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Changing the Rules: State Mortgage Foreclosure
Moratoria During the Great Depression
David C. Wheelock
Many U.S. states imposed temporary moratoria on farm and nonfarm residential mortgage foreclosures during the Great Depression. This article describes the conditions that led some states to
impose these moratoria and other mortgage relief during the Depression and discusses the economic
effects. Moratoria were more common in states with large farm populations (as a percentage of total
state population) and high farm mortgage foreclosure rates, although nonfarm mortgage distress
appears to help explain why a few states with relatively low farm foreclosure rates also imposed
moratoria. The moratoria reduced farm foreclosure rates in the short run, but they also appear to
have reduced the supply of loans and made credit more expensive for subsequent borrowers. The
evidence from the Great Depression demonstrates how government actions to reduce foreclosures
can impose costs that should be weighed against potential benefits. (JEL E44, G21, G28, N12, N22)
Federal Reserve Bank of St. Louis Review, November/December 2008, 90(6), pp. 569-583.

N

early 1 percent of U.S. home mortgages entered foreclosure during the
first quarter of 2008, and almost 2.5
percent of all home mortgages were
in foreclosure at the end of the quarter.1 The high
number of home mortgages in foreclosure or at
risk of foreclosure has prompted calls for government action. On July 30, 2008, President Bush
signed the Housing and Economic Recovery Act
of 2008 (H.R. 3221), which, among other provisions, included a $300 billion increase in Federal
Housing Administration (FHA) loan guarantees
to encourage lenders to refinance delinquent
home mortgages. Congress also has considered,
among other proposals, directing the Federal
National Mortgage Association (Fannie Mae) and
1

The stock of mortgages in foreclosure during a given quarter
includes mortgages that entered foreclosure during that quarter
and foreclosures that began in previous quarters that have not yet
been completed. These data are from the Mortgage Bankers
Association (Haver Analytics).

the Federal Home Loan Mortgage Association
(Freddie Mac) to refinance subprime mortgages,
and creating a new federal agency to acquire
and refinance delinquent mortgages.2
The creation of a new federal agency to purchase delinquent mortgages would mimic a similar
agency, the Home Owners’ Loan Corporation,
which was established to refinance delinquent
mortgages during the Great Depression. Mortgage
delinquency rates rose sharply during the
Depression. By one estimate, approximately half
of all U.S. urban home mortgages were delinquent
as of January 1, 1934 (Bridewell, 1938, p. 172).
The Home Owners’ Loan Corporation was established in 1933 and over the subsequent three years
purchased and refinanced more than 1 million
delinquent home loans. Additional steps by the
2

Fannie Mae and Freddie Mac are the two main governmentsponsored enterprises that purchase and securitize home
mortgages.

David C. Wheelock is an assistant vice president and economist at the Federal Reserve Bank of St. Louis. The author thanks Lee Alston,
Carlos Garriga, and Rajdeep Sengupta for comments on an earlier version of this article. Craig P. Aubuchon provided research assistance.

© 2008, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the
views of the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced,
published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts,
synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

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federal government to ease mortgage market
pressures during the 1930s included the creation
of the Federal Home Loan Bank System to mobilize funds for home lending, the introduction of
FHA mortgage insurance, and the creation of
Fannie Mae to purchase FHA-insured loans.3
State and local governments also responded
to the rise in mortgage foreclosures during the
Depression, mainly by changing state laws governing foreclosure. Several states enacted temporary
foreclosure moratoria. Others made permanent
changes that limited the rights or incentives of
lenders to foreclose on mortgaged property.
Recently a number of U.S. states have considered
similar steps to reduce mortgage foreclosures.
During the first six months of 2008, the state legislatures of Massachusetts, Minnesota, and New
York considered legislation to impose moratoria
on foreclosures, and legislation for a national
moratorium was introduced in the U.S. Congress.
Foreclosure moratoria are controversial.
Although moratoria can benefit some borrowers
and temporarily reduce foreclosures, critics argue
that moratoria reduce the supply of loans and
increase costs for future borrowers.4 Despite similar arguments made during the Great Depression,
27 states imposed moratoria at the time to reduce
the number of mortgage foreclosures.5 Today, the
growing sentiment for using moratoria to reduce
the current number of foreclosures prompts a
retrospective look at other episodes, such as the
Great Depression, when moratoria were used to
limit mortgage foreclosures. This article summarizes the main types of mortgage foreclosure laws
enacted by U.S. states during the 1930s. Further,
it examines why some states elected to impose
foreclosure moratoria but others did not. Finally,
3

These and other federal government responses to mortgage distress
during the Great Depression are described in Wheelock (2008).

4

For example, see Sloan (2008).

5

The federal government also enacted a moratorium on farm mortgage foreclosures during the Great Depression. The Frazier-Lemke
Farm Bankruptcy Act of 1934 authorized federal courts to grant a
five-year moratorium on foreclosure and to scale down a farmer’s
debt to the current value of his property. The act was declared
unconstitutional by the Supreme Court in 1935. Subsequently,
Congress enacted the Frazier-Lemke Farm Mortgage Moratorium
Act of 1935, which modified and limited the terms of the moratorium. The constitutionality of the latter act was upheld by the
Supreme Court in 1937.

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it summarizes empirical evidence on the costs of
foreclosure moratoria borne by borrowers.

MORTGAGE DISTRESS DURING
THE GREAT DEPRESSION
The Great Depression was a cataclysmic
event. Between 1929 and 1933, U.S. personal
income declined 44 percent, real output fell by
30 percent, and the unemployment rate climbed
to 25 percent of the labor force. U.S. real estate
markets were already showing signs of distress
before the Great Depression began. The number
of nonfarm residential real estate foreclosures
doubled between 1926 and 1929. With the onset
of the Depression, the number of foreclosures
rose still higher, from 134,900 in 1929 to 252,400
in 1933.6 The foreclosure rate, shown in Figure 1,
increased from 3.6 per 1,000 home mortgages in
1926, the first year data are available, to a high of
13.3 per 1,000 mortgages in 1933. In that year, on
average 1,000 home mortgages were foreclosed
every day (Federal Home Loan Bank Board, 1937,
p. 4). Many more homes were at risk of foreclosure—as many as half of urban home mortgages
were delinquent on January 1, 1934 (Bridewell,
1938, p. 172).
The Great Depression also sharply increased
farm mortgage foreclosures, which were unusually
high throughout the 1920s and 1930s; an average
of more than 100,000 farm mortgages entered
foreclosure each year from 1926 to 1940. Figure 2
shows that the farm foreclosure rate was especially
high from 1932 through 1934, peaking at nearly
39 foreclosures per 1,000 farms in 1933.7
The sharp increase in mortgage distress during the Great Depression was the result of precipitous declines in income and real estate values
following a period of rapid growth in mortgage
debt outstanding.8 A rising level of debt does
6

Historical Statistics of the United States, Earliest Times to the
Present: Millennial Edition (2006), series Dc1255.

7

Alston (1983, Table 1) reports average annual foreclosure rates of
3.2 per 1,000 farms for 1913-20, 10.7 for 1921-25, 19.8 for 1926-40,
3.2 for 1941-50, 1.7 for 1951-60, 1.3 for 1961-70, and 1.3 for 1971-80.

8

See Alston (1983) and Wheelock (2008) for discussion on the
growth of farm and nonfarm mortgage debt, respectively, during
the 1910s and 1920s.

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Figure 1
Nonfarm Real Estate Mortgage Foreclosure Rate, 1926–1941
Foreclosures per 1,000 Mortgages
14
12
10
8
6
4
2
0
1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941

Figure 2
U.S. Farm Foreclosure Rate, 1926–1941
Foreclosures per 1,000 Mortgages
45
40
35
30
25
20
15
10
5
0
1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940

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Figure 3
Nonfarm Residential Mortgage Debt as a Percentage of Nonfarm Residential Wealth
Percent
40
35
30
25
20
15
10
5
0

1896

1901

1906

1911

1916

1921

1926

1931

1936

1941

1946

1951

SOURCE: Grebler, Blank, Winnick (1956, table L-6).

not necessarily pose a problem for borrowers,
provided their incomes and wealth are sufficient
to make loan payments. However, between 1929
and 1932, personal disposable income and nonfarm residential wealth fell 41.0 percent and 25.7
percent, respectively, whereas the value of nonfarm residential debt fell a mere 6.8 percent. As
shown in Figure 3, nonfarm residential mortgage
debt increased sharply relative to nonfarm residential wealth during the 1920s and continued
to rise until 1932. Moreover, falling house prices
meant that homeowners who were having difficulty making their mortgage payments were
increasingly unlikely to sell their homes for more
than the outstanding balances on their loans.
Moreover, many home mortgages were shortterm, nonamortizing loans that typically were
refinanced on maturity.9 Refinancing usually

was easily accomplished during the 1920s, when
household incomes and property values were
generally rising, but next to impossible during
the Depression. Falling incomes made it increasingly difficult for borrowers to make loan payments or to refinance outstanding loans as they
came due. The failure of thousands of banks and
other lenders made refinancing difficult even for
good borrowers; customer relationships were
severed and the costs of credit intermediation
rose (Bernanke, 1983). The mix of falling household incomes and property values and short-term,
nonamortizing loans resulted in soaring mortgage
delinquency and foreclosure rates.10
Farmers faced similar problems. U.S. farm
income fell from $6.2 billion in 1929 to $2.0 billion in 1932. At the same time, farm mortgage
10

9

Mortgage lending terms varied considerably across lenders. Savings
and loan associations typically made long-term, amortizing mortgage loans. However, banks and life insurance companies often
made short-term, nonamortizing (or only partly amortizing) loans.
See Morton (1956) for more information about the mortgage market
and loan characteristics during the 1920s and 1930s.

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As discussed in Wheelock (2008), federal agencies created during
the 1930s to rescue and reform the mortgage market encouraged
the use of long-term, amortizing mortgage loans—so-called conventional loans. Nonamortizing, unconventional loans have become
more common in recent years, however, which some analysts contend has contributed to the increase in mortgage loan delinquencies
and foreclosures since 2006.

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debt outstanding rose from 40 percent of the value
of farm land and buildings in 1930 to 50 percent
in 1935.11 Hence, sharply falling incomes made
it increasingly difficult for farmers to pay the
interest and principal on their outstanding debts,
but falling property values made it less likely
that farmers could sell their properties for more
than the outstanding balance on their mortgages.
The result was a sharp increase in farm mortgage
delinquencies and foreclosures.

FORECLOSURE RELIEF
LEGISLATION
The first attempts to reduce foreclosures during the Great Depression focused on encouraging
lenders and borrowers to renegotiate loan terms
through mediation boards and other voluntary
arrangements. However, the clamor for compulsory foreclosure moratoria grew louder as the
Depression worsened and the number of foreclosures rose. On February 8, 1933, Iowa became
the first state to enact a moratorium on mortgage
foreclosures. Over the subsequent 18 months, a
total of 27 states enacted legislation to limit or
halt foreclosures (Skilton, 1944, p. 78).

Mortgage Law
Mortgages and similar loan contracts often
are used to finance the purchase of homes, farms,
and other real estate.12 The mortgage contract
specifies the terms under which the borrower is
obligated to make regular payments of principal
and interest to retire the loan. If at some point the
borrower fails to make the contracted payments,
the loan agreement and laws of the state in which
the property is located determine the actions the
lender may take to enforce the loan contract. The
mortgaged property serves as the security or col11

Historical Statistics of the United States, Earliest Times to the
Present: Millennial Edition (2006), series Da1295 (farm income)
and series Da579 (debt as a percentage of land and building value).

12

Deeds of trust are used to finance real estate purchases in some
states. Unlike a mortgage, a deed of trust involves an independent
trustee who holds a power of sale in the event of default and who
conveys the property to the borrower once the deed of trust is paid
in full. See McDonald and Thornton (2008) for basic information
about the mortgage market and mortgage finance.

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lateral for the loan, and if the borrower defaults on
the mortgage contract, the lender may foreclose
on the property against which the loan was made,
subject to the state’s laws governing foreclosure.
State laws governing the foreclosure process
vary. For example, foreclosure may be judicial or
nonjudicial. Under judicial foreclosure, the lender
sues the delinquent borrower in court for nonperformance. Typically, judicial foreclosure results
in the public sale of the mortgaged property under
court supervision, with the proceeds used to satisfy the outstanding mortgage balance and any
other outstanding liens on the property.
Under nonjudicial foreclosure by “power of
sale,” the mortgaged property is sold without
court supervision in the event of borrower default,
again with the sale proceeds used to pay the outstanding balance of the mortgage and any other
liens. Some states permit strict foreclosure, which
grants the lender unconditional title to the mortgaged property in the event of borrower default.
The laws of some states grant statutory
redemption periods during which a borrower
(mortgagor) may regain ownership of a property
after foreclosure sale by payment of the foreclosure
sale price, interest, and taxes. Generally, redemption is permitted from six months to one year
after the foreclosure sale. During the Depression,
several states modified their laws to extend or
enhance the rights of mortgagors to redeem foreclosed property.
Finally, some states allow deficiency judgments in which a mortgage holder is granted a
lien against other assets of the borrower when the
proceeds from a sale of the mortgaged property
do not cover the outstanding mortgage balance.13
During the Depression, several states enacted
reforms that limited the rights of lenders to seek
deficiency judgments against borrowers.

Examples from the Great Depression
The diversity of foreclosure proceedings
across U.S. states during the 1930s was noted in
a 1936 federal government study:
13

If the value of a property exceeds the outstanding loan balance, the
borrower generally benefits from refinancing the loan or selling the
property and paying off the outstanding loan balance rather than
losing the property through foreclosure. Hence, the proceeds from
most foreclosure sales are less than the outstanding mortgage balance.

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A general survey indicates that in twenty-eight
states foreclosure is by action in court. Ten
states use unregulated power of sale. Five states
use regulated power of sale, and the remaining
states have various other methods. Thirty-one
states provide a redemption period ranging
from four months in Oregon to two years in
Alabama. Seventeen states have no redemption period, but, of these, eight use foreclosure
in court which requires months to complete.
(Central Housing Committee, 1936, p. 2)

During the Depression, many states enhanced
borrower redemption rights, limited deficiency
judgments, or made other changes that favored
borrowers, and several states imposed moratoria
on foreclosures. The specific details of moratoria
legislation varied widely. A few states imposed
blanket moratoria that temporarily prohibited
most foreclosures of farm and nonfarm home mortgages contracted before a specified date. However,
most states limited their moratoria to specific
situations. For example, some states granted relief
only for borrowers who were current in the payment of interest and taxes but delinquent in the
payment of loan principal. For example, a New
York statute enacted in 1933 specified that “No
action for the foreclosure of a mortgage on real
estate solely on account of default in payment of
principal…shall be brought before July 1, 1937”
(Central Housing Committee, 1936, p. A-18).
Foreclosures were permitted, however, against
borrowers who had ceased to pay interest and
taxes, as well as principal.
Several states directed their state courts to
grant moratoria in deserving cases, but little
guidance was provided to the courts about how
to determine which borrowers deserved relief.
For example, in Iowa, the court was authorized
to grant a borrower’s request for relief from pending foreclosure unless “good cause is shown to
the contrary” (Skilton, 1944, p. 82). Similarly,
an Arizona statute specified that “In pending or
future real estate mortgage foreclosure suits, the
court may order a two-year continuance unless
good cause to the contrary is shown” (Central
Housing Committee, 1936, p. A-3). Not surprisingly, the extent to which courts granted relief to
delinquent borrowers varied widely, even within
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a state. Many courts determined that it was pointless to grant relief to borrowers who had no hope
of refinancing their mortgage or making payments
or who did not act in good faith toward their
lender (Skilton, 1944, pp. 98-106). In addition,
courts often required borrowers to pay rent or
interest to the lender, as well as taxes, as a condition for halting foreclosure proceedings.
In conjunction with a foreclosure moratorium,
several states extended the period during which
a mortgagor could redeem his property after foreclosure. Again, however, any extension of the
redemption period was often left to the court’s
discretion. In Kansas, for example, “the period
for redemption on real estate may be extended
for such additional time as the court shall deem
it just and equitable” (Central Housing Committee,
1936, p. A-10). In a few states, the legislation was
more specific. For example, North Dakota legislation specified that “The period within which a
mortgagor or judgment debtor may redeem from
a mortgage foreclosure or execution sale of real
estate…is extended for a period of two years”
(Central Housing Committee, 1936, p. A-21).
Several states also modified their statutes to
limit deficiency judgments. Some states restricted
judgments to the difference between the outstanding loan balance and a “fair” or “reasonable”
value of the mortgaged property, rather than the
difference between the loan balance and the price
received at a foreclosure sale. For example, a
1933 Idaho statute specified that “no deficiency
judgment may be entered in any amount greater
than the difference between the mortgage indebtedness, plus the cost of foreclosure and sale and
the reasonable value of the property” (Central
Housing Committee, 1936, p. A-7). Other states
permitted courts to invalidate foreclosure sales
for less than fair value. Most states left the determination of fair value to the discretion of a local
appraisal board or court rather than attempt to
define “fair value” in statutes.
Several states imposed new limits on the
length of time that a lender could seek a deficiency judgment after a foreclosure sale. For
example, Iowa and Ohio enacted legislation
limiting deficiency judgments to two years after
a foreclosure sale (Skilton, 1944, p. 130). Other
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states abolished the right of lenders to seek deficiency judgments altogether. For example, a 1935
Montana statute specified that “Deficiency judgments are abolished in all actions for foreclosure
of mortgages for balance of purchase price of real
property” (Central Housing Committee, 1936,
p. A-16).14

Table 1
State Mortgage Moratoria during the Great
Depression
States imposing
moratoria

States not imposing
moratoria

Arizona

Alabama

Arkansas

Colorado

WHICH STATES ADOPTED
MORATORIA AND WHY?

California

Connecticut

Delaware

Florida

Idaho

Georgia

The 27 states that adopted foreclosure moratoria during 1933 and 1934 are listed in Table 1,
and the geographic distribution of states with
moratoria is shown in Figure 4. Moratoria were
especially common among states in the Midwest
and Great Plains, but they also were imposed by
several states in the Northeast and Far West. Foreclosure moratoria were less common in New
England, the Southeast, and Mountain West.15
Foreclosure moratoria generally applied to
both farm and nonfarm residential mortgages.
However, the pressure for foreclosure moratoria
was particularly intense in midwestern states
where farm foreclosure rates were especially high
(Figure 5). Moratoria were less common in states
with relatively low farm foreclosure rates, though
a few, including New Hampshire, Pennsylvania,
and Vermont, also imposed moratoria.
Alston (1984) investigates why some, but not
all, states imposed foreclosure moratoria during
the Depression. He estimates a logit regression
model that includes a state’s farm foreclosure rate,
percentage of farms mortgaged, and percentage
of farm mortgages held by federal land banks as
explanatory variables. Alston argues that a state
was more likely to impose a moratorium the

Illinois

Indiana

Iowa

Kentucky

Kansas

Maine

Louisiana

Maryland

Michigan

Massachusetts

Minnesota

Missouri

Mississippi

New Jersey

Montana

New Mexico

Nebraska

Nevada

New Hampshire

Rhode Island

New York

Tennessee

North Carolina

Utah

North Dakota

Virginia

Ohio

Washington

Oklahoma

West Virginia

Oregon

Wyoming

14

See Central Housing Committee (1936), Poteat (1938), or Skilton
(1944) for additional information about the provisions of moratoria
and other legislation affecting the rights of mortgagors and lenders
enacted in different states during the Depression.

15

The source for Table 1 and Figure 4 is Skilton (1944, p. 78), which
lists 27 states as having had a moratorium. Other sources omit
Oregon, where a moratorium was authorized by a joint resolution
of the state legislature, rather than by statute (Poteat, 1938), or omit
both Oregon and Arkansas (Alston, 1984).

16

The Federal Farm Loan Act of 1916 established 12 regional federal
land banks to increase the supply of farm mortgage loans. See
www.fca.gov/about/history/historyFCA_FCS.html.

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Pennsylvania
South Carolina
South Dakota
Texas
Vermont
Wisconsin
SOURCE: Skilton (1944, p. 78).

higher its farm foreclosure rate, the higher its
percentage of mortgaged farms, and the lower
the percentage of mortgages held by federal land
banks (which were less likely to foreclose than
other lenders).16 He finds that the farm foreclosure
rate had the strongest impact on a state’s decision
to impose a moratorium.
As noted previously, moratoria were adopted
in a few states with relatively low farm foreclosure
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Figure 4
States Imposing Foreclosure Moratoria During the Great Depression

No Mortgage Moratoria
Mortgage Moratoria

Figure 5
Average Farm Foreclosure Rates, 1929–1932

Less Than 10 Foreclosures per 1,000 Farms
10 to 20 Foreclosures per 1,000 Farms
20 to 30 Foreclosures per 1,000 Farms
More Than 30 Foreclosures per 1,000 Farms

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Table 2
Regression Results
Model
Variable

1

2

3

4

Intercept

–1.7768
(1.7752)

–4.0343
(3.4049)

–1.5403
(2.9175)

–2.4317
(3.6759)

Farm foreclosure rate

0.0803**
(0.0366)

0.1338*
(0.0695)

–0.0183
(0.0647)

0.0419
(0.1081)

Mortgaged farm percent

2.0338
(3.4587)

3.2953
(4.3798)

1.7109
(3.7252)

2.033
(4.5092)

Federally held farm debt

–3.0984
(2.5978)

–3.4411
(–3.1007)

–6.4965*
(3.7163)

–5.5301
(3.8831)

3.5653
(5.9059)

2.9328
(5.5364)

3.6291
(5.9293)

0.0023*
(0.0013)

0.0017
(0.0016)

Owner-occupied nonfarm homes
Foreclosure rate × farm population
Midwest

–1.7877
(1.8866)

–1.0099
(2.0200)

South

–0.5345
(1.4734)

–0.6759
(1.4776)

West

–2.0764
(1.4546)

–1.3836
(1.5882)

Log likelihood
Probability > chi-square

–27.3815
0.0116

–25.8424
0.0493

–25.6897
0.0132

–25.2482
0.0537

NOTE: Standard errors are indicated in parentheses; statistically significant coefficients are in bold. *Indicates significance at the 90
percent confidence level; ** indicates significance at the 95 percent confidence level.
See the Appendix for data definitions and sources.

rates, and some states with high farm foreclosure
rates did not impose moratoria. According to
Skilton (1944), some states imposed moratoria in
response to high numbers of nonfarm home mortgage foreclosures. Unfortunately, state-level data
on nonfarm real estate foreclosures are not available for the early 1930s to test directly the impact
of nonfarm foreclosures on moratoria adoption.
Nevertheless, regional differences in farm foreclosure rates and the adoption of moratoria suggest
that nonfarm foreclosures or other considerations
may have influenced the decision to impose
moratoria in some states.
Some evidence on why states imposed foreclosure moratoria is reported in Table 2, which
presents a replication of Alston’s (1984) logit
model and some alternative specifications. The
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

dependent variable in this set of cross-sectional
regressions is a dummy variable, set equal to 1
for states that adopted a moratorium during
1933-34 and to 0 otherwise. The Appendix provides complete definitions and data sources for
the variables included in the regressions.
Model 1 replicates Alston’s model and shows
his main result: the higher a state’s farm foreclosure rate, the greater the likelihood the state
would adopt a foreclosure moratorium.17 Model 2
includes the percentage of owner-occupied nonfarm homes as an additional explanatory variable.
17

The coefficient estimates in Model 1 differ slightly from those
reported in Alston (1984). Unlike Alston, I treated Arkansas and
Oregon as having had moratoria, based on Skilton (1944), and used
the farm foreclosure rate for 1932, rather than the average farm
foreclosure rate for 1932 and 1933, as an explanatory variable.

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Figure 6
Model 1: Pearson Residuals
3
2

LA
NH

1

DE

AR
AZ
CA

IL

0
FL
AL

–1

MI
MN

KS

IA

KY

CT

NC
MT
NE
ND

SC
OK

WI
SD

VA
TN

NV

IN

WV

UT

RI

NM

MD

VT
TX

OR

NJ

GA
CO

OH

ME
MA

PA

NY

MS

ID

WA
WY

–2
–3

MO

–4

Presumably, the demand for moratoria legislation
was greater where a high percentage of homes
were mortgaged and, hence, at risk of foreclosure.
Unfortunately, state-level data on the percentage
of homes carrying a mortgage are not available
for the 1930s. However, if owner-occupied homes
were no less likely to be mortgaged than rented
homes, a higher percentage of owner-occupied
homes might reflect a greater demand for a foreclosure moratorium. Accordingly, I expect a positive coefficient on this variable. Consistent with
expectations, the coefficient estimate in Model 2
for the percentage of owner-occupied homes is
positive, though not statistically significant.
Model 2 also includes regional dummy variables. The coefficient estimates for the regional
dummies indicate that relative to the Northeast
(the omitted region), states in other regions of
the country were less likely to adopt foreclosure
moratoria. Stated differently, for a given rate of
farm foreclosures, states in the Northeast were
more likely to adopt foreclosure moratoria than
states elsewhere. This suggests that nonfarm mortgage distress had a greater influence on the decision to adopt moratoria among the more urbanized
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northeastern states than it did in other regions of
the country. However, the coefficients on the
regional dummy variables are not statistically
significant.18
Model 3 further refines the analysis by testing
whether the influence of farm foreclosures on
moratoria adoption was stronger in states with
relatively high farm populations. To test this conjecture, Model 3 includes the interaction of the
farm foreclosure rate and the percentage of state
population located on farms. The coefficient estimate on the interaction term (foreclosure rate ×
farm population) is positive and statistically
significant, and the coefficient on the farm foreclosure rate is near zero, which supports this
hypothesis. The impact of a given farm foreclosure rate was greater in states with relatively
larger farm populations.
Finally, Model 4 adds regional dummy variables to the previous specification. The coefficients on the regional dummies are again negative,
suggesting a relatively low demand for moratoria
18

The test statistic for a likelihood ratio test of the hypothesis that
the coefficients on the regional dummies are jointly zero is 3.08
(p-value = 0.38).

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Wheelock

among states outside the Northeast. However,
the contribution of the regional dummies to the
model’s explanatory power is not statistically
significant.19
For additional insights about why states
adopted (or did not adopt) foreclosure moratoria,
I examined the residuals from the logit models
reported in Table 2. The Pearson residuals for
Model 1 are shown in Figure 6.20 The residuals
for states that adopted moratoria are greater than
or equal to zero, whereas those for states that did
not adopt moratoria are less than or equal to zero.
The closer a state’s residual is to zero, the more
accurately the model explains the state’s decision
to impose (or not impose) a moratorium. Thus,
the large positive residual for Louisiana indicates
that the model explains relatively little of the
state’s decision to impose a moratorium. Similarly,
the model explains relatively little of Missouri’s
decision not to adopt a moratorium. Missouri had
a comparatively high farm foreclosure rate and,
given that fact, Model 1 predicts that Missouri
would have imposed a moratorium.
Additional information helps explain the
anomalous behavior of some states. For example,
Louisiana was the last state to adopt a debt moratorium (in July 1934). Soon thereafter, the legislation authorizing the moratorium was amended to
grant broad authority to a state debt commissioner
to “suspend all laws relating to the collection of
fundamentally all types of debts in existence at
the time of the passage of the act” (Skilton, 1944,
pp. 83-84). In effect, the state imposed a general
moratorium on all debts, not just real estate mortgage debt. The breadth of the moratorium thus
might help explain why Louisiana imposed a
moratorium, despite only a modest level of farm
distress.
New York also enacted an unusually broad
foreclosure moratorium that extended to commercial real estate, as well as to farm and nonfarm
19

The test statistic for a likelihood ratio test of the hypothesis that
the coefficients on the regional dummies are jointly zero is 0.88
(p-value = 0.83).

20

The logit models were estimated using Stata/MP 10.0. The basic
Pearson residual is the difference between the actual and modelpredicted values of the dependent variable, divided by the estimated standard deviation of the predicted values. See Stata/MP
10.0 for more details about the calculation of the Pearson residual.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

residential property. According to Skilton (1944,
pp. 76-77), property management companies and
other real estate interests had considerable influence on the moratorium legislation, and “The
lobbying of real estate operators was sufficient…
to defeat Governor Lehman’s original idea that
a moratorium should be limited to farms and
homes.” Thus, like Louisiana, the breadth of the
moratorium may help explain why Model 1,
which captures only the effects of farm distress,
does not explain well the imposition of a foreclosure moratorium in New York.
Differences in the prevailing state laws governing mortgage foreclosure might also help account
for the model’s failure to explain well the moratoria decisions of some states. For example, neither
Indiana nor Missouri adopted a foreclosure moratorium during the Depression, despite relatively
high levels of farm distress. However, a federal
study concluded that the demand for moratoria
was low in both states because their prevailing
foreclosure laws were already comparatively
favorable to borrowers (Central Housing
Committee, 1936).

ECONOMIC IMPACT OF
FORECLOSURE MORATORIA
Governments cause both immediate and
long-term effects when they rewrite the terms of
contracts between private parties. The immediate
impact is redistribution of wealth between the
parties of the affected contracts. The temporary
foreclosure moratoria and most other changes in
state mortgage laws enacted during the 1930s
favored borrowers over lenders. These actions
interfered with the rights of lenders to seize collateral pledged by borrowers to guarantee payment
of their mortgages. Several states also enhanced
the rights of borrowers to redeem foreclosed
property and limited the rights of lenders to sue
for deficiency judgments.
One immediate effect of mortgage relief legislation during the Depression was reduced farm
foreclosure rates (Rucker and Alston, 1987).21
21

I am unaware of any research on the effects of relief legislation on
nonfarm home mortgage foreclosure rates.

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However, over the longer run, foreclosure moratoria and other changes in mortgage laws may
have made loans costlier or more difficult to
obtain. Critics argued that foreclosure moratoria
induce lenders to restrict the supply of loans and
raise interest rates to compensate for the possibility that their right to foreclose on delinquent
loans or to collect deficiency judgments will be
constrained. According to a 1936 federal government report,
Statutes which provide a lengthy, expensive,
complicated or otherwise burdensome foreclosure procedure, or which interpose a long
period of redemption before title and possession to the mortgaged property can be obtained,
have a tendency to increase interest rates and
security requirements throughout the jurisdiction, since prospective lenders naturally take
into account the procedure available for realizing the debt out of the security when determining the conditions on which they will be willing
to make loans. (Central Housing Committee,
1936, p. 3)

The same report noted that in 1933-34 many
states elected to disregard such objections because
it was widely believed that “unrestricted foreclosure of farm and home mortgages under the
circumstances prevailing at the time would have
deprived large numbers of persons of essential
shelter and protection, and would have left them
without the necessary means for earning a living.
Such wholesale evictions might have seriously
endangered basic interests of society” (Central
Housing Committee, 1936, p. 2). Hence, in many
states, the societal costs of widespread foreclosures
were viewed as exceeding the costs of reduced
loan supply and higher interest rates borne by
prospective borrowers. Furthermore, foreclosure
moratoria generally were viewed as expedients
to buy time for the economy to recover and for
the federal government to initiate programs to
refinance delinquent mortgages (Skilton, 1944,
pp. 73-77). Even lenders may have benefited from
foreclosure moratoria in the short run. Although
individual lenders had an incentive to foreclose
to recoup losses on delinquent mortgages, a high
number of foreclosures in an area could reduce
property values and thereby cause still more
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foreclosures. Thus, foreclosure moratoria might
halt a downward spiral in property values and
benefit lenders as a whole.22
Although the economic and societal benefits
of lower foreclosure rates are difficult to measure,
research shows that the foreclosure moratoria of
the Great Depression did impose costs on future
borrowers. Alston (1984) investigates the impact
of foreclosure moratoria in an empirical model
of the farm mortgage market. He argues that foreclosure moratoria encouraged lenders to reduce
the supply of loans, resulting in fewer loans made
and, possibly, higher average interest rates. Consistent with this hypothesis, Alston (1984) finds
that private lenders made significantly fewer
loans in states that imposed moratoria and tended
to charge higher interest rates on the loans they
did make.
Rucker (1990) extends Alston’s (1984) study
to investigate differences in the impact of mortgage relief legislation on the supply of loans
offered by different types of private lenders. In
the 1930s, most farm mortgages were issued by
local commercial banks, private individuals,
insurance companies, and federal land banks.
Insurance companies tended to be larger and
more diversified and to have a lower cost of funds
than did banks and individual lenders. Their size
and cost advantages enabled insurance companies
to attract lower-risk borrowers and, consequently,
experience lower delinquency rates. Insurance
companies generally were also more willing to
grant extensions to delinquent borrowers. Hence,
the costs imposed by mortgage relief legislation
should have been lower for insurance companies
than for other private lenders. Rucker (1990)
finds that, indeed, mortgage relief legislation led
to significantly larger reductions in the supply
of loans from commercial banks and individual
lenders than from insurance companies.23 Both
22

Kahn and Yavas (1994) examine the short- and long-run effects of
changes in foreclosure laws (especially how they affect borrower
and lender behavior and borrower welfare) in a simple theoretical
model of the mortgage market in which renegotiation of loan contracts is possible. Jaffe and Sharp (1996) describe the economics of
foreclosure moratoria in the context of alternative legal theories
of contracts.

23

In his econometric analysis, Rucker (1990) treated legislation that
limited deficiency judgments or enhanced redemption rights for

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Wheelock

Alston (1984) and Rucker (1990) conclude that
mortgage relief legislation caused significant
reductions in the aggregate supply of loans in
states that enacted such legislation.
The findings of Alston (1984) and Rucker
(1990) on the effects of mortgage relief legislation
during the 1930s are consistent with other studies
that find significant effects of state mortgage laws
on local lending markets. Meador (1982), for
example, finds that loan interest rates tend to be
higher in states with lengthy or costly foreclosure
processes or those that prohibit deficiency judgments. More recently, Pence (2006) finds that
mortgage loans are, on average, some 3 to 7 percent
smaller in states in which foreclosure requires a
court action than in states with nonjudicial foreclosure processes, again consistent with the
hypothesis that the supply of loans is lower in
states in which foreclosure is more costly.24

CONCLUSION
In 2008, residential real estate foreclosure
rates are at their highest levels since the Great
Depression. Not surprisingly, policymakers are
considering actions similar to those taken during
the Depression to limit foreclosures. The federal
government responded to mortgage distress during
the Depression by creating new federal agencies
to refinance delinquent mortgages, insure and
finance newly issued mortgages, and expand
federal farm credit programs. By contrast, many
state governments imposed moratoria on foreclosures, limited deficiency judgments, and enhanced
the rights of borrowers to redeem foreclosed property. By halting foreclosures temporarily, states
hoped to buy time for economic recovery to take
hold, for household incomes and property values
to rise, and for the federal government to refinance
delinquent mortgages.
The earliest calls for mortgage relief were in
farming regions, and states with high farm foreborrowers, as well as foreclosure moratoria, as forms of relief legislation, whereas Alston (1984) focused exclusively on moratoria.
24

Pence (2006) compares bordering census tracts located in different
states and controls for a variety of borrower, policy, and other
census tract characteristics.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

closure rates were more likely to impose moratoria (Alston, 1984). Additional evidence indicates
that farm foreclosures had a greater impact on the
decision to impose moratoria in states in which
the farm population comprised a relatively high
percentage of total state population.
Moratoria were imposed in a few states with
comparatively little farm mortgage distress, suggesting that urban mortgage distress or other factors influenced the decision to impose moratoria
in some states. For example, in New York, lobbying by commercial real estate interests helped
shape legislation for a broad moratorium covering farm, urban residential, and commercial real
estate mortgage foreclosures.
In most states, foreclosure moratoria were
limited to borrowers who had some chance of
paying or refinancing their loans. Relief often was
denied to borrowers judged to have little prospect
of ever paying off their mortgage.
Foreclosure moratoria resulted in both winners
and losers. Although the rights of lenders to foreclose on collateral or to seek deficiency judgments
were restricted, relief legislation did apparently
contribute to a reduction in farm failures (Rucker
and Alston, 1987).
At least some contemporaries recognize that
even temporary foreclosure moratoria can impose
costs on future borrowers. Alston (1984) and
Rucker (1990) find that lenders reduced the supply of loans in response to diminution of their
rights to foreclose on collateral or to seek deficiency judgments. Thus, while to many observers
the economic and societal costs of widespread
real estate foreclosures were overwhelming, foreclosure moratoria and other relief legislation
transferred at least some of those costs to future
borrowers. The evidence from the use of foreclosure moratoria during the Great Depression
demonstrates how legislative actions to reduce
foreclosures can impose costs that should be
weighed against potential benefits.

REFERENCES
Alston, Lee J. “Farm Foreclosures in the United States
During the Interwar Period.” Journal of Economic
History, December 1983, 43(4), pp. 885-903.

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Wheelock

Alston, Lee J. “Farm Foreclosure Moratorium
Legislation: A Lesson from the Past.” American
Economic Review, June 1984, 74(3), pp. 445-57.

Meador, Mark. “The Effects of Mortgage Laws on the
Home Mortgage Rates.” Journal of Economics and
Business, 1982, 34(2), pp. 143-48.

Bernanke, Ben S. “Nonmonetary Effects of the
Financial Crisis in the Propagation of the Great
Depression.” American Economic Review, June
1983, 73(3), pp. 257-76.

Morton, Joseph E. Urban Mortgage Lending:
Comparative Markets and Experience. Princeton,
NJ: Princeton University Press, 1956.

Bridewell, David A. The Federal Home Loan Bank
Board and its Agencies: A History of the Facts
Surrounding the Passage of the Creating Legislation,
The Establishment and Organization of the Federal
Home Loan Bank Board and the Bank System, The
Savings and Loan System, The Home Owners’ Loan
Corporation, and the Federal Savings and Loan
Insurance Corporation. Washington, DC: Federal
Home Loan Bank Board, 1938.
Bridewell, David A. and Russell, Horace. “Mortgage
Law and Mortgage Lending.” Journal of Land and
Public Utility Economics, August 1938, 14(3),
pp. 301-21.
Central Housing Committee. “Special Report No. 1 on
Social and Economic Effects of Existing Foreclosure
Procedure and Emergency Moratorium Legislation.”
Horace Russell, Chairman. Submitted April 2, 1936.
Federal Home Loan Bank Board. Fifth Annual Report.
June 30, 1937.
Jaffe, Austin J. and Sharp, Jeffery M. “Contract Theory
and Mortgage Foreclosure Moratoria.” Journal of
Real Estate Finance and Economics, January 1996,
12(1), pp. 77-96.
Kahn, Charles M. and Yavas, Abdullah. “The
Economic Role of Foreclosures.” Journal of Real
Estate Finance and Economics, January 1994, 8(1),
pp. 35-51.

Pence, Karen M. “Foreclosing on Opportunity: State
Laws and Mortgage Credit.” Review of Economics
and Statistics, 2006, 88(1), pp. 177-82.
Poteat, J. Douglass. “State Legislative Relief for the
Mortgage Debtor During the Depression.” Law and
Contemporary Problems, 1938, 5, pp. 517-44.
Rucker, Randal R. “The Effects of State Farm Relief
Legislation on Private Lenders and Borrowers: The
Experience of the 1930s.” American Journal of
Agricultural Economics, February 1990, 72(1),
pp. 24-34.
Rucker, Randal R. and Alston, Lee J. “Farm Failures
and Government Intervention: A Case Study of the
1930s.” American Economic Review, September
1987, 77(4), pp. 724-30.
Skilton, Robert H. Government and the Mortgage
Debtor (1929 to 1939). PhD Dissertation, University
of Pennsylvania, Philadelphia, 1944.
Sloan, Steven. “Minnesota Foreclosure Measure
Draws Veto.” American Banker, June 3, 2008;
www.americanbanker.com/article.html?id=200806
02TJH8JBQ8&queryid=982795036&hitnum=.
Wheelock, David C. “The Federal Response to Home
Mortgage Distress: Lessons from the Great
Depression.” Federal Reserve Bank of St. Louis
Review, May/June 2008, 90(3), pp. 133-48;
research.stlouisfed.org/publications/review/08/05/
Wheelock.pdf.

McDonald, Daniel and Thornton, Daniel L. “A Primer
on the Mortgage Market and Mortgage Finance.”
Federal Reserve Bank of St. Louis Review,
January/February 2008, 90(1), pp. 31-46;
research.stlouisfed.org/publications/review/08/01/
McDonald.pdf.

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APPENDIX
Variable Definitions and Data Source Information
Variable name

Definition

Source

Moratorium

Dummy variable equal to 1
for states with mortgage
moratorium in 1933-34

Skilton, Robert H. Government and the
Mortgage Debtor (1929 to 1939).
PhD Dissertation, University of Pennsylvania,
Philadelphia, 1944, p. 78.

Farm foreclosure rate

Farm foreclosures per 1,000
mortgages in 1932

U.S. Department of Agriculture.
“The Farm Real Estate Situation, 1930-31.”
Bureau of Agricultural Economics,
circular no. 209, 1931.

Mortgaged farms (percent)

Percentage of farms mortgaged
in 1930, calculated as
(mortgaged farms/all owned
farms)

U.S. Department of Commerce.
Statistical Abstract of the United States: 1932.
Washington, DC: U.S. Government Printing
Office, 1932, Table 548, p. 589.

Federally held farm debt

Percent of mortgage debt held
by federal land banks,
calculated as (sum of amount
of loans closed 1917 to 1932/
total farm mortgage debt
in 1932)

U.S. Department of Agriculture.
Miscellaneous Publication No. 478,
“Farm Mortgage Credit Facilities in the United
States.” Washington, DC: U.S. Government
Printing Office, 1942, Table 64, p. 221 and
Table 78, p. 245.

Owner-occupied nonfarm
homes (percent)

Percentage of owned nonfarm
homes in 1930, calculated as
(sum of owned nonfarm
homes/total nonfarm homes)

U.S. Department of Commerce.
Fifteenth Census of the United States: 1930.
Population, Volume VI, Table 42, p. 35.
Washington, DC: U.S. Government Printing
Office, 1931.

Farm population

Percentage of population on
farms in 1930

U.S. Department of Commerce.
Statistical Abstract of the United States: 1932.
Washington, DC: U.S. Government Printing
Office, 1932, Table 36, p. 47.

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Mortgage Innovation, Mortgage Choice,
and Housing Decisions
Matthew S. Chambers, Carlos Garriga, and Don Schlagenhauf
This paper examines some of the more recent mortgage products now available to borrowers.
The authors describe how these products differ across important characteristics, such as the down
payment requirement, repayment structure, and amortization schedule. The paper also presents a
model with the potential to analyze the implications for various mortgage contracts for individual
households, as well as to address many current housing market issues. In this paper, the authors
use the model to examine the implications of alternative mortgages for homeownership. The authors
use the model to show that interest rate–adjustable mortgages and combo loans can help explain
the rise—and fall—in homeownership since 1994. (JEL E2, E6)
Federal Reserve Bank of St. Louis Review, November/December 2008, 90(6), 585-608.

H

ousing is a big-ticket item in the
U.S. economy. At the macro level,
residential housing investment
accounts for 20 to 25 percent of
gross private investment. In the aggregate, this
financing is about 8 trillion dollars and uses a
sizable fraction of the financial resources of the
economy. The importance of housing at the individual household level is more evident because
the purchase of a house is the largest single consumer transaction and nearly always requires
mortgage financing. This decision affects the
overall expenditure patterns and asset allocation
decisions of the household.
In recent years, interest in the role of housing
in the U.S. economy has increased, influenced
mainly by two events. During the economic
downturn in 2000, the housing sector seemed to
mitigate the slowdown in many other sectors of
the economy as residential investment remained
at high levels. More recently, the large number of

foreclosures has again focused attention on the
importance of housing. Fears have increased that
mortgage market problems will have long-lasting
effects on the credit market and thus continue to
create a drag on the economy.
Events illustrating the important role of
housing in the economy are not limited to those
of the past decade. Housing foreclosures soared
during the Great Depression as a result of two
factors. The mortgage system was very restrictive:
Homeowners were required to make down payments that averaged around 35 percent for loans
lasting only five to ten years. At the end of the
loan period, mortgage holders had to either pay
off the loan or find new financing. The 1929 stock
market collapse resulted in numerous bank failures. Mortgage issuance fell drastically, and homeowners were dragged into foreclosure. Faced with
these problems, the government developed new
housing policies as part of the New Deal legislation. The Home Owners’ Loan Corporation (HOLC)
and the Federal Housing Administration (FHA)

Matthew S. Chambers is an assistant professor of economics at Towson University. Carlos Garriga is an economist at the Federal Reserve Bank
of St. Louis. Don Schlagenhauf is a professor of economics at Florida State University. The authors are grateful for the financial support of
the National Science Foundation (grant No. SEP-0649374). Carlos Garriga also acknowledges support from the Spanish Ministry of Science
and Technology (grant No. SEJ2006-02879). Michelle T. Armesto provided research assistance.

© 2008, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the
views of the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced,
published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts,
synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

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Chambers, Garriga, Schlagenhauf

were created along with a publicly supported
noncommercial housing sector. The HOLC was
designed to help distressed homeowners avert
foreclosure by buying mortgages near or in foreclosure and replacing them with new mortgages
with much longer durations. The HOLC financed
these purchases by borrowing from the capital
market and the U.S. Treasury. The FHA introduced
new types of subsidized mortgage contracts by
altering forms and terms, as well as mortgage
insurance. In addition, Congress created Federal
Home Loan Banks in 1932 and the Federal Home
Loan Mortgage Corporation, commonly known
as Fannie Mae, in 1938. The latter organization
was allowed to purchase long-term mortgage loans
from private banks and then bundle and securitize these loans as mortgage-backed securities.1
These changes had an important impact on the
economy: The stock of housing units increased
20 percent during the 1940s, and the homeownership rate increased approximately 20 percentage
points from 1945 to 1965.
The need for increased understanding of
housing markets, housing finance, and their linkage to the economy—the objective of this paper—
should be obvious. We begin by examining the
structure of a variety of mortgage contracts. Given
the array of available mortgage products, mortgage
choice can be a complex problem for potential
home buyers. Buyers must consider many dimensions, such as the down payment, maturity of
the contract, repayment structure, the ability to
refinance the mortgage, and the impact of changes
in interest rates and housing prices. We present
examples to clarify key features of prominent
mortgage contracts. The best mortgage for one
household need not be the best mortgage for
another. In fact, a model is needed to understand
the mortgage decisionmaking process and what
the aggregate implications are for the economy.
This model must explicitly recognize the differences among households in age, income, and
1

This increased the flow of resources available in areas in which
savings were relatively scarce. The intent was to increase the opportunities for low-income families in the housing market. Because
of the implicit backing of the government, the riskiness of these
assets was perceived to be similar to the risk of U.S. Treasury
securities.

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wealth. In addition, these decisions must reflect
the complexities of the tax code that favor owneroccupied housing. Such a framework allows individual decisions to be aggregated so that the
impact of mortgage decisions for the economy
can be clearly identified.
The second part of this paper presents a model
for understanding the impact of mortgage decisions
on the economy. We use the model to show the role
that adjustable-rate mortgages (ARMs) and combo
loans have played since 1994 in the rapid rise—
and subsequent decline—in homeownership.

MORTGAGE CONTRACTS
A mortgage contract is a loan secured by real
property. In real estate markets this debt instrument uses the structure (building) and land as
collateral. In most countries mortgage lending is
the primary mechanism to finance the acquisition
of residential property. Mortgage loans typically
are long-term contracts and require periodic
payments that can cover interest and principal.
Lenders provide the funds to finance the loans.
Usually, such loans are sold to secondary market
parties interested in receiving an income stream
in the form of the borrower’s payments.
The financial marketplace offers many types
of mortgage loans, which are differentiated by
three characteristics: the payment structure, the
amortization schedule, and the term (duration) of
the mortgage loan. The payment structure defines
the amount and frequency of mortgage payments.
The amortization schedule determines the amount
of principal payments over the life of the mortgage.
This schedule differs across types of mortgage
loans and can be increasing, decreasing, or constant. Some contracts allow for no amortization
of principal and full repayment of principal at a
future, specified date. Other contracts allow negative amortization, usually in the initial years of
the loan.2 The term or duration usually refers to
the maximum length of time allotted to repay the
2

A mortgage contract with negative amortization means the monthly
payment does not cover the interest on the outstanding balance.
As a result, the principal owed actually increases. We illustrate
such a contract later in the paper.

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Chambers, Garriga, Schlagenhauf

Table 1
Types of Primary Mortgage Contracts*
Type of contract

1993*

1995

1997

1999

2003

2005

Fixed-rate mortgage

84.4

82.6

86.5

90.6

92.8

90.0

Adjustable-rate mortgage

11.0

12.3

9.3

5.9

4.3

5.9

Adjustable-term mortgage

0.2

0.0

0.8

0.8

0.3

0.4

Graduated-payment mortgage

1.0

1.0

1.2

1.0

0.7

1.2

Balloon

0.9

1.6

1.0

0.9

1.1

1.2

Other

1.7

1.6

0.1

0.0

0.1

0.1

Combination of the above
Sample size

0.8

0.9

1.1

0.8

0.7

1.1

37,183

39,026

35,999

39,034

42,411

45,450

NOTE: *Share of total contracts in percent.
SOURCE: U.S. Department of Commerce, American Housing Survey for various years.

mortgage loan. The most common mortgage contracts are for 15 and 30 years. The combination
of these three factors allows a large variety of
distinct mortgage products.
Mortgage contracts affect consumer decisions.
For example, some contracts are more effective in
allowing increased homeownership for younger
households. What types of mortgage contracts are
actually held in the United States? According to
the 2001 Residential Finance Survey (U.S. Census
Bureau, 2001), roughly 97 percent of housing
units were purchased through mortgage loans,
whereas only 1.6 percent were purchased with
cash. Table 1 summarizes the types of mortgage
contracts used in the United States. The fixed-rate
(payment) mortgage loan is the dominant contract,
and the popularity of an adjustable (or floating)
rate mortgage is substantially smaller. In contrast,
in the United Kingdom and Spain, where the
homeownership rate is 71 and 80 percent, respectively, the adjustable (or floating) rate contract is
the dominant contract. The popularity of the
fixed-rate contract in the United States is largely
a result of the policies of the FHA, Veterans
Administration, and various government incentives to sell the loan in the secondary market. This
is the role of enterprises such as Fannie Mae and
the Federal Home Loan Mortgage Corporation
(Freddie Mac), two government-sponsored enterprises (GSEs) that are among the largest firms that
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securitize mortgages. Mortgage securitization
occurs when a mortgage contract is resold in the
secondary market as a mortgage-backed security.
In the early 1990s, substantial changes occurred
in the structure of the mortgage market in the
United States. According to data in the 2007
Mortgage Market Statistical Annual, the market
share of nontraditional mortgage contracts has
increased since 2000. Nontraditional or alternative
mortgage products include interest-only loans,
option ARMs, loans that couple extended amortization with balloon-payment requirements, and
other contracts of alternative lending. For example, in 2004 these products accounted for 12.5
percent of origination loans. By 2006, this segment
increased to 32.1 percent of loan originations.
Given the declining share of conventional and
conforming loans, the structure of mortgage contracts merits further consideration.

General Structure of Mortgage Contracts
Despite all their differences, mortgage loans
are just special cases of a general representation.
Some form of notation is needed to characterize
this representation. Consider the expenditure
associated with the purchase of a house of size h
and a unit price of p. We can consider h as the
number of square feet in the house and p as the
price per square foot. If buyers purchase a house
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with cash, the total expenditure is then denoted
by ph. Most buyers do not have assets available
that allow a check to be written for ph, and therefore they must acquire a loan to finance this large
expenditure.
In general, a mortgage loan requires a down
payment equal to χ percent of the value of the
house. The amount χph represents the amount
of equity in the house at the time of purchase,
and D0 = 共1 – χ 兲ph represents the initial amount
of the loan. In a particular period, denoted by n,
the borrower faces a payment amount mn (i.e.,
monthly or yearly payment) that depends on the
size of the original loan, D0, the length of the mortgage, N, and the mortgage interest rate, r m. This
payment can be subdivided into an amortization
(or principal) component, An, which is determined
by the amortization schedule, and an interest
component, In, which depends on the payment
schedule. That is,
(1)

D n + 1 = D n − A n , ∀n .

H n +1 = H n + An ,

∀n,

where H0 = χph denotes the home equity in the
initial period.4
This representation of mortgage contracts is
very general and summarizes many of the differ3

The calculation of the mortgage payment depends on the characteristics of the contract, but for all contracts the present value of
the payments must be equal to the total amount borrowed,

D0 ≡χ ph =

588

In the United States, fixed-rate mortgages
(FRMs) typically are considered the standard mortgage contract. This loan product is characterized
by a constant mortgage payment over the term of
the mortgage, m ⬅ m1 = … = mN . This value, m,
must be consistent with the condition that the
present value of mortgage payments repays the
initial loan. That is,

mn = An + I n , ∀n,

This formula shows that the level of outstanding
debt at the start of period n is reduced by the
amount of any principal payment. A principal
payment increases the level of equity in the home.
If the amount of equity in a home at the start of
period n is defined as Hn, a payment of principal
equal to An increases equity in the house available
in the next period to Hn+1. Formally,
(3)

Mortgage Loans with Constant Payments

D0 ≡ χ ph =

where the interest payments are calculated by
In = r mDn.3 An expression that determines how
the remaining debt, Dn, changes over time can be
written as
(2)

ent contracts available in the financial markets.
For example, this formulation can accommodate
a no-down-payment loan by setting χ = 0 so that
the initial loan is equal to D0 = ph. Because this
framework can be used to characterize differences
in the amortization terms and payment schedules,
we use it to describe the characteristics of some
prominent types of mortgage loans.

m1
1+ r

+

m2

(1 + r )2

N OV E M B E R /D E C E M B E R

++

mN

(1 + r )N

2008

.

m
m
m
++
+
.
N −1
1+ r
(1 + r )
(1 + r )N

If this equation is solved for m, we can write

m = λ D0 ,
where λ = r m[1 – 共1 + r m兲–N ]–1. Because the mortgage payment is constant each period, and m =
At + It , the outstanding debt decreases over time
D0 > … > Dn. This means the fixed-payment contract front-loads interest rate payments,

(

)

Dn +1 = 1 + r m D n − m,

∀n,

and, thus, back-loads principal payments,

An = m − r m D n .
The equity in the house increases each period by
the mortgage payment net of the interest payment
component:

H n +1 = H n +  m − r m D n  ,

∀n.

We now present some examples to illustrate key
properties of the FRM contract.
4

It is important to state that for the sake of simplicity this framework assumes no changes in house prices. If house prices are
allowed to change, then the equity equation would have to allow
for capital gains and losses.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Chambers, Garriga, Schlagenhauf

Table 2
Characteristics of a Fixed-Rate Mortgage at 6 Percent*
Payment

Total payment ($)

Interest ($)

Principal ($)

Remaining
principal ($)

1

1,178.74

973.51

205.23

199,794.77

2

1,178.74

972.51

206.23

199,588.54

120

1,178.74

812.98

365.76

166,655.59

181

1,178.74

686.89

491.85

140,625.26

219

1,178.74

587.23

591.51

120,049.79

240

1,178.74

523.73

655.01

106,940.84

251

1,178.74

487.89

690.95

99,521.83

360
Total

1,178.74

5.71

1,173.03

424,346.40

224,346.40

200,000.00

0.00
—

NOTE: *Based on 30-year maturity.

Example 1. Consider the purchase of a house
with a total cost of ph = $250,000 using a loan
with a 20 percent down payment, χ = 0.20; an
interest rate of 6 percent annually; and a 30-year
maturity. This mortgage loan is for $200,000.5
Table 2 illustrates the changes in interest and
principal payments per month over the length
of the mortgage contract.
The first two rows of Table 2 show the mortgage payment in the first and second months of
the contract. The monthly payment on this mortgage is $1,178.74. In the first period, $973.51 of
the monthly payment goes to interest rate payments. This means the principal payment is only
$205.23.6 Now, let us consider the mortgage payment 10 years into the mortgage. Although the
monthly payment does not change, the principal
payment has increased to $365.76 and the interest
payment component has decreased to $812.98.
After 10 years, the homeowner has paid off only
5

Tables 2 through 9 apply to the following situation: house purchase price of $250,000 with a down payment of 20 percent (total
loan amount of $200,000). Other parameters vary as noted in the
individual examples.

6

This is the same example used in McDonald and Thornton (2008).
The numbers presented here are slightly different because of a
difference in interest rate calculation. McDonald and Thornton
calculate the monthly interest rate as 0.06/12 = 0.005. We calculate
the monthly interest as 1.06共1/12兲 –1 = 0.004868. This explains
why our payments are slightly lower.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

$33,344.41 of the original $200,000 loan. The
month after the halfway point in the mortgage
occurs at period 181. The interest payment component of the monthly payment still exceeds the
principal payment. In payment period 219—18
years and 3 months into the contract—the principal component of the monthly payment finally
exceeds the interest payment component. From
this point forward, the principal payment will be
larger than the interest payment. At the end of
20 years, or period 240, the principal component
of the $1,178.74 monthly payment is $655.01.
However, $106,941.84 is still owed on the original
$200,000 loan. The outstanding loan balance does
not drop below $100,000 until payment period
251. With a standard 30-year mortgage contract,
it takes nearly 22 years to pay off half the mortgage
loan. The remaining half of the mortgage will be
repaid in the final 8 years of this mortgage.
Example 2. Table 3 shows the standard 30year mortgage contract if the mortgage interest
rate increases from 6 percent to 7 percent. A 1
percent increase in the interest rate increases the
monthly mortgage payment from $1,178.74 to
$1,301.85—a $123.11 increase. Furthermore, the
increase in the interest rate results in additional
back-loading of principal payments. After 10
years, less than $30,000 of the original balance
is paid off. The payment period when the prinN OV E M B E R /D E C E M B E R

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Table 3
Characteristics of a Fixed-Rate Mortgage at 7 Percent*
Payment

Total payment ($)

Interest ($)

Principal ($)

Remaining
principal ($)

1

1,301.85

1,130.83

171.02

199,828.98

2

1,301.85

1,129.86

171.99

199,656.99

120

1,301.85

967.32

334.53

170,746.58

181

1,301.85

830.00

471.85

146,322.72

239

1,301.85

647.47

654.38

113,858.74

240

1,301.85

643.77

658.08

113,200.66

260

1,301.85

565.22

736.63

99,965.68

360
Total

1,301.85

7.31

1,294.54

468,666.00

268,666.00

200,000.00

0.00
—

NOTE: *Based on 30-year maturity.

cipal component exceeds the interest component
does not occur until period 239. In fact, the outstanding balance will not drop below $100,000
until payment 260—9 months later than if the
interest rate is 6 percent (as in Example 1).
This table clearly illustrates the impact of
interest rate changes on a mortgage loan. If the
total interest payments on the mortgage contract
presented in Table 2 are compared with those in
Table 3, the 1 percent increase in the interest rate
results in $44,320 of additional mortgage payments over the life of the mortgage.

Mortgage with Constant Amortization
As seen in Tables 2 and 3, the FRM accrues
little equity in the initial years of the mortgage
because most of the mortgage payment services
interest payments. Some buyers would benefit
by a combination of an FRM and faster equity
accrual. Can a mortgage contract be designed to
allow accrual of more equity in the initial periods,
and what properties would be involved in such
a contract? A mortgage contract with this benefit
is known as a constant amortization mortgage
(CAM). This loan contract allows constant contributions toward equity in each constant amortization mortgage period; that is, the amortization
schedule is An = An+1 = A. Because the interest
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N OV E M B E R /D E C E M B E R

2008

repayment schedule depends on the size of outstanding level of debt, Dn, and the loan term, N,
the mortgage payment, mn, is no longer constant
over the duration of the loan. Formally, the constant amortization term is calculated by

A=

D0 (1 − χ ) ph
=
.
N
N

If the expression for the interest payments is
used, the monthly mortgage payment, mn, will
decrease over the length of the mortgage. This
characteristic of the CAM follows from the decline
in outstanding principal over the life of the contract. The monthly payment is determined by

mn =

D0
+ r m Dn .
N

For this contract, the changes in the outstanding
level of debt and home equity are represented by

D n +1 = D n −

D0
,
N

∀n,

D0
,
N

∀n .

and

H n +1 = H n +

Example 3. We consider a $250,000 30-year
loan with a 20 percent down payment and a 6
percent annual interest rate to show the characF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Chambers, Garriga, Schlagenhauf

Table 4
Characteristics of a Constant Amortization Mortgage at 6 Percent*
Payment

Total payment ($)

Interest ($)

Principal ($)

Remaining
principal ($)

1

1,529.07

973.51

555.56

199,444.44

2

1,526.36

970.81

555.56

198,888.89

120

1,207.27

651.71

555.56

133,333.33

156

1,109.92

554.36

555.56

113,333.33

181

1,042.31

486.76

555.56

99,444.44

240

882.76

327.21

555.56

66,666.67

360

558.26

2.70

555.56

0.00

375,718.58

175,718.58

200,000.00

Total

—

NOTE: *Based on 30-year maturity.

teristics of this type of contract. Table 4 presents
the monthly mortgage payment, principal component, and interest component.
The monthly payment with this contract has
a much different profile than that of a fixed-payment mortgage loan. Clearly, the amount of the
mortgage payment declines over the life of the
loan. The initial payment is nearly three times
the size of the payment in the last period. Principal payments are constant over the life of the loan,
thus allowing for faster equity accumulation. Half
of the original principal is repaid halfway through
the loan. From a wealth accumulation perspective,
this is an attractive feature. However, the declining payment profile is not positively correlated
with a normal household’s earning pattern during
the first half of the life cycle: Mortgage payments
are highest when earnings tend to be lower. From
a household budget perspective, this could be a
very unattractive option.

Balloon and Interest-Only Loans
The key property of the CAM is the payment
of principal every period. In contrast, balloon
and interest-only loans allow no amortization of
principal throughout the term of the mortgage. A
balloon loan is a very simple contract in which
the entire principal borrowed is paid in full in
the last payment period, N. This product tends
to be more popular when mortgage rates are high
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

and home buyers anticipate lower future mortgage
rates. In addition, homeowners who expect to stay
in their homes only for a short time may find this
contract attractive as they are not concerned about
paying principal. The amortization schedule for
this contract can be written as
∀n < N
0
An = 
.
(1 − χ ) ph n = N
This means that the mortgage payment in all
periods, except the last period, is equal to the
interest rate payment, In = r mD0. Hence, the mortgage payment for this contract can be specified as
∀n < N
I n
mn = 
,
m
 1 + r D0 n = N

(

)

where D0 = 共1 – χ 兲ph. The evolution of the outstanding level of debt can be written as
D n ,
Dn +1 = 
0,

∀n < N
.
n=N

With an interest-only loan and no change in
house prices, the homeowner never accrues equity
beyond the initial down payment. Hence, An = 0
and mn = In = r mD0 for all n. In essence, the homeowner effectively rents the property from the
lender and the mortgage (interest) payments are
the effective rental cost. As a result, the monthly
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Table 5
Characteristics of a Balloon Mortgage at 6 Percent*
Total payment ($)

Interest ($)

Principal ($)

Remaining
principal ($)

1

973.51

973.51

0.00

200,000.00

2

973.51

973.51

0.00

200,000.00

180

973.51

973.51

0.00

200,000.00

181

1,670.59

973.51

697.08

199,302.92

219

1,670.59

832.25

838.34

170,141.84

240

1,670.59

742.26

928.33

151,562.86

290

1,670.59

487.16

1,183.43

98,898.87

Payment

360
Total

1,670.59

8.09

1,662.50

475,938.02

275,938.02

200,000.00

0.00
—

NOTE: *Based on 30-year maturity, 15 years interest only.

Table 6
Characteristics of an Adjustable-Rate Mortgage with a Constant Interest Rate of 6 Percent*
Total payment ($)

Interest ($)

Principal ($)

Remaining
principal ($)

1

973.51

973.51

0.00

200,000.00

2

973.51

973.51

0.00

200,000.00

36

973.51

973.51

0.00

200,000.00

37

1228.20

973.51

254.89

199,745.30

120

1,228.20

847.10

381.10

173,648.03

181

1,228.20

715.71

512.49

146,525.31

219

1,228.20

611.86

616.34

125,086.37

240

1,228.20

545.70

682.50

111,427.30

257

1,228.20

486.97

741.23

99,303.08

360

1,228.20

5.95

1,222.25

0.00

432,983.16

232,983.16

200,000.00

Payment

Total

—

NOTE: *Based on 30-year maturity, 3 years interest only.

mortgage payment is minimized because no periodic payments toward equity are made. A homeowner is fully leveraged with the bank with this
type of mortgage contract. If capital gains are
realized, the return on the housing investment is
maximized. If the homeowner itemizes tax deductions, a large interest deduction is an attractive
by-product of this contract.
592

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Example 4. This example illustrates a balloon
contract with a 15-year interest-only loan that is
rolled into a 15-year fixed-payment mortgage.
Table 5 shows the payment profiles for this contract. We also assume an interest rate of 6 percent
and a 20 percent down payment.
The interest-only part of the loan requires
180 mortgage payments of $973.51 just to cover
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Chambers, Garriga, Schlagenhauf

Table 7
Characteristics of an Adjustable-Rate Mortgage with a Rising Interest Rate*
Total payment ($)

Interest ($)

Principal ($)

Remaining
principal ($)

1

973.51

973.51

0.00

200,000.00

2

973.51

973.51

0.00

200,000.00

36

973.51

973.51

0.00

200,000.00

37

1,347.72

1,130.83

216.89

199,783.11

120

1,347.72

1,001.40

346.32

176,762.45

181

1,347.72

859.24

488.48

151,477.91

239

1,347.72

670.28

677.44

117,869.91

240

1,347.72

666.45

681.27

117,188.65

264

1,347.72

567.74

779.98

99,630.97

Payment

360
Total

1,347.72

7.57

1,340.15

471,707.64

271,707.64

200,000.00

0.00
—

NOTE: *Based on 30-year maturity, 3 years interest only at a 6 percent interest rate, and the remaining years at 7 percent.

the interest obligations on the $200,000 loan.
After 15 years, the mortgage payment increases
to $1,670.59 because the 15-year balloon loan is
rolled into a 15-year FRM. Payment number 219
denotes the month in which principal payments
exceed interest payments. In period 290, half of
the $200,000 debt will be paid off. With this type
of mortgage contract, it takes more than 24 years
to accrue $100,000 in equity.
Example 5. Some ARMs used in recent years
have a very short period of interest-only payments. Table 6 presents the payment profiles for
a 3-year interest-only ARM that rolls into a 27year standard FRM. The assumptions for the
interest rate, total contract length, and down
payment remain unchanged.
The monthly interest payments for this
interest-only ARM are $973.51. Once the standard
27-year contract takes effect, the monthly mortgage payment increases by $254.69 to $1,228.20.
This increase is not caused by an interest rate
increase, but rather payment toward principal.
Example 6. Mortgage interest rates have
begun to increase recently. What effect does this
have on an interest-only ARM? To show this
effect, we allow the interest rate to increase to
7 percent for the standard FRM that is obtained
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

after the 3-year ARM expires. Table 7 presents
the various payment patterns. A 100-basis-point
increase in the interest rate causes the monthly
payment to increase to $1,347.72 from $1,228.20—
a 38 percent increase in the mortgage payment
from the interest-only payments. This example
illustrates the risk facing homeowners when the
interest rate increases before the transition to a
standard FRM.

Graduated-Payment Mortgages
The repayment structures of the previous
contract examples are relatively rigid. Payments
are either constant during the entire contract or
proportional to the outstanding level of debt.
Mortgage contracts can be designed with a variable repayment schedule. This section focuses on
mortgage loan payments that increase over time,
m1 < … < mN. This feature could attract first-time
buyers because payments are initially lower than
payments in a standard contract. When a buyer’s
income grows over the life cycle, this loan product
allows for stable housing expenditure as a ratio to
income. However, the buyer’s equity in the home
builds at a slower rate than with the standard
contract, which may explain this product’s lack
of popularity historically. Mortgage contracts with
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Table 8
Characteristics of a Graduated-Payment Mortgage: 1 Percent Geometric Growth Rate*
Payment

Remaining
principal ($)

Total payment ($)

Interest ($)

1

195.18

973.51

–778.33

200,778.33

2

197.13

977.30

–780.17

201,558.50

120

637.79

1,459.98

–822.19

300,763.84

181

1,170.26

1,666.83

–496.57

342,933.91

220

1,725.11

1,719.49

5.57

353,260.70

240

2,104.96

1,701.52

403.44

349,161.20

344

5,924.70

508.34

5,416.36

99,017.59

360
Total

Principal ($)

6,947.18

33.65

6,913.53

682,149.10

482,149.10

200,000.00

0.00
—

NOTE: *Based on interest rate of 6 percent, 30-year maturity, and a payment growth of 1 percent.

variable repayment schedules are known as
graduated-payment mortgages (GPMs). These
contracts are of special interest because their
features are similar to those of mortgage contracts
sold to subprime borrowers.
The repayment schedule for a GPM depends
on the growth rate of these payments. The growth
rate of payments is specified in the mortgage contract, and borrowers considering this contract
must know this condition. We present examples
to illustrate why knowledge of this parameter or
condition is important. Typical GPM growth patterns are either geometric or arithmetic. We focus
on GPMs with geometric growth patterns.
With this type of contract, mortgage payments
evolve according to a constant geometric growth
rate denoted by

mn +1 = (1 + g ) mn ,
where g > 0. This means the amortization and
interest payments also increase as

mn = An + I n .
The initial mortgage payment is determined by

m0 = λg D0 ,
where λg = 共r m – g兲[1 – 共1 + r m兲–N ]–1. The law of
motion for the outstanding debt satisfies
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N OV E M B E R /D E C E M B E R

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(

)

n

Dn +1 = 1 + r m D n − (1 + g ) m0 ,
and the amortization term is An = λg D0 – r mDn.
Example 7. Table 8 shows the implications
for payments of a GPM contract when the mortgage payments grow at 1 percent per payment.
We maintain the assumption of a 30-year contract
with a 20 percent down payment and a 6 percent
annual interest rate.
Clearly, the initial payments of this mortgage
are very low, which explains why this contract is
attractive for first-time buyers. However, these low
payments come at a cost: The monthly payment
does not cover the interest on the outstanding
balance. Thus, the remaining principal increases.
This mortgage contract exhibits negative amortization. In this example, the mortgage payment
does not cover the interest on the principal for
the first 219 months. The maximum remaining
principal for this home purchase increases to more
than $350,000 from the original $200,000 debt. It
is interesting to note that the final $100,000 principal is paid in the final 16 months of this mortgage. Because the principal is back-loaded and
must be paid off, the monthly payment must
increase over time. The monthly mortgage payment tops out in the last month of the contract at
$6,913.53. A homeowner who chooses this conF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Chambers, Garriga, Schlagenhauf

Table 9
Characteristics of a Graduated-Payment Mortgage: 0.1 Percent Geometric Growth Rate*
Payment

Total payment ($)

Interest ($)

Principal ($)

Remaining
principal ($)

57.17

199,942.83

1

1,030.68

973.51

2

1,031.71

973.23

58.48

199,884.36

120

1,160.85

884.19

276.67

181,372.92

240

1,308.78

614.19

694.59

125,485.59

273

1,352.67

489.90

862.77

99,782.99

360
Total

1,475.56

7.15

1,468.41

446,356.77

246,356.77

200,000.00

0.00
—

NOTE: *Based on interest rate of 6 percent, 30-year maturity, and a payment growth of 0.1 percent.

tract pays $482,149.10 in total interest payments.
Compared with the FRM contract presented in
Table 2, total interest payments are more than
double. These characteristics make GPMs risky
from a lender’s perspective because the potential
for default is greater, which is one reason this
type of contract has not historically been a factor
in the mortgage market.
Example 8. Table 9 shows the importance of
the payment growth parameter by reducing the
monthly growth rate from 1 percent to 0.1 percent. Negative amortization does not occur with
a lower monthly growth rate. Perhaps the most
striking result is the amount of total interest payments over the length of the mortgage contract.
When the mortgage contract has a 1 percent
monthly growth rate, total interest payments
are $482,149.10. If the monthly growth rate
falls to 0.1 percent, total interest payments are
$246,356.77. Clearly there is a cost to loans with
negative amortization.

different loans. Different types of CLs are offered
in the mortgage industry; for example, an 80-15-5
loan implies a primary loan for 80 percent of the
value, a secondary loan for 15 percent, and a 5
percent down payment. Another example is the
so-called no-down-payment, or an 80-20 loan,
which consists of a primary loan with a loan-tovalue ratio of 80 percent and a second loan for
the 20 percent down payment.
Formally, the primary loan covers a fraction
of the total purchase, D1 = 共1 – χ 兲ph, with a payment schedule, m1n, and maturity, N1. The second
loan partially or fully covers the down payment,
D2 = ϑχ ph, where ϑ 僆 共0,1] and represents the
fraction of the down payment financed by the
second loan. The second loan has an interest
premium r2m = r1m + ζ (where ζ > 0), a mortgage
payment mn2 , and a maturity N2 ≤ N1. In this case,

Combo Loans

Because both loans are of a fixed-rate form, the
laws of motion are equivalent to those presented
in the FRM contract discussion. Table 10 shows
characteristics of a CL.
Example 9. Table 10 presents the profile for
an 80-20 CL for our $250,000 house. The first
$200,000 is borrowed with the standard fixedpayment mortgage at 6 percent interest. The
remaining $50,000 is financed using another

In the late 1990s a new mortgage product
became popular as a way to avoid large down
payments and mortgage insurance.7 This product
is known as the combo loan and amounts to two
7

Government-sponsored enterprises (GSEs) initiated the use of
this product in the late 1990s and it became popular in private
mortgage markets between 2001 and 2002.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

m1 + m2 Ä whenÄ N 2 ≤ n ≤ N 1
.
mn =  1
m Ä whenÄ n < N 2

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Chambers, Garriga, Schlagenhauf

Table 10
Characteristics of an 80-20 Combo Loan Mortgage*
Payment

Total payment ($)

Interest ($)

Principal ($)

Remaining
principal ($)

1

1,535.94

1,295.21

240.73

249,759.27

2

1,535.94

1,293.98

241.96

249,517.32

120

1,535.94

1,094.04

441.90

210,261.45

181

1,535.94

931.49

604.45

178,528.13

156

1,535.94

554.36

555.56

113,333.33

228

1,535.94

765.78

770.16

146,301.19

240

1,535.94

716.53

819.41

136,742.23

281

1,535.94

522.76

1,013.15

99,220.31

360

1,535.94

7.99

1,527.95

0.00

552,938.40

302,938.40

250,000.00

Total

—

NOTE: *Based on interest rate of 6 percent, 30-year maturity, and second loan rate of 8 percent.

fixed-payment mortgage that incorporates a risk
premium of 2 percent. We will assume the second
mortgage is also for 30 years. (In reality, the second mortgage is usually for 10 or 15 years.) The
second loan for $50,000 increases the monthly
payment by $357.20. The mortgage payment pattern of this CL is very similar to the basic fixedpayment mortgage. This is not surprising because
the CL is nothing more than a combination of two
FRMs. An obvious question for borrowers is why
they should not obtain just one FRM with no
down payment. The larger single loan would
require mortgage insurance. The total monthly
payment, including the mortgage insurance,
would exceed the monthly payment on the CL.
The CL is attractive for one segment of buyers who
desire to enter the housing market: young buyers
with high incomes. These buyers can afford the
mortgage payment, but they have not yet had time
to accumulate savings for the down payment.

A MODEL OF HOUSING
DECISIONS AND MORTGAGE
CHOICES
The previous section described various features and properties of mortgage contracts avail596

N OV E M B E R /D E C E M B E R

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able in the marketplace. However, the discussion
did not detail the characteristics of individuals
who might choose a particular contract. In addition, no mention was made of the ramifications
of alternative contracts for the performance of the
aggregate economy. The only way to discuss these
issues is by analyzing alternative mortgages in
the context of a model economy in which buyers
can choose from among a set of mortgage products.
In this section, we use a simplified version of the
consumer problem used by Chambers, Garriga,
and Schlagenhauf (2007a,b) to address the implications of mortgage choice for the performance of
the aggregate economy (i.e., house prices, interest
rates). This model allows us to focus on how types
of mortgages influence the homeownership decision. This modeling style allows quick analysis
of aggregate implications of mortgage markets and
yet maintains the details needed to identify implications across different income, wealth distribution, and age cohorts.

Model Features
Age Structure. We develop a life cycle model
with ex ante heterogeneous individuals. Let j
denote the age of an individual and let J represent
the maximum number of periods an individual
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Chambers, Garriga, Schlagenhauf

can live. At every period, an individual faces
mortality risk and uninsurable labor-earning
uncertainty. The survival probability, conditional
on the individual being alive at age j, is denoted
by ψj+1 僆 [0,1], with ψ1 = 1 and ψj+1 = 0. Earning
uncertainty implies that the individual is subject
to income shocks that cannot be insured via private contracts. In addition, we assume that annuity markets for mortality risk are absent. The lack
of these insurance markets creates a demand for
precautionary savings to minimize fluctuations in
consumption goods, c, and in the consumption
of housing services, s, over the life cycle.
Preferences. Individual preferences rank
goods (consumption and housing) according to
a utility function, u共c,s兲. The utility function
has the property that additional consumption
increases utility and also results in declining
marginal utility. Consumption over periods is
discounted at rate β and, thus, lifetime utility is
defined as
J

(

)

v 1 = E ∑ψ j β j −1u c j , s j .
j =1

The assumption that utility is separable over
time allows for a simple recursive structure of
preferences for every realization of uncertainty:
J

(

)

v 1 = u (c1 , s1 ) + β E ∑ j =2ψ j β j − 2u c j , s j .
Using the definition of expected lifetime utility,
we can write the previous expression as

assumption simplifies the problem because
households do not need to anticipate changes in
house prices. A housing investment of size h′ can
be thought of as the number of square feet in the
house. A house of size h′ yields s services.8 If a
household does not invest in housing, h = 0, the
household is a renter and must purchase housing
services from a rental market. The rental price
of a unit of housing services is R.
Housing investment is financed through longterm mortgage contracts and is subject to transaction costs. We need to summarize the information
required so that the monthly payment, remaining
principal, and equity position in the house can be
identified for any mortgage contract. This critical
information consists of the house size, h, the type
of mortgage contract, z, and the remaining length
of the mortgage, n. This information set can be
used to identify the desired information concerning a household’s mortgage contract.
Household Income. Household income
varies over the buyer’s life cycle and depends on
whether the individual is a worker or a retiree.
For workers younger than the mandatory retirement age, j < j*, income is stochastic and depends
on the basic wage income, w, a life cycle term
that depends on age, υj , and the persistent idiosyncratic component, ε , drawn from a probability
distribution that evolves according to the transition law, Πε,ε ′. For an individual older than j*, a
retirement benefit, θ, is received from the government equal to θ. Income can be specified as

v 1 = u (c1 , s1 ) + β Ev 2 ,

w ευ j + (1 + r ) a,
y a, ε , j , υ j = 
θ + (1 + r ) a,

(

where
J

(

v 2 = ∑ j =2ψ j β j −2u c j , s j

)

represents the future lifetime expected utility.
Asset Structure. Individuals have access to
a portfolio of assets to mitigate income and
mortality risk. We consider two distinct assets:
a riskless financial asset denoted by a′ with a
net return r and a risky housing durable good
denoted by h′ with a market price, p, where the
prime is used to denote future variables. To keep
things simple, we assume that the price of housing does not change over time, so p = p′. This

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

)

if j < j ∗,
if Ä j ≥ j ∗ .

In the presence of mortality risk and missing annuity markets, we assume borrowing constraints,
a′ ≥ 0, to prevent individuals (buyers and renters)
from dying with negative wealth. We also assume
that households are born with initial wealth
dependent on their initial income level.
The Decision Problem. Individuals make
decisions about consumption goods, c, housing
services, s, a mortgage contract type, z, and
8

For the sake of simplicity, we assume a linear relationship between
house size and services generated. In other words, s = h′.

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Chambers, Garriga, Schlagenhauf

Curr ent r enter : h = 0

 Continues renting: h ′ = 0
 Purchases a house: h ′ > 0


Curr ent owner : h > 0

Stays in house: h ′ = h
Changes size (upsize or downsize): h ′ ≠ h

Sell and rent: h ′ = 0

investment in assets, a′, and housing, h′. The
individual’s current-period budget constraint
depends on the household’s asset holdings, the
current housing investment, the remaining length
of the mortgage, labor income shock, and age.
We can isolate five possible decision problems
that a household must solve.
The household value function, v, is described
by a vector of so-called state variables that provide
sufficient information of the position of the individual at the start of the period. The state vector
is characterized by the level of assets at the start
of the period, a, the prior-period housing position,
h, the number of periods remaining on an existing
mortgage, n, the mortgage contract type, z, the
value of the current-period idiosyncratic shock,
ε , and the age of the individual, j. To shorten
notation of the individual’s characteristics, we
define x = 共a,h,n,z,ε ,j兲. Using a recursive approach,
we know that the household decisions for
c,s,z,a′ and h′ depend on the x vector. For example, suppose that x contains the following information, x = 共1000,2000,56,FRM,2,36兲. This vector
tells us that the individual has $1,000 of nonhousing wealth, a 2,000-square-foot home with a
market value given by p × 2,000, where p represents the given price per square foot, 56 pending
mortgage payments with the bank, an FRM, the
income shock this period is two times average
income, and the individual’s age is 36. The decisions made by this individual will differ from
those of an individual who has a different state
vector x = 共20000,2000,56,FRM,2,41兲, because
the second individual has more wealth and is 5
years older. For individuals who do not own a
home, the information vector would have many
zero entries, such as x = 共a,0,0,0,ε ,j 兲.
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Given all the possible options, the individual
could be in one of five situations with respect to
the housing investment and mortgage choice
decisions. These five decisions are summarized
in the box above.
We now detail the various decision problems.
First, we consider an individual who starts as a
renter and then consider an individual who starts
as a homeowner.
Renters. An individual who is currently renting (h = 0) has two options: continue renting
(h′ = 0) or purchase a house (h′ > 0). This is a
discrete choice in ownership that can easily be
captured by the value function, v (present and
future utility), associated with these two options.
Given the relevant information vector x = 共a,0,0,
0,ε ,j 兲, the individual chooses the option with the
higher value, which can be expressed as

{

}

v ( x ) = max v r ,v o .
The value associated with continued renting is
determined by the choice of consumption goods, c,
housing services, s, and investment in assets, a′,
which solves the problem

v r ( x ) = max u (c, s ) + β j +1Ev ( x ′ ),
s.t. c + a ′ + Rs = y ( x ).
The decisions are restricted to positive values
for c,s,a′ and the evolution of the state vector that
summarizes the future information as given by
x′ = 共a′,0,0,0,ε ′,j+1兲, where a′ denotes next period’s
wealth, ε ′ represents next period’s realization of
the income shock, and j+1 captures the fact that
the individual will be one period older.
The renter who chooses to purchase a house
must solve a different problem as choices must
now be made over h′ > 0, a mortgage type, z, as

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Chambers, Garriga, Schlagenhauf

well as c, s, and a′. This decision problem can be
written as

homeowner decides to stay in the current house,
the optimization problem can be written as

v o ( x ) = max u (c , s ) + β j +1Ev ( x ′ ),

v s ( x ) = max u (c, h ′ ) + β j +1Ev ( x ′ )

s.t. c + a ′ + ϕb + χ (z ′ )  ph ′ + m ( x ) = y ( x ).
It should be noted that a purchase of a house
requires two up-front expenditures: transaction
costs (i.e., realtors’ fees, closing costs) that are
proportional to the value of the house, ϕb ph′, and
a down payment to the mortgage bank for a fraction of the value of the house, χ共z′ 兲 (i.e., 20 percent of the purchase price). These payments are
incurred only at the time of the purchase. Homeowners also must make mortgage payments. These
payments are denoted by m共x兲 and depend on relevant variables, such as the loan amount, 共1 – χ 兲ph′,
the type of mortgage (i.e., FRM vs. ARM), the
length of the contract (i.e., 30 or 15 years), and the
interest rate associated with the loan. It is important to restate that a homeowner who purchases
a house of size h′ receives s units of housing consumption. The value of these housing services is
denoted by Rs h. This value does not appear in the
budget constraint because these services are consumed internally. As a result, the value of services
generated is canceled by the value of services
consumed internally. The household’s decisions
influence the information state in the following
period; that is, x′ = 共a′,h′,N共z兲 – 1,z′,ε ′,j +1兲. Again,
to determine whether an individual continues to
rent or purchases a home, we need to solve both
problems—v r共x兲 and v 0共x兲— and find the one
that yields the highest value. When v r共x兲 > v 0共x兲,
the individual continues to rent; otherwise he or
she will become a homeowner.
Owners. The decision problem for an individual who currently owns a house, (h > 0), has a
similar structure. However, a homeowner faces a
different set of options: stay in the same house,
(h′ = h), purchase a different house, (h′ ≠ h), or sell
the house and acquire housing services through
the rental market, (h′ = 0). Given the relevant
information x = 共a,h,n,z, ε,j兲, the individual solves

{

}

s.t. c + a ′ = y ( x ) − m ( x ) .
This problem is very simple, because the homeowner must make decisions only on consumption
and saving after making the mortgage payment.
If the schedule of pending mortgage payments
shows zero, n = 0, then the implied mortgage
payment is also set to zero, m共x兲 = 0. The future
state of information for this case is given by
x′ = 共a′,h′,n′, z′, ε ′,j +1兲, where n′ = max{n – 1,0}.
For the homeowner who decides to either
upsize or downsize, (h ≠ h′), the problem becomes

v c ( x ) = max u (c , h ′ ) + β j +1Ev ( x ′ )
s.t. c + a ′ + ϕb + χ (z ′ )  ph ′ + m ( x )
= y ( x ) + (1 − ϕs ) ph − D ( n, z ) .
This individual must sell the existing property
to purchase a new one. The choices depend on
the income received from selling the property, ph,
net of transactions costs from selling, ϕs , and the
remaining principal, D共n,z兲, owed to the lender.
The standing balance depends on whether the
mortgage has been paid off (n = 0 and D共n,z兲 = 0)
or not (n > 0 and D共n,z兲 > 0) and the type of loan
contract. For example, mortgage loans with a slow
amortization usually imply large remaining principal when the property is sold over the length
of the loan, whereas contracts such as the constant amortization imply a much faster repayment. A new loan, z′, must be acquired if the
individual upsizes and purchases a new house,
h′ > 0. The relevant future information is given
by x′ = 共a′,h′,N – 1, z′, ε ′,j +1兲.
Finally, we solve the problem of a homeowner
who sells the house, h > 0, and becomes a renter,
h′ = 0.9 The optimization problem is very similar
to the previous one. However, in this case the individual must sell the home and rent, Rs. Formally,

v ( x ) = max v s ,v c ,v r .
9

Each of these three different values is calculated
by solving three different decision problems. If the
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

In the last period, all households must sell h, rent housing services,
and consume all their assets, a, as a bequest motive which is not
in the model. In the last period, h′ = a′ = 0.

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Chambers, Garriga, Schlagenhauf

v r ( x ) = max u (c, s ) + β j +1Ev ( x ′ ),
s.t. c + a ′ + Rs = y ( x ) + (1 − ϕ s ) ph − D ( n, z )  ,
where the relevant future information is simply
given by x′ = 共a′,0,0,0,ε ′,j+1兲.
Given the initial information summarized in
x, the choice of whether to stay in the house,
change the housing size, or sell the house and
become a renter depends on the values of v s, v c,
and v r.

Aggregation and Parameterization
We want our model economy to be consistent
with certain features of the U.S. economy. In particular, we want to ensure that the choices of functional forms and parameter values are consistent
with key features of the U.S. housing market.
Replicating these features requires aggregating
the microeconomic behavior of all the households
in the economy. Because individuals are heterogeneous along six different dimensions—level of
wealth, housing holdings, pending mortgage payments, type of mortgage used to finance the house,
income shock, and age—our aggregation needs
to take into account the number of individuals
who have the same characteristics and the sum
across these characteristics. To aggregate these
dimensions, we define Φ共x兲 as the fraction of individuals who have a given level of characteristics
x = 共a,h,n,z, ε,j兲.
We can calculate aggregate statistics of the
economy by taking the weighted average of all the
household-level decisions across characteristics.
As an example we would generate the aggregate
housing stock, wealth, and consumption of housing services (or square feet) by calculating

H = ∫h ′ ( x ) Φ (dx ) ;
W = ∫a ′ ( x ) Φ (dx ) ;

live until age 86 (model period 23). Retirement is
assumed to be mandatory at age 65 (model period
16). Individuals survive to the next period with
probability ψj+1.10 The size of the age-specific
cohorts, µj , needs to be specified. Because of our
focus on steady-state equilibrium, these shares
must be consistent with the stationary population
distribution. As a result, these shares are determined from µj = ψj µj–1/共1 + ρ兲 for j = 1,2,…,J and

∑ jJ =1 µ j = 1,
where ρ denotes the population growth rate.
Using the resident population as the measure of
the population, the annual growth rate is set at
1.2 percent.
Functional Forms. The choice of preferences
is based on empirical evidence. The first-order
condition that determines the optimal amount
of housing consumption is denoted by

us j
uc j

where at the optimum sj = h′j . Jeske (2005) documents that the hj /cj ratio is increasing by age j. He
points out that standard homothetic preferences
over consumption and housing services,

(

600

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1

)

σ
u c j , s j = γ c σj + (1 − γ ) s σj  ,

imply a constant ratio
1

hj

 (1 − γ )  1−σ
=
,
c j  γ R 
because the parameters γ and σ and the rental
price R do not vary across age. Therefore, this
preference specification is inconsistent with the
empirical evidence over the life cycle. A preference structure consistent with the evidence is
denoted by

S = ∫s ( x ) Φ (dx ) .
The model can generate other aggregates of
interest in a similar manner. We start by discussing
how the model is parameterized.
Demographics. A period in the model is taken
to be three years. Individuals enter the labor
force at age 20 (model period 1) and potentially

= R,

u (c , s ) = γ

c 1−σ 1
s 1−σ 2
+ (1 − γ )
,
1 − σ1
1 − σ2

where the implied first-order condition is
denoted by
10

These probabilities are set at survival rates observed in 1994, and
the data are from the National Center for Health Statistics (U.S.
Department of Health and Human Services, 1994).

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Chambers, Garriga, Schlagenhauf

h σj 2
c σj 1

=

(1 − γ ) .
γR

This expression represents a nonlinear relationship between hj and cj that varies by age, j.
The coefficients, σ1 and σ2, determine the curvature of the utility function with respect to consumption and housing services. The relative ratio
of σ1 and σ2 determines the growth rate of the
housing-to-consumption ratio. A larger curvature
in consumption relative to the curvature in housing services implies that the marginal utility of
consumption exhibits relatively faster diminishing returns. When household income increases
over the life cycle (or different idiosyncratic labor
income shocks), a larger fraction of resources is
allocated to housing services. We set σ2 = 1 and
σ2 = 3 to match the observed average growth rate
while the preference parameter γ is estimated.
The discount factor, β, is set at 0.976, which is
derived from Chambers, Garriga, and Schlagenhauf
(2007a).
Endowments. Workers are assumed to have
an inelastic labor supply, but the effective quality of their supplied labor depends on two components. One component is age specific, υj , and
is designed to capture the hump in life cycle
earnings. We use U.S. Census Bureau (1994) data
to construct this variable. The other component
captures the stochastic component of earnings
and is based on Storesletten, Telmer, and Yaron
(2004). We discretize this income process into a
five-state Markov chain using the methodology
presented by Tauchen (1986). Our reported values
reflect the three-year horizon used in the model.
As a result, the efficiency values associated
with each possible productivity value, ε, are

Each household is born with an initial asset
position. This assumption accounts for the fact
that some of the youngest buyers who purchase
housing have some wealth. Failure to allow for
this initial asset distribution creates a bias against
the purchase of homes in the earliest age cohorts.
As a result, we use the asset distribution observed
in Panel Study on Income Dynamics (Institute for
Social Research, 1994) to match the initial distribution of wealth for the cohort of age 20 to 23.
Each income state has assigned the corresponding
level of assets to match the nonhousing wealthto-earnings ratio. We choose the basic level of
earnings, w, as a scaler to match labor earnings
over total earnings.
Housing. The housing market introduces a
number of parameters. The purchase of a house
requires a mortgage and down payment. In this
paper, we focus on the 30-year FRM as the benchmark mortgage. As a result of the assumption
that a period is three years, we set the mortgage
length, N, to 10 periods. The down payment, χ,
is set to 20 percent (matching facts from the 2004
U.S. Department of Commerce American Housing
Survey, AHS). Buying and selling property is
subject to transaction costs. We assume that all
these costs are paid by the buyer and set σs = 0
and σb = 0.06.
Because of the lumpy nature of the housing
investment (i.e., movement from H = 0 to H > 0),
the specification of the second point in the housing grid has important ramifications. This grid
point, h, determines the minimum house size and
has implications for the timing of investments in
housing, wealth portfolio decisions, and the
homeownership rate. We determine the size of
this grid point as part of the estimation problem
to avoid inadvertent implications on the results
caused by this variable.

ε ∈ E = {4.41, 3.51, 2.88, 2.37, 1.89},

Estimation

and the transition matrix is
0.47
0.29

π = 0.12

0.03
0.01
1

0.33 0.14
0.33 0.23
0.23 0.29
0.11 0.23
0.05 0.14

0.05 0.01 
0.11 0.03 
0.24 0.12  .

0.33 0.29 
0.33 0.47 

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

We estimate five parameters using an exactly
identified method of moments approach. The
parameters that need to be estimated are the
interest rate, r, the rental rate for housing, R, the
price of housing, p, the wage rate w, and the size
of the smallest housing investment position, h.
We identify these parameter values so that the
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Chambers, Garriga, Schlagenhauf

Table 11
Method of Moments Estimates*
Statistic

Data

Model estimate

Percent error

1. Ratio of wealth to gross domestic product

2.541

2.549

0.314

2. Ratio of housing stock to fixed capital stock

0.430

0.4298

–0.047

3. Ratio housing services to consumption of goods

0.230

0.235

2.7

4. Labor earnings over total earnings

0.700

0.71

1.4

5. Homeownership rate

0.640

0.643

0.468

Parameter

Value

1. Interest rate, r

0.0546

2. Rental price, R

0.3403

3. Housing price, p

1.4950

4. Wage rate, w

0.8768

5. Minimum house size, h

1.4480

NOTE: *Values in annual terms.

resulting aggregate statistics in the model economy are equal to five targets observed in the U.S.
economy.
i.

Wealth-to-gross income ratio (W/I ). We
find the target is the ratio of nonhousing
wealth to gross income, which is about
2.541 (annualized value), for the period
1958-2001.

ii. Housing stock-to-wealth ratio (H/W ).
For this ratio, the housing capital stock is
defined as the value of fixed assets in
owner and tenant residential property.
The housing stock data are from the fixed
asset tables of the Bureau of Economic
Analysis (1958-2001) The ratio of the housing stock to nonhousing wealth is 0.43.
iii. Housing services-to-consumption of
goods ratio (RS/C ). The targeted housing
consumption-to-nonhousing consumption
ratio is also based on National Income and
Product Accounts (NIPA) data (1958-2001),
where housing services are defined as
personal consumption expenditure for
housing while nonhousing consumption
is defined as nondurable and services
consumption expenditures net of hous602

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ing expenditures (U.S. Department of
Commerce, NIPA tables). The targeted ratio
for 1994 is 0.23, but the number does not
vary greatly over the period 1990-2000.
This value is from Jeske (2005).
iv. Labor earnings over total earnings. The
evidence from NIPA suggests that labor
share of the economy is about 70 percent.
We determine the value of w to match this
observation.
v. Homeownership ratio. This target is
based on data from the AHS (1994) for
1994 and is equal to 64.0 percent.
Table 11 summarizes the parameter estimates
and the empirical targets. The moments and the
parameter values are presented in annual terms.
The model nicely matches the moments of the
U.S. economy.

Model Evaluation
We can now take a more in-depth look at the
results from a distribution perspective. We begin
by studying the homeownership rate across both
the age and the income distribution (Table 12).
Another dimension of interest is the consumption of housing services. We measure average
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Chambers, Garriga, Schlagenhauf

Table 12
Homeownership Rates by Age
Homeownership rate (percent)
Variable

Total

20-34 years

35-49 years

50-64 years

65-74 years

75-89 years

Data 1994

64.0

40.0

64.5

75.2

79.3

77.4

Baseline model 1994

64.3

37.1

80.6

81.5

81.5

62.5

SOURCE: U.S. Census Bureau, Housing Vacancies and Homeownership (1994) and U.S. Department of Commerce, American Housing
Survey (1994).

Table 13
Owner-Occupied Housing Consumption by Age
House size (square footage)
Simulation

Total

20-34 years

35-49 years

50-64 years

65-74 years

75-89 years

Data 1994

2,137

1,854

2,220

2,301

2,088

2,045

Baseline model 1994

1,896

2,013

1,787

1,736

2,242

2,452

SOURCE: U.S. Department of Commerce, American Housing Survey (1994).

consumption of housing services by computing
the average size of an owner-occupied house.
Data from the AHS indicate the average owneroccupied house is 2,137 square feet. Our model
implies an average house size of 1,895 square feet.
Table 13 shows observed housing size by age
cohorts. The model reasonably estimates homeowners’ acquisition of appropriately sized homes.
The average size for most age cohorts is within a
few hundred square feet. Home size increases
with age of the homeowner, which is observed
only until age 65 in the data.11
Because households make savings decisions
with respect to assets, the portfolio allocations
implied by the model can be analyzed. In the
model, a household’s financial portfolio consists
of asset holding and equity in housing investment.
We use data from the 1994 Survey of Consumer
Finances (Board of Governors, 1998) to determine
the importance of housing in household portfolios.
11

It should be noted that the full equilibrium model with landlords
in Chambers, Garriga, and Schlagenhauf (2007a,b) does capture
the hump-shaped pattern in home size.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

We define assets as bond and stock holdings, and
housing is defined as the estimated value of an
existing homeowner’s house adjusted for the
remaining principal. The data indicate housing
represents a large fraction of a household’s portfolio in the youngest age cohorts. This fraction
declines with household age until around retirement age and then increases as retirees consume
their nonhousing wealth after retirement. As
shown in Figure 1, our model generates a similar
pattern.

MORTGAGE CHOICES
In this section we look at the implications of
mortgage innovation on the housing market, especially with regard to the rate of homeownership.
We focus on two of the largest mortgage innovations: ARM-type and CL mortgage contracts. In
the first example, households face an additional
decision regarding the type of mortgage to finance
their home purchase. We will allow a potential
home buyer to choose between a 30-year fixedN OV E M B E R /D E C E M B E R

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Chambers, Garriga, Schlagenhauf

Figure 1
Housing in the Portfolio by Age
Percent
70
Model Prediction
Data (SCF)
60

50

40

30

20

10

25

30

35

40

45

50

55

60

65

70

75

80

Age
SOURCE: Survey of Consumer Finances (Board of Governors of the Federal Reserve System, 1998).

payment mortgage with a 20 percent down payment and an ARM with 3 years of interest-only
payments followed by a 27-year fixed-payment
mortgage. This simulation generates an aggregate
homeownership rate of 65.83 percent, which is
an increase of 1.5 percent from the baseline simulation. The effects are even more dramatic for
homeownership rates by age.
Table 14 shows a very similar pattern to the
baseline case with a few important differences.
The biggest difference is the large increase in
homeownership by the youngest cohort. For
households younger than age 35, homeownership
has surged to nearly 50 percent. Some of this
increase in ownership is offset by a slight decrease
in ownership later in life. This difference is
explained by the labor income shocks for some
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of those who became owners by using ARM mortgages. The decision to own a home early in life
delays the accumulation of capital assets, which
insures the homeowner against bad income
shocks. The average house size in this economy
is 1,759 square feet. This implies that the introduction of ARMs leads to a large increase in the
purchase of smaller homes, which tend to be purchased by lower-income households, who tend
to be more exposed to labor income shocks. With out protection against income shocks, some homeowners are unable to make mortgage payments
and thus become renters.
When considering mortgage finance and
selection, we find that 51.7 percent of homeowners have some form of mortgage debt. As for the
type of mortgage, 35.5 percent have a fixed-payF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Chambers, Garriga, Schlagenhauf

Table 14
Homeownership (Including an ARM) by Age
Homeownership rate (percent)
Simulation

Total

20-34 years

35-49 years

50-64 years

65-74 years

75-89 years

Benchmark

64.3

37.1

80.6

75.2

79.3

77.4

Model

65.8

49.1

80.3

76.3

72.9

64.7

SOURCE: Data generated by the model.

Table 15
Homeownership (Including Combo Loans) by Age
Homeownership rate (percent)
Simulation

Total

20-34 years

35-49 years

50-64 years

65-74 years

75-89 years

Benchmark model 1994

64.3

37.1

80.6

81.5

81.5

62.5

Model

68.6

42.2

88.0

81.6

83.2

66.9

SOURCE: Data generated by the model.

ment mortgage and 16.2 percent have an ARM
mortgage. Only households with ARMs are in
the bottom quintile of income distribution. ARMs
can be attractive to many homeowners, but those
who decide to become homeowners because of
these loans are low-income households. Thus,
mortgage contracts can influence asset decisions
over the life cycle.
The next example considers the choice
between a standard FRM and a CL when 80 percent of the home value is financed with a traditional fixed-payment mortgage and the other 20
percent is financed with another fixed-payment
mortgage with a 2 percent interest rate premium.
The aggregate homeownership rate in this economy is 68.65 percent. The introduction of a CL
increases the homeownership rate by 4.3 percent.
Table 15 shows how the homeownership rate
decreases by age in this situation after the young est cohort period. Just as with an ARM, the homeownership rate of the youngest cohort increases
from 37 to nearly 43 percent. However, because
the payments of the typical CL combo loan are
higher than a corresponding ARM, income conF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

straints prevent some young households from
entering the market. Unlike the ARM, CL appears
to have a positive effect across the entire age profile. Every age cohort has a homeownership rate
at or above that in the baseline case.
The average home size in this economy is
1,909 square feet. This fact implies that the CL
encourages the purchase of larger homes, which
are affordable only for higher-income households.
For this group, only 45.3 percent of the households have mortgage debt; 32.6 percent have a
fixed-payment mortgage, and 12.7 percent have
a CL. In addition, CLs are used in the bottom 40
percent of the income distribution. The income
of an ARM household is lower than that of the
average CL household.

CONCLUSION
This paper addresses several issues facing
mortgage finance and potential home buyers.
Recent innovations in the mortgage market have
greatly expanded the types of loans available to
home buyers. These products vary greatly in terms
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Chambers, Garriga, Schlagenhauf

of payment size, composition of interest versus
principal, and amortization schedule. Some products, such as interest-only loans, increase affordability by reducing payment size. However, these
products typically slow accumulation of equity
and thus become less attractive for wealth accumulation. Some mortgage types can generate
negative amortization, which would seem highly
unattractive to potential mortgage lenders. Other
products, such as CLs, seek to increase affordability by reducing down payment requirements.
These mortgages are characterized by larger mortgage payments. Given the typical government
stance of seeking greater homeownership, both
types of products appear successful in this regard.
In a standard macroeconomic model, we find
that the typical ARM should generate large
increases in the homeownership rate of young
households. However, because of a delay in capital asset accumulation, lower homeownership
may be found for older households. CLs also tend
to drive up homeownership. For young households this increase in homeownership is not as
pronounced as with ARMs, but with no apparent
reduction in homeownership later in the life cycle.
Thus, it should come as no surprise that the introduction of these mortgage products coincided
with the observed increase in homeownership
from 1995 through 2005. It should also not be
surprising that the homeownership rate declines
as these instruments are removed from the mortgage market.

REFERENCES
Chambers, Matthew; Garriga, Carlos and
Schlagenhauf, Don. “Accounting for Changes in
the Homeownership Rate.” International Economic
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Schlagenhauf, Don. “The Tax Treatment of
Homeowners and Landlords,” Working Paper,
Florida State University, July 2007b.
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Social Research, University of Michigan;
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Jeske, Karsten. “Macroeconomic Models with
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McDonald, Daniel J. and Thornton, Daniel L.
“A Primer on the Mortgage Market and Mortgage
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Storesletten, Kjetil, C.; Telmer, Chris I. and Yaron,
Amir. “Consumption and Risk Sharing over the
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2004, 51(3), pp. 609-33.
The Mortgage Market Statistical Annual. Bethesda,
MD: Inside Mortgage Finance Publications, 2007.
Tauchen, George. “Finite State Markov-Chain
Approximation to Univariate and Vector
Autoregressions.” Economic Letters, 1986, 20(2),
pp. 177-81.
U.S. Bureau of Economic Analysis. National Income
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U.S. Census Bureau. Housing Vacancies and
Homeownership; www.census.gov/hhes/
www/housing/hvs/hvs.html.
U.S. Census Bureau. Residential Finance Survey:
2001—Census 2000 Special Reports (report
CENSR-27); www.census.gov/prod/2005pubs/
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U. S. Department of Commerce, Bureau of the
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life94_2.pdf.

APPENDIX
Alm, James and J. Follain, James R., Jr. “Alternative Mortgage Instruments, the Tilt Problem and Consumer
Welfare.” Journal of Financial and Quantitative Analysis, March 1984, 19(1), pp. 113-26.
Berkovec, James and Fullerton, Don. “A General Equilibrium Model of Housing, Taxes and Portfolio Choice.”
Journal of Political Economy, April 1992, 100(2), pp. 390-429.
Campbell, John Y. “Household Finance,” Journal of Finance, August 2006, 61(4), 1553-604.
Campbell, John Y. and Cocco, Joao F. “Household Risk Management and Optimal Mortgage Choice.” Quarterly
Journal of Economics, November 2003, 118(4), pp. 1449-94.
Chambers, Matthew; Garriga, Carlos and Schlagenhauf, Don. “The Loan Structure and Housing Tenure Decisions
in an Equilibrium Model of Mortgage Choice.” Working Paper 2008-024A, July 2008, Federal Reserve Bank
of St. Louis; http://research.stlouisfed.org/wp/2008/2008-024.pdf, July 2008, WP 2008-024A.
Cooley, Thomas F. and Prescott, Edward C. “Economic Growth and Business Cycles” in Thomas F. Cooley, ed.,
Frontiers of Business Cycle Research. Princeton, NJ: Princeton University Press, 1995, pp. 1-38.
Dhillon, Upinder S; Shilling, James D. and Simans, C.F. “Choosing Between Fixed and Adjustable Rate
Mortgages.” Journal of Money, Credit and Banking, May 1987, 19(2), pp. 260-67.
Dunn, Kenneth B. and Spatt, Chester S. “An Analysis of Mortgage Contracting: Prepayment Penalties and the
Due-on Sales Clause.” Journal of Finance, March 1985, 40(1), 293-308.
Fernández-Villaverde, Jesús and Krueger, Dirk. “Consumption and Savings over the Life-Cycle: How Important
Are Consumer Durables?” Working Paper, University of Pennsylvania, December 19, 2005;
www.econ.upenn.edu/~dkrueger/research/durables12192005sec.pdf.
Follain, James R. “Mortgage Choice.” American Real Estate and Urban Economic Associations Journal, Summer
1990, 18(2), pp. 125-44.
Gouveia, Miguel and Strauss, Robert P. “Effective Federal Individual Income Tax Functions: An Exploratory
Empirical Analysis.” National Tax Journal, June 1994, 47, pp. 317-39.
Gervais, Martin. “Housing Taxation and Capital Accumulation.” Journal of Monetary Economics, October 2002,
49(7), pp. 1461-89.

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Heathcoate, Jonathan and Davis, Morris. “Housing and the Business Cycle.” International Economic Review,
August 2005, 46(3), pp. 751-84.
Henderson, J. Vernon and Ioannides, Yannis M. “A Model of Housing Tenure Choice.” American Economic
Review, March 1983, 73(1), pp. 98-113.
Jeske, Karsten and Krueger, Dirk. “Housing and the Macroeconomy: The Role of Implicit Guarantees for
Government-Sponsored Enterprises.” Federal Reserve Bank of Atlanta Working Paper 2005-15, August 2005;
www.frbatlanta.org/filelegacydocs/wp0515.pdf.
Kearl, James R. “Inflation, Mortgages, and Housing.” Journal of Political Economy, October 1979, 87(5, Part 1),
pp. 1115-38.
LeRoy, Stephen F. “Mortgage Valuation Under Optimal Repayment.” Review of Financial Studies, Autumn 1996,
9(3), pp. 817-44.
Li, Wenli. “Moving Up: Trends in Homeownership and Mortgage Indebtedness.” Federal Reserve Bank of
Philadelphia Business Review, First Quarter 2005, pp. 26-34; www.philadelphiafed.org/files/br/brq105wl.pdf.
Li, Wenli and Yao, Rui. “The Life-Cycle Effects of House Price Changes.” Journal of Money, Credit and Banking,
September 2007, 39(6), pp. 1375-409.
Nakajima, Makoto. “Rising Prices of Housing and Non-Housing Capital and Rising Earnings Instability: The Role
of Illiquidity of Housing.” Working Paper, 2003, University of Pennsylvania.
Ortalo-Magne, François and Rady, Sven. “Housing Market Dynamics: On the Contribution of Income Shocks
and Credit Constraints.” Review of Economic Studies, April 2006, 73(2), pp. 459-85.
Ríos-Rull, José-Victor. “Life Cycle Economies and Aggregate Fluctuations.” Review of Economic Studies, July
1996, 63(3), 465-89.
Ríos-Rull, José-Victor. “Population Changes and Capital Accumulation: The Aging of the Baby Boom.” The BE
Journal of Macroeconomics, 2001, 1(1), article 7.
Ríos-Rull, José-Victor and Sanchez-Marcos, Virginia. “An Aggregate Economy with Different House Sizes.”
Working Paper, September 2006, University of Pennsylvania; www.econ.umn.edu/~vr0j/papers/houaug06.pdf.
Sánchez, José Miguel. “An Estimable Dynamic Model of Housing Tenure Choice.” Unpublished manuscript,
2007, Instituto de Economía, Pontificia Universidad Católica de Chile.
Stanton, Richard and Wallace, Nancy. “Mortgage Choice: What’s the Point?” Real Estate Economics, June 1998,
26(2), pp. 73-205.

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Real Interest Rate Persistence:
Evidence and Implications
Christopher J. Neely and David E. Rapach
The real interest rate plays a central role in many important financial and macroeconomic models,
including the consumption-based asset pricing model, neoclassical growth model, and models of
the monetary transmission mechanism. The authors selectively survey the empirical literature that
examines the time-series properties of real interest rates. A key stylized fact is that postwar real
interest rates exhibit substantial persistence, shown by extended periods when the real interest
rate is substantially above or below the sample mean. The finding of persistence in real interest
rates is pervasive, appearing in a variety of guises in the literature. The authors discuss the implications of persistence for theoretical models, illustrate existing findings with updated data, and
highlight areas for future research. (JEL C22, E21, E44, E52, E62, G12)
Federal Reserve Bank of St. Louis Review, November/December 2008, 90(6), pp. 609-41.

T

he real interest rate—an interest rate
adjusted for either realized or expected
inflation—is the relative price of consuming now rather than later.1 As such,
it is a key variable in important theoretical models
in finance and macroeconomics, such as the consumption-based asset pricing model (Lucas, 1978;
Breeden, 1979; Hansen and Singleton, 1982,
1983), neoclassical growth model (Cass, 1965;
Koopmans, 1965), models of central bank policy
(Taylor, 1993), and numerous models of the monetary transmission mechanism.
The theoretical importance of the real interest
rate has generated a sizable literature that exam1

Heterogeneous agents face different real interest rates, depending
on horizon, credit risk, and other factors. And inflation rates are
not unique, of course. For ease of exposition, this paper ignores
such differences as being irrelevant to the economic inference.

ines its long-run properties. This paper selectively
reviews this literature, highlights its central findings, and analyzes their implications for theory.
We illustrate our study with new empirical results
based on U.S. data. Two themes emerge from our
review: (i) Real rates are very persistent, much
more so than consumption growth; and (ii)
researchers should seriously explore the causes
of this persistence.
First, empirical studies find that real interest
rates exhibit substantial persistence, shown by
extended periods when postwar real interest rates
are substantially above or below the sample mean.
Researchers characterize this feature of the data
with several types of models. One group of studies
uses unit root and cointegration tests to analyze
whether shocks permanently affect the real interest rate—that is, whether the real rate behaves like
a random walk. Such studies often report evidence

Christopher J. Neely is an assistant vice president and economist at the Federal Reserve Bank of St. Louis. David E. Rapach is an associate
professor of economics at Saint Louis University. This project was undertaken while Rapach was a visiting scholar at the Federal Reserve
Bank of St. Louis. The authors thank Richard Anderson, Menzie Chinn, Alan Isaac, Lutz Kilian, Miguel León-Ledesma, James Morley,
Michael Owyang, Robert Rasche, Aaron Smallwood, Jack Strauss, and Mark Wohar for comments on earlier drafts and Ariel Weinberger for
research assistance. The results reported in this paper were generated using GAUSS 6.1. Some of the GAUSS programs are based on code
made available on the Internet by Jushan Bai, Christian Kleiber, Serena Ng, Pierre Perron, Katsumi Shimotsu, and Achim Zeileis, and the
authors thank them for this assistance.

© 2008, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the
views of the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced,
published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts,
synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

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Neely and Rapach

of unit roots, or—at a minimum—substantial persistence. Other studies extend standard unit root
and cointegration tests by considering whether
real interest rates are fractionally integrated or
exhibit significant nonlinear behavior, such as
threshold dynamics or nonlinear cointegration.
Fractional integration tests typically indicate that
real interest rates revert to their mean very slowly.
Similarly, studies that find evidence of nonlinear
behavior in real interest rates identify regimes in
which the real rate behaves like a unit root process.
Another important group of studies reports evidence of structural breaks in the means of real
interest rates. Allowing for such breaks reduces
the persistence of deviations from the regimespecific means, so breaks reduce local persistence.
The structural breaks themselves, however, still
produce substantial global persistence in real
interest rates.
The empirical literature thus finds that persistence is pervasive. Although researchers have
used sundry approaches to model persistence,
certain approaches are likely to be more useful
than others. Comprehensive model selection
exercises are thus an important area for future
research, as they will illuminate the exact nature
of real interest rate persistence.
The second theme of our survey is that the
literature has not adequately addressed the economic causes of persistence in real interest rates.
Understanding such processes is crucial for assessing the relevance of different theoretical models.
We discuss potential sources of persistence and
argue that monetary shocks contribute to persistent fluctuations in real interest rates. While identifying economic structure is always challenging,
exploring the underlying causes of real interest
rate persistence is an especially important area
for future research.
The rest of the paper is organized as follows.
The next section reviews the predictions of economic and financial models for the long-run
behavior of the real interest rate. This informs
our discussion of the theoretical implications of
the empirical literature’s results. After distinguishing between ex ante and ex post measures of the
real interest rate, the third section reviews papers
that apply unit root, cointegration, fractional
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integration, and nonlinearity tests to real interest
rates. The fourth section discusses studies of
regime switching and structural breaks in real
interest rates. The fifth section considers sources
of the persistence in the U.S. real interest rate and
ultimately argues that it is a monetary phenomenon. The sixth section summarizes our findings.

THEORETICAL BACKGROUND
Consumption-Based Asset Pricing Model
The canonical consumption-based asset pricing model of Lucas (1978), Breeden (1979), and
Hansen and Singleton (1982, 1983) posits a representative household that chooses a real consumption sequence, {ct }⬁t = 0 , to maximize
∞

∑t =0 βtu (ct ),
subject to an intertemporal budget constraint,
where β is a discount factor and u共ct 兲 is an instantaneous utility function. The first-order condition
leads to the familiar intertemporal Euler equation,
(1)

{

}

Et β u ′ (ct +1 ) / u ′ (ct ) (1 + rt ) = 1,

where 1 + rt is the gross one-period real interest
rate (with payoff at period t + 1) and Et is the conditional expectation operator. Researchers often
assume that the utility function is of the constant
α
relative risk aversion form, u共ct 兲 = c1–
t /共1 – α兲,
where α is the coefficient of relative risk aversion.
Combining this with the assumption of joint lognormality of consumption growth and the real
interest rate implies the log-linear version of the
first-order condition given by equation (1) (Hansen
and Singleton, 1982, 1983):
(2)

κ − α Et ∆log (ct +1 )  + Et log (1 + rt )  = 0,

where ∆log共ct+1 兲 = log共ct+1 兲 – log共ct 兲, κ = log共β 兲 +
0.5σ 2, and σ 2 is the constant conditional variance
of log[β 共ct+1 /ct 兲–α 共1 + rt 兲].
Equation (2) links the conditional expectations
of the growth rate of real per capita consumption
[∆log共ct+1 兲] with the (net) real interest rate
[log共1 + rt 兲 ≅ rt ]. Rose (1988) argues that if equation (2) is to hold, then these two series must have
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Neely and Rapach

Figure 1
U.S. Ex Post Real Interest Rate and Real Per Capita Consumption Growth, 1953:Q1–2007:Q2
Percent
10

8

6

4

2

0

–2

–4

Ex Post Real Interest Rate
Per Capita Consumption Growth

–6
1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

NOTE: The figure plots the U.S. ex post 3-month real interest rate and annualized per capita consumption growth. Consumption is
measured as the sum of nondurable goods and services consumption.

similar integration properties. Whereas ∆log共ct+1 兲
is almost surely a stationary process [∆log共ct+1 兲 ~
I共0兲], Rose (1988) presents evidence that the real
interest rate contains a unit root [rt ~ I共1兲] in many
industrialized countries. A unit root in the real
interest rate combined with stationary consumption growth means that there will be permanent
changes in the level of the real rate not matched
by such changes in consumption growth, so equation (2) apparently cannot hold.
Figure 1 illustrates the problem identified
by Rose (1988) using U.S. data for the ex post 3month real interest rate and annualized growth
rate of per capita consumption (nondurable goods
plus services) for 1953:Q1–2007:Q2. The two series
appear to track each other reasonably well for long
periods, such as the 1950s, 1960s, and 1984-2001,
but they also diverge for significant periods, such
as the 1970s, early 1980s, and 2001-05.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

The simplest versions of the consumptionbased asset pricing model are based on an endowment economy with a representative household
and constant preferences. The next subsection
discusses the fact that more elaborate theoretical
models allow for some changes in the economy—
for example, changes in fiscal or monetary policy—to alter the steady-state real interest rate
while leaving steady-state consumption growth
unchanged. That is, they permit a mismatch in
the integration properties of the real interest rate
and consumption growth.

Equilibrium Growth Models and the
Steady-State Real Interest Rate
General equilibrium growth models with a
production technology imply Euler equations
similar to equations (1) and (2) that suggest sources
of a unit root in real interest rates. Specifically, the
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Cass (1965) and Koopmans (1965) neoclassical
growth model with a representative profitmaximizing firm and utility-maximizing household predicts that the steady-state real interest rate
is a function of time preference, risk aversion,
and the steady-state growth rate of technological
change (Blanchard and Fischer, 1989, Chap. 2;
Barro and Sala-i-Martin, 2003, Chap. 3; Romer,
2006, Chap. 2). In this model the assumption of
constant relative risk aversion utility implies the
following familiar steady-state condition:
(3)

r* = ζ + α z ,

where r* is the steady-state real interest rate,
ζ = –log共β 兲 is the rate of time preference, and z is
the (expected) steady-state growth rate of laboraugmenting technological change. Equation (3)
implies that a permanent change in the exogenous
rate of time preference, risk aversion, or long-run
growth rate of technology will affect the steadystate real interest rate.2 If there is no uncertainty,
the neoclassical growth model implies the following steady-state version of the Euler equation
given by (2):
(4)

−ζ − α ∆ log (c ) * + r* = 0,

where [∆log共c兲]* represents the steady-state
growth rate of ct . Substituting the right-hand side
of equation (3) into equation (4) for r*, one finds
that steady-state technology growth determines
steady-state consumption growth: [∆log共c兲]* = z.
If the rate of time preference (ζ ), risk aversion
(α ), and/or steady-state rate of technology growth
(z) change, then (3) requires corresponding
changes in the steady-state real interest rate.
Depending on the size and frequency of such
changes, real interest rates might be very persis tent, exhibiting unit root behavior and/or structural breaks. Of these three factors, a change in
the steady-state growth rate of technology—such
as those that might be associated with the “productivity slowdown” of the early 1970s and/or the
“New Economy” resurgence of the mid-1990s—is
the only one that will alter both the real interest
rate and consumption growth, producing non2

Changes in distortionary tax rates could also affect r* (Blanchard
and Fischer, 1989, pp. 56-59).

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stationary behavior in both variables. Thus, it
cannot explain the mismatch in the integration
properties of the real interest rate and consumption growth identified by Rose (1988).
On the other hand, shocks to the preference
parameters, ζ and α , will change only the steadystate real interest rate and not steady-state consumption growth. Therefore, changes in
preferences potentially disconnect the integration
properties of real interest rates and consumption
growth. Researchers generally view preferences
as stable, however, making it unpalatable to
ascribe the persistence mismatch to such changes.3
In more elaborate models, still other factors
can change the steady-state real interest rate.
For example, permanent changes in government
purchases and their financing can also affect the
steady-state real rate in overlapping generations
models with heterogeneous households
(Samuelson, 1958; Diamond, 1965; Blanchard,
1985; Blanchard and Fischer, 1989, Chap. 3;
Romer, 2006, Chap. 2). Such shocks affect the
steady-state real interest rate without affecting
steady-state consumption growth, so they potentially explain the mismatch in the integration
properties of the real interest rate and consumption growth examined by Rose (1988).
Finally, some monetary growth models allow
for changes in steady-state money growth to affect
the steady-state real interest rate. The seminal
models of Mundell (1963) and Tobin (1965) predict that an increase in steady-state money growth
lowers the steady-state real interest rate, and more
recent micro-founded monetary models have
similar implications (Weiss, 1980; Espinosa-Vega
and Russell, 1998a,b; Bullard and Russell, 2004;
Reis, 2007; Lioui and Poncet, 2008). Again, this
class of models permits changes in the steadystate real interest rate without corresponding
changes in consumption growth, potentially
explaining a mismatch in the integration properties of the real interest rate and consumption
growth.
3

Some researchers appear more willing to allow for changes in
preferences over an extended period. For example, Clark (2007)
argues that a steady decrease in the rate of time preference is responsible for the downward trend in real interest rates in Europe from
the early medieval period to the eve of the Industrial Revolution.

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Transitional Dynamics
The previous section discusses factors that
can affect the steady-state real interest rate. Other
shocks can have persistent—but ultimately transitory—effects on the real rate. For example, in
the neoclassical growth model, a temporary
increase in technology growth or government
purchases leads to a persistently (but not permanently) higher real interest rate (Romer, 2006,
Chap. 2). In addition, monetary shocks can persistently affect the real interest rate via a variety
of frictions, such as “sticky” prices and information, adjustment costs, and learning by agents
about policy regimes. Transient technology and
fiscal shocks, as well as monetary shocks, can
also explain differences in the persistence of real
interest rates and consumption growth. For example, using a calibrated neoclassical equilibrium
growth model, Baxter and King (1993) show that
a temporary (four-year) increase in government
purchases persistently raises the real interest rate,
although it eventually returns to its initial level.
In contrast, the fiscal shock produces a much less
persistent reaction in consumption growth. As we
will discuss later, evidence of highly persistent
but mean-reverting behavior in real interest rates
supports the empirical relevance of these shocks.

TESTING THE INTEGRATION
PROPERTIES OF REAL INTEREST
RATES
Ex Ante versus Ex Post Real Interest
Rates
The ex ante real interest rate (EARR) is the
nominal interest rate minus the expected inflation
rate, while the ex post real rate (EPRR) is the
nominal rate minus actual inflation. Agents make
economic decisions on the basis of their inflation
expectations over the decision horizon. For example, the Euler equations (1) and (2) relate the
expected marginal utility of consumption to the
expected real return. Therefore, the EARR is the
relevant measure for evaluating economic decisions, and we really wish to evaluate the EARR’s
time-series properties, rather than those of the
EPRR.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Unfortunately, the EARR is not directly observable because expected inflation is not directly
observable. An obvious solution is to use some
survey measure of inflation expectations, such
as the Livingston Survey of professional forecasters, which has been conducted biannually
since the 1940s (Carlson, 1977). Economists are
often reluctant, however, to accept survey forecasts as expectations. For example, Mishkin (1981,
p. 153) expresses “serious doubts as to the quality
of these [survey] data.” Obtaining survey data at
the desired frequency for the desired sample might
create other obstacles to the use of survey data.
Some studies have used survey data, however,
including Crowder and Hoffman (1996) and Sun
and Phillips (2004).
There are at least two alternative approaches
to the problem of unobserved expectations. The
first is to use econometric forecasting methods to
construct inflation forecasts; see, for example,
Mishkin (1981, 1984) and Huizinga and Mishkin
(1986). Unfortunately, econometric forecasting
models do not necessarily include all of the relevant information agents use to form expectations
of inflation, and such models can fail to change
with the structure of the economy. For example,
Stock and Watson (1999, 2003) show that both
real activity and asset prices forecast inflation but
that the predictive relations change over time.4
A second alternative approach is to use the
actual inflation rate as a proxy for inflation expectations. By definition, the actual inflation rate at
time t (πt ) is the sum of the expected inflation rate
and a forecast error term (εt ):
(5)

π t = E t −1π t + εt .

The literature on real interest rates has long
argued that, if expectations are formed rationally,
Et –1πt should be an optimal forecast of inflation
(Nelson and Schwert, 1977), and εt should there4

Atkeson and Ohanian (2001) and Stock and Watson (2007) discuss
the econometric challenges in forecasting inflation. One might
also consider using Treasury inflation-protected securities (TIPS)
yields—and/or their foreign counterparts—to measure real interest rates. But these series have a relatively short span of available
data, in that the U.S. securities were first issued in 1997, are only
available at long maturities (5, 10, and 20 years), and do not correctly measure real rates when there is a significant chance of
deflation.

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fore be a white noise process. The EARR can be
expressed (approximately) as
(6)

rtea = it − Et π t +1 ,

where it is the nominal interest rate. Solving
equation (5) for Et 共πt +1兲 and substituting it into
equation (6), we have
(7)

rtea = it − (π t +1 − εt +1 )
= it − π t +1 + εt +1 = rtep + εt +1 ,

where rtep = it – πt +1 is the EPRR. Equation (7)
implies that, under rational expectations, the
EPRR and EARR differ only by a white noise component, so the EPRR and EARR will share the
same long-run (integration) properties. Actually,
this latter result does not require expectations to
be formed rationally but holds if the expectation
errors (ε t +1) are stationary.5 Beginning with Rose
(1988), much of the empirical literature tests the
integration properties of the EARR with the EPRR,
after assuming that inflation-expectation errors
are stationary.
Researchers typically evaluate the integration
properties of the EPRR with a decision rule. They
first analyze the individual components of the
EPRR, it and πt +1. If unit root tests indicate that it
and πt +1 are both I共0兲, then this implies a stationary EPRR, as any linear combination of two I共0兲
processes is also an I共0兲 process.6 If it and πt+1
have different orders of integration—for example,
if it ~ I共1兲 and πt +1 ~ I共0兲—then the EPRR must
have a unit root, as any linear combination of an
I共1兲 process and an I共0兲 process is an I共1兲 process.
Finally, if unit root tests show that it and πt +1 are
both I共1兲, researchers test for a stationary EPRR
by testing for cointegration between it and πt+1—
that is, testing whether the linear combination
5

Peláez (1995) provides evidence that inflation-expectation errors
are stationary. Also note that Andolfatto, Hendry, and Moran (2008)
argue that inflation-expectation errors can appear serially correlated in finite samples, even when expectations are formed rationally, due to short-run learning dynamics about infrequent changes
in the monetary policy regime.

6

The appendix, “Unit Roots and Cointegration Tests,” provides
more information on the mechanics of popular unit root and
cointegration tests.

7

The presence of θ0 allows for a constant term in the cointegrating
relationship corresponding to the steady-state real interest rate.

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it – [θ0 + θ1πt+1] is a stationary process—using
one of two approaches.7 First, many researchers
impose a cointegrating vector of 共1,–θ1兲′ = 共1,–1兲′
and apply unit root tests to rtep = it – πt +1. This
approach typically has more power to reject the
null of no cointegration when the true cointegrating vector is 共1,–1兲′. The second approach is to
freely estimate the cointegrating vector between
it and πt +1, as this allows for tax effects (Darby,
1975).
If it , πt+1 ~ I共1兲, then a stationary EPRR requires
it and πt+1 to be cointegrated with cointegrating
coefficient, θ1 = 1, or, allowing for tax effects,
θ1 = 1/共1 – τ 兲, where τ is the marginal investor’s
marginal tax rate on nominal interest income.
When allowing for tax effects, researchers view
estimates of θ1 in the range of 1.3 to 1.4 as plausible, as they correspond to a marginal tax rate
around 0.2 to 0.3 (Summers, 1983).8 It is worth
emphasizing that cointegration between it and
πt +1 by itself does not imply a stationary real
interest rate: θ1 must also equal 1 [or 1/共1 – τ 兲],
as other values of θ1 imply that the equilibrium
real interest rate varies with inflation.
Although much of the empirical literature
analyzes the EPRR in this manner, it is important
to keep in mind that the EPRR’s time-series properties can differ from those of the EARR—the
ultimate object of analysis—in two ways. First,
the EPRR’s behavior at short horizons might differ
from that of the EARR. For example, using survey
data and various econometric methods to forecast
inflation, Dotsey, Lantz, and Scholl (2003) study
the behavior of the EARR and EPRR at businesscycle frequencies and find that their behavior
over the business cycle can differ significantly.
Second, some estimation techniques can generate different persistence properties between the
EARR and EPRR; see, for example, Evans and
Lewis (1995) and Sun and Phillips (2004).

Early Studies
A collection of early studies on the efficient
market hypothesis and the ability of nominal
8

Data from tax-free municipal bonds would presumably provide a
unitary coefficient. Crowder and Wohar (1999) study the Fisher
effect with tax-free municipal bonds.

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Neely and Rapach

interest rates to forecast the inflation rate foreshadows the studies that use unit root and cointegration tests. Fama (1975) presents evidence
that the monthly U.S. EARR can be viewed as
constant over 1953-71. Nelson and Schwert (1977),
however, argue that statistical tests of Fama (1975)
have low power and that his data are actually not
very informative about the EARR’s autocorrelation
properties. Hess and Bicksler (1975), Fama (1976),
Carlson (1977), and Garbade and Wachtel (1978)
also challenge Fama’s (1975) finding on statistical
grounds. In addition, subsequent studies show
that Fama’s (1975) result hinges critically on the
particular sample period (Mishkin, 1981, 1984;
Huizinga and Mishkin, 1986; Antoncic, 1986).

Unit Root and Cointegration Tests
The development of unit root and cointegration analysis, beginning with Dickey and Fuller
(1979), spurred the studies that formally test the
persistence of real interest rates. In his seminal
study, Rose (1988) tests for unit roots in short-term
nominal interest rates and inflation rates using
monthly data for 1947-86 for 18 countries in the
Organisation for Economic Co-operation and
Development (OECD). Rose (1988) finds that augmented Dickey-Fuller (ADF) tests fail to reject
the null hypothesis of a unit root in short-term
nominal interest rates, but they can consistently
reject a unit root in inflation rates based on various price indices—consumer price index (CPI),
gross national product (GNP) deflator, implicit
price deflator, and wholesale price index (WPI).9
As discussed above, the finding that it ~ I共1兲 while
πt ~ I共0兲 indicates that the EPRR, it – πt+1, is an I共1兲
process. Under the assumption that inflationexpectation errors are stationary, this also implies
that the EARR is an I共1兲 process. Rose (1988) easily rejects the unit root null hypothesis for U.S.
consumption growth, which leads him to argue
that an I共1兲 real interest rate and I共0兲 consumption
growth rate violates the intertemporal Euler equation implied by the consumption-based asset pricing model. Beginning with Rose (1988), Table 1
summarizes the methods and conclusions of sur9

The appendix discusses unit root and cointegration tests.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

veyed papers on the long-run properties of real
interest rates.
A number of subsequent papers also test for
a unit root in real interest rates. Before estimating
structural vector autoregressive (SVAR) models,
King et al. (1991) and Galí (1992) apply ADF unit
root tests to the U.S. nominal 3-month Treasury
bill rate, inflation rate, and EPRR. Using quarterly
data for 1954-88 and the GNP deflator inflation
rate, King et al. (1991) fail to reject the null hypothesis of a unit root in the nominal interest rate,
matching the finding of Rose (1988). Unlike Rose
(1988), however, King et al. cannot reject the unit
root null hypothesis for the inflation rate, which
creates the possibility that the nominal interest
rate and inflation rate are cointegrated. Imposing
a cointegrating vector of 共1,–1兲′, they fail to reject
the unit root null hypothesis for the EPRR. Using
quarterly data for 1955-87, the CPI inflation rate,
and simulated critical values that account for
potential size distortions due to moving-average
components, Galí (1992) obtains unit root test
results similar to those of King et al. Despite the
failure to reject the null hypothesis that it – πt +1 ~
I共1兲, Galí nevertheless assumes that it – πt +1 ~ I共0兲
when he estimates his SVAR model, contending
that “the assumption of a unit root in the real
[interest] rate seems rather implausible on a priori
grounds, given its inconsistency with standard
equilibrium growth models” (Galí, 1992, p. 717).
This is in interesting contrast to King et al., who
maintain the assumption that it – πt+1 ~ I共1兲 in their
SVAR model. Shapiro and Watson (1988) report
similar unit root findings and, like Galí, still
assume the EPRR is stationary in an SVAR model.
Analyzing a 1953-90 full sample, as well as a
variety of subsamples for the nominal Treasury
bill rate and CPI inflation rate, Mishkin (1992)
argues that monthly U.S. data are largely consistent with a stationary EPRR. With simulated critical values, as in Galí (1992), Mishkin (1992) finds
that the nominal interest rate and inflation rate
are both I共1兲 over four sample periods: 1953:01–
1990:12, 1953:01–1979:10, 1979:11–1982:10, and
1982:11–1990:12. He then tests whether the nominal interest rate and inflation rate are cointegrated
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Table 1
Selective Summary of the Empirical Literature on the Long-Run Properties of Real Interest Rates
Study

Sample

Countries

Nominal interest rate and price data

A: 1892-70, 1901-50
Q: 1947-86
M: 1948-86

18 OECD countries

Long-term corporate bond yield, shortterm commercial paper rate, GNP
deflator, CPI, implicit price deflator, WPI

King et al. (1991)

Q: 1949-88

U.S.

3-month U.S. Treasury bill rate, implicit
GNP deflator

Galí (1992)

Q: 1955-87

U.S.

3-month U.S. Treasury bill rate, CPI

Mishkin (1992)

M: 1953-90

U.S.

1- and 3-month Treasury bill rates, CPI

Wallace and Warner
(1993)

Q: 1948-90

U.S.

3-month Treasury bill rate, 10-year
government bond yield, CPI

Engsted (1995)

Q: 1962-93

13 OECD countries

Mishkin and Simon
(1995)

Q: 1962-93

Australia

Crowder and Hoffman
(1996)

Q: 1952-91

U.S.

Rose (1988)

Koustas and Serletis Q: Data begin from
(1999)
1957-72; all data
end in 1995

Long-term bond yield, CPI

13-week government bond yield, CPI

3-month Treasury bill rate, implicit
consumption deflator, Livingston
inflation expectations survey, tax data
from various sources

11 OECD countries

Various short-term nominal interest rates,
CPI

Bierens (2000)

M: 1954-94

U.S.

Federal funds rate, CPI

Rapach (2003)

A: Data begin in
1949-65; end in
1994-96

14 industrialized countries

Rapach and Weber
(2004)

Q: 1957-2000

16 OECD countries

Long-term government bond yield, CPI

Rapach and Wohar
(2004)

Q: 1960-1998

13 OECD countries

Long-term government bond yield, CPI
marginal tax rate data (Padovano and
Galli, 2001)

Long-term government bond yield,
implicit GDP deflator

NOTE: A, Q, and M indicate annual, quarterly, and monthly data frequencies; GNP denotes gross national product.

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Results on the long-run properties of nominal interest rates, inflation rates, and real interest rates
ADF tests fail to reject a unit root for nominal interest rates but do reject for inflation rates, indicating a unit root
in EPRRs. ADF tests do reject a unit root for consumption growth.

ADF tests fail to reject a unit root for the nominal interest rate, inflation rate, and EPRR.

ADF tests with simulated critical values that adjust for moving-average components fail to reject a unit root in the
nominal interest rate, inflation rate, and EPRR.
ADF tests with simulated critical values that adjust for moving-average components fail to reject a unit root in the
nominal interest rate and inflation rate. AEG tests typically reject the null of no cointegration, indicating a
stationary EPRR.
ADF tests fail to reject a unit root in the long-term nominal interest rate and inflation rate. Johansen (1991)
procedure provides evidence that the variables are cointegrated and that the EPRR is stationary.
ADF tests fail to reject a unit root in nominal interest rates and inflation rates, while cointegration tests present
ambiguous results on the stationarity of the EPRR across countries.
ADF tests fail to reject a unit root in the nominal interest rate and inflation rate. AEG tests typically fail to reject the
null hypothesis of no cointegration, indicating a nonstationary EPRR.
ADF test fails to reject a unit root in the nominal interest rate and inflation rate after accounting for moving-average
components. Johansen (1991) procedure rejects the null of no cointegration and supports a stationary EPRR.

ADF tests usually fail to reject a unit root in nominal interest rates and inflation rates, while KPSS tests typically
reject the null of stationarity, indicating nonstationary nominal interest rates and inflation rates. AEG tests typically
fail to reject the null of no cointegration, indicating a nonstationary EPRR.
New test provides evidence of nonlinear cotrending between the nominal interest rate and inflation rate, indicating
a stationary EPRR. New test, however, cannot distinguish between nonlinear cotrending and linear cointegration.
ADF tests fail to reject a unit root in all nominal interest rates and in 13 of 17 inflation rates. This indicates a
nonstationary EPRR for the four countries with a stationary inflation rate. AEG tests typically fail to reject a unit
root in the EPRR for the 13 countries with a nonstationary inflation rate, indicating a nonstationary EPRR for these
countries.
Ng and Perron (2001) unit root tests typically fail to reject a unit root in nominal interest rates and inflation rates.
Ng and Perron (2001) and Perron and Rodriguez (2001) tests usually fail to reject the null of no cointegration,
indicating a nonstationary EPRR in most countries.
Lower (upper) 95 percent confidence band for the EPRR’s ρ is close to 0.90 (above unity) for nearly every country.

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Table 1, cont’d
Selective Summary of the Empirical Literature on the Long-Run Properties of Real Interest Rates
Study

Sample

Countries

Karanasos, Sekioua,
and Zeng (2006)

A: 1876-2000

U.S.

Lai (1997)

Q: 1974-2001

8 industrialized and
8 developing countries

Tsay (2000)

M: 1953-90

U.S.

1- and 3-month Treasury bill rates, CPI

Sun and Phillips (2004)

Q: 1934-94

U.S.

3-month Treasury bill rate, inflation
forecasts from the Survey of
Professional Forecasters, CPI

Pipatchaipoom and
Smallwood (2008)

M: 1971-2003

U.S.

Eurodollar rate, CPI

Maki (2003)

M: 1972-2000

Japan

10-year bond rate, call rate, CPI

M: 1951-99

U.S.

3-month Treasury bill rate, CPI

Christopoulos and
León-Ledesma (2007)

Q: 1960-2004

U.S.

3-month Treasury bill rate, CPI

Koustas and Lamarche
(2008)

A: 1960-2004

G-7 countries

Garcia and Perron (1996)

Q: 1961-86

U.S.

Clemente, Montañés,
and Reyes (1998)

Q: 1980-95

U.S., U.K.

Million (2004)

Nominal interest rate and price data
Long-term government bond yield, CPI

1- to 12-month Treasury bill rates, CPI,
Data Resources, Inc. inflation forecasts

3-month government bill rate, CPI

3-month Treasury bill rate, CPI

Long-term government bond yield, CPI

Caporale and Grier (2000) Q: 1961-86

U.S.

3-month Treasury bill rate, CPI

Bai and Perron (2003)

U.S.

3-month Treasury bill rate, CPI

Q: 1961-86

NOTE: A, Q, and M indicate annual, quarterly, and monthly data frequencies; GNP denotes gross national product.

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Results on the long-run properties of nominal interest rates, inflation rates, and real interest rates
95 percent confidence interval for the EPRR’s ρ is (0.97, 0.99). There is evidence of long-memory, mean-reverting
behavior in the EPRR.
ADF and KPSS tests indicate a unit root in the nominal interest rate, inflation rate, and expected inflation rate.
There is evidence of long-memory, mean-reverting behavior in the EARR and EPRR.
There is evidence of long-memory, mean-reverting behavior in the EPRR.
Bivariate exact Whittle estimator indicates long-memory behavior in the EARR. There is no evidence of a fractional
cointegrating relationship between the nominal interest rate and expected inflation rate.

Exact Whittle estimator provides evidence of long-memory, mean-reverting behavior in the EARR.

Breitung (2002) nonparametric test that allows for nonlinear short-run dynamics provides evidence of cointegration
between the nominal interest rate and inflation rate; cointegrating vector is not estimated, however, so it is not
known if the cointegrating relationship is consistent with a stationary EPRR.
Luukkonen, Saikkonen, and Teräsvirta (1988) test rejects linear short-run dynamics for the adjustment to the longrun equilibrium EPRR. A smooth transition autoregressive model exhibits asymmetric mean reversion in the EPRR,
depending on the level of the EPRR.
Choi and Saikkonen (2005) test provides evidence of nonlinear cointegration between the nominal interest rate and
inflation rate. Exponential smooth transition regression (ESTR) model fits best over the full sample and the first
subsample (1960-78), while a logistic smooth transition regression (LSTR) model fits best over the second
subsample (1979-2004). Estimated ESTR model for 1960-78 is not consistent with a stationary EPRR for any inflation
rate, and estimated LSTR model for 1979–2004 is consistent with a stationary EPRR only when the inflation rate is
above approximately 3 percent.
ADF and KPSS tests provide evidence of a unit root in the nominal interest rate and inflation rate. Bec, Ben Salem,
and Carassco (2004) nonlinear unit root and Hansen (1996, 1997) linearity tests indicate that the EPRR can be
suitably modeled as a three-regime self-exciting autoregressive (SETAR) process in Canada, France, and Italy.
An estimated autoregressive model with a three-state Markov-switching process for the mean indicates that the
EPRR was in a “moderate”-mean regime for 1961-73, a “low”-mean regime for 1973-80, and a “high”-mean regime
for 1980-86. EPRR is stationary with little persistence within these regimes.
ADF tests that allow for two structural breaks in the mean reject a unit root in the EPRR, indicating that the EPRR is
stationary within regimes defined by structural breaks.
Bai and Perron (1998) methodology provides evidence of multiple structural breaks in the mean EPRR.
Bai and Perron (1998) methodology provides evidence of multiple structural breaks in the mean EPRR.

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Table 1, cont’d
Selective Summary of the Empirical Literature on the Long-Run Properties of Real Interest Rates
Study
Lai (2004)

Sample

Countries

M: 1978-2002

U.S.

1-year Treasury bill rate, inflation
expectations from the University of
Michigan Survey of Consumers, CPI,
federal marginal income tax rates for
four-person families

13 OECD countries

Long-term government bond yield,
CPI, marginal tax rate data (Padovano
and Galli, 2001)

Rapach and Wohar (2005) Q: 1960-98

Lai (2008)

Q: 1974-2001

8 industrialized and
8 developing countries

Nominal interest rate and price data

1- to 12-month Treasury bill rate, deposit
rate, CPI

NOTE: A, Q, and M indicate annual, quarterly, and monthly data frequencies; GNP denotes gross national product.

ing a cointegrating vector and testing for a unit
root in it – πt+1. Mishkin (1992) rejects the null
hypothesis of no cointegration for the 1953:01–
1990:12 and 1953:01–1979:10 periods, but finds
less frequent and weaker rejections for the
1979:11–1982:10 and 1982:11–1990:12 periods.10
Mishkin and Simon (1995) apply similar tests to
quarterly short-term nominal interest rate and
inflation rate data for Australia. Using a 1962:Q3–
1993:Q4 full sample, as well as 1962:Q3–1979:Q3
and 1979:Q4– 1993:Q4 subsamples, they find
evidence that both the nominal interest rate and
the inflation rate are I共1兲, agreeing with the results
for U.S. data in Mishkin (1992). There is weaker
evidence that the Australian nominal interest rate
and inflation rate are cointegrated than there is
for U.S. data. Nevertheless, Mishkin and Simon
(1995) argue that theoretical considerations warrant viewing the long-run real interest rate as stationary in Australia, as “any reasonable model of
the macro economy would surely suggest that
10

Although they use essentially the same econometric procedures
and similar samples, Galí (1992) is unable to reject the unit root
null hypothesis for the EPRR, while Mishkin (1992) does reject
this null hypothesis. This illustrates the sensitivity of EPRR unit
root and cointegration tests to the specific sample. In addition,
the use of short samples, such as the 1979:11–1982:10 sample
period considered by Mishkin (1992), is unlikely to be informative
about the integration properties of the EPRR. To infer long-run
behavior, one needs reasonably long samples.

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real interest rates have mean-reverting tendencies which make them stationary” (Mishkin and
Simon, 1995, p. 223).
Koustas and Serletis (1999) test for unit roots
and cointegration in short-term nominal interest
rates and CPI inflation rates using quarterly data
for 1957-95 for 11 industrialized countries. They
use ADF unit root tests as well as the KPSS unit
root test of Kwiatkowski et al. (1992), which takes
stationarity as the null hypothesis and nonstationarity as the alternative. ADF and KPSS unit root
tests indicate that it ~ I共1兲 and πt+1 ~ I共1兲 in most
countries, so a stationary EPRR requires cointegration between the nominal interest rate and inflation rate. Koustas and Serletis (1999), however,
usually fail to find strong evidence of cointegration using the AEG test. Overall, their study finds
that the EPRR is nonstationary in many industrialized countries. Rapach (2003) obtains similar
results using postwar data for an even larger number of OECD countries.
In a subtle variation on conventional cointegration analysis, Bierens (2000) allows an individual time series to have a deterministic component
that is a highly complex function of time—essentially a smooth spline—and a stationary stochastic
component, and he develops nonparametric procedures to test whether two series share a common
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Neely and Rapach

Results on the long-run properties of nominal interest rates, inflation rates, and real interest rates
ADF tests allowing for a structural break in the mean reject a unit root in the tax-adjusted or unadjusted EARR,
indicating that the EARR is stationary within regimes defined by the structural break.

The Bai and Perron (1998) methodology provides evidence of structural breaks (usually multiple) in the mean EPRR
and mean inflation rate for all 13 countries.

ADF tests allowing for a structural break in the mean reject a unit root in the EPRR for most countries, indicating
that the EPRR is stationary within regimes defined by the structural break.

deterministic component (“nonlinear cotrending”).
Using monthly U.S. data for 1954-94, Bierens
(2000) presents evidence that the federal funds
rate and CPI inflation rate cotrend with a vector
of 共1,–1兲′, which can be interpreted as evidence
for a stationary real interest rate. Bierens shows,
however, that his tests cannot differentiate
between nonlinear cotrending and linear cointegration in the presence of stochastic trends in
the nominal interest rate and inflation rate. In
essence, the highly complex deterministic components for the individual series closely mimic
unit root behavior.
A number of studies use the Johansen (1991)
system–based cointegration procedure to test for
a stationary EPRR. Wallace and Warner (1993)
apply the Johansen (1991) procedure to quarterly
U.S. nominal 3-month Treasury bill rate and CPI
inflation data for a 1948-90 full sample and a
number of subsamples. Their results generally
support the existence of a cointegrating relationship, and their estimates of θ1 are typically not
significantly different from unity, in line with a
stationary EPRR. Wallace and Warner (1993) also
argue that the expectations hypothesis implies
that short-term and long-term nominal interest
rates should be cointegrated, and they find evidence that U.S. short and long rates are cointeF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

grated with a cointegrating vector of 共1,–1兲′. In
line with the results for the nominal 3-month
Treasury bill rate, Wallace and Warner find that
the nominal 10-year Treasury bond rate and inflation rate are cointegrated.
With quarterly U.S. data for 1951-91, Crowder
and Hoffman (1996) also use the Johansen (1991)
procedure to test for cointegration between the
3-month Treasury bill rate and implicit consumption deflator inflation rate. As in Wallace and
Warner (1993), they reject the null of no cointegration between the nominal interest rate and
inflation rate. Their estimates of θ1 range from
1.22 to 1.34, which are consistent with a stationary tax-adjusted EPRR. Crowder and Hoffman
(1996) also use estimates of average marginal tax
rates to directly test for cointegration between
it 共1 – τ 兲 and πt +1. The Johansen (1991) procedure
supports cointegration and estimates a cointegrating vector not significantly different from 共1,–1兲′,
in line with a stationary tax-adjusted EPRR.
Engsted (1995) uses the Johansen (1991) procedure to test for cointegration between the nominal long-term government bond yield and CPI
inflation rate in 13 OECD countries using quarterly
data for 1962-93. In broad agreement with the
results of Wallace and Warner (1993) and Crowder
and Hoffman (1996), Engsted (1995) rejects the
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Neely and Rapach

Table 2
Unit Root Test Statistics, U.S. data, 1953:Q1–2007:Q2
ADF

MZα

3-Month Treasury bill rate

–2.49 [7]

–4.39 [8]

PCE deflator inflation rate

–2.72* [4]

–5.20 [5]

Ex post real interest rate

–3.06** [6]

–18.83*** [2]

Per capita consumption growth

–4.99*** [4]

–42.07*** [2]

Variable

NOTE: The ADF and MZα statistics correspond to a one-sided (lower-tail) test of the null hypothesis that the variable has a unit root
against the alternative hypothesis that the variable is stationary. The 10 percent, 5 percent, and 1 percent critical values for the ADF
statistic are –2.58, –2.89, and –3.51; the 10 percent, 5 percent, and 1 percent critical values for the MZα statistic are –5.70, –8.10, and
–13.80. The lag order for the regression model used to compute the test statistic is reported in brackets. *, **, and *** indicate significance at the 10 percent, 5 percent, and 1 percent levels. PCE denotes personal consumption expenditures.

null hypothesis of no cointegration for almost all
countries. The estimates of θ1 vary quite markedly
across countries, however, and the values are
often inconsistent with a stationary EPRR.
Overall, unit root and cointegration tests
present mixed results with respect to the integration properties of the EPRR. Generally speaking,
single-equation methods provide weaker evidence
of a stationary EPRR, while the Johansen (1991)
system–based approach supports a stationary
EPRR, at least for the United States. Unfortunately,
econometric issues, such as the low power of
unit root tests and size distortions in the presence
of moving-average components, complicate inference about persistence.
To address these econometric issues, Rapach
and Weber (2004) use unit root and cointegration
tests with improved size and power. Specifically,
they use the Ng and Perron (2001) unit root and
Perron and Rodriguez (2001) cointegration tests.
These tests incorporate aspects of the modified
ADF tests in Elliott, Rothenberg, and Stock (1996)
and Perron and Ng (1996), as well as an adjusted
modified information criterion to select the autoregressive (AR) lag order, to develop tests that
avoid size distortions while retaining power.
Rapach and Weber (2004) use quarterly nominal
long-term government bond yield and CPI inflation rate data for 1957-2000 for 16 industrialized
countries. The Ng and Perron (2001) unit root and
Perron and Rodriguez (2001) cointegration tests
provide mixed results, but Rapach and Weber
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interpret their results as indicating that the EPRR
is nonstationary in most industrialized countries
over the postwar era.

Updated Unit Root and Cointegration
Test Results for U.S. Data
Tables 2 and 3 illustrate the type of evidence
provided by unit root and cointegration tests for
the U.S. 3-month Treasury bill rate, CPI inflation
rate, and per capita consumption growth rate for
1953:Q1–2007:Q2 (the same data as in Figure 1).
Table 2 reports the ADF statistic, as well as
the MZα statistic from Ng and Perron (2001), which
is designed to have better size and power properties than the former. Consistent with the literature,
neither test rejects the unit root null hypothesis
for the nominal interest rate. The results are mixed
for the inflation rate: The ADF statistic rejects the
unit root null at the 10 percent level, but the MZα
statistic does not reject at conventional significance levels. The ADF test result that it ~ I共1兲 while
πt ~ I共0兲 means that the EPRR is nonstationary, as
in Rose (1988).11 The MZα statistic’s failure to
reject the unit root null for either inflation or nomi11

A significant moving-average component in the inflation rate could
create size distortions in the ADF statistic that lead us to falsely
reject the unit root null hypothesis for that series. The fact that we
do not reject the unit root null using the MZα statistic—which is
designed to avoid this size distortion—supports this interpretation.
Rapach and Weber (2004), however, do reject the unit root null
for the U.S. inflation rate using the MZα statistic and data through
2000. Inflation rate unit root tests are thus particularly sensitive
to the sample period.

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Neely and Rapach

Table 3
Cointegration Test Statistics and Cointegrating Coefficient Estimates, U.S. 3-Month Treasury
Bill Rate and Inflation Rate (1953:Q1–2007:Q2)
Cointegration tests
MZα

Trace

–17.11** [2]

19.96* [4]

AEG
–3.07* [6]
Coefficient estimates
Estimation method

θ0

θ1

Dynamic OLS

2.16** (1.01)

0.86*** (0.24)

Johansen (1991) maximum likelihood

0.39 (1.21)

1.44***(0.29)

NOTE: The AEG and MZα statistics correspond to a one-sided (lower-tail) test of the null hypothesis that the 3-month Treasury bill
rate and inflation rate are not cointegrated against the alternative hypothesis that the variables are cointegrated. The 10 percent, 5
percent, and 1 percent critical values for the AEG statistic are –3.07, –3.37, and –3.96; the 10 percent, 5 percent, and 1 percent critical
values for the MZα statistic are –12.80, –15.84, and –22.84. The trace statistic corresponds to a one-sided (upper-tail) test of the null
hypothesis that the 3-month Treasury bill rate and inflation rate are not cointegrated against the alternative hypothesis that the variables are cointegrated. The 10 percent, 5 percent, and 1 percent critical values for the trace statistic are 18.47, 20.66, and 24.18. The
lag order for the regression model used to compute the test statistic is reported in brackets. *, **, and *** indicate significance at the
10 percent, 5 percent, and 1 percent levels. Standard errors are reported in parentheses.

nal interest rates argues for cointegration analysis
of those variables to ascertain the EPRR’s integration properties. When we prespecify a 共1,–1兲′
cointegrating vector and apply unit root tests to
the EPRR, we reject the unit root null at the 5
percent level using the ADF statistic and at the
1 percent level using the MZα statistic. The U.S.
EPRR appears to be stationary.
To test the null hypothesis of no cointegration
without prespecifying a cointegrating vector,
Table 3 reports the AEG statistic, MZα statistic
from Perron and Rodriguez (2001), and trace statistic from Johansen (1991). The AEG and trace
statistics reject the null hypothesis of no cointegration at the 10 percent level, and the MZα statistic rejects the null at the 5 percent level. Table
3 also reports estimates of the cointegrating coefficients, θ0 and θ1. Neither the dynamic ordinary
least squares (OLS) nor Johansen (1991) estimates
of θ1 are significantly different from unity, indicating a stationary U.S. EPRR. The cointegrating
vector is not estimated precisely enough to
determine whether there is a tax effect.
Tables 2 and 3 provide evidence that the U.S.
EPRR is stationary, although some of the rejections
are marginal. Unit root and cointegration test
results, however, are sensitive to the test proceF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

dure and sample period. Studies such as Mishkin
(1992), Wallace and Warner (1993), and Crowder
and Hoffman (1996) find evidence of a stationary
U.S. EPRR, but Koustas and Serletis (1999) and
Rapach and Weber (2004) generally do not. In
contrast, per capita consumption growth is clearly
stationary, as the ADF and MZα statistics in Table 2
both strongly reject the unit root null hypothesis
for this variable. The fact that integration tests
give mixed results for the EPRR’s stationarity and
clear-cut results for consumption growth highlights differences in the persistence properties of
the two variables.

Confidence Intervals for the Sum of the
Autoregressive Coefficients
The sum of the AR coefficients, ρ, in the AR
representation of it – πt+1 equals unity for an I共1兲
process, while ρ < 1 for an I共0兲 process. It is inherently difficult, however, to distinguish an I共1兲
process from a highly persistent I共0兲 process, as
the two types of processes can be observationally
equivalent (Blough, 1992; Faust, 1996).12 To ana12

In line with this, Crowder and Hoffman (1996) emphasize that
impulse response analysis indicates that shocks have very persistent effects on the EPRR, although the U.S. EPRR appears to be I共0兲.

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Neely and Rapach

lyze the theoretical implications of the time-series
properties of the real interest rate, however, we
want to determine a range of values for ρ that are
consistent with the data, not only whether ρ is
less than or equal to 1. That is, a series with a ρ
value of 0.95 is highly persistent, even if it does
not contain a unit root per se, and it is much more
persistent than a series with a ρ value of, say, 0.4.
To calculate the degree of persistence in the
data—rather than simply trying to determine if
the series is I共0兲 or I共1兲—Rapach and Wohar (2004)
compute 95 percent confidence intervals for ρ
using the Hansen (1999) grid-bootstrap and
Romano and Wolf (2001) subsampling procedures.13 Using quarterly nominal long-term government bond yield and CPI inflation rate data
for 13 industrialized countries for 1960-68, Rapach
and Wohar (2004) report that the lower bounds
of the 95 percent confidence interval for ρ for the
tax-adjusted EPRR are often greater than 0.90,
while the upper bounds are almost all greater
than unity. Similarly, Karanasos, Sekioua, and
Zeng (2006) use a long span of monthly U.S. longterm government bond yield and CPI inflation
data for 1876-2000 to compute a 95 percent confidence interval for the EPRR’s ρ. Their computed
interval, (0.97, 0.99), indicates that the U.S. EPRR
is a highly persistent or near-unit-root process,
even if it does not actually contain a unit root.
With the same U.S. data underlying the
results in Tables 2 and 3, we use the Hansen (1999)
grid-bootstrap and Romano and Wolf (2001) subsampling procedures to compute a 95 percent
confidence interval for ρ in the it – πt+1 process.
The grid-bootstrap and subsampling confidence
intervals are (0.77, 0.97) and (0.71, 0.97), and the
upper bounds are consistent with a highly persis tent process. In contrast, the grid-bootstrap and
subsampling 95 percent confidence intervals or
13

Andrews and Chen (1994) argue that the sum of the AR coefficients,
ρ, characterizes the persistence in a series, as it is related to the
cumulative impulse response function and the spectrum at zero
frequency. While conventional asymptotic or bootstrap confidence
intervals do not generate valid confidence intervals for nearly
integrated processes (Basawa et al., 1991), Hansen (1999) and
Romano and Wolf (2001) show that their procedures do generate
confidence intervals for ρ with correct first-order asymptotic coverage. Mikusheva (2007) shows, however, that while the Hansen
(1999) grid-bootstrap procedure has correct asymptotical coverage,
the Romano and Wolf (2001) subsampling procedure does not.

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ρ for per capita consumption growth are (0.34,
0.70) and (0.37, 0.64). The upper bounds of the
confidence intervals for ρ for consumption growth
are less than the lower bounds of the confidence
intervals for ρ for the EPRR. This is another way
to characterize the mismatch in the persistence
properties of the EPRR and consumption growth.

Testing for Fractional Integration
Unit root and cointegration tests are designed
to ascertain whether a series is I共0兲 or I共1兲, and
the I共0兲/I共1兲 distinction implicitly restricts—perhaps inappropriately—the types of dynamic
processes allowed. In response, some researchers
test for fractional integration (Granger, 1980;
Granger and Joyeux, 1980; Hosking, 1981) in the
EARR and EPRR. A fractionally integrated series
is denoted by I共d兲, 0 ≤ d ≤ 1. When d = 0, the series
is I共0兲, and shocks die out at a geometric rate;
when d = 1, the series is I共1兲, and shocks have
permanent effects or “infinite memory.” An intermediate case occurs when 0 < d < 1: The series is
mean-reverting, as in the I共0兲 case, but shocks now
die out at a much slower hyperbolic (rather than
geometric) rate. Series in which 0 < d < 1 exhibit
“long memory,” mean-reverting behavior, and
can be substantially more persistent than even a
highly persistent I共0兲 series.
A number of studies, including Lai (1997),
Tsay (2000), Karanasos, Sekioua, and Zeng (2006),
Sun and Phillips (2004), and Pipatchaipoom and
Smallwood (2008), test for fractional integration
in the U.S. EPRR or EARR. Using U.S. postwar
monthly or quarterly U.S. data, Lai (1997), Tsay
(2000), and Pipatchaipoom and Smallwood (2008)
all present evidence of long-memory, meanreverting behavior, as estimates of d for the U.S.
EPRR or EARR typically range from 0.7 to 0.8 and
are significantly above 0 and below 1. Using a
long span of annual U.S. data (1876-2000),
Karanasos, Sekioua, and Zeng (2006) similarly
find evidence of long-memory, mean-reverting
behavior in the EPRR. Sun and Phillips (2004)
develop a new bivariate econometric procedure
that estimates the EARR’s d parameter in the
0.75 to 1.0 range for quarterly postwar U.S. data.
Overall, fractional integration tests indicate
that the U.S. EPRR and EARR do not contain a
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Neely and Rapach

unit root per se but are mean-reverting and very
persistent. We confirm this by estimating d for the
EPRR using our sample of U.S. data for 1953:Q1–
2007:Q2 with the Shimotsu (2008) semiparametric
two-step feasible exact local Whittle estimator
that allows for an unknown mean in the series.
This estimator refines the Shimotsu and Phillips
(2005) exact local Whittle estimator, and these
authors show that such local Whittle estimators
of d have good properties in Monte Carlo experiments. The estimate of d for the EPRR is 0.71, with
a 95 percent confidence interval of (0.51, 0.90),
so we can reject the hypothesis that d = 0 or d = 1.
This evidence of long-memory, mean-reverting
behavior is consistent with the results from the
literature discussed previously. The estimate of
d for per capita consumption growth is 0.15 with
a standard error of 0.10, so we cannot reject the
hypothesis that d = 0 at conventional significance
levels. This is another manifestation of the discrepancy in persistence between the real interest
rate and consumption growth.

Testing for Threshold Dynamics and
Nonlinear Cointegration
The empirical literature on the real interest
rate typically uses models that assume both the
cointegrating relationship and short-run dynamics
to be linear.14 Recently, researchers have begun
to relax these linearity assumptions in favor of
nonlinear cointegration or threshold dynamics,
which allow for the cointegrating relationship or
mean reversion to depend on the current values
of the variables. For example, a threshold model
might permit the EPRR to be approximately a
random walk within ±2 percent of some long-run
equilibrium value but to revert strongly to the ±2
percent bands when it wanders outside the
bands.15
Million (2004) presents evidence that the U.S.
EPRR adjusts in a nonlinear fashion to a long-run
equilibrium level using a logistic smooth transi14

Studies that allow for fractional integration or structural breaks
also relax some linearity assumptions but in a different way than
those reviewed in this subsection.

15

The purchasing power parity literature often uses these threshold
models (Sarno and Taylor, 2002).

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

tion autoregressive (LSTAR) model and monthly
U.S. 3-month Treasury bill rate and CPI inflation
rate data for 1951-99. The Lagrange multiplier
test of Luukkonen, Saikkonen, and Teräsvirta
(1988) rejects the null hypothesis of a linear
dynamic adjustment process, and there is evidence
of stronger (weaker) mean reversion in the EPRR
for values of the EPRR below (above) a threshold
level of 2.2 percent. Million (2004) notes that the
weak mean reversion in the upper regime is consistent with the fact that the U.S. real interest rate
was persistently high during much of the 1980s,
and he observes that the Federal Reserve’s priority on fighting inflation, following the stagflation
of the 1970s, could explain this period of high
real rates. In a vein similar to that of Million,
Koustas and Lamarche (2008) estimate threeregime self-exciting threshold autoregressive
(SETAR) models to characterize the monetary
policy strategy of “opportunistic disinflation”
(Blinder, 1994; Orphanides and Wilcox, 2002).
Based on the nonlinear unit root test of Bec, Salem,
and Carassco (2004) and Hansen (1996, 1997)
linearity tests, Koustas and Lamarche (2008) conclude that the EPRR can be suitably modeled as
a three-regime SETAR process in Canada, France,
and Italy over the postwar period.16
Christopoulos and León-Ledesma (2007)
examine quarterly U.S. 3-month Treasury bill
rate and CPI inflation rate data for 1960-2004,
permitting the cointegrating relationship itself
to be nonlinear. More precisely, they allow the
cointegrating coefficient (θ1) to vary with the
inflation rate by estimating logistic and smooth
exponential transition regression (LSTR and
ESTR) models. Christopoulos and León-Ledesma
(2007) find significant evidence of nonlinear
cointegration between the nominal interest rate
and inflation rate using the Choi and Saikkonen
(2005) test. Using estimation techniques from
Saikkonen and Choi (2004), the authors conclude
16

Maki (2003) uses the Breitung (2002) nonparametric procedure
that allows for nonlinear adjustment dynamics to test for cointegration between the Japanese nominal interest rate and CPI inflation rate for 1972:01–2000:12. While Maki (2003) finds significant
evidence of cointegration between the nominal interest rate and
inflation rate using the Breitung (2002) test, he does not estimate
the cointegrating vector, so it is not clear that the long-run equilibrium relationship is consistent with a stationary EPRR.

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Neely and Rapach

that the ESTR model fits best over the full sample
(1960:Q1– 2004:Q4) and the first subsample
(1960:Q1–1978:Q1), whereas the LSTR model
fits best over the second subsample (1979:Q1–
2004:Q4). The estimated ESTR model for 1960:Q1–
1978:Q1 is not consistent with a stationary real
EPRR for any inflation rate, and the estimated
LSTR model for 1979:Q1–2004:Q4 is consistent
with a stationary EPRR only when the inflation
rate moves above approximately 3 percent.
In summary, recently developed econometric
procedures provide some evidence of threshold
behavior or nonlinear cointegration in the EPRR
in certain industrialized countries. In some cases,
the threshold models accord well with our intuition about changes in central bank policies.
Although evidence of threshold behavior in real
interest rates is potentially interesting, the models
do not obviate the persistence in real interest rates,
as there are still regimes where the real interest
rate behaves very much like a unit root process.

TESTING FOR REGIME
SWITCHING AND STRUCTURL
BREAKS IN REAL INTEREST RATES
Building on the work of Huizinga and Mishkin
(1986), another strand of the empirical literature
tests for structural breaks in real interest rates.
Accounting for such breaks can substantially
reduce the persistence within the regimes defined
by those breaks (Perron, 1989). Similarly, failing
to account for structural breaks can produce spurious evidence of fractional integration (Jouini
and Nouira, 2006).
Using quarterly U.S. 3-month Treasury bill
rate and CPI inflation rate data for 1961-86, Garcia
and Perron (1996) use Hamilton’s (1989) Markovswitching approach to test for regime shifts in the
U.S. EPRR. Specifically, they allow the unconditional mean of an AR(2) process to follow a threestate Markov process. The three estimated states
correspond to high, middle, and low regimes with
means of approximately 5.5 percent, 1.4 percent,
and –1.8 percent, respectively. The filtered probability estimates show that the EPRR was likely
in the middle regime from 1961-73, the low regime
from 1973-81, and the high regime from 1981-86.
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There is very little persistence within each regime,
as the estimated AR coefficients (ρ1 and ρ2 in
equation (A1)) are near 0 within regimes. Overall,
Garcia and Perron (1996) argue that the U.S. real
interest rate occasionally experiences sizable
shifts in its mean value, while the real interest
rate is close to constant within the regimes.
Applications of Markov-switching models
typically assume that the model is ergodic, so the
current state will eventually cycle back to any
possible state. Structural breaks have some similar
properties to Markov-switching regimes, but they
are not ergodic—they do not necessarily tend to
revert to previous conditions. Because real interest
rates in Garcia and Perron (1996) exhibit no obvious tendency to return to previous states, structural breaks might be considered more appropriate
for modeling real interest rate changes than Markov
switching. Bai and Perron (1998) develop a powerful methodology for testing for multiple structural breaks in a regression model, and Caporale
and Grier (2000) and Bai and Perron (2003) apply
this methodology to the mean of the U.S. EPRR.
Both studies use quarterly U.S. short-term nominal
interest rate and CPI inflation rate data for 1961-86,
and the estimated break dates are very similar:
1967:Q1, 1972:Q4, and 1980:Q2 in Caporale and
Grier (2000) and 1966:Q4, 1972:Q3, and 1980:Q3
in Bai and Perron (2003). The breaks correspond
to a decrease in the mean EPRR in 1966/1967, a
further decrease in 1972, and a sharp increase in
1980. Caporale and Grier argue that changes in
political regimes—party control of the presidency
and Senate—produce these regime changes.
Rapach and Wohar (2005) extend the work of
Caporale and Grier (2000) and Bai and Perron
(2003) by applying the Bai and Perron (1998)
methodology to the EPRR in 13 industrialized
countries using tax-adjusted nominal long-term
government bond yield and CPI inflation rate data
for 1960-98. They find significant evidence of
structural breaks in the mean of the EPRR in each
of the 13 countries. Rapach and Wohar (2005) also
find that breaks in the mean inflation rate often
coincide with breaks in the mean EPRR for each
country’s data. Furthermore, increases (decreases)
in the mean inflation rate are almost always associated with decreases (increases) in the mean EPRR.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Neely and Rapach

Table 4
Bai and Perron (1988) Test Statistics and Estimation Results for the U.S. ex post Real Interest
Rate (1953:Q1–2007:Q2)
Test statistic
UDmax

Estimated ex post
real interest rate mean

Regime
14.84***

1953:Q1–1972:Q3 [1969:Q2, 1973:Q4]

1.22*** (0.17)

WDmax (5%)

27.06**

1972:Q4–1980:Q3 [1979:Q1, 1980:Q4]

F(1|0)

12.92***

1980:Q4–1989:Q3 [1984:Q3–1994:Q2]

4.58*** (0.71)

F(2|1)

17.89***

1989:Q4–2007:Q2

1.82*** (0.52)

F(3|2)

17.89***

F(4|3)

10.37*

F(5|4)

10.37

–0.55 (0.38)

NOTE: *, **, and *** indicate significance at the 10 percent, 5 percent, and 1 percent levels. The bracketed dates in the Regime column
denote a 90 percent confidence interval for the end of the regime. Numbers in parentheses in the last column denote standard errors
for the estimated mean.

This finding is consistent with the hypothesis
that monetary easing increases inflation and generates a persistent decline in the real interest rate.
In a comment on Rapach and Wohar (2005),
Caporale and Grier (2005) examine whether political regime changes affect the mean U.S. EPRR,
after controlling for the effects of regime changes
in the inflation rate. Caporale and Grier (2005)
find that political regime changes associated with
changes in the party of the president or control
of Congress do not affect the mean EPRR after controlling for inflation. However, the appointments
of Federal Reserve Chairmen Paul Volcker in 1979
and Alan Greenspan in 1987 are associated with
shifts in the mean EPRR even after controlling
for changes in the mean inflation rate.
The previous papers test for structural breaks
under the assumption of stationary within-regime
behavior. In the spirit of Perron (1989), a number
of studies test whether the real interest rate is I共0兲
after allowing for deterministic shifts in the mean
real rate. Extending the methodology of Perron
and Vogelsang (1992), Clemente, Montañés, and
Reyes (1998) test the unit root null hypothesis for
the U.K. and U.S. EPRR using quarterly long-term
government bond yield and CPI inflation rate data
for 1980-95, allowing for two breaks in the mean
of the EPRR. They find that the EPRR in the United
Kingdom and United States is an I共0兲 process
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

around an unconditional mean with two breaks.
Using monthly U.S. 1-year Treasury bill rate data
for 1978-2002 and expected inflation data from
the University of Michigan’s Survey of Consumers,
Lai (2004) finds that the EARR is an I共0兲 process
with a shift in its unconditional mean in the early
1980s. Lai (2008) extends Lai (2004) by allowing
for a mean shift in quarterly real interest rates for
eight industrialized countries and eight developing countries and finds widespread support for a
stationary EPRR after allowing for a break in the
unconditional mean.
To further illustrate the prevalence of structural
breaks, we use the Bai and Perron (1998) methodology to test for such instability in the unconditional mean of the U.S. EPRR for 1953:Q1–
2007:Q2.17 Table 4 reports the results. The procedure finds three changes in the mean that occur
at 1972:Q3, 1980:Q3, and 1989:Q3 and are similar
to those previously identified for the United
States.18 The breaks are associated with substan17

We focus on the Bai and Perron (1998) methodology in analyzing
mean real interest rate shifts in updated U.S. data. It would be
interesting in future research to consider regime-switching models
and recently developed structural break tests such as described
by Elliott and Müller (2006).

18

Rapach and Wohar (2005) discuss how the statistics reported in
Table 4 imply that there are three significant breaks in the unconditional mean.

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Neely and Rapach

Figure 2
U.S. Ex Post Real Interest Rate and Regime-Specific Means, 1953:Q1–2007:Q2
Percent
10

8

6

4

2

0

–2

–4

Ex Post Real Interest Rate
Regime-Specific Means

–6
1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

NOTE: The figure plots the U.S. ex post real interest rate and means for the regimes defined by the structural breaks estimated using
the Bai and Perron (1998) methodology.

tial changes in the average annualized real interest rate in the different regimes. The average real
rate is 1.22 percent for 1953:Q1–1972:Q3, is not
significantly different from zero for 1972:Q4–
1980:Q3, increases to 4.58 percent for 1980:Q4–
1989:Q3, and falls to 1.82 percent for 1989:Q4–
2007:Q2. Figure 2 depicts the EPRR and the mean
for each of the four regimes defined by the three
breaks.19 In contrast to this evidence for breaks
in the real rate, the Bai and Perron (1998) methodology fails to discover significant evidence of
structural breaks in the mean of per capita consumption growth. (We omit complete results for
brevity.)
19

The test results of Bai and Perron (1998) for structural breaks in the
mean EPRR do not appear sensitive to whether the tax-adjusted or
tax-unadjusted EPRR is used (Rapach and Wohar, 2005). Neither
do estimates of the sum of the AR coefficients nor tests for fractional
integration hinge critically on whether the EPRR is tax adjusted.

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In interpreting structural break results, we
emphasize that such breaks only reduce withinregime or local persistence in real interest rates.
The existence of breaks still implies a high degree
of global persistence, and the breaks themselves
require an economic explanation.

THEORETICAL IMPLICATIONS
AND A MONETARY EXPLANATION
OF PERSISTENCE
This section considers what types of shocks
are most likely to produce the persistence in the
U.S. real interest rate. The empirical literature
devotes relatively little attention to this important
issue. We argue that monetary shocks likely drive
the persistence in the U.S. real interest rate.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Neely and Rapach

Before discussing potential sources of real
interest rate persistence, we briefly make the
case that the U.S. real interest rate is ultimately
mean-reverting. As we emphasize, unit root and
cointegration tests have difficulty distinguishing
unit root processes from persistent but stationary
alternatives. Nevertheless, unit root and cointegration tests with good size and power, applied to
updated data, provide evidence that the U.S. real
interest rate is an I共0兲—and thus mean-reverting—
process (see Table 2).20 Tests for fractional integration nest the I共0兲/I共1兲 alternatives, and they concur
that the U.S. real interest rate is a mean-reverting
process. Using an updated sample, we confirm the
findings of Lai (1997), Tsay (2000), Pipatchaipoom
and Smallwood (2008), and Karanasos, Sekioua,
and Zeng (2006) that demonstrate long-memory,
mean-reverting behavior in the U.S. real interest
rate. Our updated sample also provides evidence
of structural breaks in the U.S. real interest rate.
Curiously, the regime-specific mean breaks for the
EPRR largely cancel each other in the long run
(see Table 4): The estimated mean real rate in 2007
is close to that estimated for 1953.21 We speculate that although structural breaks appear to
describe the data better than a constant, linear
data generating process, these breaks appear to
exhibit a certain type of mean-reverting behavior.
With sufficient data—much more than we have
now—one could presumably model this meanreversion in regimes.
These facts lead us to tentatively claim that
the U.S. real interest rate is best viewed as a very
persistent but ultimately mean-reverting process.
We emphasize the tentative nature of this claim,
and we consider careful econometric testing of
this proposition to be an important area for future
research. Even if real interest rates ultimately
mean-revert, they are clearly very persistent.
Recall the underlying motivation for learning
about real interest rate persistence: In a simple
20

Recall, however, that unit root and cointegration tests are sensitive
to the particular sample used.

21

One might wonder if the observed mean-reversion in structural
breaks contradicts our contention that the breaks should not be
modeled as a Markov process because they are not ergodic. We do
not think, however, that observing one state twice and two states
once provides sufficient information for a Markov process.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

endowment economy, the real interest rate should
have the same persistence properties as consumption growth. In fact, however, real rates are much
more persistent than consumption growth. Permanent technology growth shocks can create a nonstationary real rate but affect consumption growth
in the same way, so they cannot account for the
mismatch in persistence. More complex equilibrium growth models potentially explain this persistence mismatch through changing fiscal and
monetary policy, as well as transient technology
growth shocks. We consider fiscal, monetary, and
transient technology shocks as potential causes
of persistent fluctuations in the U.S. real interest
rate.
Figures 1 and 2 reveal two episodes of pronounced and prolonged changes in the U.S. EPRR:
the protracted decrease in the EPRR in the 1970s
and subsequent sharp increase in the 1980s. Fiscal
shocks appear to be an unlikely explanation for
the large decline in real rates from 1972-79. The
U.S. did not undertake the sort of contractionary
fiscal policy that would be necessary for such a
fall in real rates.22 In fact, fiscal policy in the 1970s
largely tended toward modest deficits. Given the
substantial budget deficits beginning in 1981,
expansionary fiscal shocks are a more plausible
candidate for the increase in real rates at this time.
Monetary shocks appear to fit well with the
overall pattern in the real interest rate, including
the multiyear decline in the real rate during the
1970s, the very sharp 1980 increase, and subsequent gradual decline during the “Great
Disinflation.” One interpretation of the “Great
Inflation” that began in the late 1960s and lasted
throughout the 1970s is that the Federal Reserve
pursued an expansionary monetary policy—either
inadvertently or to reduce the unemployment rate
to unsustainable levels—and this persistently
reduced the real interest rate (Delong, 1997; Barsky
and Kilian, 2002; Meltzer, 2005; Romer, 2005).
After Paul Volcker’s appointment as Chairman,
the Federal Reserve sharply raised short-term
nominal interest rates to reduce inflation from
its early 1980 peak of nearly 12 percent, and this
22

The recent analyses by Romer and Romer (2008) and Ramey (2008)
indicate that the U.S. economy did not experience sizable contractionary fiscal policy shocks during the 1970s.

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Neely and Rapach

Figure 3
Romer and Romer (2004) Measure of Monetary Policy Shocks, 1969:Q1–1996:Q4
1.5

1

0.5

0

–0.5

–1

–1.5
1970

1975

1980

1985

1990

1995

NOTE: A positive (negative) value corresponds to a contractionary (expansionary) monetary policy shock.

produced a sharp and prolonged increase in the
real interest rate. The structural breaks manifest
these pronounced swings: The mean EPRR falls
from 1.22 percent in 1972:Q3 to essentially zero
and then rises to 4.58 percent beginning in
1980:Q4 (see Table 4). Furthermore, Rapach and
Wohar (2005) report evidence of breaks in the
mean U.S. inflation rate in 1973:Q1 and 1982:Q1
that increase and decrease the average inflation
rate. The timing and direction of the breaks are
consistent with a monetary explanation that also
accounts for the mismatch in persistence between
the real interest rate and consumption growth. In
each case, negative (positive) breaks to the real
rate of interest coincide with positive (negative)
breaks in the mean rate of inflation. The data are
in line with the hypothesis that central banks
change monetary policy and inflation through
persistent effects on the real rate of interest.
Turning to technology shocks, the paucity of
independent data on technology shocks makes it
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difficult to correlate such changes with real interest rates. In addition, researchers have traditionally viewed technology growth as reasonably
stable. One might think that other sorts of supply
shocks, such as oil price increases, might influence
the real rate, and they surely do to some degree;
Barro and Sala-i-Martin (1990) and Caporale and
Grier (2000), for example, consider this possibility. It is unlikely, however, that oil price shocks
alone can account for the pronounced swings in
the U.S. real interest rate: Why would rising oil
prices in 1973 reduce the real interest rates but
rising oil prices in 1979 dramatically raise the
real rate?23
While we interpret the timing of major swings
in the U.S. real rate to strongly suggest a monetary explanation, we ultimately need to estimate
23

Furthermore, Barsky and Kilian (2002) argue that the timing of
increases in U.S. inflation in the early 1970s is more consistent
with a monetary rather than an oil price shock explanation.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Neely and Rapach

Figure 4
U.S. Ex Post Real Interest Rate Response to a Contractionary Romer and Romer (2004)
Monetary Policy Shock
Percent
4

3

2

1

0

–1
0

2

4

6

8

10

12

14

16

18

20

Quarters After Shock

NOTE: The response is based on an autoregressive distributed lag model estimated for 1969:Q1–1996:Q4. Dashed lines delineate
two-standard-error bands. The response is to a shock of size 0.5.

structural models to analyze the relative importance of various shocks. Galí (1992) is one of the
few studies providing evidence on the economic
sources of real interest rate persistence. His SVAR
model finds that an expansionary money supply
shock leads to a very persistent decline in the real
interest rate, and money supply shocks account
for nearly 90 percent of the variance in the real
rate at the one-quarter horizon and still account
for around 60 percent of the variance at the 20quarter horizon. Galí’s (1992) evidence is consistent with our monetary explanation of real interest
rate persistence.24
We present tentative additional evidence in
support of a monetary explanation of real interest
24

King and Watson (1997) and Rapach (2003) use SVAR frameworks
to estimate the long-run effects of exogenous changes in inflation
on the real interest rate. Both studies find evidence that an exogenous increase in the steady-state inflation rate decreases the
steady-state real interest rate.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

rate persistence based on the new measure of
monetary shocks developed by Romer and
Romer (2004). They cull through quantitative
and narrative Federal Reserve records to compute
a monetary policy shock series for 1969-96 that
is independent of systematic responses to anticipated economic conditions. Figure 3 plots the
Romer and Romer (2004) monetary policy shocks
series, where expansionary (i.e., negative) shocks
in the late 1960s and early 1970s and large contractionary (i.e., positive) shocks in the late 1970s
and early 1980s appear to match well with the
decline in the U.S. real interest rate in the 1970s
and subsequent sharp increase around 1980.
Romer and Romer (2004) estimate autoregressive distributed lag (ARDL) models to examine
the effects of a monetary policy shock on real
output and the price level. They find that a contractionary shock creates persistent and sizable
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Neely and Rapach

declines in both real output and the price level.
In similar fashion, we estimate an ARDL model via
OLS to measure the effects of a monetary policy
shock on the real interest rate. The ARDL model
takes the form,
8

(8)

8

rtep = a0 + ∑ a j rtep
− j + ∑ b j St − j + ut ,
j =1

j =0

where rtep is the EPRR and St is the Romer and
Romer measure of monetary policy shocks.
Figure 4 illustrates the response of the EPRR
to a monetary policy shock of size 0.5, which is
comparable to some of the contractionary shocks
experienced in the late 1970s and early 1980s
(see Figure 3). Romer and Romer’s (2004) Monte
Carlo methods provide the two-standard-error
bands. A contractionary monetary policy shock
produces a statistically and economically significant increase in the U.S. EPRR, which remains
statistically significant after approximately two
years. Note that the response in Figure 4 is nearly
identical to the response of rtep to a shock to St
obtained from a bivariate VAR(8) model that orders
St first in a Cholesky decomposition. Together,
Figures 3 and 4 show that expansionary (contractionary) monetary policy shocks can account for
the pronounced and prolonged decrease (increase)
in the U.S. real interest rate in the 1970s (early
1980s). We emphasize that this evidence is suggestive. Of course, structural identification is a
thorny issue, and more research is needed to
determine the veracity of the monetary explanation for U.S. real interest rate persistence.

CONCLUSION
Rose’s (1988) seminal study spurred a sizable
empirical literature that examines the time-series
properties of real interest rates. Our survey details
the evidence that real interest rates are highly
persistent. This persistence manifests itself in
the following ways:
• Under the assumption of a constant data
generating process, many studies indicate
that real interest rates contain a unit root.
While econometric problems prevent a
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dispositive resolution of this question, real
interest rates display behavior that is very
persistent, close to a unit root.
• Estimated 95 percent confidence intervals
for the sum of the AR coefficients from the
literature have upper bounds that are greater
than or very near unity.
• Real interest rates appear to display longmemory behavior; shocks are very longlived, but the real interest rate is estimated
to be ultimately mean-reverting.
• Studies allowing for nonlinear dynamics
in real interest rates identify regimes where
the real interest behaves like a unit root
process.
• Structural breaks in unconditional means
characterize real interest rates. Although
the breaks reduce within-regime persistence, the real interest rate remains highly
persistent because the regimes have different means.
Although researchers have used a variety of
econometric models to analyze the time-series
properties of real interest rates, relatively little
work has been done to discriminate among these
sundry models. Model selection could tell us, for
example, whether we should think of persistent
changes in real interest rates in terms of changes
in the steady-state real rate—which are consistent
with unit root behavior—or long-lived shocks
that eventually decay to a stable steady-state real
rate—which are consistent with mean-reverting
behavior. While model selection raises challenging econometric (and philosophical) issues, outof-sample forecasting exercises and analysis of
posterior model probabilities in a Bayesian context might identify the best way to model real
interest rate persistence.
Finally, structural analysis is necessary to
identify the sources of the persistence in real
interest rates. Theoretical models suggest that a
variety of shocks can induce real rate persistence,
including preference, technology growth, fiscal,
and monetary shocks. We suggest a tentative
monetary explanation of U.S. real interest rate
persistence based on timing, lack of persistence
in consumption growth, and large and persistent
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Neely and Rapach

real interest rate responses to a Romer and Romer
(2004) monetary policy shock. The literature
would greatly benefit from further analysis of the
relative importance of different types of shocks
in explaining real interest rate persistence.

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APPENDIX
Unit Root and Cointegration Tests
This appendix briefly describes the basic framework for unit root and cointegration testing;
Hamilton (1994) details the subject. Following Dickey and Fuller (1979) and Said and Dickey (1984),
unit root tests are typically based on the autoregressive (AR) representation of a time series, which can
be written as follows:

y t − µ = ρ1 ( y t −1 − µ ) +  + ρk ( yt − k − µ ) + et ,

(A1)

where et is a white noise disturbance term. When the sum of the AR coefficients in equation (A1),
k

ρ = ∑ j =1 ρ j ,
equals 1, shocks to yt persist forever—yt has a unit root and thus has no tendency to revert to an unconditional mean. Testing the null hypothesis that yt ~ I共1兲 against the alternative hypothesis that yt ~ I共0兲
is equivalent to testing
k

k

∑ j =1 ρ j = 1 versus ∑ j =1 ρ j < 1.
Researchers usually ignore the possibility that ρ > 1, since this would imply an explosive process, which
we do not observe in the data. The t statistic on γ in the following augmented Dickey-Fuller (ADF)
regression provides a convenient test statistic for the unit root null hypothesis:
∆y t = δ + γ y t −1 + ρ1 ∆y t −1 +  + ρ k −1∆y t − ( k −1) + et ,

(A2)

where δ = µ共1 – ρ兲, γ = –共1 – ρ兲, and
k
ρ i = −∑ j = i +1 ρ j . 25

Under the null hypothesis that yt ~ I共1兲, γ = 0, while γ < 0 under the alternative hypothesis that yt ~ I共0兲.
The t statistic on γ in equation (A2) has a nonstandard distribution, necessitating simulation methods
to obtain critical values.
Cointegration tests are closely related to unit root tests in that they ask whether any linear combination of some set of I共1兲 processes (say, yt and xt ) are stationary or cointegrated. The popular, residualbased augmented Engle and Granger (1987, AEG) procedure uses the following ordinary least squares
(OLS) regression as a first step in testing the null hypothesis of no cointegration:
(A3)

y t = θ0 + θ1 xt + ut .

The cointegrating vector, which defines the stable long-run relationship between yt and xt (if it exists),
is given by 共1,–θ1 兲′. One then runs an ADF-type unit root test—with no constant—on the regression
residuals, ût = yt – 共θˆ0 + θˆ1xt 兲, where θˆ0 and θˆ1 are the OLS estimates of θ0 and θ1 . The AEG test statistic—
the ADF test statistic from the residual regression—also has a nonstandard asymptotic distribution,
which requires simulated critical values. When yt and xt are cointegrated, θˆ0 and θˆ1 are superconsistent,
converging to their probability limits faster than the usual rate of
1 T.
25

The unit root tests developed by Phillips and Perron (1988) are closely related to ADF tests and are frequently used in the literature. We refer
to both ADF and Phillips and Perron (1988) tests simply as ADF tests in our discussion of the empirical literature in the text.

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Endogeneity bias, however, renders conventional OLS standard errors incorrect. When yt and xt are
cointegrated, fully modified OLS (FM-OLS; Phillips and Hansen, 1990) and dynamic OLS (DOLS;
Saikkonen, 1991; Stock and Watson, 1993) procedures efficiently estimate θ0 and θ1 with appropriate
standard errors.
Johansen (1991) develops a cointegration test procedure based on the likelihood function of a system
of equations that simultaneously tests the null hypothesis of no cointegration and consistently and
efficiently estimates the cointegrating vector (if it exists). This system-based approach is also popular
in applied research and is potentially more powerful than the single-equation–based AEG approach
(Pesavento, 2004).
Unit root and cointegration tests have two significant problems. First, they have low power to reject
the null if the true model is a highly persistent but stationary process (DeJong et al., 1992). Second,
moving-average components in the underlying data-generating process complicate inference from unit
root and cointegration tests. Schwert (1987, 1989) shows that ADF unit root tests can have substantial
size distortions that lead to spurious rejections of the unit root null hypothesis in the presence of a
significant moving-average component.26 Lütkepohl and Saikkonen (1999) show that such size distortions can also affect cointegration tests. This is potentially relevant when analyzing the EPRR, as Perron
and Ng (1996) and others show that inflation rates often have sizable moving-average components.27

26

There are two strategies for dealing with a significant moving-average component in the data-generating process when performing ADF unit
root tests: (i) include a large number of lags when estimating (A2), as an autoregressive moving average process with finite-order lag polynomials can be expressed as an infinite-order AR process; (ii) include the moving-average component in the data generating process when simulating critical values.

27

Perron (1994) observes that the inflation rate could exhibit a substantial moving-average component if the monetary authority offsets inflationary
or disinflationary shocks away from a target price level path.

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Drug Prices Under the Medicare
Drug Discount Card Program
Emin M. Dinlersoz, Rubén Hernández-Murillo, Han Li, and Roger Sherman
In early 2004, the U.S. government initiated the Medicare Drug Discount Card Program (MDDCP),
which allowed card subscribers to obtain discounts on prescription drugs. Pharmacy-level prices
were posted on the program website weekly with the hope of promoting competition among card
sponsors by facilitating consumer access to prices. A large panel of pharmacy-level price data
collected from this website indicates that price dispersion across cards persisted throughout the
program. Prices declined initially when consumers were choosing cards, but rose later when subscribers were restricted to commit to their card choices. In contrast, contemporaneous prices from
online drug retailers, which were unrelated to the program, rose steadily over time, indicating that
program prices evolved in a way different from the general evolution of prices outside the program.
(JEL D43, D83, I11, I18, L11, L13, L50)
Federal Reserve Bank of St. Louis Review, November/December 2008, 90(6), pp. 643-66.

O

n April 29, 2004, in conjunction
with the Medicare Drug Discount
Card Program and Transitional
Assistance Program (MDDCP), the
U.S. government activated a website to publicize
prices offered by discount cards for more than
800 prescription drugs at individual pharmacy
levels across all zip code areas in the United
States. The MDDCP was initiated as a transition
to the broader Medicare Part D prescription drug
assistance program that took effect in January
2006, aiming to lower the cost of drugs and
therapy for elderly and handicapped individuals
covered by Medicare. The price information on
the MDDCP website was updated on a weekly
basis for the duration of the program. This
mandatory release of prices continues under the
Medicare Part D program, and it is unmatched

in scale in the history of government policy on
information transparency.
The MDDCP and its successor program,
Medicare Part D, were intended to induce competition among drug card sponsors, largely
through the extensive amount of price information
that drug card sponsors were required to release
on the website. The premise was that the ease of
consumer search for prices in the program website would enable them to choose the lowest-price
card sponsor, leading to intensified competition
among sponsors. However, at the same time that
the MDDCP generated price information with the
intent to boost competition among drug cards,
the program design also required subscribers to
commit to a single drug card once they subscribed,
rather than being allowed to switch cards at will.
This institutional constraint on consumer switching, among other factors, could inhibit competi-

Emin M. Dinlersoz is a senior economist at Cornerstone Research, Washington, DC. Rubén Hernández-Murillo is a senior economist at the
Federal Reserve Bank of St. Louis. Han Li is an associate professor at the Research Institute of Economics and Management, Southwestern
University of Finance and Economics, Chengdu, Sichuan, China. Roger Sherman is professor emeritus, Department of Economics, University
of Houston.

© 2008, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the
views of Cornerstone Research, the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be
reprinted, reproduced, published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation
are included. Abstracts, synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank
of St. Louis.

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Dinlersoz, Hernández-Murillo, Li, Sherman

tion by preventing consumers from switching to
low-price providers. Thus, a major question is
whether MDDCP competition among the drug
card sponsors was indeed effective in lowering
drug prices as intended by the program initiators.
This paper studies the dynamics of prices
over the course of the program by using a large
sample of prices collected from the MDDCP website for several weeks. The empirical analysis
indicates that the program resulted in economically significant and persistent price dispersion
across cards. More importantly, the evidence
points to a nonmonotonic time path for prices.
Drug prices declined in the early phases of the
program when card subscription was still diffusing across consumers, and they rose later when
new card subscriptions slowed and consumers
could no longer switch cards, although the magnitudes of these shifting trends were not exceptionally large relative to the overall average of
program prices. As a benchmark for comparison,
contemporaneous prices unrelated to the program
were collected from online drug retailers, and
these prices exhibited a steady upward trend. In
particular, when MDDCP prices declined, online
prices rose, and when both sets of prices rose, the
rise in MDDCP prices was actually greater than
the rise in online prices. Thus, MDDCP prices
evolved differently from the general evolution of
drug prices outside the MDDCP, indicating that
the time path of prices within the MDDCP cannot
be explained simply by general trends in regular
online drug prices.
The analysis of the evolution of prices under
the MDDCP is relevant because of the potentially
large welfare consequences of government policies aimed at increasing competition, which continue under Medicare Part D. At the time of the
study, the population eligible for drug cards was
around 7.5 million, and it has continued to grow
since Medicare Part D took effect in 2006. The
design of a viable prescription drug program for
the elderly is still a major policy issue and the
success of the ongoing Medicare Part D remains
to be seen. Therefore, lessons learned from the
MDDCP experience are valuable in assessing the
success of government-sponsored competition
and information dissemination about prices. By
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increasing program awareness, making the price
information publicly available through its website, and helping eligible consumers choose
cards, the program’s goal was to increase competition among rival prescription drug suppliers
and to help establish a market in which such
increased competition persisted in the long run
even after the broader Medicare Part D took
effect. The belief, at least in part, was that effective
consumer search for lower prices would discipline
the pricing behavior of suppliers and lead to lower
prices. Certain theories of consumer search (e.g.,
Stahl, 1989) suggest that easier consumer search
can exert downward pressure on prices in a market. Related empirical work (notably, Brown and
Goolsbee, 2002) also demonstrated that the diffusion of consumer search can be associated with
lower prices, provided consumers were uninhibited in switching to lower-priced suppliers. Yet,
the results here suggest that no systematic and
economically significant decline in prices occurred
when the overall price dynamics within the program are considered.
Official surveys and studies on the marketing
performance of the MDDCP point to several reasons that appear to have prohibited effective
search by consumers, which could have allowed
the reallocation of consumers to lower-priced
cards.1 Efforts to inform potential beneficiaries
about drug cards and the enrollment process were
limited, particularly about the cost of cards and
the extent of the discounts available. In addition,
the program’s website and the existing help lines
were not particularly useful in guiding consumers
to choose the card that was best for them. Thus,
these studies do not suggest any strong indication
that consumers were able to make highly informed
and close to ideal choices. Consumers also were
often confused about the abundance of cards and
pharmacies from which to choose, which made
it difficult to make the best choice. Furthermore,
the low inherent propensity of Internet usage and
searching capability among elderly individuals
prevented effective usage of the website for consumer decisionmaking. All these impediments
1

See, for instance, the 2005 U.S. Government Accountability Office
study GAO-06-13R.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Dinlersoz, Hernández-Murillo, Li, Sherman

seem to have led to price dynamics in the program
that did not coincide with the program’s intended
effects.
The rest of this paper is organized as follows.
The next section provides background for the
MDDCP. The third section presents some theoretical guidance, followed by a description of the
data. Empirical analysis and results are then
described before our concluding section.

THE MDDCP BACKGROUND
The design and the institutional environment
of the MDDCP are crucial for understanding the
functioning of the retail drug markets created by
the program. The MDDCP allowed qualified drug
card sponsors to make arrangements with drug
manufacturers to obtain discounts and pass these
discounts on to Medicare recipients. Eligible consumers could subscribe on a strictly voluntary
basis to a card of their choice and obtain their
prescriptions at a discount specified by the card
sponsor. Prescriptions were available either from
retail pharmacies or by mail from mail-order
pharmacies that had arrangements with the card
sponsor. An individual consumer subscribed to
a card by paying a fixed annual fee (for at most
two years), ranging between $0 and $30, and thereafter was entitled to receive that card’s discounts.
The consumer’s problem consisted of two stages:
first, choosing a drug card that provided the best
discount on the bundle of drugs used by the consumer and second, choosing a retail (or mail-order)
pharmacy that sold the drugs of interest.
Certain institutional aspects of the program
were relevant for the dynamics of program prices.
First, a card sponsor was not required to commit
to a given level of discount on drugs over time.
This flexibility in card prices left the door open
for price fluctuations that could result from competition among cards, above and beyond general
fluctuations in drug prices such as those related
to changes in manufacturers’ costs or changes in
demand after the introduction of a generic. For a
given card, there was also no prior commitment
for prices to be the same across all pharmacies
that offered discounts under the card.
Second, in addition to the usual consumer
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

search and switching costs that contribute to price
dispersion in drug retail markets (see ScottMorton, 1997, and Sorensen, 2000, 2001), prohibitive consumer switching costs were inherent
in the very design of the program.2 Once enrolled
in a card program, a consumer was not allowed
to switch to another card, except in certain special
cases, such as moving to a new location or a card
sponsor exiting the market. This restriction on
switching introduced additional friction and
inertia into the market, which may have impeded
reallocation of consumers to low-price card sponsors over time. The MDDCP had a nationally coordinated switching period between November 15
and December 31, 2004, during which consumers
were allowed to review their card choices and
change them if they wished to do so. After this
period, a consumer who was already enrolled in
a card was not allowed to switch to another card
until the end of the program, subject to the exceptions mentioned. The prevention of switching
after the switching period and the timing of the
switching period could potentially lead to price
dynamics driven by the card sponsors’ incentives
to charge lower prices in the early stages of the
program to attract subscribers, and then to increase
their prices once consumers were locked in to
their card choices.
Third, the diffusion of card enrollment among
eligible consumers was expected to be gradual,
not instantaneous. Consumers had to evaluate
card choices before making a decision. One of
the main criticisms of the MDDCP was the complexity of the card choice process related to the
abundance of alternative plans whose benefits
were hard to assess. This criticism applies equally
to Medicare Part D. Available evidence indicated
that the diffusion of card enrollment was indeed
gradual. According to enrollment data from the
Center for Medicare and Medicaid Services (CMS),
about 6.4 million beneficiaries were enrolled in
the drug card program as of September 2005,
2

Usual switching costs in the context of prescription drugs include
consumer learning costs about the side effects of a new drug that
can substitute for the consumer’s existing drug and physicians’
inertia in changing prescriptions because of rewards and loyalty
programs offered by the manufacturer or the wholesaler of that drug.

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Dinlersoz, Hernández-Murillo, Li, Sherman

toward the end of the program.3 Roughly twothirds of participants enrolled early in the program
(May through July 2004). Enrollment was much
faster between May and October 2004 and reached
about 6 million participants (about 80 percent of
the total Medicare population) around October
2004. It rose little thereafter, essentially staying
level after January 2005, when the switching
period ended.
Moreover, most consumers eligible for cards
were 65 years or older, not a group of particularly
Internet-savvy consumers. Shortly before the
program took effect, Fox (2004) estimated that 22
percent of adults aged 65 and older had access to
the Internet. Of this group, an estimated 66 percent
used the Internet to locate health information,
implying that only about 14 percent of the relevant
population used the Internet for health information searches. Thus, the overall propensity to use
the Internet as a price search tool was not impressively high in the eligible population.
Further evidence of consumers’ enrollment
and experience with the program comes from an
October 2005 report on the progress of the MDDCP
program prepared by Abt Associates, Inc., on
request from the CMS.4 Based on an extensive
survey of card enrollees and non-enrollees, the
report found that widespread awareness of the
MDDCP was obtained within a few months of
the program. Although a majority of respondents
reported that they had more than enough information to make a choice among the cards, one
quarter to half did not consider more than just
one drug card. Some consumers simply took the
first card available, whereas others were enrolled
automatically. About 13 percent of survey participants obtained information from the Medicare
website, either directly or with the help of a
family member, friend, or counselor who accessed
the website for them. Overall, the available evidence indicates that both the rate of learning about
cards and the search rate for lower prices were
rather low.
3

For more details of the enrollment patterns, see the 2005 U.S.
Government Accountability Office study GAO-06-13R.

4

See Hassol et al. (2005).

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THEORETICAL CONSIDERATIONS
Consumer search is an important source of
price dispersion in retail drug markets (e.g.,
Sorensen, 2000, 2001). Static models of search
are abundant in the literature (see, e.g., Salop and
Stiglitz, 1977, Reinganum, 1979, Burdett and
Judd, 1983, and Stahl, 1989). For instance, Stahl
(1989) shows that as the proportion of consumers
who are fully informed of prices increases, average price falls monotonically. Price dispersion
exhibits nonmonotonic behavior, initially increasing for low values of the informed proportion,
but decreasing for higher values. Although comparative statics from this static model can be used,
as in Brown and Goolsbee (2002), to draw some
conclusions for a dynamic framework, the
MDDCP’s institutional environment introduces
further considerations for firms’ and consumers’
behavior over time, which call for a dynamic
framework.
Given the available evidence on intensity of
search discussed in the previous section, it is hard
to argue that consumer search worked as effectively as in ordinary, nonprogram retail prescription drug markets. Factors in the previous section
suggest that there may have been little consumer
search in the market created by MDDCP, and the
abundance of choices and the complexities of
the program design may have inhibited search.
Another major constraint of the program is that
it prevented consumers from using more than one
card or from changing their card choices after they
subscribed, with few exceptions. The prohibitive
switching cost could have induced card sponsors
to lower their prices in the early stages of the program to attract consumers who had not yet chosen
a card. But as more and more consumers were
locked in to their choices, card sponsors would
have incentives to raise prices. After the switching
period, prices may be expected to rise as sponsors
take advantage of consumers’ inability to change
cards.
This nonmonotonic time path of prices indeed
arises in certain models of dynamic price competition with consumer switching costs, such as
those of Klemperer (1987) and Farrell and Shapiro
(1988). The MDDCP had a lifetime of less than
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Dinlersoz, Hernández-Murillo, Li, Sherman

two years, and cards were differentiated in many
dimensions beyond just price. These main features
of the program are captured nicely by the model
of Klemperer (1987), which presents a two-period
differentiated-products duopoly in which consumers are partially locked in by switching costs
that they face in the second period. Switching
costs make demand more inelastic in the second
period. Prices are lower in the first period as firms
compete to build a customer base that is valuable
later. However, prices may be higher in both
periods than they would be in a market without
switching costs.
Two main considerations under the MDDCP
may make the price dynamics differ from those in
Klemperer (1987). First, Klemperer (1987) assumes
perfect consumer information about prices,
whereas the evidence discussed above suggests
that many card enrollees under the MDDCP chose
their drugs with imperfect information about the
cards’ benefits and prices. Lack of perfect information about prices would not change the competition in the second period, because the constraints
on switching would prevent consumers from
abandoning their firms even if they were informed
of a lower price at some point. However, the intensity of competition in the first period could change.
Firms could take advantage of consumers’ imperfect information and not lower their prices as
much as they would in the case of perfect information. Obviously, a related issue is that each card
sponsor itself probably did not have good information on the general pattern of card enrollment
and on imperfections in consumers’ information
about cards. If card sponsors believed, at least initially until firm evidence on enrollment patterns
emerged, that consumers would make informed
decisions, they would have incentives to lower
their prices.
Second, the MDDCP’s allowance for a round
of card switching in the middle of the program
created incentives for a potential price war by card
sponsors. One implication is that, in addition to
lower prices at the early phases of the program,
lower prices would be expected during the switching period compared with nonswitching periods.
There is no artificially introduced “switching
period” in Klemperer (1987).
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Other considerations, however, could prevent
this predicted nonmonotonic path for prices.
Given the continuing nature of the prescription
drug program with Part D, card sponsors who
use bait-and-switch strategies could harm their
reputations. Although the MDDCP itself lasted
only two years, many card sponsors continued
to participate in Medicare Part D when it started
in January 2006, so sponsors faced the possibility
of alienating consumers because of bait-andswitch price strategies. One of the program’s goals,
as stated in the Medicare program–related website, was to prevent bait-and-switch behavior.
However, the program did not spell out any strict
guidelines as to what exactly constitutes bait-andswitch and how it would be prevented.
The discussion so far suggests that the level of
program prices may not have declined steadily
over time. In view of the institutional environment of the program and the predictions arising
from models of dynamic competition with switching costs, it is possible to observe a nonmonotonic
path for prices. Given the underlying complexities of the program design and the fact that consumer search was not exceptionally high in this
market, the pattern the program prices followed
is ultimately an empirical issue.

DATA
In this section we describe the drugs for
which data were collected, the geographic areas
covered, the timing of data collection, and the
other prices obtained for control purposes.

Drugs
Prices were collected for 28 prescription drugs,
which were chosen based on the following three
criteria. First, all the drugs were in the top 100
drugs in claims filed by the elderly in 2001, and
in the top 200 highest-selling drugs for the elderly
in 2003. This selection of relatively popular drugs
ensures that each drug had sufficiently large
demand. The relatively high demand for these
drugs implies that the price dynamics we are seeking are likely to have been apparent and economically important. Second, half of the drugs are
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Drugs Used in the Empirical Analysis
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Rank in
claims by
elderly (2001)

Typical
indications

Generic
available?

Typical
dosage

Among top
50 drugs for
elderly (2001)?

1

5

Cholesterol

No

10 mg

Yes

2

12

Cholesterol

No

20 mg

Yes

13

2

Cardiovascular

No

5 mg

Yes

7

27

Depression

No

50 mg

Yes

4

Cardiovascular

Yes

10

Cardiovascular

No

75 mg

Yes

Typical usage
duration

Total sales
rank (2003)

Lipitor

Long term

Zocor

Long term

Norvasc

Long term

Zoloft

Long term

Lanoxin

Long term

NA

Plavix

Long term

12

Isosorbide mononitrate Long term

Drug name

0.125 mg

Yes

NA

20

Cardiovascular

Yes

60 mg

Yes

Long term

18

38

Cholesterol

No

20 mg

Yes

Atenolol

Long term

175

45

Cardiovascular

Yes

25 mg

Yes

Metoprolol

Long term

NA

28

Cardiovascular

Yes

50 mg

Yes

Pravachol

Glucophage

Long term

99

9

Diabetes

Yes

500 mg

Yes

Detrol

Long term

86

32

Urinary

No

1 mg

Yes

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Glucotrol XL

Long term

127

40

Diabetes

No

10 mg

Yes

Zestril

Long term

NA

33

Cardiovascular

Yes

10 mg

Yes

Amoxicillin

Short term

NA

> 100

Antibiotics

Yes

500 mg

No

Augmentin

Short term

177

> 100

Antibiotics

Yes

500 mg

No

Zithromax

Short term

NA

> 100

Antibiotics

No

500 mg

No

Minocycline

Short term

NA

> 100

Antibiotics

Yes

100 mg

No

Levaquin

Short term

25

> 100

Antibiotics

No

500 mg

No

Carisoprodol

Short term

NA

> 100

Pain

Yes

350 mg

No

Cephalexin

Short term

171

> 100

Antibiotics

Yes

250 mg

No

Ambien

Short term

31

> 100

Insomnia

No

10 mg

No

Cipro

Short term

48

> 100

Antibiotics

No

500 mg

No

Biaxin

Short term

138

> 100

Antibiotics

No

500 mg

No

Skelaxin

Short term

132

> 100

Pain

No

400 mg

No

Flexeril

Short term

NA

> 100

Pain

Y es

10 mg

No

Cefzil

Short term

152

> 100

Antibiotics

No

500 mg

No

Doxycycline hyclate

Short term

NA

> 100

Antibiotics

Yes

50 mg

No

Dinlersoz, Hernández-Murillo, Li, Sherman

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Table 1

Dinlersoz, Hernández-Murillo, Li, Sherman

Table 2
Variables Used in the Empirical Analysis
Variable

Description

LONG_TERM

Dummy variable, 1 if the drug is a maintenance drug, 0 if the drug is primarily for shortterm use

GENERIC

Dummy variable, 1 if the drug has a generic equivalent or is itself generic, 0 if the drug is
brand name

PRES_2003

The total number of prescriptions for a drug in 2003

PAT_EXPIRE

Dummy variable, 1 if the drug’s patent had expired by 2004, 0 otherwise

PAT_EXCLUSIVE

Dummy variable, 1 if the drug has an exclusive patent for a specific condition, 0 otherwise

FDA_YEAR

The year a drug was approved by the FDA

WALGREENS

Dummy variable, 1 if the pharmacy is a Walgreens store, 0 otherwise

CVS

Dummy variable, 1 if the pharmacy is a CVS store, 0 otherwise

ECKERD

Dummy variable, 1 if the pharmacy is an Eckerd store, 0 otherwise

GEO

Dummy variable, 1 if the card offers national coverage, 0 otherwise

FEE

The fixed one-time enrollment fee to a given card in dollars

MFG

The number of manufacturers with which a card has a contract for discount prices

ASSIST

Dummy variable, 1 if the card offers enrollment assistance, 0 otherwise

MAIL

Dummy variable, 1 if the card has a mail-order option for drugs, 0 otherwise

FORMULARY

Dummy variable, 1 if the drug offers the entire formulary of Medicare-approved drugs,
0 otherwise

FRAC65+

Fraction of people ≥ 65 years or older in a zip code

MEDHINC

Median household income in a zip code

RENT

Median rent for renter-occupied housing units in a zipcode

FRACWHITE65+

Fraction of people ≥ 65 years in a zip code who are white

FRACFEM65+

Fraction of people ≥ 65 years in a zip code who are female

POP65+

Population in a zip code ≥ 65 years

POPWHITE65+

Population in a zip code ≥ 65 years and white

POPFEM65+

Population in a zip code ≥ 65 years and female

SOURCE: FDA, U.S. Food and Drug Administration.

short-term drugs, such as antibiotics and pain killers, and the other half are long-term, maintenance drugs, such as those used for diabetes and
cardiovascular diseases. The evolution of shortterm drug prices is expected to differ from that
of maintenance drugs, for which consumers are
likely to search more intensely for a bargain.
Finally, drug dosages were selected to reflect the
most frequently prescribed dosages for the drugs,
so that the demand is large relative to what it
would be with unusually high or low dosages.5
Each drug price pertains to a 30-day supply. The
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

drugs and some of their attributes are presented
in Table 1.

Geographic Areas
The price data from the MDDCP website
were listed at the level of zip codes. Ninety zip
codes were chosen by a random stratified sampling, designed to oversample zip codes with a
5

Drug-specific information was obtained from Mosby’s Drug Consult
(2004, 2005), which features information on the typical usage and
dosages of drugs.

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Dinlersoz, Hernández-Murillo, Li, Sherman

greater proportion of the population composed
of elderly residents, defined as individuals who
are 65 years of age or older. To determine any
demand side effects on prices, we needed to
ensure a sufficient variation in market size and
other demand shifters, such as income, for discount drugs. The population of residents 65 or
older in a zip code is a proxy for the local market
size for MDDCP cards. The proportion of elderly
people in a zip code population varies in our
sample from a low of 3 percent to a high of 92.6
percent; the average is 28 percent and the standard
deviation is 25 percent. We also gathered zip
code–level demographic data from the U.S. Census
Bureau’s 2000 Zip Code Statistics to analyze the
price effect of demand shifters such as income
and race composition (Table 2).
The program’s price search engine listed
prices for all pharmacies within a circle of a certain radius whose center coincides with the center
of the selected zip code area. The search engine
allowed for a choice of four different radii for any
given zip code, and these radii varied by zip code.
For densely populated urban areas, radii tended
to be much smaller, whereas for less densely populated suburban and rural areas, the radii were
larger, so that cardholders in these areas could
obtain price information for a sufficient number
of pharmacies. We collected price data for all
pharmacies within the smallest and the secondsmallest radii around a given zip code. This selection enabled us to assess the sensitivity of our
results to the choice of radius.

Timing of Data Collection
The price data were updated weekly on the
Medicare website between April 29, 2004, and
December 31, 2005. As shown in Figure 1, the
sample in this paper was collected for several
weeks to cover important periods when the
MDDCP was in effect.6 Prices were first made
available online on April 29, 2004, card enrollment began on May 3, 2004, and cards went into
effect on June 1, 2004. Data collection was initiated
6

The data collection process was automated using iOpus Internet
Macros software that allowed periodic recording of the data from
the Medicare website.

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on June 21, 2004, three weeks after subscribers
were first allowed to use their cards under the
program.7
The first wave of data was collected each week
for a period of seven weeks during the summer
of 2004. We refer to this period as the preswitching period. The second wave was collected during
the last week of December 2004. This week is
within the period between November 15 and
December 31, which was the nationally coordinated switching period. Price observations from
this period enable us to test whether card sponsors lowered their prices in an effort to induce
switches. Finally, the third wave was collected
after the end of the switching period to assess the
behavior of prices when switching cards was not
allowed. We label this period the postswitching
period. During the postswitching period, the collection process took place over nine collection
cycles, which included data from March 7, 2005,
through August 15, 2005.
Each price observation pertains to a drug
sold by a pharmacy at a given location under the
discount offered by a given card at one point in
time. The prices are posted prices, not necessarily
transaction prices. Transactions may have taken
place at only a subset of the posted prices, and
some cards may have had little or no sales for
some drugs. Therefore, posted prices do not necessarily coincide with the set of prices at which
transactions take place. Lacking sales data, we
are unable to make any statements on these issues.
No card sponsor imposed explicit restrictions on
the geographic or time variation in prices.8 Geographic variation may have occurred for several
reasons, including the changing demand and cost
conditions or simply the changing composition
of cards across locations.
7

The price data during the initial weeks of the program contained
certain glitches, as noted by others (see Antos and Pinell, 2004).
Some prices reported by pharmacies were found to be inaccurate
and incorrect. However, these problems were fixed to a large extent
within the first few weeks of the program. To ensure reliable data,
we started collection in the fourth week after the cards went into
effect.

8

A brochure offered by a Walgreens store in Houston, Texas,
specifically stated that prices were subject to change from store to
store and over time.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Figure 1
Chronology of Important Events and Data Collection
Important Events in the MDDCP

May 3, 2004
Card enrollment
begins
June 1, 2004
April 29, 2004
Weekly online price
posting begins

Card usage
begins

November 15, 2004

December 31, 2004

December 31, 2005

Switching period
begins

Switching period
ends

Program terminates

January 1, 2006

April 1, 2004
Second Wave

Third Wave

One week
between December 20
and December 27, 2004

Nine weeks
between March 15
and August 31, 2005

2008

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Dinlersoz, Hernández-Murillo, Li, Sherman

N OV E M B E R /D E C E M B E R

Three Waves
of Data Collection

First Wave
Seven consecutive weeks
between June 21 and
August 15, 2004

Dinlersoz, Hernández-Murillo, Li, Sherman

Other Price Data
Part of our analysis aims to assess the magnitude of savings offered through card usage by controlling for changes in the general level of drug
prices unrelated to the MDDCP. Ideal control data
for this purpose would be comparable pharmacylevel, nonprogram retail price data collected at a
weekly frequency to match the sample of MDDCP
prices. Unfortunately, such detailed data are difficult to find. Instead, we collected nationwide
wholesale prices for the drugs in our sample. The
prices listed here are from Mosby’s Drug Consult
(2004, 2005), which provides prices for major drug
wholesalers by dosage and duration. They are a
representative sample of the wholesale prices
typically used to reimburse patients for their prescriptions.9 Unlike the card prices, however, these
prices are not available by geographic units.
Rather, a single nationwide price is reported by
each supplier, usually a manufacturer. In addition,
the price quotes are not available at a weekly frequency. Instead, they are representative of the
price levels for the year the database was formed.
Despite their shortcomings, these prices are the
best readily available benchmarks and can be used
to approximate savings. As we will show, the
MDDCP prices exhibit little or no geographic dispersion. Thus, the nationwide prices in Mosby’s
Drug Consult can serve as a reasonable benchmark.
To attribute the evolution of prices to program
specifics, the general trends exhibited by drug
prices over the course of the program also need
to be eliminated. For this purpose, we collected
concurrent weekly prices posted by Internet drug
retailers for the same drugs and dosages as in the
program data. We used a major Internet prescription drug search engine, which quoted prices
from several Internet drug retailers.10
9

The nature of these prices is described in Mosby’s reference book
as follows: “Prices are AWP (average wholesale price), a benchmark
price used for reimbursement. AWP represents what a retail pharmacist or a dispensing physician might pay for a product, without
any special discounts. There are, however, many discounts already
in place, so the AWP can often approximate the price that a consumer might pay. The prices listed here are not intended to serve as
an up-to-date substitute for supplier price lists. The price listings
give the reader a good idea of the range between the high and low
prices.”

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Unlike program prices, online prices exhibit
no geographic variation. Because they are subject
to general nationwide trends in drug prices, they
can serve as a good comparison group for the
prices posted by card sponsors. The purpose of
this comparison is twofold: First, it allows us to
assess whether consumers would be able to obtain
lower prices simply by purchasing at regular
online prices available to general consumers,
rather than going through the complicated process
of choosing a card and hunting for lower prices.
Second, and more importantly, online prices can
be used to control for general changes in drug
prices unrelated to the program. Drug prices can
change over time because of changes in manufacturers’ costs, availability of new substitute drugs,
general inflation, or other factors. All such general
trends are expected to apply in similar ways to
MDDCP prices and online prices. Therefore, if
different time patterns are observed for program
prices versus other online prices, it is likely that
program effects are an important cause. However,
online prices may not reflect the exact set of nonprogram prices available to Medicare-eligible
consumers. These consumers typically do not
buy at regular online prices. Thus, online prices
should not be viewed as an exact control group
for Medicare-eligible consumers, but rather as a
benchmark to control for general trends.

ANALYSIS
We begin with an analysis of the variation in
price levels, followed by estimates of the extent
of savings possible through the MDDCP. We then
focus on price dynamics using the second-smallest
radius for each zip code. The results were very
similar when the smallest radius was used instead.

Analysis of Price Variation
The starting point of our analysis is understanding whether significant price dispersion
10

Once again, the data were collected by using iOpus Internet Macros
from the website destinationrx.com. Our sample includes eight
online retailers. Online stores of two major discount retailers
(costco.com and walmart.com), online stores of two large drug
retail chains (cvs.com and homemed.com), and the pharmacy
branch of one major health care service provider (aarpharmacy.com).

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Dinlersoz, Hernández-Murillo, Li, Sherman

Figure 2
Lipitor Price Dispersion: Week of June 28 to July 3, 2004
All Prices

Average Prices by Card

Frequency

Frequency

10,000

25

8,000

20

6,000

15

4,000

10

2,000

5

0

64

66

68

70

72

0

74

64

66

68

70

72

74

Dollars

Dollars

Standard Deviation within Card

Coefficient of Variation within Card

Frequency

Frequency

25

30

20
20
15
10

10

5
0

0

.5

1

1.5

0

Dollars

existed in the market for drug discount cards and,
if so, what drove that dispersion. Figure 2 illustrates the dispersion of prices for one drug, Lipitor,
for the week of June 28–July 3, 2004. The upperleft panel is the histogram of the entire set of
Lipitor prices observed across cards, zip codes,
and pharmacies. The upper-right panel is the
distribution of the average price within a given
card. The average price for a card is calculated
using all price observations pertaining to the card.
The average price varies between about $65 and
$74. However, as shown in the two lower panels,
the dispersion of price within a card is usually
very small, amounting to an economically negligible variation across pharmacies within a card,
even though such lack of variation was not explicitly guaranteed a priori by any card.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

0

.005

.01

.015

.02

Avg/SD

To determine whether the pattern in Figure 2
is typical of all drugs, we consider a general
expression for the price pdrczt of drug d offered
by card c at pharmacy r in zip code z at time t:
(1)

pdrczt = µ + fd + f r + fc + f z + ft + edrczt ,

where µ is a constant, fi is a fixed effect for i 僆
{d,r,c,z,t}, and edrczt is a zero mean error term
that accounts for remaining unobserved factors.
The contribution of each of the main factors to
the overall variation in price can be analyzed by
using analysis of variance (ANOVA) to understand
the components of variation in prices. Because
pharmacies are “nested” within zip codes, a
nested ANOVA was performed to decompose the
total variation in prices for each drug. Results of
the ANOVA for the first week of data (June 21-27,
N OV E M B E R /D E C E M B E R

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Dinlersoz, Hernández-Murillo, Li, Sherman

2004) showed that the variation in price of any
drug across cards is the major component of the
total variation in drug prices. On average, about
87 percent (standard deviation [SD] 15.3 percent)
of the total variation in price is explained by the
variation across cards, and there is little variation
within cards. The variation across zip codes was
only 0.5 percent (SD 2.1 percent) of the total variation on average, and the variation across pharmacies accounted, on average, for only 1.3 percent
(SD 1.8 percent) of the total variation. The hypothesis that the average price of a drug is equal across
cards is rejected strongly for all drugs. We repeated
the ANOVA for other weeks and the findings
supported the same conclusions.11
The finding of little variation in retail prices
across zip codes raises the issue of how much
geography affects pharmacies’ pricing behavior.
By the effect of geography, we mean the locationspecific factors that may affect prices, such as
income level of residents, population, and age
composition in a location, which are particularly
relevant as demand shifters. The ability to control
for all other factors is important in investigating
geographic variation in prices. The ideal experiment would look at the geographic variation in
prices for a given drug and card combination,
holding constant the pharmacy composition
across zip codes. Such an experiment is impossible, however, because pharmacy composition
changes across zip codes. Nevertheless, a close
approximation to this ideal experiment is possible by looking at the prices charged by the stores
of a given pharmacy chain across zip codes. The
individual stores of a chain, such as Walgreens
or CVS, tend to have very similar structures and
practices, so a good approximation can be
obtained by assuming that the store-level features
are roughly constant across zip codes for a given
chain. We calculated the coefficient of variation
of prices across all stores of a pharmacy chain
for each drug and card combination. In almost
all cases, the coefficient of variation was either
11

We also performed the ANOVA for mail-order prices for cards
with a mail-order option. Not surprisingly, the entire variation in
the case of mail-order prices (excluding shipping charges) was
attributable to the cards.

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exactly zero or very close to zero. Thus, price
variation across zip codes arose mainly because
the composition of cards and pharmacies changed
across zip codes.
Although the analysis of variance in prices
clearly indicates that much of the cross-sectional
variation was attributable to the variation across
cards, it does not provide information about specific factors responsible for this variation. Identifying key demand and supply factors that affect
prices is important for understanding why prices
differed across drugs, cards, pharmacies, or zip
codes.
Consider the following version of equation
(1) that includes explanatory variables explicitly
for a given a time period (week):
(2) pdrcz = µ + βd X d + βr X r + βc X c + βz X z + εdrcz ,
where βi is a Ki × 1 vector of coefficients and Xi is
a Ki × N matrix of observables, for i = d,r,c,z. Each
Xi has the form
 x 1 x 2 … x K ′ ,
i 

where xj is an N × 1 vector that contains variables specific to cluster j = 1,…,Ki within group
i = d,r,c,z.
The structure of the error term in equation (2)
is assumed to be
(3)

εdrcz = εd + ε r + εc + ε z + edrcz ,

where edrcz is the error term in equation (1) and
is assumed to be uncorrelated across observations.
The error terms εi (i 僆 {r,d,c,z}) represent the
remaining unobserved part of the fixed effect fi
in (1) after the observable Xi is added to the specification in equation (1) to obtain equation (2).
Specification (3) implies that error terms are correlated within drugs, cards, pharmacies, and zip
codes because of the presence of cluster-specific
errors εi (i 僆 {r,d,c,z}). Because the component εi
is fixed within cluster i, we can include dummy
variables for drugs, cards, pharmacies, and zip
codes to account for these unobserved components. The error term defined in equation (3)
then reduces to edrcz as in equation (1), which is
assumed to be uncorrelated across observations
within a cluster, and we can implement the regresF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Dinlersoz, Hernández-Murillo, Li, Sherman

Table 3
Static Price Regression
Dependent variable: Price
Independent variables

I

II

LONG_TERM

–51.10 (0.04)

–51.10 (0.04)

GENERIC

–11.58 (0.07)

–11.58 (0.07)

PRES_2003

–0.0000027 (0.0000001)

–0.0000027 (0.0000001)

PAT_EXPIRE

48.09 (0.06)

48.09 (0.06)

192.93 (0.09)

192.93 (0.09)

1.89 (0.02)

1.89 (0.02)

PAT_EXCLUSIVE
FDA_YEAR
WALMART

0.14 (0.05)

0.16 (0.06)

–0.94 (0.06)

–0.94 (0.06)

ECKERD

0.69 (0.03)

0.68 (0.04)

GEO

4.94 (0.61)

5.14 (0.61)

CVS

FEE

0.07 (0.01)

0.08 (0.01)

MFG

–0.44 (0.06)

–0.47 (0.06)

ASSIST

–4.15 (0.7)

–4.17 (0.7)

MAIL
FORMULARY

2.04 (0.48)

2.13 (0.48)

1.82 (0.15)

1.73 (0.17)

FRAC65+

–0.33 (0.09)

MEDHINC

–0.00037 (0.000013)

–0.00022 (0.000097)

0.0064 (0.00037)

0.0066 (0.00039)

RENT

—

FRACWHITE65+

–0.29 (0.03)

—

FRACFEM65+

–0.24 (0.02)

—

POP65+

—

POPWHITE65+

—

0.029 (0.0017)

POPFEM65+

—

0.0024 (0.0003)

Card dummies

Y

Y

Drug dummies

Y

Y

Zip code dummies

Y

Y

Pharmacy dummies

–0.03 (0.002)

Y

Y

N

1,230,215

1,230,215

R2

0.98

0.98

NOTE: Robust standard errors are listed in parentheses.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

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655

Dinlersoz, Hernández-Murillo, Li, Sherman

sion in equation (2) without using any cluster
effects.12
The results of the regression are shown in
Table 3 for two specifications for the week of
June 21-27, 2004. We used the same specification
for other time periods and the results were robust.
In evaluating the results, it should be noted that
the drugs in our sample form only a subset of all
drugs (28 of more than 800 drugs) covered by the
MDDCP. Therefore, some characteristics that
would apply in general to the drugs in the entire
list of the MDDCP may not be fully represented
in this relatively small sample.
The explanatory variables, including the
dummies, account for 98 percent of the variation
in prices. Given the large number of observations,
almost all coefficients are precisely estimated.
Long-term maintenance drugs in our sample were,
on average, cheaper than the short-term drugs,
based on the prices for 30-day supplies.13 Generic
drugs and brand-name drugs for which generic
alternatives are available were cheaper compared
with drugs that do not have generic alternatives.
The prices were also lower for drugs that are prescribed more frequently. In addition, newer drugs
had higher prices, as indicated by the positive
coefficient on the year of approval by the FDA.
The coefficients on selected pharmacy chains
suggest that Wal-Mart had slightly higher prices,
by about 14 cents, than those of the omitted category of all remaining pharmacies, while CVS
prices were lower by about a dollar than those
of the omitted category. Eckerd, which merged
with CVS in the spring of 2004 shortly before the
MDDCP took effect, had prices that were higher
by about 70 cents than those of the omitted
category.
12

Because of the large number of dummy variables in this regression
(>1,000 pharmacy dummies), we use the “de-meaned” regression
approach (Greene, 1993, pp. 468-69). By de-meaning the observations by pharmacy, we eliminate the pharmacy dummies and still
obtain the usual ordinary least square (OLS) estimates of the coefficients of interest.

13

The price difference should not be taken as evidence that the cost
of therapy is lower for long-term drugs in general, because longterm prescriptions typically are renewed for several months and
some short-term prescriptions are prescribed for periods shorter
than a month (antibiotics such as Zithromax, which are used for
intense treatment for a week in certain cases). If the drug is used
only seven days, the cost of therapy will be low.

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Cards with national coverage and with a mailorder service tended to have higher prices than
cards that did not have national coverage and
mail-order service. Cards with higher subscription fees and with a broader formulary also tended
to have higher prices. Cards that had arrangements
to provide discounts with a larger number of drug
manufacturers and those that provided enrollment assistance had lower prices than the cards
that did not offer these benefits. Certain quality
dimensions, such as formulary breadth, extensive
geographic coverage, and cost-reducing features
such as association with a larger number of manufacturers, apparently were important for the
differences in price across card sponsors.
Demographic characteristics of zip code areas
also influenced prices to some extent. Zip codes
with a higher proportion of elderly people in the
population had lower prices. Zip codes with a
higher median household income also had lower
prices, whereas zip codes with higher housing
costs were associated with higher drug prices;
but these effects are relatively small.

Estimates of Savings
The finding of differences in prices across
cards noted in the previous section raises the
following question: Were the differences large
enough to reward searching for lower prices
across cards? Several small-scale studies tried to
assess the extent of the discounts in the early
phases of the program with only a handful of
drugs and a few zip codes.14 Such investigations
generally found some savings accruing to cardholders, but the small scale of these investigations
prevented any general conclusions. In the following text, we ignore the card enrollment fee, which
in most cases was zero and could not exceed $30,
and look only at the savings a cardholder could
obtain from using the card to purchase drugs at
card prices versus purchasing at regular retail or
online prices.
14

See, for example, Antos and Ximena (2004). Their approach first
identifies a few health conditions that are common among the
elderly and then calculates the total price of a bundle of drugs
typically prescribed to remedy these conditions.

F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Dinlersoz, Hernández-Murillo, Li, Sherman

Let p–dct be the average price of drug d for card
c in week t, where the average is taken across all
pharmacies selling drug d offered by card c. Define
min
as the average and the minimum of
p–dt and pdt
–
p dct across cards in week t. Similarly, define the
average and minimum regular prices obtained
from Mosby’s (2004) database as p–dMosby and
pdMosby, min, where the average and the minimum
are calculated across the wholesalers listed in the
Mosby’s database for a given drug. In addition to
the prices in Mosby’s database, a separate, independent source is the set of prices we collected
from online pharmacies as described earlier.
Define the average and minimum prices for online
online
online, min
and pdt
.
retailers in week t as p–dt
We now define several alternative measures
of potential savings. The first measure is the savings a naive (or nonsearching, or uninformed)
consumer could obtain. A naive consumer is
defined as one who purchases randomly with
equal probabilities across cards. For a single purchase of the drug at a given point in time, if this
consumer uses a card instead of buying at the
regular wholesale price (i.e., outside the discount
program), the savings are the percentage difference
between the average regular price and the average
card price. We report the average of these savings
across all weeks in the data in percentage form
as follows:
(4)

Sdnaive =

Mosby
− pdt 
100 T  pd
∑

.
Mosby
T t =1  Pd


The second measure is the savings that
accrued to an Internet searcher, who uses the
program website to search for the lowest-price
card for a given drug, but otherwise would purchase randomly in the regular market (outside
the program) because of higher search costs (as
opposed to searching for discounted prices online).
The savings of such a consumer are defined as the
percentage difference between the average price
in the regular market and the minimum price in
the discount card market averaged across weeks,
and are obtained simply by replacing p–dt in equamin
.
tion (4) by pdt
The third measure we consider is the savings
an expert consumer could obtain. An expert conF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

sumer is defined as one who is fully informed of
prices in both markets and thus is always able to
purchase at the minimum price. The average savings across weeks for such a consumer are formally
defined as the percentage difference between the
minimum price in the regular market and the
minimum price in the discount card market averaged across weeks, and are obtained by replacing
min
.
p–dMosby in equation (4) by pdMosby,min and p–dt by pdt
Following Baye, Morgan, and Scholten (2003),
we also define the “value of information” in the
drug discount card market, which is the saving
of a consumer informed of all card prices with
respect to that of a naive consumer,
(5)

Vdcard =

100 T  pdt − pdmin 
∑
.
T t =1 
pdt


We also report the value of information for online
prices and prices from Mosby’s database.
The defined savings measures and the values
of information are reported by drug in Table 4. A
naive consumer could obtain an average savings
of 11.2 percent. The average savings were even
higher for a searcher—about 25 percent. An expert
consumer, on the other hand, had little to gain
from purchasing in the discount card market: An
average savings of only 2.3 percent accrued to such
a consumer. Because most drug card users were
likely non-experts in searching, the estimate of
savings to naive consumers, or at best to searchers,
is likely to be the most reasonable estimate.
A somewhat different picture emerges when
we consider the savings with respect to online
prices. A searcher could obtain an average savings
of 8.7 percent by purchasing at the minimum card
price instead of purchasing randomly from one
of the online pharmacies. However, the benefit
for a naive consumer was negative (but statistically insignificant), and an expert consumer could
obtain positive (again statistically insignificant)
savings. Thus, compared with online prices, card
prices did not appear to provide substantial savings. The average value of information also was the
highest for regular prices, indicating the biggest
rewards to searching, with an average savings for
an informed consumer that amounted to around
20 percent of the average price. These savings were
N OV E M B E R /D E C E M B E R

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657

Estimates of Savings from Drug Discount Cards
N OV E M B E R /D E C E M B E R

Savings (percent)
Regular versus card prices

2008
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Drug

Naive†

Searcher‡

Ambien
Amoxicillin
Atenolol
Augmentin
Biaxin
Carisoprodol
Cefzil
Cephalexin
Cipro
Detrol
Doxycycline hyclate
Flexeril
Glucophage
Glucotrol XL
Isosorbide mononitrate
Lanoxin
Levaquin
Lipitor
Metoprolol
Minocycline
Norvasc
Plavix
Pravachol
Skelaxin
Zestril
Zithromax
Zocor
Zoloft
Average
SD
Median
Interquartile range

5.2
50.1
54.4
–1.6
5.7
38.7
14.3
NA
5.0
5.9
63.4
6.8
–25.1
–12.2
59.6
–2.8
10.1
5.7
NA
–46.3
6.8
–2.0
–9.5
–16.4
28.5
14.2
24.4
8.0
11.2#
25.9
6.3
23.7

17.5
63.6
75.6
8.3
9.0
89.4
16.5
NA
9.8
11.1
79.2
21.9
–11.0
–3.6
81.8
11.5
14.2
11.3
NA
24.7
12.0
3.1
–1.9
–8.6
36.1
20.3
42.9
14.0
24.9#
29.1
14.1
24.1

Expert§

14.2
10.8
67.4
–29.3
–22.0
43.5
–12.7
NA
–12.2
1.9
79.3
3.7
–137.6
–71.4
74.8
–38.9
14.2
6.5
NA
24.7
2.0
–17.0
–1.9
–30.9
31.7
20.3
34.1
5.3
2.3
44.9
4.5
39.5

Online versus card prices (with shipping)*
Naive*

12.0 (10.8)
–42.0 (–66.3)
22.8 (9.7)
3.2 (2.6)
–4.0 (–5.1)
48.6 (43.7)
–19.1 (–19.4)
69.2 (66.2)
5.2 (4.4)
–1.39 (–3.2)
NA
–4.2 (–7.8)
NA
–31.2 (–39.9)
–19.2 (–27.2)
4.0 (–9.4)
–1.4 (–1.8)
4.2 (2.1)
–23.6 (–48.8)
47.9 (46.6)
1.2 (–2.0)
2.1 (0.8)
–4.8 (–6.5)
–9.1 (–10.8)
–31.6 (–35.8)
–2.6 (–2.9)
–20.2 (–21.5)
3.0 (1.2)
0.4 (–4.6#)
25.1 (28.1)
–1.4 (–3.0)
20.8-19.7

Searcher||

Expert

13.6 (12.6)
0.7 (–0.4)
–16.9 (–27.0)
–54.4 (–70.5)
45.7 (45.7)
–1.7 (–1.7)
5.0 (3.8)
–5.1 (–6.5)
3.4 (1.9)
–0.08 (–1.6)
57.3 (57.3)
–147.6 (–147.6)
–17.3 (–17.8)
–20.2 (–20.7)
77.6 (73.2)
47.1 (36.7)
8.8 (8.0)
4.0 (3.1)
3.4 (–0.4)
–2.3 (–6.4)
NA
NA
5.9 (2.6)
–31.7 (–37.3)
NA
NA
–29.8 (–37.3)
–41.6 (–49.8)
–19.2 (–27.2) –222.3 (–244.2)
16.1 (16.1)
2.4 (2.4)
3.9 (3.2)
–0.8 (–1.5)
8.7 (7.1)
2.9 (1.2)
24.8 (24.8)
–23.9 (–23.9)
61.6 (61.6)
25.4 (25.4)
6.5 (5.4)
1.1 (–0.09)
5.5 (4.9)
0.5 (–0.02)
1.2 (0.4)
–6.1 (–7.0)
–1.5 (–4.7)
–8.1 (–11.7)
–25.5 (–29.2)
–44.4 (–48.7)
–2.6 (–2.9)
–10.4 (–10.8)
–15.9 (–15.9)
–53.4 (–53.4)
6.9 (5.1)
0.5 (–1.6)
8.7# (–19.0#) –22.6# (–26.0#)
26.3 (20.6)
53.8 (57.0)
5.2 (–10.3)
–3.7 (–6.4)
14.7-23.1
32.4-37.2

Value of information
Online

1.8 (2.0)
18.2 (22.4)
29.0 (39.0)
1.8 (1.2)
7.2 (6.7)
16.8 (24.1)
1.9 (1.6)
27.5 (20.8)
3.8 (3.8)
4.7 (2.7)
NA
9.8 (9.5)
7.6 (11.5)
1.3 (2.4)
0.0 (0.0)
12.6 (23.2)
12.6 (23.2)
4.6 (5.0)
39.1 (49.5)
25.4 (27.2)
25.4 (27.2)
3.4 (4.2)
5.6 (6.5)
8.3 (6.3)
4.1 (4.3)
4.1 (4.3)
0.0 (0.0)
4.0 (3.9)
9.1# (10.6*)
10.0 (12.4)
5.0 (4.9)
7.7-13.6

Card

Regular

13.0
24.1
46.2
9.6
3.5
82.6
2.5
57.6
5.0
5.6
43.1
16.3
11.3
7.9
54.4
13.9
4.6
6.0
39.3
48.5
5.5
5.0
6.9
6.6
11.3
7.0
24.4
6.5
20.3#
21.1
10.5
22.2

3.8
59.3
25.5
29.0
25.4
81.2
25.9
NA
19.6
9.4
0.0
19.0
39.5
53.3
27.8
36.3
0.0
5.1
NA
0.0
10.2
17.2
0.0
17.1
6.5
0.0
13.4
9.2
20.5#
20.3
17.1
22.7

NOTE: *The figures within parentheses include shipping fees. The figures outside the parentheses are based on the online base prices. †“Naive” is defined as a consumer who
is uninformed and purchases randomly in both markets. ‡“Searcher” is defined as a consumer who is informed of the minimum card price but otherwise purchases randomly
in the regular market. §“Expert” is defined as a consumer who is fully informed in both markets. ||“Searcher” is defined as a consumer who is informed of the minimum online
price but otherwise purchases randomly in the discount card market. #Indicates difference from zero at 5 percent or lower levels.

Dinlersoz, Hernández-Murillo, Li, Sherman

658

Table 4

Dinlersoz, Hernández-Murillo, Li, Sherman

followed closely by card prices. The value of information in the online market was the lowest.

taking the difference of the prices for two consecutive time periods, t and t ′, we obtain

Dynamics of Prices

(7)

We now turn to the evolution of prices. Price
changes using two balanced panels of pharmacies
from the preswitching period and the postswitching period are examined in the first subsection
below. Next, we investigate the behavior of prices
around the switching period. The evolution of
online prices is examined for comparison with
program prices, followed by consideration of the
evolution of price dispersion within the program.

where dct , ddt , and dt are the obvious time differences for the corresponding fixed effects and
εdrczt = 共εdrczt – εdrczt兲. Because differencing works
only if we have the same pharmacies across the
two time periods, we restrict attention to a balanced panel.
Now, consider the following ordinary least
squares (OLS) regression based on equation (6):
(8)

Results from the Balanced Panels
Using a slight modification of equation (1), a
price observation can be written as
(6) pdrczt = µ + ft + fct + fdt + fd + fc + f r + f z + ηdrczt ,
where we introduced the interaction terms, fct , a
card- and time-specific effect, and fdt , a drug- and
time-specific effect. The term fct captures potentially different behavior of cards over time. Different cards may have had different pricing policies
that may have depended on time as competition
among card sponsors changed. In addition, the
time and drug interaction effect, fdt , captures the
possibility of different drugs experiencing different price changes over time (e.g., cards may have
competed more intensely in certain popular drug
categories). The fixed effect, ft, can be interpreted
as the general time effect on prices, which is a
combination of the program’s effect on price and
general fluctuations in drug prices outside the
program.
The specification in equation (6) can be estimated using our unbalanced panel of observations.
This approach has two drawbacks. First, a very
large number of effects (both pure and interaction
effects) must be estimated. Second, and more
importantly, the included effects are not guaranteed to exhaust the set of relevant effects, which
may lead to omitted variable bias, and the timeinvariant fixed effects can potentially be correlated
with the error term. One approach to alleviate
these concerns is to use time differencing, which
eliminates the time-invariant fixed effects. By
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

∆pdrczt = dct + ddt + dt + εdrczt ,

∆pdrczt = βct Dct + βdt Ddt + βt Dt + εdrczt ,

where Dct , Ddt , and Dt are dummies for the differenced effects dct , ddt , and dt . The error term εdrczt
has serial correlation, which we take into account
in estimating the standard errors.
One problem with this approach is that the
balanced panel has a low cross-sectional dimension if we restrict attention only to observations
common across all weeks of data in the sample
period. Because of errors in accessing the MDDCP
website that occurred randomly during the data
collection, there was some attrition in our sample
and the balanced panel that can be constructed
across all weeks of observation is limited in size.
However, because this attrition was entirely random, a systematic bias is not a concern. Consequently, we implement regression (8) separately
for the seven weeks in the preswitching period
and then for the nine weeks in the postswitching
period. This approach provides a large, but different, number of cross-sectional observations for
both periods. We handle the data for the switching
period separately as discussed below.
We first consider the evolution of prices using
a panel from weeks 4 to 10 of the program, the
preswitching period. The results of the difference
regression for this period are shown on the left side
of Table 5. The estimates of βt are all negative and
statistically significant, except for week 5 of the
program. Most of the drop in prices in this period
took place between the fifth and eighth weeks,
resulting in a decline in general level of prices of
about $4.77. By the end of the 10th week, the
prices were lower by about $4.63. However, this
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Dinlersoz, Hernández-Murillo, Li, Sherman

Table 5
Estimated Coefficients of Time Dummies from the Difference Regressions
Dependent variable: first difference in price
Independent variables:
dummy for the week of

Estimates for
preswitching period

Independent variables:
dummy for the week of

Estimates for
postswitching period

6/28/2004

0.21 (0.27)

4/4/2005

2.85 (0.11)

7/5/2004

–2.25 (0.38)

5/16/2005

4.53 (0.16)

7/11/2004

–3.73 (0.47)

6/6/2005

6.54 (0.20)

7/18/2004

–4.77 (0.54)

6/20/2005

7.74 (0.23)

7/25/2004

–4.64 (0.61)

7/11/2005

7.74 (0.26)

8/2/2004

–4.63 (0.66)

7/18/2005

7.7 (0.28)

8/1/2005

7.8 (0.31)

8/15/2005

7.83 (0.33)

N

92,700

N

18,280

R2

0.53

R2

0.51

NOTE: Robust standard errors are shown in parentheses. Omitted time dummy is the first week for each regression: 6/21/2004 for
the preswitching period and 3/7/2005 for the postswitching period.

reduction represents a small portion (5.5 percent)
of the average ($81.90) of all price observations
during the fourth week of the program when data
collection began.
We repeated the analysis for the postswitching
period using a balanced panel. The evolution of
the prices in the sample of weeks from the postswitching period shows a different pattern compared with the preswitching period, as seen on
the right side of Table 5. In fact, the estimated βt
coefficients are all positive and statistically significant. Between the starting and ending weeks
of the sample in the postswitching period, prices
rose by about $8, controlling for drug and card
effects. Much of this increase took place between
the end of the switching period and the end of
June 2005. Thereafter, prices stabilized somewhat.
Between the end of the switching period and the
end of June, prices rose at a pace of about $2 a
month. The total rise in prices represents about
9.5 percent of the average drug price in the fourth
week of the program.
Figure 3 displays the discrepancy in the average evolution of prices for different cards and
drugs. Specifically, the upper two histograms
660

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display the frequency distributions of the time
average of the card-time effects plus the puretime effects,
(9)

1 T
βˆ c = ∑ βˆ t + βˆ ct ,
T t =1

(

)

for the preswitching and postswitching periods,
on the left and the right panels, respectively.
Analogously, the bottom two panels contain the
frequency distributions of the time average, of
the drug-time plus the pure-time effects,
(10)

1 T
βˆ d = ∑ βˆ t + βˆ dt ,
T t =1

(

)

for the preswitching period on the left and the
postswitching period on the right. As is evident
from the histograms on the left-hand side of the
upper and lower panels, most cards and drugs had
lower prices during the preswitching period.
However, the right tails of these histograms show
a few outlier cards and drugs that exhibited an
average upward trend in prices even during this
period. In contrast, for the postswitching period,
all cards and drugs exhibited an average upward
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Dinlersoz, Hernández-Murillo, Li, Sherman

Figure 3
Frequency Distribution of Average Card–Time and Drug–Time Effects
Card–Time Effects
Preswitching Period*

Postswitching Period*

Frequency

Frequency

15

10
8

10

6
4

5

2
0
−10

−5

0

5

0

2

3

4

5

6

Drug–Time Effects
Preswitching Period**

Postswitching Period**

Frequency

Frequency
5

10

4
3
5

2
1

0

−5

0

5

0

2

4

6

8

NOTE: *As defined in equation (9). **As defined in equation (10).

trend in price (seen in the histograms on the
right-hand side of the upper and lower panels).
Overall, these histograms suggest that prices of
cards and drugs on average moved in the same
direction within the preswitching and postswitching periods with few exceptions.
We repeated the estimation in equation (8)
by adding a long-term drug dummy interaction
with a time dummy to explore whether long-term
drugs exhibited any different behavior compared
with short-term drugs. We found that during the
preswitching period, the prices for long-term
drugs actually fell less, and during the postswitching period they rose less compared with shortterm drugs. This pattern does not support the
hypothesis that consumers searched more vigorously for bargains on these drugs. If this were the
case, we would have expected to see a steeper
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

decline for these prices compared with the prices
of short-term drugs.15

The Switching Period
For the nationally coordinated card-switching
period between November 15 and December 31,
2004, we were able to collect only one week of
price data because of technical problems in
accessing the website during much of that period.
As a result, we were able to collect data for only
15 drugs, and the generally smaller number of
observations for that period precluded us from
including the switching period in the balanced
15

One possible explanation is that consumers with an existing prescription for a given long-term drug who have purchased from
their preferred pharmacy for a long time may not have found it
worthwhile to search vigorously for a card and a possibly different
pharmacy—which illustrates another form of switching costs.

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Dinlersoz, Hernández-Murillo, Li, Sherman

Table 6
Analysis of Price Changes Around the Switching Period
(Switching period price) –
(Preswitching period price)
Average
difference ($) Paired t statistic

Drug

p Value

(Postswitching period price) –
(Switching period price)
Average
difference ($) Paired t statistic

p Value

Ambien

–1.99

–6.91

0.00

0.31

5.42

0.00

Amoxicillin

–2.28

–26.56

0.00

1.33

11.38

0.00

Atenolol

–0.77

–9.62

0.00

0.18

0.67

0.49

Augmentin

–3.07

–2.46

0.01

0.72

2.88

0.00

Biaxin

–2.65

–10.55

0.00

2.80

22.66

0.00

Carisoprodol

–0.63

–1.29

0.04

1.50

3.29

0.00

Cefzil

–2.93

–17.94

0.00

–0.10

–0.89

0.37

Cipro

–4.81

–5.00

0.00

3.69

3.35

0.00

Detrol

–2.09

–4.18

0.00

3.27

12.47

0.00

0.58

8.73

0.00

0.21

4.25

0.00

–0.70

–3.18

0.00

2.61

16.08

0.00

0.34

7.92

0.00

1.03

14.00

0.00

Doxycycline hyclate
Flexeril
Glucotrol XL

–3.36

–14.22

0.00

2.30

1.31

0.18

Lanoxin

1.32

22.87

0.00

0.05

0.60

0.54

Levaquin

–3.80

–10.78

0.00

2.48

12.42

0.00

Average

–1.79

1.49

0.45

0.33

Isosorbide mononitrate

Standard error

NOTE: “Switching period price” is the price during the one week of data available from the switching period. “Preswitching period price”
is the price during the last week (week of 8/2/2004) of price observations in our preswitching period sample. “Postswitching period
price” is the price during the first week (week of 4/4/2005) of price observations in our postswitching period sample. Bold t statistics
indicate significance at 5 percent or lower levels.

panel analysis of the previous section. Instead,
we compared the average price level for each drug
using two paired t tests. For each drug, we perform two paired t tests across common cards and
pharmacies: one for the difference between the
week from the switching period and the last week
of the preswitching period, and the other for the
difference between the first week of the post switching period and the week from the switching period. The paired t test approach eliminates
the fixed effects that are common across the two
periods and isolates the time effects, just like the
balanced panel used previously.
As shown in Table 6, both tests indicated a
statistically significant decline in prices for most
drugs (12 of 15) between the last week of the pre 662

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switching period and the week of the switching
period, and a subsequent statistically significant
rise for most drugs (11 of 15) between the week
of the switching period and the first week of the
postswitching period. The magnitude of price
drops and raises varied across drugs. Overall,
prices declined on average by about $1.80 between
the week of August 2, 2004, and the week of
December 20, 2004, and rose on average by about
$1.50 between the week of December 20, 2004,
and March 7, 2005.
Given the nature of the timing of data collection, we cannot say precisely whether the decline
in prices between the week of August 2, 2004, and
the week of December 20, 2004, was confined to
the switching period only. Because card enrollF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Dinlersoz, Hernández-Murillo, Li, Sherman

ment continued during this period, card sponsors
could have continued to reduce their prices to
some extent to attract additional consumers, as
they did in the initial phases of the program.
Some card sponsors, in anticipation of the switching period, may have also lowered prices in an
effort to deter consumers from switching. Thus,
some of the observed price decline in this period
could have occurred even before the switching
period. We are more comfortable attributing the
rise in prices after the switching period to the
existence of switching costs, because during that
period card enrollment diffused to a large extent
and enrolled consumers were committed until
the end of the program.
In summary, the evidence from the balanced
panel estimation and the paired t tests points to
initially declining but later rising prices, even
though the magnitudes of change in price levels
were not exceptionally large compared with the
average price level across drugs. The pattern
exhibited by prices lends more support to a model
in which prices move in a nonmonotonic path,
falling when consumers could switch cards and
rising when they could not switch cards.

Evolution of Nonprogram Online Prices
We now consider the evolution of online drug
prices as a benchmark for the evolution of program
prices. If the time effects found in the evolution
of program prices are specific to the program
rather than being driven entirely by general trends
in drug prices, the same time effects should not
emerge for online prices unrelated to the program.
To explore this possibility we consider a regression of the form
(11)

pdit = α + βt Dt + βi Di + βd Dd + εdit ,

where Dt is a time dummy, Di is a dummy for
online retailer i, and Dd is a dummy for drug d.
The focus is once again on the estimates of the
coefficients of time dummies.
Few problems were encountered in data collection of online prices over time, so our sample
includes a larger number of weeks and the price
changes can be observed with a higher frequency
over a longer period, sometimes even more freF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

quently than once a week. Table 7 presents the
results of the estimation in equation (11). The time
dummies have almost uniformly positive and
significant coefficients, and the coefficients are
almost monotonically increasing over time. By
the last week of data, prices were higher by about
$3.39, controlling for vendor and drug fixed effects.
We repeated the estimation in equation (11)
using the total price (base price plus shipping
fee) as the dependent variable and the results
were very similar. The total price increased over
time by about $3.53 and the estimated coefficients were uniformly positive and statistically
significant in almost all cases.
Finally, we also used a balanced panel
approach as in equation (8) to estimate the time
effects for online prices. The size of this panel
was much smaller than that of the unbalanced
panel used in equation (11), because we did not
have prices for all sellers and for all drugs every
week. The average growth rate of price between
the first and the last periods of observation was
3.31 percent (SD 0.11 percent). Only four drugs
exhibited a decline in price. Overall, the results
from the balanced panel were similar qualitatively to the estimates of time dummy coefficients in Table 7.
The observed pattern for online drug prices
thus indicates that the evolution of program
prices was indeed different from the evolution of
prices outside the program. Online prices
tended to rise over time, in contrast to the program prices, which first declined and later
increased. Because online prices are subject to
general trends in drug prices, but not to the
effects of the program, the patterns suggest that
the evolution of program prices is at least in
part driven by program effects, rather than
entirely by general trends. First, online prices
rose during the preswitching period when the
program prices exhibited a clear decline. The
decline in program prices is consistent with the
predictions of dynamic price competition models, suggesting an escalated competition in the
early stages of a market when sellers lower their
prices to lure consumers. Second, the overall
rise in online prices fell short of the rise in program prices during the postswitching period.
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Dinlersoz, Hernández-Murillo, Li, Sherman

Table 7
Estimated Time Dummies for Online Price Regression
Independent
variables
Dummy for the date:

Dependent
variable
Base price

Total price

Preswitching period

Independent
variables
Dummy for the date:

Dependent
variable
Base price

Total price

Postswitching period

6/28/2004

0.00 (0.58)

0.00 (0.58)

1/13/2005

1.95 (0.63)

1.99 (0.63)

7/8/2004

0.00 (0.58)

0.00 (0.58)

5/6/2005

2.62 (0.62)

2.66 (0.62)

7/15/2004

0.00 (0.58)

0.00 (0.58)

5/27/2005

2.81 (0.62)

2.85 (0.62)

7/26/2004

1.73 (0.60)

1.74 (0.60)

6/10/2005

2.81 (0.62)

2.85 (0.62)

8/3/2004

1.73 (0.60)

1.74 (0.60)

6/20/2005

2.81 (0.62)

2.85 (0.62)

8/10/2004

1.73 (0.60)

1.74 (0.60)

7/11/2005

3.25 (0.62)

3.31 (0.62)

8/17/2004

1.73 (0.60)

1.74 (0.60)

7/29/2005

3.25 (0.62)

3.31 (0.62)

8/24/2004

1.73 (0.60)

1.74 (0.60)

8/1/2005

3.30 (0.62)

3.36 (0.62)

9/1/2004

1.81 (0.61)

1.87 (0.61)

8/18/2005

3.33 (0.66)

3.38 (0.66)

9/13/2004

1.82 (0.62)

1.87 (0.62)

9/16/2005

3.39 (0.66)

3.53 (0.66)

9/15/2004

1.83 (0.61)

1.85 (0.61)

9/29/2005

3.39 (0.66)

3.53 (0.66)

9/21/2004

1.86 (0.60)

1.91 (0.61)

10/4/2005

3.39 (0.66)

3.53 (0.66)

9/24/2004

1.86 (0.60)

1.91 (0.61)

10/16/2005

3.39 (0.66)

3.53 (0.66)

9/28/2004

1.86 (0.60)

1.91 (0.61)

10/17/2005

3.39 (0.66)

3.53 (0.66)

10/20/2005

3.39 (0.66)

3.53 (0.66)

10/5/2004

1.81 (0.63)

1.85 (0.63)

10/15/2004

1.88 (0.63)

1.89 (0.64)

10/20/2004

1.55 (0.64)

1.56 (0.64)

12/10/2004

1.93 (0.62)

1.97 (0.62)

12/29/2004

1.89 (0.62)

1.93 (0.62)

N

2,955

R2

0.98

Switching period

NOTE: Robust standard errors are shown in parentheses. Total price includes shipping fee for standard delivery for each vendor.
Dates refer to the day the price data were collected. Preswitching period: before 12/2004; switching period: 12/2004; postswitching
period: after 12/2004.

Indeed, the program prices actually increased
about $4 more than online prices by the end of
this period. Therefore, the upward trend in program prices after the switching period cannot be
explained simply by a general rise in drug prices
caused by nonprogram effects.
In addition to the evolution of levels of prices,
we also investigated the evolution of price dispersion. To measure price dispersion at any point
in time, we first calculated the average of a drug’s
price within a card. Next, we computed the dis664

N OV E M B E R /D E C E M B E R

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persion of that average around its mean across
cards. We then used the balanced panel of observations to test the hypothesis that the price dispersion remained the same over time versus the
alternative that dispersion changed. We found no
overwhelming evidence that the dispersion of
average price across cards changed substantially
during the preswitching or the postswitching
periods. The dispersion of prices was persistent
over the course of the program.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

Dinlersoz, Hernández-Murillo, Li, Sherman

CONCLUSION
We used a large panel of drug prices to assess
the effects of government-sponsored release of
price information over the Internet under the
MDDCP. The designers of the program began with
the premise that access to price information by
consumers would lower prices over time. In contrast, the card prices and their dispersion did not
steadily decline over time, as some models of
improved access to price information suggest.
Instead, prices declined during the initial phases
of the program but then increased later when
consumers were unable to switch cards. The
evolution of program prices exhibited significant
deviation from the general evolution of prices
outside the program.
The nonmonotonic evolution of program
prices can be reconciled with the predictions of
certain models of dynamic price competition
with consumer switching costs, such as that of
Klemperer (1987). The very design of the program
left consumers vulnerable to price changes by
card sponsors. Card sponsors appeared to have
reduced their prices initially, possibly in an effort
to lure customers to subscribe, but then raised
their prices in the later stages of the program to
take advantage of consumers when they were
locked in to their choices. However, we are unable
to provide any direct evidence on the actual subscription patterns by card or whether consumers
switched cards at all.
The extent to which these patterns will carry
over to Medicare’s Part D prescription drug
assistance program currently in effect remains
to be seen. Although Part D has a much more
complicated structure, some drivers of price
dynamics under MDDCP also apply to Part D. For
instance, consumers can switch plans only from
November 15 through December 31 of every year,
except in special cases. There are also certain
differences between the two programs. Consumer
non-enrollment in Part D carries a financial penalty
that becomes gradually more severe, unlike in
the case of the MDDCP, where enrollment was
voluntary. Also, the prescription drug benefit
providers engage in a multiperiod, long-horizon
competition under Part D, instead of the twoperiod interaction under the MDDCP. This broader
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W

time horizon introduces considerations of market
growth. Thus, prescription drug benefit providers
will set prices for a broader horizon, probably
considering the trade-off between charging lower
prices to attract newcomers and higher prices to
already committed consumers. The differences
between the two programs notwithstanding, the
evidence from the MDDCP does not straightforwardly suggest a secular decline in the level and
the dispersion of prices under Part D.

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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W