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More Money: Understanding Recent Changes
in the Monetary Base
William T. Gavin
The financial crisis that began in the summer of 2007 took a turn for the worse in September 2008.
Until then, Federal Reserve actions taken to improve the functioning financial markets did not
affect the monetary base. The unusual lending and purchase of private debt was offset by the
sale of Treasury securities so that the total size of the balance sheet of the Fed remained relatively
unchanged. In September, however, the Fed stopped selling securities as it made massive purchases
of private debt and issued hundreds of billions of dollars in short-term loans. The result was a
doubling of the size of the monetary base in the final four months of 2008. This article discusses
the details of the programs that the Fed has initiated since the crisis began, shows which programs
have grown as the monetary base grew, and discusses some factors that will determine whether
this rapid increase in the monetary base will lead to rapid inflation. (JEL E31, E42)
Federal Reserve Bank of St. Louis Review, March/April 2009, 91(2), pp. 49-59.

he monetary base is the sum of currency in circulation and bank deposits
at Federal Reserve Banks. Between midSeptember and December 31, 2008,
the U.S. monetary base increased from approximately $890 billion to $1,740 billion, doubling
in a little more than 3 months.1 This is a concern
because, under normal circumstances, we would
associate such a rapid rise in the monetary base
with a sharp acceleration of inflation. But today,
more people seemed to be worried about deflation
than a sudden rebound of inflation. The purpose
of this article is to explore the sources of growth
in the monetary base and to ask whether or not
1

These data are derived from the Fed’s H4.1 release
(www.federalreserve.gov/releases/h41/). This measure of the
monetary base is named as the series WSBASE on the Federal
Reserve Bank of St. Louis’s FRED database. For technical reasons
(adjustments for seasonal factors, reserve requirements, carryover,
“as of,” and cash items in process of collection), the numbers here
do not correspond to either the Board of Governor’s measure of
the monetary base on the H3 release or the St. Louis adjusted
monetary base.

we should expect to see high inflation following
such rapid monetary growth.
Figure 1 shows that this rapid surge in the
monetary base is concentrated entirely in the
accumulation of bank reserves. (Throughout this
article, the generic word “bank” is used instead
of the official term, “depository financial institution.”) Bank deposits at the Fed include three
components. Two are small and have changed
little since the economic crisis began in August
2007; they are deposits used to satisfy reserve
requirements and those used to satisfy required
clearing balances.2 The third component, “excess
reserves,” accounts for the doubling of the monetary base. This rapid increase is directly related to
Federal Reserve programs initiated or expanded
2

See Stevens (1993) for a description of required clearing balances.
See Anderson and Rasche (2001) for a description of the sweep
programs that reduced the amount of required reserves essentially
to that which would normally be held as a buffer for clearing checks
and meeting uncertain cash withdrawals.

William T. Gavin is a vice president and economist at the Federal Reserve Bank of St. Louis. The author thanks Dick Anderson, Bob Rasche,
and Dave Kemme for helpful comments. Chris Martinek provided research assistance.

© 2009, 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.

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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Gavin

It would be an error to believe that the Fed’s
new programs to improve the functioning of credit
markets began only in September 2008; they did

not. But a major change did occur in September:
The Fed stopped selling Treasury securities as it
increased lending to financial institutions and
purchased non-Treasury assets. As Figure 1 shows,
before mid-September 2008, the Fed’s practice of
selling Treasuries as it purchased other financial
instruments largely insulated the monetary base
from these new programs—bank deposits at the
Fed increased little.4
Table 1 presents a somewhat simplified view
of the Fed’s balance sheet to help illustrate the
sources and uses of the monetary base today.5 The
big changes in the traditional items on the asset
side of the balance sheet are in outright holdings
of Treasury securities, which fell from $778.9
billion in 2007 to $475.2 billion in 2009. This has
virtually wiped out the Fed’s holdings of Treasury
bills, which fell from $277 billion to $18.4 billion.
The Fed’s holding of notes and bonds was reduced
from $467.9 billion to $412.9 billion. But of those
the Fed still holds, $125.1 billion has been lent
through the Term Securities Lending Facility
(TSLF) to securities dealers. Note that changes
in the TSLF do not affect the size of the balance
sheet, but they do reduce the liquidity of the Fed’s
security portfolio.
Holdings of federal agency debt rose from 0
to $26.7 billion. Note that in December 2008, the
FOMC authorized the Trading Desk of the Federal
Reserve Bank of New York to purchase up to
$100 billion of agency debt in the first half of
2009. Repurchase agreements (repos) decreased
from $27.5 billion to $17.1 billion. Another big
change among the traditional assets was the big
increase in primary lending: from $0.3 billion in
the week ending January 17, 2007, to $65.0 billion
in the week ending January 28, 2009. A new part
of this lending program was the very public campaign to eliminate the “stigma” associated with
borrowing at the discount window, an obstacle
to overcome if these lending facilities were to be
implemented as intended.

See Thornton (2009).

This information can be found in the H4.1 release in the table showing factors that supply and absorb reserves. These factors are found
primarily on the Fed’s balance sheet, but also include monetary
items from Treasury’s balance sheet.

since September that seek to improve the functioning of financial markets under stress.
Since lowering its federal funds rate target to
the range of 0 to 0.25 percent, the Federal Open
Market Committee (FOMC) has referred to its
latest policy actions as “credit policy.” These new
programs are distinguished from traditional monetary policy by the type of assets purchased by the
Federal Reserve. Traditional programs involve the
purchase and sale of U.S. Treasury securities,
whereas the new credit-oriented policies involve
the purchase of non-Treasury securities, including
commercial paper and asset-backed securities. By
purchasing such assets, the Fed hopes to reduce
risk premiums and improve flows through the
specific private markets (Bernanke, 2009). Yet,
although the emphasis of these credit programs
is on the types of non-Treasury securities being
purchased (that is, the composition of the Fed’s
assets), nontraditional and traditional programs
share one common characteristic: The purchase
of any asset by the Fed, unless offset by some
other action, increases simultaneously both the
Fed’s balance sheet assets and its liabilities.
The next section of this article shows the
Fed’s balance sheet in January 2007 and again
in January 2009, highlighting the balance sheet
changes since the summer of 2007.3 It highlights
the new programs and shows which have contributed most to the recent surge in the monetary
base. The following section then discusses economic and institutional factors that will influence
the Fed’s ability to maintain price stability as the
economy recovers from the recession and the
financial crisis.

THE FED’S BALANCE SHEET—
BEFORE AND AFTER

See Balbach and Burger (1976) for an elementary introduction to
the derivation of the monetary base from the central bank’s balance
sheet. Their appendix includes an application of their method to
the Fed’s balance sheet in 1976. See Anderson and Rasche (1996)
for the technical details in the derivation of the St. Louis adjusted
monetary base.

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Gavin

Figure 1
Monetary Base
Weekly Average, $ Billions
1,800
Reserve Balances with Federal Reserve Banks
1,600

Currency in Circulation

1,400

1,200

1,000

800

600

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9
/0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0
30 8/6 /13 /20 /27 9/3 /10 /17 /24 0/1 0/8 /15 /22 /29 1/5 /12 /19 /26 2/3 /10 /17 /24 /31 1/7 /14 /21 /28
1 1 1
9 9 9 1 1 10 10 10 1 11 11 11 1 12 12 12 12
8 8 8

From January 17, 2007, to January 28, 2009, the
traditional items on the asset side of the balance
sheet decreased by $224.5 billion. The decline in
outright holdings of Treasury securities, repos,
and float was partially offset by increases in primary lending and federal agency debt. The other
longtime items on the balance sheet are either
unchanged or relatively small. These include the
gold stock, special drawing rights, other assets,
lending through the traditional channels, secondary and seasonal lending, and float.
Next, we turn to the new programs established
after the crisis began. The Trading Desk has just
begun to buy mortgage-backed securities (adding
$6.8 billion as of January 28, 2009) under instructions from the FOMC to purchase as much as
$500 billion in the first half of 2009. Also included
on the balance sheet is a total of $415.9 billion in
loans to banks through the Term Auction Facility
(TAF).6 Figure 2 shows the history of lending
6

For information about the acronyms and new programs, go to
www.federalreserve.gov/newsevents/recentactions.htm.

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

under this program initiated in December 2007—
the same time that the Fed began lending securities to primary dealers through the TSLF.
On January 28, 2009, there were $32.1 billion
in loans outstanding in the Primary Dealer Credit
Facility (PDCF) and other broker-dealer loans,
$14.6 billion in loans through the Asset-Backed
Commercial Paper Money Market Mutual Fund
Liquidity Facility (AMLF), and $38.3 billion in
direct loans to the American Insurance Group
(AIG). Figure 3 shows the history of lending under
these three new programs, as well as the traditional discount window lending of primary credit.
Certain new programs operate as specialpurpose vehicles (SPVs) wholly owned by the
Federal Reserve Bank of New York. The assets
and liabilities of these SPVs are included on the
Federal Reserve’s balance sheet. The next item in
Table 1 (under “New program portfolio”) is the
sum of the private assets purchased under new
programs; the total was $389.9 billion the week
ending January 28, 2009. Among these SPVs is
the Commercial Paper Funding Facility (CPFF)
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Gavin

Table 1
Factors Affecting Reserve Balances ($ billions)
Week Ending
January 17, 2007

January 28, 2009

Assets supplying reserves
Gold stock

11.0

Special drawing rights
Treasury securities*

11.0

2.2

778.9

475.2

Bills

277

Notes and bonds (nominal)

467.9

412.9

30.2

39.4

3.8

4.5

Notes and bonds (inflation-indexed)
Inflation compensation
Federal agency debt

Mortgage-backed securities
Repurchase agreements
Term Auction Facility (TAF)‡
Loans and discounts including float

NA (01/05/09)†

18.4

26.7
6.8

27.5

17.1

NA (12/17/07)

415.9

0.1

148.0

Primary

0.3

65.0

Secondary

0.0

Seasonal

0.0

Float

–0.2

–2.0

Primary Dealer Credit Facility (PDCF) and other broker-dealer loans

NA (03/17/08)

32.1

Asset-Backed Commercial Paper (ABCP)
Money Market Mutual Fund (MMMF) Liquidity Facility (AMLF)

NA (09/19/08)

14.6

Loans to American Insurance Group (AIG)

NA (09/16/08)

New program portfolio

—

38.3
389.9

Commercial Paper Funding Facility (CPFF)

NA (10/27/08)

316.2

Money Market Investor Funding Facility (MMIFF)

NA (11/24/08)

0.0

Maiden Lane

NA (06/26/08)

27.0

Maiden Lane II

NA (11/10/08)

19.7

Maiden Lane III

NA (11/25/08)

27.0

NA (12/12/07)

465.9

39.6

44.4

Central bank liquidity swaps
Other assets
Memo item
Treasury coin outstanding (TCO)
Total factors supplying reserves = Total assets + TCO

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38.3

38.8

897.5

2,041.9

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

Gavin

Table 1, cont’d
Factors Affecting Reserve Balances ($ billions)
Week Ending
January 17, 2007

January 28, 2009

Liabilities absorbing reserves
Federal Reserve notes held by Treasury

0.2

Reverse repos, international accounts, and dealers (RRP)
Treasury deposits
General account
Supplemental financing account

0.3

30.5

73.1

4.7

230.4

4.7

55.5

NA (09/17/08)

174.8

Foreign official

0.1

0.2

Service-related and other demand deposits

7.2

7.9

Other liabilities and capital

36.7

50.4

Total factors other than the monetary base absorbing reserves

79.4

362.3

Monetary base

818.1

1,679.6

Currency in the hands of the public (in circulation)

757.6

830.6

Vault cash in depository institutions

50.3

53.5

Counted as required reserves

32.3

41.2

Counted as surplus cash

Depository institution reserve balances

10.2

12.3
795.5

Held as required reserves

6.1

26.3

Held as excess reserves

4.1

769.2

897.5

2,041.9

Total liabilities plus Treasury coin outstanding

NOTE: Components may not sum to totals because of rounding. Data are from the H4.1 release (Federal Reserve Statistical Release:
Factors Affecting Reserve Balances); see www.federalreserve.gov/releases/h41/.
*Includes $125.1 billion lent to primary dealers through the Term Securities Lending Facility.
† NA refers to an item that was created after the financial crisis was under way. The date refers to the day that the Fed announced the
program or began to purchase this asset.
‡For information about the new programs created to solve the financial crisis, go to: www.federalreserve.gov/newsevents/recentactions.htm.

created to support activity in the market for the
highest-rated (A1/P1) commercial paper. This
program, created in the aftermath of the troubles
at AIG, Lehman Brothers, and Merrill Lynch, has
grown rapidly to $316.2 billion, with the Fed providing most of the new lending in this market.
Also included are three new structured investment vehicles created to buy and hold certain
troubled assets of specific insolvent institutions.
Through Maiden Lane, the Fed owns $27.0 billion
of the poorer-quality assets from the troubles at
Bear Stearns. Through Maiden Lane II and Maiden
Lane III, it owns $19.7 billion and $27.0 billion,
respectively, of troubled assets purchased in supF 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

port of the insurance firm AIG. Figure 4 shows
the history of assets purchased under these new
programs.
On December 12, 2007, the Federal Reserve
established temporary swap lines with foreign
central banks. Under these swap arrangements,
the Federal Reserve provides U.S. dollar deposits
at the Federal Reserve in exchange for an amount
of foreign currency deposits at the foreign central
bank. The amount is determined by the prevailing
exchange rate. The currency is swapped back at
a future date at the swap exchange rate used in
the original transaction. All exchange rate risk is
the burden of the borrowing central bank. Figure 5
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Gavin

Figure 2
Term Auction Facility Assets
Weekly Average, $ Billions
500
Reserve Bank Credit: Term Auction Credit (average)

450
400
350
300
250
200
150
100
50
0
7

/
12

/
10

/
11

Figure 3
Total Loans and Discounts
Weekly Average, $ Billions
400
Credit Extended to AIG (average)
350

Reserve Bank Credit: Asset-Backed Commercial Paper
MM Fund Liquidity Facility (average)

300

Reserve Bank Credit: Primary Dealer Credit Facility
(average)
Reserve Bank Credit: Primary Credit to
Depository Institutions (average)

250
200
150
100
50
0
08

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3
4/

2
8/

1
9/

1
0/

1
1/

/
12

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Figure 4
New Program Portfolio
Weekly Average, $ Billions
450
Net Portfolio Holdings of Commercial Paper Funding Facility LLC

400

Net Portfolio Holdings of Maiden Lane II LLC (average)
Net Portfolio Holdings of Maiden Lane III LLC (average)

350

Net Portfolio Holdings of Maiden Lane LLC (average)
300
250
200
150
100
50
0

3
7/

2
8/

2
9/

1
1/

1
2/

1
1/

2
0/

Figure 5
Foreign Exchange Swaps
Weekly Average, $ Billions
700
Currency Swaps

600
500
400
300
200
100
0

3
7/

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

2
8/

2
9/

2
0/

1
1/

1
2/

1
1/

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Gavin

Figure 6
Total Factors Other than Monetary Base Absorbing Reserves
Weekly Average, $ Billions
900

Factors Absorbing Reserve Funds: Treasury Supplemental
Financing Account (average)

800

Factors Absorbing Reserve Funds:
Treasury Deposits with Federal Reserve Banks
(average)

700

Other Liabilities Absorbing Reserves

600
500
400
300
200
100
0
8

shows the dramatic rise in foreign exchange assets
from currency swap arrangements; these swaps
totaled $465.9 billion as of the week ending
January 28, 2009.
Overall, total assets added by the Federal
Reserve’s nontraditional credit programs were
$1,363.5 billion the week ending January 28, 2009.
Total factors supplying monetary base skyrocketed
that week to a little more than $2 trillion, with
almost all the increase coming after mid-September
2008.
Next, we turn to the liability side of the Fed’s
balance sheet. Not all liabilities of the Fed are
included in the monetary base. Most items on
the liability side of the Fed’s balance sheet that
are not included in the monetary base are small
or relatively unchanged. There has been a relatively large increase—from $30.5 billion to $73.1
billion—in reverse repos with dealers, foreign
official, and other international accounts. The
other—and the most important item absorbing
reserves—is the Treasury deposit account. The
56

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2009

/
10

/
11

/
12

Treasury general account rose from $4.7 billion
to $55.5 billion; for more than 20 years, the Fed
has maintained its general account (used for tax
collection and government disbursements) near
a $5 billion balance. In September 2008, the
Treasury created a new “supplemental financing
account,” which held $174.8 billion on January
28, 2009. At inception, this account held $500
billion obtained by the Treasury as proceeds from
selling a special issue of Treasury bills to the
public. The mechanism for this sale was quite
simple: Each purchaser of a Treasury bill paid
with a bank check or debit. When these transactions cleared, the Federal Reserve transferred the
amounts from bank deposits (reserve accounts)
to the Treasury account (which absorbs reserves,
but is not part of the monetary base). In the second
half of January, the Treasury allowed the special
issue of Treasury bills to mature, to avoid hitting
statutory debt limits. As the Treasury repaid the
owners of these bills, deposits were transferred
from the Treasury’s deposits at the Fed to 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

Gavin

deposits of the banks whose customers owned
the maturing bills. Doing so increases the monetary base, dollar for dollar.
Overall, other factors absorbing reserves rose
from $79.4 billion in January 2007 to $362.3 billion in January 2009. Figure 6 shows the total
factors other than the monetary base that absorb
reserves, with detail shown for Treasury deposits
(both the general account and the supplemental
financing account).
The bottom section in Table 1 lists the components of the monetary base. The “monetary
base” is defined as currency in circulation and
bank demand deposits at the Fed. Currency in
circulation includes vault cash (coin and Federal
Reserve notes held by the depository institutions)
and cash held by the general public. Bank reserve
deposits are sometimes referred to as federal funds.
Thus, the federal funds rate is the interest rate
that banks pay to borrow Federal Reserve deposits
from other banks. The monetary base includes
coin and Federal Reserve notes held overseas
because we have no measure of the amount held
overseas, only the total amount outstanding.7
And, regardless of where they are held, Federal
Reserve notes are a liability of the Fed.
Between January 17, 2007, and January 28,
2009, currency in the hands of the public grew
from $757.6 billion to $830.6 billion. Vault cash
grew from $50.3 billion to $53.5 billion. In January
2007, $32.3 billion of the vault cash was used to
meet reserve requirements; in January 2009, $41.2
billion of vault cash was used. In the early period,
$18.0 billion of vault cash was counted as surplus
vault cash; in January 2009, $12.3 billion was
counted as surplus vault cash.
The interesting change in the monetary base
was in reserve balances held in demand deposits
at the Federal Reserve. These deposits grew from
$10.2 billion the week ending January 17, 2007,
to $795.5 billion the week ending January 28,
2009. Of this large amount, $769.2 billion was
held as excess reserves at the Fed.
7

See Porter and Judson (1996) for estimates of the amount of currency held abroad.

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

WILL RAPID GROWTH IN THE
MONETARY BASE CAUSE RAPID
INFLATION?
The enormous accumulation of excess reserves
began at the time of the Lehman bankruptcy and
rescue of AIG in mid-September. Whether this
large increase in the monetary base is a harbinger
of rapid inflation in the future depends on how
the Federal Reserve and the U.S. government act
when financial markets return to more-normal
behavior and the recession ends.
The difficulty of maintaining price stability
will depend on the size the balance sheet reaches
before the crisis ends, the quality of the assets in
the portfolio, and the policy followed to manage
the interest rate paid on reserves. Any attempt to
predict whether inflation will occur must rely on
predictions about the Fed’s response to events and
its exit from these new programs (that is, reducing the size of the balance sheet) as the economy
recovers from recession and financial crisis.
Analysis of future monetary policy must
consider the October 1, 2008, Congressional
authorization for the Fed to pay interest to banks
on both required reserve and excess reserve balances. By increasing this rate relative to the federal
funds rate target, the Fed provides an incentive
for banks to hold more deposits at the Fed. By
reducing this rate the Fed encourages banks to
expand their lending—and the money supply.
When the FOMC set the federal funds rate target
to the range 0 to ¼ percent on December 16, 2008,
it also set the interest paid on both required and
excess reserves equal to ¼ percent.
A logical question might be why depository
institutions would choose to hold $800 billion
in excess reserves that are earning so little. Two
answers are important, one at the level of the
individual bank and one at an aggregate level.
First, for the individual bank, the risk-free rate of
¼ percent must be the bank’s perception of its best
investment opportunity. Note that on January 28,
2009, the interest rate on the 3-month Treasury
bill was less than ¼ percent. The other is that,
perhaps because of market conditions—the dramatic decline in the price of bank stocks and the
fall in the market value of assets—the bank finds
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Gavin

Table 2
New Program Use and Authorization ($ billions)
Assets supplying reserves
Mortgage-backed securities
Term Auction Facility (TAF)

Week ending
January 28, 2009

500

6.8

600

415.8

Primary Dealer Credit Facility (PDCF)

No announced limit

32.1

Asset-Backed Commercial Paper (ABCP) Money Market
Mutual Fund (MMMF) Liquidity Facility (AMLF)

No announced limit

14.6

Loans to American Insurance Group (AIG)

38.3

Commercial Paper Funding Facility (CPFF)

No announced limit

316.2

Money Market Investor Funding Facility (MMIFF)

540

Maiden Lane

27.0

Maiden Lane II

22.5

19.7

Maiden Lane III

27.0

No announced limit

465.9

Swaps

itself undercapitalized. In such conditions, the
bank is likely to hold relatively more safe assets
while it builds capital by cutting costs, raising fee
income, and hoping for a recovery in both the
economy and its stock price.
Second, the banking system as a whole cannot
create or destroy bank deposits at the Fed. Only
the Fed (and technically, the Treasury) can create
or destroy bank reserves. If one bank makes a loan
and the funds are deposited in another bank, then
the ownership of the deposits at the Fed would
change, but the total bank deposits at the Fed
would remain the same. In theory, the banking
system reduces excess reserves—but only by
expanding loans and the money supply in a way
that increases required reserves by an equivalent
amount. The key is that the Fed will have to drain
reserves when the economy begins to recover if
it is to prevent a rapid acceleration of inflation.
That necessity drives the current discussion of
exit strategies.8
The ease with which the Fed can reduce the
size of its balance sheet in the future depends on
many factors, including the term of its loan portfolio, the quality of assets that it holds outright,
and the market’s appetite for repurchasing these
8

Announced authorization

See Bernanke (2009).

MARCH/APRIL

2009

financial instruments. The authorization for the
ultimate size of new programs varies and has
grown since the beginning of the crisis. Table 2
lists each new program and the upper limit authorized as of January 28, 2009. Of course, in some
cases the limits will be determined by the available assets and/or by the demand for the program.
(Note that there are zero assets in the MMIFF,
which has an authorization of $540 billion.)
When the time comes to shrink the monetary
base, the Fed could allow the lending programs
to expire as loans mature and sell the assets that
it holds outright. If the crisis is over, the assets
should be priced in the market and the Fed should
expect to recover most of its investment in such
assets.
Inflation does not appear to be a risk in the
current environment: The economy is in recession. Inflation is falling and is not expected to
return before the recession ends. If inflation
resumes but the economy does not recover, policymakers will face a difficult choice. Monitoring
the size and composition of the monetary base as
the economy recovers will help us understand
what actions are needed (and should be taken)
by the Fed and the Congress to prevent a return
to a high-inflation economy.
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

Gavin

REFERENCES
Anderson, Richard G. and Rasche, Robert H. “Retail
Sweep Programs and Bank Reserves, 1994-1999.”
Federal Reserve Bank of St. Louis Review,
January/February 2001, 83(1), pp. 51-72;
http://research.stlouisfed.org/publications/review/
01/0101ra.pdf.
Anderson, Richard G. and Rasche, Robert H. “A
Revised Measure of the St. Louis Adjusted Monetary
Base.” Federal Reserve Bank of St. Louis Review,
March/April 1996, 78(2), pp. 3-14;
http://research.stlouisfed.org/publications/review/
96/03/9603ra.pdf.
Balbach, Anatol and Burger, Albert E. “Derivation of
the Monetary Base.” Federal Reserve Bank of St.
Louis Review, November 1976, pp. 2-8;
http://research.stlouisfed.org/publications/review/
76/11/Derivation_Nov1976.pdf.
Bernanke, Ben S. “The Crisis and the Policy
Response.” The Stamp Lecture, London School of
Economics, London, England, January 13, 2009;
www.federalreserve.gov/newsevents/speech/
bernanke20090113a.htm.
Porter, Richard D. and Judson, Ruth A. “The Location
of U.S. Currency: How Much Is Abroad?” Federal
Reserve Bulletin, October 1996, 82, pp. 883-903;
www.federalreserve.gov/paymentsystems/coin/
1096lead.pdf.
Stevens, Edward J. “Required Clearing Balances.”
Federal Reserve Bank of Cleveland Economic
Review, Quarter IV 1993, 29(4), pp. 2-14;
http://clevelandfed.org/Research/Review/1993/
93-q4-stevens.pdf.
Thornton, Daniel L. “The Fed, Liquidity, and Credit
Allocation.” Federal Reserve Bank of St. Louis
Review, January/February 2009, 91(1), pp. 13-21;
http://research.stlouisfed.org/publications/review/
09/01/Thornton.pdf.

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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

Foreign Direct Investment, Productivity,
and Country Growth: An Overview
Silvio Contessi and Ariel Weinberger
The authors review the empirical literature that studies the relationship between foreign direct
investment, productivity, and growth using aggregate data and focus on two questions: Is there
evidence of a positive relationship between foreign direct investment and national growth? And
does the output of the “multinational sectors” exhibit higher labor productivity? The authors also
briefly discuss how the microeconomic evidence and a number of aggregation and composition
problems might help explain the ambiguous results in this literature. (JEL E32, F21, F32, F36)
Federal Reserve Bank of St. Louis Review, March/April 2009, 91(2), pp. 61-78.

“Today’s policy literature is filled with extravagant claims about positive spillovers from FDI
but the evidence is sobering.”1

he notable growth of foreign direct
investment (FDI) in the past 30 years
continues to trigger conflicting reactions, in both industrial and emerging
countries (Coughlin, 1992). In short, FDI is an
investor’s acquisition of “long-term influence”
in the management of a firm in another country.
(See the next section for a more complete definition.) In the developed world, countries that
export capital and countries that import capital
both raise concerns about FDI: The former are
concerned that capital leaving their countries
might be detrimental to domestic investment;
the latter’s politicians and workers fear foreign
ownership of domestic firms. Emerging, transition, and developing countries (and at times local
governments) usually welcome FDI, assuming
that investment through this multinational activity will bring additional capital, managerial
expertise, and technology.
1

From Rodrik (1999).

In economics, multinational activity (essentially foreign firms with U.S. production units
and U.S. firms with foreign production units,
described in more detail later) is also viewed as a
positive contribution to the technological progress
of the host economies. An established literature
that dates back to Findlay (1978) develops models
in which multinational firms own and transfer
technology—which may not be available in the
host country—that allows them to be more productive and profitable than firms that are not
multinational in nature. Because such a transfer is
assumed to contribute to the technical progress
of the host economies, it is also assumed to contribute ultimately to their growth.
Rivera-Batiz and Rivera-Batiz (1991) develop
a formal model that allows for increasing returns
due to specialization as a result of FDI. Borensztein,
De Gregorio, and Lee (1998) stress the interaction
between FDI and investment in human capital.
Helpman, Melitz, and Yeaple (2004) and Yeaple
(2008) show that only the most productive firms
in a country become multinationals, whereas progressively less productive firms enter progressively
more attractive countries.

Silvio Contessi is an economist and Ariel Weinberger is a research analyst at the Federal Reserve Bank of St. Louis.

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Figure 1
National Regulatory Changes, 1992-2006
250

Number of Countries that Introduced Changes
Number of Measures in Favor of FDI
Number of Measures Limiting FDI

200

150

100

1992

1994

1996

1998

2000

2002

2004

2006

SOURCE: UNCTAD Database on National Laws and Regulations.

Some other studies highlight reasons why FDI
may not accelerate growth: Aitken and Harrison
(1999) argue that increased local competition
caused by multinationals may crowd out domestic
firms; Boyd and Smith (1992) show that FDI distorts resource allocation and slows growth when
other distortions are present in the financial sector,
prices, or trade. This would imply that FDI does
not necessarily contribute to growth, and countries
could be harming their economies with provisions
that favor FDI.
As mentioned, overall FDI has increased in
many countries. In Figure 1, we plot an index of
the time series of the number of national regulatory changes between 1992 and 2006, which we
obtained from various annual surveys on national
laws and regulations.2 If we consider these series
as proxies for the amount of intervention aimed
at expanding and restricting FDI activities, the
graph illustrates clearly the existence of a grow2

Specifically, we used various issues of The World Investment
Report, an annual publication from the United Nations Commission
on Trade and Development (UNCTAD) that focuses on FDI trends
based partially on public data and partially on proprietary datasets
and surveys and covers a different special topic every year:
www.unctad.org.

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ing trend over the past 15 years of introduction
of polices aimed at promoting FDI. Since 1992
at least 80 percent of regulatory changes have
been favorable to FDI, particularly those in the
1990s.3 Furthermore, the absolute number of
favorable changes has steadily increased since
1992, with some countries introducing more
provisions and others that previously had no
favorable provisions now passing legislation to
encourage foreign investment.
This paper attempts to lay out the empirical
evidence on each side. We review a number of
macroeconomic studies that mostly fail to show
convincing evidence that FDI contributes to
growth. In particular, we organize our discussion
around two questions: Is there evidence of a positive relationship between FDI and growth in
macroeconomic data? And does the output of the
3

Specific examples of positive changes include the creation of new
special economic zones in India, many of which offer tax holidays
or other incentives, and variations in corporate taxes such as the
change in Egypt’s corporate tax from a base rate of 40 percent (32
percent for industrial and export activities) to a standard rate of
20 percent. Examples of negative changes include the restriction
to a ceiling of 49 percent participation in Algerian state-owned oil
and gas enterprises or the restriction to foreign participation in the
Russian strategic sector, such as defense-related activities, aviation,
and natural resources.

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Contessi and Weinberger

multinational sector exhibit higher labor productivity? After explaining how to define and identify
FDI in the next section, we discuss the evidence
based on aggregate data and then the evidence
regarding labor productivity. The final section
offers a possible interpretation of this evidence.

DEFINITIONS, MEASUREMENT,
AND RELEVANCE
The Definition of FDI
The most widely accepted definition of FDI is
known as “the IMF/OECD benchmark definition”
because it was provided by a joint workforce of
these two international organizations with the
objective of providing standards to national statistical offices for compiling FDI statistics.4 The
gist of the definition is that FDI is an international
venture in which an investor residing in the home
economy acquires a long-term “influence” in the
management of an affiliate firm in the host economy. According to the definition, the existence
of such long-term influence should be assumed
when voting shares or rights controlled by the
multinational firm amount to at least 10 percent
of total voting shares of rights of the foreign firm.5
Aggregate FDI flows are the sum of equity capital, reinvested earnings, and other direct investment capital; hence, aggregate FDI flows and
stocks include all financial transfers aimed at
financing of new investments, plus retained earnings of affiliates, internal loans, and financing of
cross-border mergers and acquisitions. FDI flows
can be observed from the perspective of the host
economy, which records them as inward FDI along
with other liabilities in the balance of payments,
or from the perspective of the home economy,
4

The fourth revision of the OECD Benchmark Definition of Foreign
Direct Investment (OECD, 2008) can be found here: www.oecd.org/
dataoecd/26/50/40193734.pdf. This collection of operational guidelines sets the world standard for FDI statistics, indicating to national
statistical agencies the best practice to measure FDI activity. The
benchmark definition was first published in 1983 based on a report
by the OECD Group of Financial Statisticians, with revisions in
1990, 1992, and 2008.
Voting shares give the stockholder the right to vote on matters of
corporate policymaking and on the appointment of the board of
directors. If the equity share of control is 50 percent or more, the
controlled firm is often defined as a subsidiary.

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

which records them as outward FDI, a category
of assets.6
The sum of all direct capital owned by nonresidents in a given country j in a certain time
period t constitutes the existing stock of FDI at
that time. We will refer to the stock of foreign
direct capital as KjtI . Hence, in each period FDIjt
is the per-period increase in the stock of foreign
direct capital, FDIjt = KjtI – KjtI –1, in country j.
These measures can be sufficiently accurate
in the short run. However, the value of the capital
stock changes over longer periods, causing problems with the adjustment of its valuation. Over
20 years, the value of the stock of FDI at current
prices may become three times as large as its historical value. For example, Ihrig and Marquez
(2006) show that if one simply adds up net direct
investment flows from 1982 to 2004, then the
United States has net claims on foreigners of
approximately $250 billion; whereas, if one
adjusts the values of assets and liabilities for inflation and changes in exchange rates (current cost),
then net claims on foreigners in 2004 soar to
almost $600 billion. The difference between these
two measures of the net direct investment position results from valuation adjustments over this
time period. Another way to adjust the value is
to calculate the net position at market value, a
procedure that brings the net direct investment
position to $500 billion in 2004.
Table 1 describes the composition of U.S.
outward FDI, using stocks and flows in 2006.
The data we use for this table do not capture the
ultimate destination of flows that most statistical
agencies try to report, but only the initial destination. Initial and final destinations might differ
because multinational firms try to minimize the
tax burden from multinational activity by exploiting the differences of fiscal regimes across countries. For example, the main FDI partners of the
United States in 2006 include the Netherlands,
6

Three main types of private capital flows appear in the balance of
payment accounts of a country: international debt, international
portfolio flows, and FDI. FDI and portfolio investment are both a
form of international equity investment, i.e., they represent shares
of ownership of foreign firms, unlike private and public debt that
is pledged to be returned at the end of the life of the international
loan that generates it. The difference between FDI and portfolio
equity, instead, is that the latter lacks the objective of influencing
the management decisions of the controlled firm, and as such is
generally more liquid and more short term.

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Contessi and Weinberger

Table 1
U.S. Outward FDI by Destination Country in 2006, Stocks and Flows
Stock of U.S. FDI holdings
in other countries (percent)

Country

U.S. outward FDI
by country (percent)

U.K.

15.29

6.88

Netherlands

11.43

18.42

Canada

9.37

3.67

Bermuda

5.48

8.53

Switzerland

4.69

5.07

Japan

3.76

4.56

Luxembourg

3.85

7.91

Mexico

3.39

3.96

Germany

3.92

2.42

Other

38.82

Total

100

Bermuda, and Luxembourg, which offer particularly favorable fiscal regimes, although the final
investment is likely to refer to an affiliate located
in a third country.
Besides the problems with data reporting,
the definitions used by statistical agencies may
differ from the legal treatment of multinational
firms in international treaties, such as the ones
managed by the World Trade Organization (WTO)
or NAFTA, that aim at reducing legal barriers to
FDI. Although many efforts in this direction have
been undertaken over the years, no encompassing
multilateral treaty with the aim of setting standards for the liberalization of multinational activity exists, with two partial exceptions. The WTO
treaties include (i) some specific measures aimed
at the liberalization of FDI in the service sector
in the General Agreement on Trade in Services
(GATS) and (ii) some provisions meant to prevent members’ actions aimed at restricting traderelated FDI in the Trade-Related Investment
Measures (TRIMs) Agreement. No agreement exists
to regulate FDI in the manufacturing sector.

Measurement and Relevance
Typically available macroeconomic time series
for FDI include the nominal value of the flows in
or out of a country (inward and outward) and
64

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38.59
100

stock values. Both measures have problems that
sometimes undermine the cross-country comparability of the series, especially because statistical
agencies of different countries may use different
definitions of FDI. For example, in Estonia, the
10 percent benchmark for equity ownership suggested by the International Monetary Fund/
Organisation for Economic Co-operation and
Development (IMF/OECD) definition of FDI has
been applied only since the beginning of 2000,
whereas the previous threshold was 20 percent.
Prior to 1997, Poland used a criterion of “effective voice in management” that might not have
amounted to 10 percent or more ownership—a
criterion they later adopted in compliance with
international standards (IMF, 2003). In both cases,
the series are clearly not comparable before and
after the change in methodology, and large changes
in their levels may either be a purely statistical
artifact or have an economic basis to them.
A second problem with datasets available
from international organizations, such as the ones
available from the IMF, the World Bank, and the
UNCTAD, is that they often have missing data
points, particularly for developing countries.
A third issue with the use of aggregate data in
studying FDI is that the records may not capture
a part of the investment in the foreign project. The
fact that multinational activities can be financed
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Contessi and Weinberger

Figure 2
Inward FDI Flows as a Percentage of Gross Fixed Capital Formation
Percent
25

United States
World

20
15
10
5
0
1970

1974

1978

1982

1986

1990

1994

1998

2002

2006

1982

1986

1990

1994

1998

2002

2006

Percent
25

Developed Economies
Developing Economies

20
15
10
5
0
1970

1974

1978

SOURCE: UNCTAD.

using local or foreign financial markets implies
that measures of FDI flows and stock that capture
only the foreign financing of the projects provide
a potentially distorted measure of the extent of
multinational activity across countries, as we discuss in the next paragraph. When foreign owners
raise capital in the host country by issuing bonds
or shares, no international capital flow is recorded
in the balance of payment data of the source and
the host country, and hence it does not show up in
FDI statistics (Marin and Schnitzer, 2006). Therefore, using the flow of FDI might lead to incorrect
inference, as part of the capital used to finance
the multinational activity might be raised locally
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 hence not be recorded as an international
capital flow in the balance of payments.
A common way to gauge the relevance of FDI
is by comparing FDI with domestic investment.
Figure 2 plots inward FDI flows as a percentage
of gross fixed capital formation for developed and
developing countries, as well as the world and
the United States. The time series show clearly
that these ratios were basically flat during the
1970s and part of the 1980s and subsequently
started growing during the 1980s, eventually
crossing the threshold of 5 percent.
Looking at groups of countries hides large
variability in individual countries and regional
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Contessi and Weinberger

Figure 3
FDI Inflows in Developed (top) and Developing (bottom) Countries (percent)
1988

2005

1996

38
43

54
62

Primary
Manufacturing

1988
2

1996

2005

Services
Unspecified

39
50
49

SOURCE: UNCTAD.

experiences, even during these early years. Beginning in the mid-1980s, the ratio started to grow
quite steeply and later accelerated in the mid1990s to reach a peak at the end of the 1990s.7
After the large correction of equity prices of
the late 1990s and the early 2000s recession, the
flows of FDI as a share of gross fixed capital formation returned to the levels of the late 1980s.
More recently, however, the slowdown reached
a turning point and the ratio is back to a level
between 5 and 10 percent for the world as a
whole. It remains to be seen whether the 2008
credit contraction in OECD countries will mark
another turning point.8
7

Part of the steep increase in the 1990s is due to the wave of crossborder mergers and acquisitions across OECD countries at the time.

Contessi, De Pace, and Francis (2008) show that industrial countries’
outward and inward FDI is significantly procyclical, whereas
emerging countries’ inward FDI is significantly countercyclical.

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2009

The figures prompt two additional observations. First, the cyclical nature of FDI flows
emerges quite clearly for the United States and
developed countries, with at least three (long)
boom-bust cycles with a first peak around 1980,
a second peak around 1988, and a third peak in
2000-01. The second observation is that developing countries stand out because they experienced
steady trend growth until 2000, rather than boombust cycles; moreover, in these countries the early
2000s correction is much less pronounced than
in developed countries and certainly much less
than in the United States. Inward flows to developing countries now make up a larger percentage
of total inward investment when compared with
developed countries.
Industrial and developing countries differ in
other dimensions regarding FDI. In Figure 3 we
compare the industry composition of FDI in indusF 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

Contessi and Weinberger

trial and emerging countries for three years, 1988,
1996, and 2005. Looking at both developed and
developing countries one can see how the share
of services in total flows has increased quite substantially—by almost 50 percent in fact—whereas
the share of manufacturing has dropped to 50 percent of what it was in 1988 in industrial countries.
This shift is likely due to the rise of the service
sector; the elimination of many restrictions to
foreign entry and ownership, particularly in the
banking and telecommunications sector; and the
commitments contained in the GATS agreement
and other regional agreements.9 The pie charts
in Figure 3 also reveal that the share of manufacturing FDI is consistently larger for developing
countries than for developed countries, although
less so as time goes by. Finally, this shift is also
likely to be a response to comparative advantage
and the emergence of vertical fragmentation of
manufacturing production over the past decades.

Do the Aggregate Data Show Evidence
of a Positive Relationship Between FDI
and Growth?
Output is assumed to be produced according
to the following production function:
(1)

(

)

Y j = Z j f K Dj , K Ij , LDj , LIj, M j ,... ,

where final output of country j in time t (subscript
omitted) is a function of a set of inputs, such as
potentially different domestic and foreign capital
(K jD, K jI ), domestic and possibly foreign labor (L jD,
L jI ), intermediate inputs (Mj ), and other factors are
combined using a technology f 共.兲 common across
firms and scaled by a total factor productivity
parameter Zj to produce Yj units of real output.
Researchers who use aggregate data normally
postulate that the aggregate production function
is a Cobb-Douglas production function. Equation
(1) then has the functional form
9

For example, many provisions aimed at completing the European
Single Market or NAFTA’s Chapter 11 contain specific FDI provisions that protect firms and individuals investing in Mexico,
Canada, and the United States.

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

(2)

β0

I ϕ
j

( ) (L ) (X)

Y j = Z j K Ij

)

D D
j , L j , M j , ...

and is transformed in logarithmic form and studied in first differences. The final regression estimate is
(3) Yj = α j + β0 FDI j + β1 FDI j × x j + γ X j + ε j ,

(

)

where α j is a constant, the matrix Xj contains a
number of non-FDI factors assumed to affect
growth and varies greatly across studies, and the
interaction term (FDIj × xj ) takes care of possible
interactions between FDI and other regressors,
that is, other non-FDI factors that are assumed to
affect growth and contained in Xj .10 Researchers
then test whether the estimated coefficient β0̂ is
positive and significant in the regression.
The most common and somewhat natural
way to measure growth in these studies is to use
real per capita GDP growth. Measures of FDI may
vary, but gross FDI inflows as a share of GDP, FDI
inflows per capita, or multinational sales are common choices. FDI stocks are more troublesome
not only because time series of flows date back
to the 1970s at the earliest, making stocks series
difficult to reconstruct for a sufficient number of
countries, but especially because the values of
firms and of the FDI stock change over time, introducing a substantive discrepancy between the
originally recorded book value and the market
value.
The matrix Xj is a set of control variables and
the specification leaves room for interaction terms
between FDIj and one or multiple variables in Xj .
The latter may include various measures of initial
per capita income, average years of schooling of
the working population, government size, inflation, openness to trade, black market premium,11
private credit, and so on. Loosely speaking, regression analysis including only the FDIj term usually
reveals nonsignificant effects of FDIj alone through
β0, while regression analysis including an inter10

Estimation techniques vary but usually range from ordinary least
squares to dynamic panels.

This is the percentage differential between the black market and
the official exchange rate.

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Contessi and Weinberger

action term with one of the variables in Xj reveals
a positive relationship.
Various panel and cross-sectional studies
show the importance of different complementary
variables. Balasubramanyam, Salisu, and Sapford
(1996) use exports as a measure of openness to
trade; Borensztein, De Gregorio, and Lee (1998) a
proxy for human capital; and Alfaro et al. (2004)
various proxies for financial development.12 They
all find that FDIj has a positive impact only if an
additional variable is interacted with it. Hence,
the more the country is financially developed,
open to trade, or endowed with human capital,
the more FDI increases growth. Unfortunately,
the most sophisticated in this group of studies,
Carkovic and Levine (2005), demonstrates the
lack of a robust positive correlation between FDI
and growth once the temporal dimension of international data is exploited using panel data.13
There are at least two important caveats that
might affect the reading of such results. The first
more general caveat is common to cross-country
growth regressions—that is, these studies are
plagued by a multiplicity of issues of parameter
heterogeneity, outliers, omitted variables, model
uncertainty, measurement error, and endogeneity,
as eloquently discussed in Rodrik (2005). Inference based on results that do not discuss the
potential biases in these studies should be taken
with a grain of salt. The second caveat was raised
in Blonigen and Wang (2005), who argue that
pooling rich and poor countries without distinguishing between levels of development (i.e.,
assuming the same β 0 for all countries and hence
underestimating cross-country heterogeneity)
leads to incorrect inference, an argument that
squares nicely with the evidence discussed in the
studies just cited.14 In particular, they show that
12

Borensztein, De Gregorio, and Lee (1998) average data over 10year periods, because annual flows might not have a discernible
effect on growth over longer periods.

Carkovic and Levine (2005) use 72 countries over the period
1960-95. They average data over non-overlapping, 5-year periods,
so that there are seven observations per country (1961-65, 1966-70,
and so on).

Results in Contessi, De Pace, and Francis (2008), for example,
echo this argument: They show that FDI inflows are clearly procyclical in developed countries but countercyclical in emerging
countries and discuss how pooling all countries together would
not reveal any pattern of cyclicality.

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it is not the use of panel technique, but the pooling of countries with different levels of wealth,
that makes the evidence of a positive relationship
between FDI stocks and growth disappear. This
is consistent with a previous study by Blomström,
Lipsey, and Zejan (1994), which found no significant effect of foreign capital on economic growth
of lower-income developing countries (as opposed
to relatively richer developing countries), suggesting that the relationship may be positive for
“sufficiently wealthy” countries.
In Figures 4 and 5, we plot the ratio of the
inward FDI stock to GDP in 1990 and 2000 on
the horizontal axis; on the vertical axis, we plot
real GDP growth for the 1990-2000 period and
for the 2000-05 period for the largest groups of
countries for which these data are available in
each of the periods.15 The scatter diagrams in the
bottom part of each graph do not distinguish
among different levels of development, whereas
the top graphs do, in a way that isolates industrial
countries (squares) and emerging and transition
countries (triangles) from other less-developed
countries (dots). Although we make no attempt
at formal inference, we think that the picture
alone suggests that the relationship between FDI
and growth that we could infer from these relationships is quite different depending on the composition of the group of countries and the time period
under scrutiny.
What do we learn from these studies? The positive relationship between FDI—whether flows,
flows to GDP, or stocks—and growth emerges in
macroeconomic data, when “some other factor”
is present. However, the presence of FDI is likely
to be affected by the presence of these factors,
making the issue of endogeneity hard to resolve.
If FDI has a positive impact on economic growth,
it increases market size, and a larger market size
attracts more FDI. Hence, FDI and growth are interdependent in a nontrivial way that needs to be
somehow addressed in the econometric analysis,
which has made two possible solutions available
for similar problems: The first, the use of random15

We obtained GDP growth data from the 2007 World Development
Indicators of the World Bank and the stock of inward FDI to GDP
from the “External Wealth of Nations—Mark II” dataset that has
been publicly released by Lane and Milesi Feretti (2007).

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Contessi and Weinberger

Figure 4
FDI Stock-to-GDP Ratio and Real GDP Growth (1990-2000)
Real GDP Growth 1990-2000 (percent)
12
10
8
6
4
2
0
0

100

FDI Stock-to-GDP Ratio in 1990

Real GDP Growth 1990-2000 (percent)
12
10
8
6
4
2
0
0

FDI Stock-to-GDP Ratio in 1990
NOTE: In the top panel, triangles represent emerging economies, squares represent industrial countries, and dots represent all other
countries. In the bottom panel, all countries are pooled together. The straight line is a linear trendline for each group.
SOURCE: 2007 World Development Indicators of the World Bank and “External Wealth of Nations–Mark II” dataset (Lane and Milesi
Ferreti, 2007).

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Contessi and Weinberger

Figure 5
FDI Stock-to-GDP Ratio and Real GDP Growth (2000-05)
Real GDP Growth 2000-05 (percent)
16
14
12
10
8
6
4
2
0

100

150

FDI Stock-to-GDP Ratio in 2000

Real GDP Growth 2000-05 (percent)
16
14
12
10
8
6
4
2
0

100

150

FDI Stock to GDP Ratio in 2000
NOTE: In the top panel, triangles represent emerging economies, squares represent industrial countries, and dots represent all other
countries. In the bottom panel, all countries are pooled together. The straight line is a linear trendline for each group.
SOURCE: 2007 World Development Indicators of the World Bank and “External Wealth of Nations–Mark II” dataset (Lane and Milesi
Ferreti, 2007).

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ized trials, is clearly impossible in growth regressions. However, Carkovic and Levine (2005) argue
that the second, the use of more sophisticated
panel techniques, can substantially alleviate the
problem of endogeneity.16
In the discussion of Carkovic and Levine
(2005) and Blonigen and Wang (2005), Melitz
(2005) puts forward the possibility that certain
types of FDI ventures known in the literature as
export platform FDI may have a potentially larger
effect on growth. Hence, export-oriented countries may benefit more from FDI than importsubstituting countries, an idea originally discussed
in Bhagwati (1988) and tested explicitly in
Balasubramanyam, Salisu, and Sapford (1996).
For example, the Volkswagen automobile plant
in Puebla, Mexico, is the only assembly unit of
this multinational in North America but meets
the demands of the three NAFTA countries.
Although the motivations of this venture are
both cost saving through lower input costs and
access to the sizeable North American consumer
markets, the factory benefits the Mexican economy more than it would if its production were
sold only in Mexico.
A part of the literature that uses aggregate
data has focused on regional, rather than county,
growth. The methods used are very similar to
studies we just described: Authors attempt to disentangle the various variables affecting productivity growth to single out the individual effect
that can be attributed to foreign investment.
Although cross-country models attempt to measure the “average” effects that FDI has on countrywide economic outcomes as a whole, they cannot
measure how certain subnational units might be
affected. Regional growth studies deal with very
specialized locales and can focus on the effects of
foreign investment in the particular community
where multinational firms establish their operations. In particular, although evidence suggests
foreign investment increases wages and growth,
it is unclear whether certain areas benefit suffi16

Carkovic and Levine (2005) argue that instrumental variables and
the use of dynamic panels estimated by generalized method of
moments can help in this context. Given the nontechnical level of
our article, we invite the interested reader to consult this article
for further details.

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

ciently to outweigh the costs incurred, particularly in terms of incentives to locate in the area.
Figlio and Blonigen (2000) and Ford, Rork, and
Elmslie (2008) find that foreign investment has
more positive effects than domestic investment,
but with substantial costs to local communities
in terms of reduction of budget expenditures.
Foreign investment’s worst effect appears to
be the crowding out of domestic investment.
Figlio and Blonigen (2000) use a detailed countylevel panel dataset from South Carolina to compare foreign manufacturing firms with domestic
manufacturing firms using share of employment.
They estimate the following model:
(4)

I
w jkt = α 0L jkt + α 1l jkt
+ δγ kt + δ j ,

where j and t are, respectively, counties and years
for each industry k. In the model, wjkt is the average
annual wage, Ljkt is total manufacturing employI
is the level of employees in foreign-owned
ment, ljkt
establishments, and γkt and δj are unobserved
county-specific differences in wages and timevarying effects, respectively.17 The authors also
estimate a similar model that replaces wages with
budget expenditures. They find that a marginal
new foreign manufacturing job has seven times
the effect on wages as does a new domestic job,
but also that the new foreign job is associated with
twelve times the revenue reduction and eight
times the expenditure reduction. Therefore, the
findings suggest that although new foreign investment can have a positive effect on wages, the welfare effect on the local community will depend
on the magnitude of benefits versus the costs of
investment in the community; and the costs can
be nontrivial.
Finally, a study by Ford, Rork, and Elmslie
(2008), similar to the panel studies described
above, adds an interaction term of FDI with human
capital and finds that FDI has a greater impact
on growth per capita than domestic investment
in U.S. states, conditional on a minimum human
capital threshold, exactly as occurs in studies that
use country data. This implies that FDI is posi17

Notice that the total manufacturing employment measure, however, does not exclude the level of employees in foreign-owned
“greenfield” plants, a feature that might introduce a bias in the
estimates.

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tively related to states’ growth only when a sufficient level of human capital is present and that
only states with a comparatively well-trained
workforce can take advantage of the presence of
foreign technology and should try to attract FDI.

DOES THE OUTPUT OF THE
MULTINATIONAL SECTOR EXHIBIT
HIGHER LABOR PRODUCTIVITY?
There is important information contained in
aggregate data about FDI and labor productivity,
as studied in Corrado, Lengermann, and Slifman
(forthcoming) for the United States and Criscuolo
(2005) for a group of OECD countries.
Corrado, Lengermann, and Slifman (forthcoming) focus on labor productivity in the United
States. The United States is a particularly interesting country in that productivity has increased at
a particularly high average annual rate of 1.84
percent between 1977 and 2006, faster than in
most other industrial countries, at least since 1995.
Moreover, the United States is both a major recipient of FDI from abroad and an especially major
source of FDI for the rest of the world. The authors
separate U.S. gross domestic product and productivity growth into that produced by exclusively
domestic firms and that produced by the so-called
multinational sector (i.e., the “industry” composed
of foreign firms with U.S. production units and
U.S. firms with foreign production units—not only
foreign firms in the United States). Labor productivity estimates are then calculated by sector: In
each year, productivity levels are defined as real
value added per total hours worked of all persons.
Private multinational nonfarm, nonfinancial firms
(again, not just foreign producers in the United
States) contribute only 40 percent of the output
of nonfinancial corporations but more than 75
percent of the increase in labor productivity
between 1977 and 2000. Moreover, all of this new
productivity in nonfinancial corporate sectors in
the late 1990s can be traced back to multinationals
(Figure 6 and Table 2).
Does the evidence for the United States carry
over to a broader set of industrial countries?
Criscuolo (2005) evaluates the direct contribution
72

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2009

of the affiliates of foreign multinational firms to
labor productivity for a large set of OECD host
countries and shows that the productivity advantage of affiliates of multinational firms varies
greatly across countries in both the manufacturing
and service sectors.18 In the United States, France,
and Sweden, foreign affiliates have approximately
the same level of measured labor productivity as
domestic firms. In Spain, Hungary, and the United
Kingdom, foreign affiliates are twice as productive and this advantage appears to be markedly
larger in low-tech sectors, such as food products,
beverages, tobacco, textile and garment, leather,
and footwear. Two possible explanations for the
lack of affiliates’ advantage in the United States,
France, and Sweden are that domestic firms in
these countries are at the technological frontier in
many sectors and that domestic firms’ productivity might have increased as a response to early
trade openness and foreign competition. Hence,
the data might be revealing that openness to competition induces survival and development of
more-productive firms that in turn are more likely
to become multinationals and contribute to their
home country’s productivity growth—as the
Corrado, Lengermann, and Slifman (forthcoming)
study would suggest. In Criscuolo (2005), however, the contribution to total productivity growth
is quite heterogeneous, ranging from 32 percent
in the United States to 42 percent in Finland, 164
percent in the Czech Republic, and an astonishing
251 percent in Norway (the highest).19 Her study
is consistent with Corrado, Lengermann, and
Slifman (forthcoming) because they define the
multinational sector as the sum of foreign affiliates
in the United States and U.S. firms that are multinational and control affiliates in other countries.
Interestingly, Criscuolo (2005) also shows how
in a given time period, for example one year, the
contribution to labor productivity growth can be
decomposed into two components: a within effect,
18

The sources of data are three OECD maintained datasets: the STAN
productivity database, the AFA (Activity of Foreign Affiliates)
database, and the FATS (Foreign Affiliates’ Trade in Services)
statistics. The time period considered is 1995-2001.

Contributions larger than 100 percent are explained by a steep
increase in the presence of affiliates with a higher labor productivity or by negative labor productivity growth of domestic firms,
as in the United Kingdom.

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

Contessi and Weinberger

Figure 6
Growth of U.S. Labor Productivity
Percent Change at Annual Rate
6
Multinational Corporations
5

Domestically Oriented
Financial Corporations

Nonfarm, Noncorporate Businesses

3
2
1
0
1997-1989

1989-1995

1995-2000

SOURCE: Corrado, Lengermann, and Slifman (forthcoming).

attributed to existing multinationals located in a
country, and a between effect, attributed to the
increase in the share of the employment of multinational affiliates. In her article, the within component drives the results in the United States,
Hungary, and the Netherlands, while in all other
countries the between component is the main
contributor. The author also shows that the within
effect is stronger in high-tech sectors, which are
presumably information technology–intensive,
which is a result that is consistent with the findings in microdata, as in Bloom, Sadun, and Van
Reenen (2007).
Finally, a different dimension of disaggregation, industry composition, might be important
in understanding the FDI contribution to growth.
Based on an industry-level analysis, Fillat Castejón
and Wörz (2006) argue that disaggregating flows by
industry conveys important information because
industrial specialization and composition are
different across countries and this may affect the
ability of a country as a whole to take advantage
of the multinationals’ technology. Even at the
industry level, and in line with previous studies,
Fillat Castejón and Wörz (2006) find that an
additional factor needs to be included in the
cross-country or cross-industry regression. Their
analysis confirms previous analysis in terms of
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

Table 2
Composite of U.S. GDP, 1997 and 2002 (%)
1977

2002

Multinational corporations

25.5

26.2

Domestically oriented

39.3

Financial corporations
Noncorporate businesses

4.6

9.2

25.3

SOURCE: Corrado, Lengermann, and Slifman (forthcoming).

requiring “other factors”—namely, export orientation and domestic investment in this case—to
find a positive relationship between FDI and
growth in the data.

WHAT DO AGGREGATE DATA
HIDE?
As Criscuolo (2005) shows, disaggregating the
data helps illuminate the effects of multinational
affiliates’ activity on productivity and ultimately
on growth.
Imagine dividing the population of firms in
the host economy into a foreign multinational
component (indexed by I ) and a purely domestic
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Contessi and Weinberger

component (indexed by D). Then total final output, Yj , could be also reinterpreted as the sum of
two components produced by domestic and foreign firms, Yj = YjD + YjI. In each time period a
total of NjD domestic firms and NjI affiliates of
multinational firms produce and sell locally YjD
and YjI, and perhaps a share of these firms sells
abroad as exporters. (In this context, the distinction can be neglected without loss of generality.)
One of the issues with estimation of aggregate data
models like equation (3) is that variables referring
to foreign firms are not excluded from the aggregate and the dependent variable is the growth rate
of total output. If we distinguish domestic from
foreign firms and the real output they produce,
then we are really considering two production
functions and observing total output as the sum
of the output of the domestic firms and the multinational firms:
(5)

Y j = Y jD + Y jI

(6)

Y jD = Z Dj f K Dj , X Dj

(7)

(
(

)

Y jI = Z Ij f K jI , X Ij .

There are at least two dimensions along
which microeconomic heterogeneity affects
econometric analyses that use aggregate data.
First, there may be important aggregation
effects that might mirror microeconomic heterogeneity in terms of directly measurable productivity advantages (ZjI > ZjD ). If there is a large
heterogeneity of multinational firms across countries and over time, and cross-country or panel
studies that do not account for it, the average
impact of FDI on growth may have little economic
meaning. Contessi (2009a,b) discusses how
thinking of multinational firms as heterogeneous
agents in the sense of Ghironi and Melitz (2005)
may help to reconcile the evidence on superior
productivity leadership with the aggregate evidence discussed in this paper. Ghironi and Melitz
(2005) assume that a firm’s labor productivity is
the product of an idiosyncratic time-invariant
productivity level and a time-varying aggregate
productivity level that is common across all firms
74

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2009

in the economy.20 The idiosyncratic productivity
level can be interpreted as the management’s
ability to appropriate and scale up (or down) the
existing technology available to all firms. If one
assumes the existence of fixed costs to export (as
in Ghironi and Melitz, 2005) or to engage in multinational production (as in Contessi, 2009b), then
some firms will export, some firms will be multinational, and the participation of firms in international markets evolves over time with entry and
exit dynamics.
If firms incur a fixed cost to become multinationals, and either this cost decreases over time
because of FDI liberalization or the attractiveness
of foreign markets increases due to their growth,
then entrants sort according to their own productivity. The most productive firms become multinationals earlier, while firms that are relatively
less productive enter host economies later, a fact
documented by Yeaple (2008) using firm-level
data for U.S. multinationals. Specifically, Yeaple
(2008) finds that a 10 percent increase in a host
country’s GDP is associated with a 5.4 percent
increase in the number of U.S. firms owning an
affiliate there, but also with a 1.4 percent decrease
in the average productivity of the entrants. Entry
of relatively less-productive firms then reduces
the average productivity of the “multinational sector” in the host economy, exactly while the stock
of FDI increases. Hence, while we expect countries
with larger stocks of FDI to grow faster, the contribution of multinational firms to the host countries’ productivity level, and growth, decreases.
Second, there may be relevant positive externalities (spillovers) that regressions based on
aggregate data are likely to miss. The presence
of spillovers implies that the mere presence of a
foreign firm increases the productivity of domestic
firms—or, in our discussion, ∂ZjD /∂NtI >0. There
are at least three groups of intra-industry spillovers. Javorcik (2008) contains an updated survey
of the literature on spillovers from FDI and an
interesting discussion of the reasons why their
presence is difficult to measure and appears to
vary greatly across countries.
20

By idiosyncratic productivity, we mean firm-specific labor or
total factor productivity that is not common to other firms.

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

Contessi and Weinberger

The demonstration effect is the first type of
positive agglomeration externality: Although
foreign firms have a strong incentive to protect
their firm-specific product or process knowledge,
domestic companies can still observe their practices to some extent and learn about new technology, marketing techniques, and product
development. Second, domestic firms may hire
workers who were employed, and hence trained,
by multinationals in the past; in this case, spillovers occur through workers’ mobility. Third,
intra-industry spillovers may also occur through
the so-called competition effect: Domestic firms
must increase their productivity to compete with
the foreign firms and survive their competition,
while nonprofitable firms are likely eliminated
from the market.
There are various ways in which the presence
of spillovers from FDI may alter our reading of
growth regressions that study FDI, as discussed
in Hale and Long (forthcoming). On the one hand,
if aggregate output measurements include the output of both the domestic sector and the output of
foreign multinationals in the country, then the
impact of FDI will always be positive (β0̂ > 0),
even if domestic productivity is not affected by
the foreign presence, just because the output measurement already incorporates the multinational
output growth that will always positively correlate to multinational presence. Hence, one would
want to use only domestic output as a dependent
variable.
On the other hand, estimating the presence
of spillovers using data that focus on domestic
variables is conducive to a second type of bias.
A large part of recorded FDI consists of acquisition, rather than new establishments. Hence, a
selection bias problem, called cherry-picking in
the literature, has to be dealt with in formal
analyses. If acquired affiliates are picked from
the upper tail of the productivity distribution
(firms with high productivity ex ante), the postacquisition distribution is truncated from above.
This means that the larger the number of acquisitions, the lower the share of domestically owned
firms with relatively lower productivity left in
the population of “domestic” firms. If one estimates a regression such as the one in equation
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

(3), then the effect of FDIj will be negative (β0̂ < 0).
Therefore, the researcher should estimate a model
with sample selection in the tradition of Heckman
(1979) using firm- or plant-level data.
These issues are likely to be at least in part
responsible for the lack of evidence of a relationship between FDI and growth that we discussed
earlier in this article.

CONCLUSION
The contributions that multinational firms
make toward economic growth of the host economies have been studied extensively, but little
consensus has emerged as to whether FDI is boon
or bane for a country as a whole. Quite simply, the
evidence is as mixed now as it was when Rodrik
(1999) wrote the line quoted at the beginning of
this article. Lacking unambiguous empirical evidence, it is difficult to formulate solid expectations
on how proposed FDI policies will affect the entry
of foreign firms. Current empirical evidence provides little guidance as to whether one should
support or oppose policies. As we have discussed
in this article, studies that use a growth regression
approach and aggregate data are not likely to
help researchers sort out the growth effect of FDI
because of methodological problems and huge
heterogeneity hidden by the data. The prior 10
years of research have confirmed that the (aggregate) evidence is still sobering.
However, a large body of empirical research
that uses firm- and plant-level data has documented that multinational firms and their affiliates (compared with domestic firms) are larger,
are more capital intensive, make more abundant
use of skilled workers, invest more in physical
and intangible capital, and pay higher wages
(Barba Navaretti and Venables, 2004). Because the
evidence based on microdata shows that firms
investing and producing in foreign countries
have superior productivity at home, foreign affiliates should also enjoy a productivity advantage
compared with local firms in the host economy.
Indeed, we have discussed some of the evidence
that reveals such an effect in aggregated data.
Recent developments in the use of microdata
to study aggregate productivity such as the ones
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Contessi and Weinberger

proposed by Petrin and Levinsohn (2005) might
prove to be key in overcoming the methodological difficulties and the problems arising with
the use of aggregate data; ultimately, these developments may increase our understanding of this
relationship between FDI, productivity, and
growth.

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Quick Exits of Subprime Mortgages
Yuliya S. Demyanyk
All holders of mortgage contracts, regardless of type, have three options: keep their payments
current, prepay (usually through refinancing), or default on the loan. The latter two options terminate the loan. The termination rates of subprime mortgages that originated each year from 2001
through 2006 are surprisingly similar: about 20, 50, and 80 percent, respectively, at one, two, and
three years after origination. For loans originated when house prices appreciated the most, terminations were dominated by prepayments. For loans originated when the housing market slowed,
defaults dominated. The similarity of the loan termination rates for all vintages in the sample suggests that subprime mortgage loans were intended to be “bridge” (i.e., temporary) loans. In addition,
between 2001 and 2006, the number of terminated subprime purchase-money loans (loans used to
purchase rather than refinance a house) outweighed the estimated number of first-time-homebuyers
with subprime mortgages. The effect of the subprime lending on the increase of homeownership
in the United States—a potentially positive outcome of subprime mortgages—most likely has been
overstated. (JEL D12, G1, G21)
Federal Reserve Bank of St. Louis Review, March/April 2009, 91(2), pp. 79-93.

he subprime mortgage market boomed
between 2001 and 2006 and began to
collapse in 2007.1 Initial signs of the
collapse were poor performance and
even default of loans,2 often within months of
their origination: The delinquency, default, and
foreclosure rates of subprime loans that were
originated in 2006 and 2007 were three times
higher than in earlier years. In 2008, the sub1

The term “subprime,” at times used imprecisely, essentially can
describe (i) borrowers with a low credit score, history of delinquency
or bankruptcy, or poor employment history; (ii) lenders specializing
in high-cost loans and selling fewer loans to government-sponsored
enterprises; (iii) securities that encompass a subprime loan (the
most- to least-risky of which are subprime, Alt-A, and prime); and
(iv) certain mortgages (e.g., 2/28 or 3/27 “hybrid” mortgages) generally not available in the prime market.

Here, “default” is used to indicate the protracted failure to meet
the terms of a mortgage loan agreement, ending in foreclosure;
“early default” is defined later in the paper.

prime securitized market froze completely and
essentially died.
Researchers, policymakers, journalists, and
other individuals have offered many explanations
for the collapse of the subprime mortgage market,
including mortgage interest rate resets, fraud, poor
underwriting, discrimination, a housing market
slowdown, and deterioration of loan quality (due
to unobserved or unexplored borrower information). The negative consequences of this market’s
collapse are well known and well publicized. The
effects include foreclosures and defaults, impaired
credit histories for borrowers, reduced housing
values, destabilized neighborhoods as a result of
vacant properties, and an overall slowdown in
many segments of the economy.
But aside from these pitfalls, did subprime
lending have any benefits, even if they were much

Yuliya S. Demyanyk is a senior research economist at the Federal Reserve Bank of Cleveland. The data analysis for this article was conducted
when she was an economist in the Banking Supervision and Regulation Division of the Federal Reserve Bank of St. Louis.

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less obvious than the problems? Anecdotal evidence suggests that the subprime market, with
its easier mortgage financing, may have promoted
U.S. homeownership. The rationale is that, even
if default rates are about 20 percent for the most
recent vintage of subprime mortgages, 80 percent
of subprime borrowers are still making their
monthly payments. Given this view, the financial
innovation that spawned subprime lending may
have promoted homeownership, and thus the
majority of borrowers benefited because they most
likely would not have qualified for mortgages
under terms in the prime market.
This paper attempts to analyze whether borrowers intended to keep their subprime mortgages
long enough to substantiate an increase in homeownership or planned a quick exit strategy at origination, using subprime loans as bridge financing
to speculate on house prices (i.e., quickly sell the
house for a profit after its value increases).
“Exit” from a subprime mortgage can take
two forms: prepayment or default. In this study,
a mortgage loan is considered “prepaid” if a borrower has either paid the mortgage loan in full or
refinanced it within a certain period after the loan
was originated. A mortgage loan is “in default” if
(i) a borrower has missed more than two mortgage
payments, (ii) the property is in the process of
foreclosure (after more missed payments), (iii) the
property is “real-estate owned” (i.e., has been
taken over by the lender as part of the loan termination3 process) within a certain period of time
after origination, or (iv) the borrower defaults on
the contract (“walks away”).
The paper is organized as follows. First, it
briefly describes the evolution of the U.S. subprime mortgage market, the crisis, and some of
the earlier research that analyzes factors associated with loan termination (exit from the market).
Second, it outlines the empirical analysis of
explanatory factors of prepayment, default, and
termination (prepayment and default combined)
within two years of loan origination; it further
compares the number of prepaid and defaulted
loans per year within two years of origination.
3

In this paper, the terms “exit” and “termination” are used
interchangeably.

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Third, it points to the quick termination of subprime loans, indicating that these loans must
have been designed and intended to be temporary
and their existence most likely did not contribute
to increased homeownership rates in the United
States between 2001 and 2006.

SUBPRIME MORTGAGE CRISIS:
HIGH DEFAULT RATES
The boom and subsequent collapse of the subprime mortgage market has drawn the attention
of numerous researchers and policymakers. This
analysis of delinquencies and foreclosures is not
new. For example, Von Furstenberg and Green
(1974) analyzed the causes of mortgage delinquencies, apart from foreclosures and defaults, for
mortgages originated between 1961 and 1972.
They refer to and confirm findings published as
early as 1969 and 1970 (by Von Furstenberg) that
such factors as high loan-to-value (LTV) ratios (or
equity-to-value ratios) and low borrower income
are important determinants of mortgage default,
ceteris paribus. Thus, these findings were known
some three decades before these subprime issues
unfolded, before very large LTVs were deemed
“acceptable,” and so-called no-income, nodocumentation, no-asset mortgage loans were
introduced.
In a more recent, but precrisis analysis, Cutts
and Van Order (2005) suggest that several economic models can, in fact, explain the main characteristics of the subprime market. In particular,
“option-based” models are consistent with pricing
and loan characteristics of subprime mortgages
(for example, improving a borrower’s credit score
makes refinancing more likely); “separating equilibrium” models sort borrowers into prime and
subprime markets through signaling mechanisms;
and “adverse selection” models are consistent
with the choice between the lower costs of the
secondary market and the information advantages
of the primary market. However, many issues
were and still are beyond fundamental and conventional economic modeling. For instance,
Demyanyk (2008) shows that the Fair Isaac and
Company (FICO) credit score failed to predict 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

Demyanyk

subprime mortgage crisis, even though it is one of
the most important determinants of serious delinquency and foreclosure in mortgage lending.4
Pennington-Cross and Chomsisengphet (2007)
studied a sample of subprime securitized loans—
first-lien, fixed-rate, homeowner-occupied—that
originated between 1996 and 2003. The authors
note that borrowers with subprime mortgages are
more likely to cash-out refinance compared with
those with prime mortgages.5 Moreover, subprime
borrowers seem to substitute mortgage debt for
credit card debt and auto loans: They tend to
refinance their mortgages when interest rates on
credit cards and auto financing rise. Analyzing
the performance of subprime loans, the authors
observed that cash-out refinances tend to default
and prepay less frequently than non-cash-out
refinances. Demyanyk and Van Hemert (2008)
observed that cash-out refinances between 2001
and 2007 tended to default less frequently than
even purchase-money mortgages.
Demyanyk and Van Hemert (2008) were
among the first to analyze the subprime mortgage
crisis in detail. Using loan-level data, they first
showed that—contrary to popular belief—the
subprime crisis of 2007 was not confined to a
particular market segment, such as loans with
mortgage rates scheduled to increase or nodocumentation loans. Instead, it was a (subprime)
marketwide phenomenon. Second, they identified
factors most likely to be associated with a larger
probability that a subprime mortgage loan would
become seriously delinquent: FICO credit score,
combined LTV (CLTV) ratio, mortgage interest rate,
and house price appreciation between the period
of loan origination and the loan-performance
evaluation. These factors were not sufficiently
different in the crisis years (2006 and 2007) than
in the earlier years and thus do not entirely explain
the crisis, its magnitude, or its timing. Even house
price appreciation does not explain—by itself or
in a combination with other factors (a phenome4

For a more detailed discussion of delinquency and foreclosure
determinants, see Demyanyk and Van Hemert (2008).

A term “cash-out” refinance refers to a situation when a borrower
refinances an existing mortgage loan into a larger one, taking cash
out. This, by definition, means that a borrower is extracting the
equity from the house.

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

non called risk layering)—why the subprime
crisis was so rapid and large.
Demyanyk and Van Hemert (2008) also
showed the presence of nonmeasurable risk in
these mortgage contracts and the increased risk
over time. More specifically, they first adjusted
mortgage performance for values of observable
borrowers’ characteristics at origination (e.g.,
credit scores, LTV ratios, debt-to-income ratios),
loan characteristics (e.g., fixed-rate mortgage [FRM]
or hybrid mortgage, if homeowner-occupied,
presence of prepayment penalty clause), and
macroeconomic conditions (e.g., change in unemployment, household income, house price appreciation since origination). Second, they calculated
the adjusted performance of the loans for all
vintage/loan age combinations in their sample;
this exercise revealed that the market has worsened each year, monotonically and dramatically,
since 2001. In other words, the crisis did not
emerge suddenly in 2007 or 2008. It had been
brewing for at least six years prior.
Even though this scenario and time frame are
not readily observable by looking at the data—a
statistical exercise is needed to see the deterioration of the subprime market—Demyanyk and
Van Hemert (2008) show that securitizers, those
who mostly dictated mortgage rates in the market,
were to some extent aware of this gradual deterioration. The decline in loan quality was monotonic but not equally spread among different types
of borrowers. Over time, loans with high LTV
ratios had higher adjusted delinquency, foreclosure, and defaults rates. Securitizers started to link
mortgage interest rates to LTV ratios; obviously,
they did not do so enough. Loan quality deteriorated while loan riskiness increased every year
from 2001 to 2007; however, the price of risk—
the subprime-prime markup—in fact, declined.
The combination of increasing loan riskiness and
decreasing prices was not sustainable. In 2008,
the market collapsed and massive foreclosures,
bank failures, and a credit crunch followed.
Haughwout, Peach, and Tracy (2008) took the
analysis by Demyanyk and Van Hemert (2008) a
step further and analyzed early defaults of subprime mortgages. “Early default” is defined as
either delinquency (missed payments) for more
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than 60 days or foreclosure within the first year
after origination. Haughwout, Peace, and Tracy
(2008) confirm the finding of Demyanyk and Van
Hemert (2008) that, although credit/lending standards are important determinants of early default,
they alone cannot explain the timing and the
magnitude of the crisis in 2007 and 2008. They
also confirm that, even if depreciation in house
prices is an important determinant of increased
delinquencies and foreclosures in the immediate
precrisis years, a large portion of the increase in
serious delinquencies remains unexplained. On
the other hand, Keys et al. (2008) found that
(observed) lending standards in the subprime
mortgage market did deteriorate; and the main
driving force of the deterioration was the securitization of those loans.
In their analysis of the subprime crisis, Mian
and Sufi (2008) suggest that securitization of
mortgage assets may have increased the supply
of credit in geographic areas that had relatively
more mortgage application rejections a decade
before the crisis (in 1996); such credit allowed
more home purchases and thereby could have led
to the rapid increases in house prices between 2001
and 2005. When housing values started declining,
between 2005 and 2007, defaults followed.
Gerardi, Shapiro, and Willen (2007), using a
unique dataset covering the homeownership
experience in Massachusetts between 1989 and
2007, found that homeownership that began with
a subprime mortgage ended in foreclosure 20 percent of the time; importantly, this number is about
six times larger than a corresponding share of
homeowners who started with prime mortgages.
Foote et al. (2008) find that, based on the same
dataset, almost half of residential foreclosures
are concentrated in subprime mortgages, even if
the subprime mortgage was a refinance of a prime
loan.
Foote, Gerardi, and Willen (2008) argue that
even though borrowers facing negative equity in
their houses are more likely to default, they may
not default in the absence of an idiosyncratic
shock, such as illness, divorce, or the loss of a
job. Also, borrowers need to consider if the cost
of default—which includes the cost of renting
after the default—outweighs a potential (future)
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benefit from home equity, should the home price
increase in the future. In other words, negative
equity is a necessary but not a sufficient condition for default.

EMPIRICAL ANALYSIS OF LOAN
TERMINATIONS
A simple logit model was used to calculate
the impact of a set of explanatory factors—such
as borrower and loan characteristics and house
price appreciation in the area surrounding the
property—on the probability of either prepayment
or default. According to the estimated results, the
main factors affecting the probability of prepayment within two years of origination are (i) house
price appreciation (pre-origination and postorigination), (ii) the presence of prepayment penalties, (iii) the resetting structure of mortgage rates
(as with hybrid mortgages), and (iv) the CLTV
ratio, which measures the amount of equity in the
house. The main factors affecting the probability
of default within two years of origination are (i)
the FICO credit score, (ii) the CLTV ratio, (iii) the
mortgage rate, and (iv) post-origination house
price appreciation. Notably, the credit score affects
only the likelihood of default, not prepayment;
and pre-origination house price appreciation
affects only prepayment, not default. Borrowers
with hybrid mortgages do tend to prepay and
default more often than those with FRMs (see
Demyanyk and Van Hemert, 2008, for supporting
evidence); however, ceteris paribus, the sole fact
that a mortgage loan is a hybrid is not a strong
predictor of default.
The factors that most affect prepayments and
defaults were not substantially different in the
precrisis years, with the exception of house price
appreciation. For loans originated in 2003 and
2004, high house price appreciation is the main
contributing factor for high prepayment rates.
For loans originated in 2005 and 2006, low house
price appreciation is the main contributor for the
high default rates. Although house price depreciation is the main contributing factor, it is not the
sole explanation for the magnitude of the crisis:
The default rates are higher than what can be
explained by housing market factors alone.
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Borrowers’ options to prepay or default on
their mortgages have been analyzed in the context
of the pricing of mortgage contracts for decades.
Deng, Quigley, and Van Order (2000) provide an
extensive literature review describing earlier
analysis of prepayment only, default only, and
default and prepayment as joint options. The
authors theoretically unify several economic
models to analyze prepayment and default options
considered by borrowers simultaneously and
empirically test this model on a sample of fixedrate, fully amortized loans that originated
between 1976 and 1983 and observed until the
first quarter of 1992. All these loans were purchased by Freddie Mac. Even though the loans
were made and their performance evaluated long
before subprime issues emerged, the implications of this research are important: The authors
found evidence of the interdependence of the
decisions to prepay (akin to exercising a call
option) or default (akin to exercising a put option).
Forecasts that ignore this interdependence can
lead to serious errors in estimating the default
risk. For a related analysis, see Pennington-Cross
and Chomsisengphet (2007).
The following logit regression model is estimated to analyze a random sample of subprime
securitized loans (between 2001 and 2006) as a
cross section:
Probability 共Z 兲 = Φ共β ′X 兲,
where Z is either prepayment or default on (and
thus exit from) a subprime mortgage loan within
24 months of origination; Φ共x 兲 = 1/共1 + exp共–x 兲兲
is the logit function; x = β ′X ; X is the vector of
explanatory variables; and β is the vector of
regression coefficients.
The explanatory factors used in the analysis
are the FICO credit score, a dummy variable indicating whether full documentation was provided
at origination, a dummy variable indicating
whether a prepayment penalty is present, the
debt-to-income ratio (back-end), a dummy variable
indicating whether a debt-to-income ratio is not
provided, the mortgage interest rate, a dummy
variable indicating whether a borrower is an
investor, a dummy variable indicating whether a
mortgage was a refinance at origination, the origiF 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

nation amount, the CLTV ratio, a margin for hybrid
loans, a dummy variable indicating whether a
mortgage is a hybrid, a dummy variable indicating
whether a mortgage is an adjustable rate-mortgage
(ARM, nonhybrid), a dummy variable indicating
whether a mortgage is a balloon, post-origination
house price appreciation (from loan origination
up to the point of loan performance evaluation,
up to three years later), and pre-origination house
price appreciation (from two years before origination up to origination).
When to evaluate loan performance (within
two years of origination) was a choice driven
mainly by two factors: the FICO credit score and
the popularity of hybrid mortgages in the sample.
The FICO credit score, as with any credit score,
measures the creditworthiness of individuals or
businesses. Lenders/securitizers use these scores
to estimate the likelihood of eventual delinquency
or default. By design, the higher the credit score,
the less likely it is that a borrower will miss payments or go into default on a loan within one or
two years after the score has been calculated
(Demyanyk, 2008). The prevalence of hybrid
mortgages is also important. More than half of
subprime securitized mortgage loans are ARMs,
and almost all are so-called hybrid contract types,
which means they carry a fixed interest rate for
an initial period (usually two or three years) after
which the rate resets. Starting the analysis at two
(or three) years after origination eliminates the
effect on these loans of mortgage rates resetting
into a mostly larger market-driven rate plus a
margin. (See Demyanyk and Gopalan, 2007, for a
more detailed description and definitions.)

DATA AND VARIABLE
DEFINITIONS
Loan-level data used for the analysis are
provided by the First American CoreLogic
LoanPerformance database, as of July 2008. In
the dataset, loan, borrower, and property characteristics are provided for about half of all U.S. subprime mortgages. All loans in this dataset have
been securitized. According to the Mortgage
Market Statistical Annual (2008), securitization
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rates are as follows: 60.7 percent (2001), 63.0 percent (2002), 67.5 percent (2003), 62.6 percent
(2004), 67.7 percent (2005), 67.6 percent (2006),
74.2 percent (2007), and 77.3 percent (first six
months of 2008). Among all subprime mortgages,
the portion securitized ranged from 54 percent
in 2001 to 75 percent in 2006. For the empirical
analysis of this study, only first-lien subprime
mortgages are used. The variables used in the
analysis are defined as follows:

Investor: A dummy variable that equals 1
if the borrower is an investor and does not
owner-occupy the property and 0 otherwise.

Cash-out: A dummy variable that equals 1 if
the mortgage loan is a cash-out refinancing
loan at origination and 0 otherwise.

Missing debt-to-income: A dummy variable
that equals 1 if the back-end debt-to-income
ratio was not provided in the data (reported
as 0); the variable takes a value of 0 otherwise. In the data, the debt-to-income value
was not reported for approximately 30 percent of loans.

CLTV ratio: The combined mortgage values
of all liens divided by the value of the
house at loan origination.
Debt-to-income ratio: The back-end debtto-income ratio; it is defined as total
monthly debt payments divided by gross
monthly income at origination. A higher
debt-to-income ratio (i.e., a higher degree of
indebtedness) makes it harder for a borrower
to make the monthly mortgage payment.
Default: A dummy variable that equals 1 if
(i) the borrower has missed more than two
monthly mortgage payments, (ii) the borrower has defaulted on the loan (with the
foreclosure procedure finalized), or (iii) the
property is in foreclosure or is real-estate
owned (taken over by the lender) within the
first two years of origination; the variable
takes a value of 0 otherwise.
Documentation: A dummy variable that
equals 1 if full documentation on the loan
is provided and 0 otherwise.
FICO score: The FICO credit score at origination. The FICO score was recommended
for use in mortgage lending by Fannie Mae
and Freddie Mac in 1995 as a measure of
borrowers’ creditworthiness. The higher
the FICO score, the less likely a borrower
will default on a loan within about two
years of loan origination. Given the nature
of FICO scores, it is expected that a relationship will be found between borrowers’
scores and the incidence of default and foreclosure during the subprime mortgage crisis.
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Margin: The additional percentage points
for an ARM or hybrid mortgage over an
index interest rate, usually the six-month
LIBOR rate, applicable after the first interest
rate reset. The higher the margin, the higher
the interest rate after the reset, which
increases the monthly mortgage payments.

Mortgage rate: The initial interest rate as
of the first payment date. A higher interest
rate makes monthly mortgage payments
larger and, therefore, can make it more
difficult for a borrower to make timely
monthly mortgage payments.
Origination amount: The size of the mortgage loan. Loan size can affect the size of a
monthly mortgage payment: The larger the
loan, the larger the monthly payment, and
the harder it can be for a borrower to make
those payments in a timely manner. Also,
a borrower’s creditworthiness can affect the
size of the loan: Less-risky borrowers may
be expected to get larger loans. Which of
the two effects is dominant is an empirical
question addressed later in this study.
Post-origination house price appreciation:
The metropolitan statistical area (MSA)–
level house price appreciation from the time
of loan origination to the time the performance of the loan is evaluated. Appreciation is measured as a ratio of the house price
indexes reported by the Office of Federal
Housing Enterprise Oversight (now the
Federal Housing Finance Agency) for the
two corresponding periods.
Pre-origination house price appreciation:
The MSA-level house price appreciation
two years before mortgage origination and
origination period.
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Prepayment: A dummy variable that equals
1 if a borrower has either paid off or refinanced a mortgage loan within two years
of origination; the variable takes a value of
0 otherwise.
Prepayment penalty: A dummy variable
that equals 1 if a prepayment penalty is
associated with a loan and 0 otherwise.
Product type: Major types in the subprime
mortgage market include FRMs, hybrid
mortgages, ARMs, and balloons. Three
dummy variables for the latter three are
included in the regression analysis; the
magnitude of their impact therefore should
be interpreted as the effect on the probability of prepayment, default, or exit relative
to an FRM. The FRM is chosen as a benchmark because FRMs show the smallest
expected and realized probability of default.
Termination: A dummy variable that equals
1 if a borrower has either defaulted or prepaid the mortgage loan within two years
of origination; the variable takes a value of
0 otherwise.

EXPLANATORY FACTORS OF
PREPAYMENT, DEFAULT, AND EXIT
Prepayment
House price appreciation occurring within
two years of origination has the largest impact
on the probability of a borrower to prepay or
refinance a loan (see Table 1, column 1). An
increase in house price appreciation of 1 standard
deviation (SD) above its mean is associated with
a 13-percentage-point increase in the likelihood
that a loan will be prepaid, ceteris paribus. If
house prices in the area appreciated 1 SD above
the mean two years before origination, there is a
7-percentage-point increase in the likelihood a
loan will be prepaid. This perhaps indicates that
individuals build their expectations about future
home values based on immediate past values (or
the past trends).
Borrowers with hybrid mortgages tend to prepay more often; all other factors being the same,
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 a loan is a hybrid and has a mortgage rate scheduled to reset in two or three years, the probability
of prepayment increases by about 5.5 percentage
points. Loan originators and securitizers must have
been aware of this pattern; and so, to compensate
for the expected losses of interest payments (payments borrowers never make if they prepay the
loan before the end of the term), they imposed
prepayment penalties on about 70 percent of subprime securitized mortgages. The prepayment
penalty factor has its expected effect on the probability of prepayment: It decreases it—specifically,
by about 6 percent within two years of origination.
The mortgage rate at origination plays an
important role as well: The higher the rate, the
higher the chance a loan will be prepaid within
its first two years. The marginal effect of the mortgage rate is approximately 5 percentage points.
A loan’s purpose at origination also affects
prepayment. If a mortgage is originated to refinance an existing mortgage, it is more likely to be
refinanced again after two years or less, compared
with home purchase (purchase-money) loans.
Also, the smaller the down payment at origination, the less likely a borrower is to prepay or
refinance a loan within two years of origination.
In unfavorable economic circumstances, such as
a housing market slowdown or job loss, ceteris
paribus, a borrower would be expected to default
rather than refinance a mortgage that had little
equity.
The more expensive a property was at origination, the more likely its mortgage will be refinanced or prepaid. A larger origination amount
is associated with larger monthly mortgage payment. The greater incentive to refinance more
expensive properties may be a desire to lower
monthly payments or a need to extract cash to
cope with those (larger) monthly payments.

Default
The marginal effects of individual factors on
the probability of default are listed in column 2
of Table 1. Four major factors seem to most affect
the probability of default two years after origination: post-origination house price appreciation,
FICO credit score, CLTV ratio, and the mortgage
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Table 1
Impact of Individual Factors on the Probability of Prepayment, Default, or Exit within Two Years
of Mortgage Loan Origination (2001-06)
Explanatory factor

Prepayment

Default

Exit

FICO credit score

0.19*

–3.28***

–4.11***

If full documentation is provided (dummy)

0.38***

–1.31***

–1.21***

If prepayment penalty is present (dummy)

–6.27***

0.65***

–5.29***

1.58***

1.28***

3.12***

Debt-to-income ratio (back end)
If debt-to-income ratio is not provided (dummy)

1.17***

1.01***

2.28***

Mortgage interest rate

5.23**

2.27***

7.76***

If an investor (dummy)

–1.05***

0.93***

0.00

2.68***

–1.08***

If a mortgage is for refinancing at origination (dummy)
Origination amount
Combined loan-to-value ratio

0.73***

3.03***

0.75***

4.16***

–4.24***

4.34***

–0.89***

Margin for hybrid loans

0.46***

0.85***

2.26***

If a hybrid (dummy)

5.53***

0.36***

4.30***

If an ARM (dummy)

1.60***

0.05

1.64***

If a balloon (dummy

0.72***

0.51***

1.48***

Post-origination house price appreciation

13.28***

–4.29***

7.31***

Pre-origination house price appreciation

7.31***

–0.46***

6.39***

NOTE: A mortgage loan is considered “prepaid” if a borrower has either prepaid or refinanced a mortgage loan within a certain period
after loan origination. A mortgage loan is considered in “default” if a borrower has defaulted on a loan or has missed more than two
mortgage payments or the property is in the process of foreclosure or is real-estate owned (i.e., is likely to default) within 2 years of
origination. “Exit” from a subprime mortgage is either prepayment or default. The reported results are the marginal effects of each
variable i calculated as follows:
–
–
MEFFi = Φ(β ′X + βi σi ) – Φ(β ′X ),
–
where Φ(β ′X ) is the likelihood that event Z will occur; Z is either prepayment (column 1), default (column 2), or exit (column 3) from
a subprime mortgage loan within two years of origination; Φ(.) is the logistic function; X is the vector of explanatory variables, σi is
the standard deviation of variable i, and β is the vector of regression coefficients.
*, **, and *** indicate statistical significance at the 10 percent, 5 percent, and 1 percent levels, respectively.

interest rate. This finding is consistent with the
results obtained by Demyanyk and Van Hemert
(2008), who estimated the effects of those factors
on the probability of serious delinquency one year
after origination. According to the estimates, a
1 SD increase in the FICO credit score, ceteris
paribus, is associated with a decrease in a probability of default by 3.3 percentage points. Note
that the credit score has almost no explanatory
power for prepayment but is a critical factor in
explaining defaults.
According to the estimates, a 1 SD increase in
house value appreciation measured at the MSA86

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level is associated with a 4.3-percentage-point
decrease in the likelihood of default; the effect on
prepayments and refinancing is about three times
larger and has the opposite sign as expected. The
difference in the absolute values of the marginal
effects reflects an asymmetry in how equity
affects different actions taken by the borrower. An
increase in appreciation increases the probability
of prepayment much more than it decreases the
probability of default. Pre-origination house price
appreciation, even though it has an economically
significant impact on prepayments, has almost no
effect on defaults.
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The CLTV ratio’s effect on default is comparable in magnitude (but opposite in sign) to its effect
on prepayment. Less equity in the house, or a
larger LTV ratio, is associated with an increased
probability of default but decreased probability
of prepayment. In both cases, the marginal effect
is about 4.3 percentage points.
The mortgage interest rate has a marginal
effect on the probability of default of 2.3 percentage points; recall that in the case of refinancing
it is about double that number. This evidence
seems to indicate that a high mortgage rate gives
borrowers incentives to exit the mortgage through
either prepayment or default.

Exit
Column 3 of Table 1 reports the estimates of
the logit regression with the “exit” being a dependent variable; that is, each factor is being analyzed
for its impact on prepayment and default combined. According to the estimates, the factors that
have a significant effect on either prepayment or
default have a significant impact on both of these
options combined. 6 The only exception is the
CLTV ratio, where the effects on prepayment and
default cancel each other in a joint regression.

ANNUAL FACTOR CONTRIBUTION
TO PREPAYMENT AND DEFAULT
Through the boom and the subsequent bust
of the subprime mortgage market, almost half of
the subprime loan borrowers in the sample terminated their original mortgages through prepayment
or default. The shares of prepayment and default
among the terminated loans, however, varied by
the vintage of those loans. For example, Figure 1
shows that the largest rates of prepayment within
two years of origination were observed for loans
6

Deng, Quigley, and Van Order (2000) and Pennington-Cross and
Chomsisengphet (2007) analyze the determinants of mortgage
termination empirically, using a maximum likelihood framework
analogous to the one used in the current study. However, a simpler
approach has been undertaken here. Instead of a multinomial logit
model (as in the study by Pennington-Cross and Chomsisengphet,
2007) or hazard functions (as in Deng, Quigley, and Van Order, 2000,
or Demyanyk and Van Hemert, 2008), a simple logit function is estimated in this study for each of the outcomes of a loan termination.

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

originated in 2002-04.7 This section attempts to
empirically answer the following question: What
observable factors, individually or in combination,
can explain changes in prepayment and default
ratios?
This study uses a method similar to the one
developed by Demyanyk and Van Hemert (2008)
to measure the extent each factor explains the
likelihood of prepayment or default for different
mortgage vintages. Specifically, for each year Y
in the sample, the impact of each explanatory
variable i is calculated as the difference between
the logit function Φ where, for one variable i, the
overall mean is substituted by its mean value in
year Y (the values of all other variables remain at
their overall mean values) and the logit function
where all variables are at their overall mean values. More formally, the annual factor contribution
(AFCiY ) for prepayment or default of each variable
i and year Y is calculated by

(

)) ( )

AFC Yi = Φ β ′X + βi X iyear Y − X i − Φ β ′X ,
–
where Φ共β ′X 兲 is the likelihood that prepayment
or default will occur within 24 months of mortgage
loan origination, Φ共.兲 is the logistic function, X is
the vector of explanatory variables, and β is the
vector of regression coefficients.
As shown in Figure 1, within two years of
origination, loans originated in 2001 had delinquency and default rates almost as high as loans
originated in 2005. Column 1 of Table 2 shows
the contribution of each factor for this origination year plus prior and subsequent house price
appreciation.
Table 2 also shows how low FICO credit
scores, high mortgage interest rates, and relatively
low house price appreciation within two years
of origination contributed to high default rates
for the 2001 vintage loans. The mortgage interest
rate continued to be a factor in defaults for vintage
2002 loans but was of a much smaller magnitude.
For 2003 and 2004 vintage loans, only postorigination house price appreciation (fast and
7

The rates for all subprime loans in the sample (originated as both
refinancings and purchase-money) are remarkably similar to those
documented in Figure 1.

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Demyanyk

Figure 1
Termination of Subprime Purchase-Money Loans Within 12, 24, and 36 Months of Origination by
Origination Year

2001
2002
2003
12 Months 2004
2005
2006
2001
2002
2003
24 Months 2004
2005
2006
2001
2002
2003
36 Months 2004
2005
2006

Delinquency, Foreclosure, and Default Rate (percent)
Prepayment and Refinance Rate (percent)

NOTE: All loans used for this figure were securitized, originated as purchase-money, are first-lien mortgages, and have the borrower
and loan characteristics reported in the data.
SOURCE: Author’s calculations based on FirstAmerican CoreLogic LoanPerformance loan-level dataset, as of July 2008.

positive) contributed to low default rates; defaults
were substituted by prepayment and refinancing
options exercised by borrowers, as discussed
below in greater detail.
For 2005 and 2006 vintage loans, the only
factor that contributed to higher default rates than
those in all other years in the sample was postorigination house price depreciation. For these
loans, house price appreciation contributed 2.6
and 7.5 percentage points, respectively, in 2005
and 2006 to the increase in the default rates two
years after origination. However, the default rates
for those loans were in fact about 20 to 30 percent,
much higher than the rates explained by house
price appreciation alone.
As shown in Table 3, column 1, the main
contributing factor for high refinance rates within
two years of origination for 2001 vintage loans was
a high mortgage interest rate; its value accounted
for 6.3 percentage points of the average prepayment rate. Post-origination and pre-origination
88

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house price appreciation contributed negatively
to prepayment rates: 4 and 3.4 percentage points,
respectively. A somewhat important factor was the
CLTV ratio prevailing in the market. In 2001, its
value at origination contributed to a 1.2-percentagepoint larger probability of prepayment two years
later.
The value of the prevailing mortgage interest
rate for loans that originated in 2002 was again
the most important contributor to explaining prepayment rates. However, the impact of this factor
(see Table 3, column 2) is much smaller compared
with its effect on loans that originated in 2001.
The important contribution of post-origination
house price appreciation is no longer present, as
it was with the 2001 vintage loans, and the contribution of the CLTV ratio has decreased.
For 2003 and 2004 vintage loans, the primary
contributing factor to high prepayment rates
was the house price appreciation that took place
between the origination period and the subsequent
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

Demyanyk

Table 2
Annual Factor Contribution to Mortgage Loan Default (2001-06)
Explanatory factor

2001

FICO credit score
If full documentation is provided (dummy)
If prepayment penalty is present (dummy)

2002

2003

2004

2005

2006

1.03

0.52

–0.15

–0.14

–0.32

–0.09

–0.31

–0.11

–0.03

0.02

0.10

0.13

0.05

0.04

0.01

0.00

–0.01

–0.03

–0.18

–0.23

–0.02

0.06

–0.01

0.30

If debt-to-income ratio is not provided (dummy)

0.10

0.17

–0.01

–0.06

0.03

–0.19

Mortgage interest rate

2.77

1.07

–0.40

–0.87

–0.58

0.66

Debt-to-income ratio (back end)

If an investor (dummy)

0.00

If a mortgage is for refinancing at origination (dummy)

–0.09

–0.05

–0.07

–0.03

0.06

0.10

Origination amount

–0.30

–0.20

–0.07

0.01

0.14

0.19

Combined loan-to-value ratio

–0.96

–0.79

–0.31

0.10

0.46

0.69

Margin for hybrid loans

–0.17

0.01

–0.12

0.02

0.08

0.09

If a hybrid (dummy)

–0.07

–0.01

–0.04

0.04

0.05

–0.08

If an ARM (dummy)

0.00

If a balloon (dummy)

0.04

–0.06

–0.09

–0.11

–0.02

0.40

Post-origination house price appreciation

2.07

–0.20

–3.00

–2.22

2.63

7.51

Pre-origination house price appreciation

0.23

0.22

0.05

–0.19

–0.20

NOTE: The annual factor contribution is
–
–
–
–
AFCiY = Φ(β ′X + β i (X iyear Y – X i )) – Φ(β ′X ),
where for each year Y, the impact of each explanatory variable i (first column) is calculated as the difference between the logit function
Φ, where, for one variable i, the overall mean is substituted by its mean value in year Y (all other variables remain at their overall mean
values) and the logit function where all variables are at their overall mean values.
–
Φ(β ′X ) is the likelihood that default will occur within two years of mortgage loan origination, Φ(.) is the logistic function, X is the
vector of explanatory variables, and β is the vector of regression coefficients.
A mortgage loan is considered in default if a borrower has defaulted on a loan or has missed more than two mortgage payments,
property is in the process of foreclosure, or is real-estate owned (i.e., is likely to default).

two years. For 2003 vintage loans, a diminishing
factor was the pre-origination house price appreciation, which contributed to the decline in the
prepayment rates. For the 2004 vintage loans,
the mortgage interest rate also diminished prepayment incentives for subprime borrowers.
For 2005 and 2006 vintage loans, the sole contributing factor for the prepayment and refinance
rate, again, was house price appreciation. However, because the housing market slowdown
reversed the trend and house prices depreciated,
the contribution was of the opposite sign compared with earlier years. With all other factors
equal, pre-origination house price appreciation
contributed positively, tending to increase refiF 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

nance rates; however, post-origination housing
values declined and the lower refinance rates prevailed. In other words, the door to refinancing
opportunity was closed by declining housing
prices and refinancing was largely overtaken by
defaults in the termination rates of subprime
mortgages.

Quick Exits
Surprisingly, almost every other loan exited
the subprime market (in one way or another)
within two years of origination. Moreover, just 30
to 40 percent of all subprime loans in the sample
were purchase-money (used to purchase rather
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Demyanyk

Table 3
Annual Factor Contribution to Mortgage Loan Prepayment (2001-06)
Explanatory factor

2001

2002

2003

2004

FICO credit score

2005

2006

–0.05

–0.02

0.01

0.00

If full documentation is provided (dummy)

0.09

0.03

0.01

0.00

–0.03

If prepayment penalty is present (dummy)

–0.53

–0.39

–0.14

0.00

0.12

0.28

Debt-to-income ratio (back end)

–0.25

–0.30

–0.03

0.08

–0.01

0.39

If debt-to-income ratio is not provided (dummy)

0.12

0.20

–0.01

–0.07

0.04

–0.24

Mortgage interest rate

6.26

2.57

–1.02

–2.24

–1.48

1.60

If an investor (dummy)

0.00

0.01

0.00

If a mortgage is for refinancing at origination (dummy)

0.21

0.13

0.16

0.08

–0.13

–0.24

–1.26

–0.82

–0.31

0.05

0.56

0.77

1.21

0.99

0.37

–0.12

–0.54

–0.79

Origination amount
Combined loan-to-value ratio
Margin for hybrid loans

–0.09

0.01

–0.07

0.01

0.04

0.05

If a hybrid (dummy)

–1.10

–0.19

–0.59

0.65

0.78

–1.28

If an ARM (dummy)

0.02

0.01

–0.04

–0.02

0.01

0.00

If a balloon (dummy)

0.05

–0.08

–0.14

–0.16

–0.02

0.57

Post-origination house price appreciation

–4.12

0.45

8.32

5.79

–5.09

–11.66

Pre-origination house price appreciation

–3.39

–3.27

–3.30

–0.81

2.88

3.15

NOTE: See first note to Table 2.
A mortgage loan is considered “prepaid” if a borrower has either paid off or refinanced a mortgage loan within 2 years of origination.

than refinance a house). The remaining borrowers
refinanced their existing homes, and refinances
do not contribute to an increase in homeownership.
Jaffee (2008) summarized research that analyzed what went wrong with the subprime market
that could cause the crisis and what went right—
potential benefits from subprime lending that
might offset consequences of the subprime crisis.
Jaffee calculated that the subprime mortgage market funded approximately 5 million home purchases between 2000 and 2006, with slightly more
than 1 million loans to first-time homebuyers.
Jaffee suggests that the subprime mortgage market
had at least one benefit to the economy: the
increase in homeownership.
However, as shown in Figure 1, for all
purchase-money mortgage loans originated
between 2001 and 2006, between 15 and 25 percent were terminated in the first year, about 50
percent in the first 2 years, and 80 percent in the
90

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first three years. For all origination years, of only
first-lien, home-purchase (purchase-money)
mortgages that were securitized and for which
reliable data were provided, more than 600,000
loans were terminated within the first year after
origination. Within two years, approximately
1.9 million loans were terminated. Among the
terminated loans, about 1 million were seriously
delinquent or in default; the remaining million
were refinanced or prepaid. For subprime mortgages, the data seem to suggest that the number
of foreclosed homes, with mortgages funding the
home purchases, already exceeds the estimated
number of first-time homebuyers with subprime
mortgages.
The number of prepaid and refinanced properties is less informative because the data do not
provide the after-prepayment outcome of the
mortgages. A refinanced loan can be either a
new subprime loan that follows the original path
described above (a borrower would either default
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

Demyanyk

or prepay again) or a prime loan (which borrowers
can also default on or prepay). Given the degree
of uncertainty on this issue, no inference based
on the number of prepaid loans is made here.
Even if borrowers refinanced their initial subprime loans into more stable subprime or prime
mortgages (those observed in the data before prepayment or refinance), the 80 percent termination
rate within the first three years after origination
would indicate that the initial boom in subprime
lending could have, at most, accelerated growth
of homeownership, even if temporarily. In other
words, in a hypothetical “success” example, if a
borrower took out a subprime loan in 2001, say
as a first-time homebuyer, and then refinanced
into a better loan in 2004, the same borrower most
likely could have skipped the subprime step and
become a first-time homebuyer in 2004, starting
with a more stable loan and avoiding high interest
rate payments and prepayment penalties. Given
the impossibility of knowing when any first-time
homebuyer who used a subprime mortgage would
have become a homeowner with a prime loan, if
ever, the data do not support the argument that
subprime mortgages increased homeownership.
Given that the percentages of terminated loans
in the sample are almost the same for all loan
vintages (origination years), one can infer that
subprime loans rarely were expected or intended
to last much longer than three years. Lenders
must have known that these loans were temporary
(i.e., it would be impossible to collect sufficient
interest payments to cover loan origination costs).
Therefore, prepayment penalties were imposed,
high interest rates and fees were charged, and
complicated loan modifications were designed.
(As well, the securitization structure is very complex, rendering individual loan modifications
almost impossible.) In addition, borrowers must
have been planning to use subprime mortgages
for so-called bridge financing. If subprime borrowers were planning a quick exit from the very
beginning, then these loans were risky not only
from a credit-risk perspective but also from the
standpoint of interest rate risk (would rates go up?)
and liquidity risk (would there be a possibility
to refinance?). Given these risks, lenders and
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

investors could experience much higher losses
than expected purely on the basis of credit risk.
In hindsight, we know that the risks did materialize and the losses did skyrocket.

CONCLUSION
The subprime mortgage crisis of 2007 resulted
in a massive wave of foreclosures and serious
delinquencies, a large proportion of which consisted of mortgages originated in 2006 and 2007.
Much of the debate among researchers and policymakers involves causes, consequences, and remedies for these early defaults and foreclosures. Still
unexplained, however, is the temporary nature
of subprime loans. This study shows that loans
that originated in any year from 2001 to 2006
generally had a life of less than three years. In
fact, almost half of these loans exited the market
through either prepayment or default within the
first two years after origination; about 80 percent
of them did so within three years.
Even though mortgage termination rates have
been remarkably similar for all origination years
evaluated one, two, or three years after origination,
the split between default and prepayment rates
varied. There is a J shape in the graphed representation of defaults for origination years 2001 to
2006. The trough of the pattern corresponds to
the years 2003 and 2004, when the housing market was booming. When default rates are small,
refinancing rates are high. When the trend in the
housing market reversed, refinancing became
impossible and defaults took their place.
The evidence in this paper is consistent with
that reported by Demyanyk and van Hemert
(2008), who explain that the crisis—the unusually
high default rates among 2006 and 2007 vintage
loans—did not occur because these loans were
in some respects much worse than all loans that
originated earlier. Subprime mortgages were very
risky all along; however, their true riskiness was
hidden by rapid house price appreciation, allowing mortgage termination by refinancing/prepayment to take place. When prepayment became
very costly (with zero or negative equity in the
house increasing the closing costs of a refinancing), defaults took their place.
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Demyanyk

The results in this paper also suggest that
subprime lending did not increase homeownership: The number of defaults in a limited sample
(about 50 percent) of subprime purchase-money
mortgages within two years of origination is almost
equal to the estimated number of first-time homebuyers who took subprime mortgages. If the data
for the rest of the market were available, the number of defaults would no doubt be even greater.
Several questions remain and require further
attention. First, the available data do not help
identify what happened to loans that were terminated but did not end in default (i.e., prepaid or
refinanced loans). Mortgages originated for refinancing tend to be refinanced again within a couple of years and tend to default as well. If more
comprehensive data become available, further
analysis on the homeownership policy discussion
may be fruitful. Foote et al. (2008) raise the same
question and explain the difficulty in answering
it. Second, several studies indicate that most of
the materialized risks associated with subprime
mortgage lending had been neither observable
nor measurable (e.g., the credit score did not
predict likelihood of default; see Demyanyk and
Van Hemert, 2008, and Haughwout, Peach, and
Tracy, 2008). Little is known about these risks
except that they existed and increased over time.
More sophisticated models and comprehensive
data are needed to answer these questions.

REFERENCES
Cutts, Amy C. and Van Order, Robert A. “On the
Economics of Subprime Lending.” Journal of Real
Estate Finance and Economics, March 2005, 30(2),
pp. 167-96.
Dell’Ariccia, Giovanni; Igan, Deniz and Laeven, Luc.
“Credit Booms and Lending Standards: Evidence
from the Subprime Mortgage Market.” Working
Paper IMF WP/08/106, International Monetary Fund,
April 2008; www.imf.org/external/pubs/ft/wp/
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Demyanyk, Yuliya. “Did Credit Scores Predict the
Subprime Crisis?” Federal Reserve Bank of St. Louis

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2009

Regional Economist, October 2008, pp. 12-13;
http://stlouisfed.org/publications/re/2008/d/pages/
mortgage.html.
Demyanyk, Yuliya and Gopalan, Yadav. “Subprime
ARMs: Popular Loans, Poor Performance.” Federal
Reserve Bank of St. Louis Bridges, Spring 2007,
pp. 4-5; http://stlouisfed.org/publications/br/2007/
a/pages/2-article.html.
Demyanyk, Yuliya and Van Hemert, Otto.
“Understanding the Subprime Mortgage Crisis.”
Review of Financial Studies, forthcoming;
http://ssrn.com/abstract =1020396 (posted
December 5, 2008).
Deng, Yongheng; Quigley, John M. and Van Order,
Robert A. “Mortgage Terminations, Heterogeneity
and the Exercise of Mortgage Options.”
Econometrica, March 2000, 68(2), pp. 275-308.
Foote, Christopher L.; Gerardi, Kristopher; Goette,
Lorenz F. and Willen, Paul. “Subprime Facts: What
(We Think) We Know about the Subprime Crisis
and What We Don’t.” Public Policy Discussion
Paper No. 08-2, Federal Reserve Bank of Boston,
May 30, 2008; www.bos.frb.org/economic/ppdp/
2008/ppdp0802.pdf.
Foote, Christopher; Gerardi, Krisopher and Willen,
Paul. “Negative Equity and Foreclosure: Theory
and Evidence.” Journal of Urban Economics,
September 2008, 64(2), pp. 234-45.
Gerardi, Kristopher; Shapiro, Adam and Willen,
Paul. “Subprime Outcomes: Risky Mortgages,
Homeownership Experiences, and Foreclosures.”
Working Paper 07-15, Federal Reserve Bank of
Boston, May 4, 2008; www.bos.frb.org/economic/
wp/wp2007/wp0715.pdf.
Haughwout, Andrew; Peach, Richard and Tracy,
Joseph. “Juvenile Delinquent Mortgages: Bad Credit
or Bad Economy?” Staff Report No. 341, Federal
Reserve Bank of New York, August 2008;
www.newyorkfed.org/research/staff_reports/sr341.pdf.
Inside Mortgage Finance Publications. Mortgage
Yearbook First Half 2008 Special Edition. Bethesda,
MD: Inside Mortgage Finance Publications, 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

Demyanyk

Jaffee, Dwight, M. “The U.S. Subprime Mortgage
Crisis: Issues Raised and Lessons Learned.”
Working Paper No. 28, Commission on Growth and
Development and the World Bank, 2008;
http://faculty.haas.berkeley.edu/jaffee/Papers/
DJSubprimeMay5.pdf.
Keys, Benjamin J.; Mukherjee, Tanmoy; Seru, Amit
and Vig, Vikrant. “Did Securitization Lead to Lax
Screening? Evidence from Subprime Loans.” Athens
Meetings Paper, European Finance Association,
December 2008; http://papers.ssrn.com/sol3/
papers.cfm?abstract_id=1093137.
Mayer, Christopher and Pence, Karen. “Subprime
Mortgages: What, Where, and to Whom?” Finance
and Economics Discussion Series Working Paper
2008-29, Federal Reserve Board, December 7, 2007;
www.federalreserve.gov/pubs/feds/2008/200829/
200829pap.pdf.
Mian, Atif and Sufi, Amir. “The Consequences of
Mortgage Credit Expansion: Evidence from the
2007 Mortgage Default Crisis.” NBER Working
Paper 13936, National Bureau of Economic Research,
April 2008; www.nber.org/papers/w13936.
Pennington-Cross, Anthony and Chomsisengphet,
Souphala. “Subprime Refinancing: Equity Extraction
and Mortgage Termination.” Real Estate Economics,
2007, 35(2), pp. 233-63.
Von Furstenberg, George M. and Green, R. Jeffery.
“Home Mortgage Delinquencies: A Cohort Analysis.”
Journal of Finance, December 1974, 29(5),
pp. 1545-48.
Von Furstenberg, George M. “Default Risk on FHAInsured Home Mortgages.” Journal of Finance,
June 1969, 24(3), pp. 459-77.
Von Furstenberg, George M. “Risk Structures and the
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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

Firm Volatility and Credit:
A Macroeconomic Analysis
Leo Kaas
This paper examines a tractable real business cycle model with idiosyncratic productivity shocks
and binding credit constraints on entrepreneurs. The model shows how firm volatility increases
in combination with credit market development. It further generates the observed comovement
of credit and firm volatility with output at business cycle frequencies in response to aggregate
productivity shocks. (JEL E32, E44, O16)
Federal Reserve Bank of St Louis Review, March/April 2009, 91(2), pp. 95-106.

arallel to the decline in macroeconomic
volatility over the past decades (see
Blanchard and Simon, 2001, and Stock
and Watson, 2002), there is some evidence that volatility at the firm level has increased
during the same period. For the United States,
such evidence is available for idiosyncratic stock
returns (Campbell et al., 2001), as well as for
employment, sales, and investment. Comin and
Mulani (2004) and Comin and Philippon (2005)
document similar results for other countries.1
There are different explanations for an increase
in firm volatility. One is that deregulation and
intensified global competition force firms to adjust
prices and business strategies faster. Another is
that financial development leads to more risktaking by entrepreneurs or facilitates leverage,
which both could potentially drive up firm volatility. Indeed, Comin and Philippon (2005) find some
support for both hypotheses. They also show that
the increase in firm volatility is driven neither by
the growing share of small firms in the sample nor
1

Davis et al. (2006) demonstrate, however, that firm-level employment volatility has increased only for publicly traded firms and
not for privately held firms.

changes in firm ownership, including merger and
acquisition activities.
This paper puts the link between financial
development and firm volatility in a macroeconomic perspective. To this end, I develop a tractable real business cycle model with idiosyncratic
productivity shocks and collateral-based borrowing constraints. Productive entrepreneurs borrow
up to the value of their collateral. Because their
capital return exceeds the capital cost, the leveraged return on equity exceeds the equity return
of less-productive entrepreneurs. An increase in
credit market development relaxes borrowing
constraint and increases leverage, and thereby
also the spread between internal rates of return
across firms. As a result, firm growth rates become
more volatile.
Another implication of my model is that both
credit market development and firm volatility
respond positively to an aggregate productivity
shock. Higher productivity raises the value of
pledgeable assets, thus softening credit constraints
and leverage. Hence, both the volume of firm
credit and firm-level volatility are procyclical. In
the following section, I demonstrate that such

Leo Kaas is a professor of economics at the University of Konstanz and was a visiting scholar at the Federal Reserve Bank of St. Louis when
this paper was written. The author thanks Costas Azariadis and Carlos Garriga for helpful comments and the German Research Foundation
for financial support (grant No. KA 1519/3).

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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Kaas

Figure 1
Business Credit (Share of GDP) and Firm Volatility (Annual U.S. Data 1955-2000)
0.25

0.8
0.7

0.20
0.6
0.5

0.15

0.4
0.10

0.3
0.2
Business Credit/GDP (left axis)

0.1
0
1955

Firm Volatility (right axis)
1960

1965

1970

1975

procyclicality is indeed observable in postwar
U.S. data. In the quantitative section, I match the
model to the U.S. business cycle and show that
it replicates reasonably well the comovements
among the three key variables of output, credit,
and firm volatility. However, the amplification
of firm volatility is twice as large as in the data,
and its cross-correlations with output and credit
are somewhat too low. The model can also be used
to investigate the effects of a financial crisis; in
particular, a severe crisis where collateral value
drops temporarily by 20 percent features a decline
of gross domestic product (GDP) below trend by
3.5 percent.
By adopting collateral-based borrowing constraints in combination with logarithmic utility
and Cobb-Douglas production technologies, my
model is essentially a variation of the approach
of Kiyotaki (1998) and Kiyotaki and Moore (2008),
who also develop tractable business cycle models
with binding credit constraints. Other theoretical
contributions on idiosyncratic production risk
and finance constraints in dynamic equilibrium
models are those of Hopenhayn and Vereshchagina
(2003) and Meh and Quadrini (2006). But while
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1980

1985

1990

1995

0
2000

they examine risk-taking in incomplete-market
environments, the effect of borrowing constraints
on firm leverage is the driving force of this paper.
Further, the model of this paper has closed-form
solutions, which make its basic mechanics particularly clear.

THE EVIDENCE
For the purpose of this paper, the appropriate
measure of credit market development is the share
of business credit in GDP, where “business credit”
includes all credit market debt owed by nonfinancial firms, including corporations and noncorporations.2 Figure 1 illustrates the substantial
financial deepening during the period 1955 to
2000; as a share of GDP, business credit roughly
doubled. Real business credit actually increased
by a factor of 8.9.3
2

See Board of Governors of the Federal Reserve (2008).

Real business credit is defined as business credit divided by the
GDP deflator. Over the same horizon, by comparison, real household debt increased by a factor of 9.5, real government debt by a
factor of 4.9, and real credit market debt of the financial sector by
a factor of 99.5.

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

Kaas

Figure 2
Detrended Real Business Credit and Firm Volatility (Annual U.S. Data 1955-2000)
0.15

0.10

0.05

–0.05

–0.10

Real Business Credit
Firm Volatility

–0.15
1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

NOTE: Both variables are reported in logs as deviations from a Hodrick-Prescott trend with smoothing parameter 100.

Figure 1 also shows the increase in firm volatility during the same period. I use the “median sales
volatility” reported in Comin and Philippon (2005,
table 1) as a volatility measure. Specifically, Comin
and Philippon calculate a rolling standard deviation (SD) of sales growth for nearly every firm in
the Compustat database; the median of the cross
section then measures firm volatility at every
point in time. It becomes evident from the figure
that firm volatility also doubled between 1955 and
2000. Of note, firm volatility is quite dispersed in
the cross section. For example, in the 1990s, sales
growth volatility was below 0.1 for 25 percent of
firms and above 0.3 for another 25 percent of firms
(see Figure 2 in Comin and Philippon, 2005).
Figure 1 further suggests that business credit
and firm volatility are positively correlated at the
business cycle frequency. To see this more clearly,
note that Figure 2 shows the detrended time series
of real business credit and of firm volatility, where
the trend is a Hodrick-Prescott (H-P) filter with
λ = 100 and the cyclical components are reported
as log deviations from trend. Particularly since
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

Table 1
Descriptive Statistics (Annual U.S. Data
1955-2000)
Output

Credit

Volatility

Standard deviation

0.021

0.042

0.050

Annual autocorrelation

0.546

0.826

0.675

Output

0.460

0.257

Credit

—

0.567

Volatility

—

Correlation matrix

NOTE: All variables are reported in logs as deviations from an
H-P trend with smoothing parameter 100.

the 1970s, the two cycles are closely synchronized
and the percentage deviations from trend are
similar in magnitude.
Table 1 summarizes the detrended data of
output, real business credit, and firm volatility.
Both firm volatility and credit have higher variance than output, and they are positively correMARCH/APRIL

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lated with contemporaneous output, where the
correlation between credit and output is stronger
than the one between volatility and output. The
correlation coefficient between credit and volatility increases from 0.567 to 0.775 when the period
is restricted to the years 1975 to 2000.

THE MODEL
Consider a one-sector growth model with infinitely lived entrepreneurs and workers in which
either group is a continuum of mass one. All agents
derive logarithmic utility from consumption and
discount future utility with the factor β < 1. All
workers supply one unit of labor inelastically.
Entrepreneurs do not supply labor; they employ
workers and capital to produce output with a
Cobb-Douglas technology, which is subject to
idiosyncratic productivity shocks. Specifically,
entrepreneur i in period t uses capital Kti and labor
Lti to produce output Yti = Ati共Kti 兲α 共Lti 兲1– α, where
the entrepreneur’s productivity attains the high
level Ati = At (productive state) with probability
π and the lower level Ati = B < A (unproductive
state) otherwise. These productivity realizations
are independent across time and across entrepreneurs. Thus, a fraction π of entrepreneurs is productive in every period. The assumption that
productivity states are independent of history
simplifies the exposition but can easily be generalized to allow for autocorrelated productivity
states. The only complication is that the model
must then be augmented by another state variable,
which is the share of wealth in the hands of productive entrepreneurs.
Factor productivity at the technology frontier
At is subject to aggregate productivity shocks. In
particular, lnAt follows an AR(1) process with coef–
ficient ρ < 1, mean lnA , and normally distributed
shocks with SD σ. The assumption that only the
frontier A fluctuates while the inferior technology
parameter B is fixed again simplifies the exposition and can be generalized. What is crucial for
the results, though, is that B fluctuates less than
proportionately with productivity at the frontier.
Output produced in period t becomes available
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for entrepreneurs’ investment and consumption
purposes in the next period. To obtain closedform solutions, capital fully depreciates within
every period. Equivalently, Yti can be interpreted
to include both output and undepreciated capital.
In the calibration exercise, I use this interpretation and choose the capital share parameter α
accordingly.
Each period, all agents have access to a capital
market where they can borrow and lend at gross
interest rate Rt. Borrowing can be against collateral
only, however. Because labor income cannot be
collateralized, workers are not permitted to borrow. Further, I show that in any steady state with
constrained entrepreneurs, R < 1/β holds, which
implies that in any stochastic equilibrium near
the steady state, workers do not save; hence,
workers simply consume their wage income in
every period.
Entrepreneurs, in turn, can pledge a fraction
λ < 1 of their output, where the “collateral share”
parameter λ plausibly depends both on technological features (e.g., what part of capital is alienable)
and on the institutional framework and market
environment (e.g., creditors’ rights and availability
of credit market instruments). Every entrepreneur’s
principal and interest on debt Dti may not exceed
the value of collateral. That is, the credit constraint
takes the form Rt Dti ≤ λYti. Credit repayments
occur at the beginning of the next period before
realization of the next period’s productivity.
For any realization of technology shocks
共At 兲t ≥ 0, a competitive equilibrium is a list of
consumption plans, production plans, and debt
positions (Cti, Kti, Lti, Dti ) for every entrepreneur;
consumption plans and debt positions for workers
(Ctw, Dtw ); and factor prices for labor and capital
(wt , Rt ) such that in every period t ≥ 04:
(i) Cti, Kti, Lti, Dti maximizes entrepreneur i’s
expected utility subject to budget and debt
constraints; that is, it solves
4

In the initial period, t = 0, all debt positions are assumed zero, and
there is some given distribution of wealth across entrepreneurs.

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

Kaas

max Et ∑ β s −t lnC si

s.t.

s ≥t

C si

+ K si

(

− Dsi = Asi −1 K si −1

1−α
i
s −1

) (L )

−w s −1Lis −1 − Rs −1Dsi −1, s ≥ t ,
α

i 1−α
s

( ) (L )

Rs Dsi ≤ λ Asi K si
(ii)

Ctw,

, s ≥ t.

Dtw

maximizes workers’ expected utility
subject to budget and zero debt constraints;
that is; it solves
max Et ∑ β s −t lnC sw

C sw −

s ≥t
w
Ds = w s

(iii) Markets for labor and capital clear:
1 i

∫0 Ltdi = 1,
i

As is shown in the appendix, all entrepreneurs’ capital investments are linear in their
equity. Hence, aggregation over entrepreneurs
with identical technologies is straightforward,
and I write

K tA =

Dsw ≤ 0, s ≥ t .

EQUILIBRIUM

s.t.

− Rs −1Dsw−1, s ≥ t ,

∫0 Dt di + Dt

put level is below the one in the first-best economy. A parameter restriction explained below
will ensure that such an equilibrium exists.

= 0.

The appendix characterizes the solutions to
the agents’ utility maximization problems. Particularly in the neighborhood of a steady-state
equilibrium with binding constraints, workers
do not save; hence, Dtw = 0 for all t ≥ 0. Further,
all entrepreneurs save a constant fraction β of
their wealth.
Before discussing an equilibrium with binding
debt constraints, it is instructive to see how the
economy acts when the collateral value λ is large
enough. In every period, then, all capital flows to
productive entrepreneurs who also hire the total
workforce. Because β is the entrepreneurs’ savings
rate and because total entrepreneur wealth is share
α of output, the aggregate capital stock evolves
according to Kt+1 = βα At Ktα. The model’s dynamics
thus resemble those in the standard real business
cycle model with logarithmic utility, Cobb-Douglas
production, and full depreciation.
The following section characterizes equilibrium when productive entrepreneurs are credit
constrained and unproductive entrepreneurs do
not lend all their capital but also produce. Hence,
production is inefficient and the steady-state outF 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

∫i: A = A Kt di and Kt = ∫i: A =B Kt di
i
t

i
t

to denote aggregate capital investment of productive and unproductive entrepreneurs. LtA and LtB
are similarly defined, and the absence of a superindex indicates an aggregate across all entrepreneurs. Let kts = Kts/Lts, s = A,B, denote capital
intensities for the two types of entrepreneurs.
Because labor moves freely between employers, the real wage is
α

( )

w t = At (1 − α ) ktA

( )

= B (1 − α ) ktB

which implies that
(1)

1α

ktB = ϕt ktA with ϕt ≡ ( At B )

> 1.

Because labor is perfectly mobile and capital is
not, unproductive entrepreneurs operate their
technology with a higher capital intensity than
productive entrepreneurs. The labor and capital
markets are in equilibrium if
(2)

B
LA
t + Lt = 1,

(3)

A
B B
LA
t kt + Lt kt = K t .

Let Dt denote total borrowing of productive entrepreneurs, which equals total lending of unproductive entrepreneurs because workers do not
participate in the credit market. Because productive entrepreneurs own π Kt units of the capital
stock, their capital input is the sum of equity and
debt:
(4)

A
LA
t kt = π K t + Dt .

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Because the credit constraint binds on each
productive entrepreneur, it also holds with
equality in the aggregate:
α

( )

Rt Dt = λ At ktA

(5)

LA
t .

Unproductive entrepreneurs are indifferent
between lending capital at gross return Rt or producing themselves, which leads to the following
arbitrage condition:
α −1

( )

Rt = α B ktB

(6)

From equations (1), (5), and (6), it follows that
borrowing is proportional to investment:
(7)

Dt =

λ At A
k
αB t

B 1−α
t

( ) (k )

LA
t =

λϕt A A
k L ;
α t t

Now equations (1), (2), (3), (4), and (7) can be
solved for the capital intensity of productive
entrepreneurs as follows:

ktA = C t Kt with Ct ≡

where Ct < 1 follows from condition (9) when ϕt
is close to its steady-state value, so that Ct is close
–
to its steady-state level, C < 1. This also implies
that ktB = ϕt Ct Kt > Kt . Employment is allocated
according to

LA
t =

(8)

To ensure that unproductive entrepreneurs
produce, their lending may not exceed their capital
holdings; that is, Dt must be strictly smaller than
共1 − π兲Kt . Together with equation (8), this necessitates λϕt < 共1 − π兲α . Because At fluctuates around
–
–
A , ϕt fluctuates around ϕ– ⬅ 共A /B兲1/α. To guarantee
a production-inefficient equilibrium in the neighborhood of the steady state, it must therefore be
assumed that
(9)

λϕ < (1 − π )α .

The explanation of this condition is as follows.
If the collateral share were too large, productive
agents would borrow all resources from their
unproductive counterparts and production would
be efficient. The same would apply if either ϕ or
π were too large: With a large productivity spread,
production becomes less attractive than lending
for unproductive agents, and a large share of borrowers raises credit above the funds supplied by
lenders. Similarly, a too-low capital share would
depress the interest rate, driving up the demand
for credit above lenders’ resources.
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α (Ct − π ) − Ct λϕt
απ
and LBt =
,
C t (α − λϕt )
Ct (α − λϕt )

so aggregate output is
α

( )

Yt = At ktA

and substitution into equation (4) yields

πλϕt
Dt =
Kt .
α − λϕt

α − λϕt − απ + απϕt
< 1,
ϕt (α − λϕt )

( )

LAt + B ktB

LBt = At Ctα K tα ,

with total factor productivity At Ctα < At. Because
workers earn share 1− α of output and do not save
and because all entrepreneurs save share β of
their wealth, the aggregate saving rate is αβ.
Hence, the capital stock evolves according to

K t +1 = αβ At Ctα K tα .
In the absence of technology shocks, the capital
stock converges to its steady-state level:

(

K = αβ AC α

)(

1 1−α )

–
Note that the steady-state interest rate is R =
–
1/共ϕ– C β 兲 < 1/β; hence, workers indeed do not
save when entrepreneurs are credit constrained.
The steady-state credit share in output is
calculated as
(10)

D αβ D αβπλϕ
=
=
.
α − λϕ
Y
K

An unproductive entrepreneur’s capital grows
–
at rate β R , whereas a productive entrepreneur’s
–
capital grows at β R̃ > β R , where

R = A k A

α −1 α

( )

(α − λ )

α − λϕ

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

Kaas

is the return on equity.5 Therefore, the SD of a
firm’s growth rate in steady state is
(11) σ = π (1 − π )β R − R =

(

)

α (ϕ − 1)
.
α − λϕ − απ + απϕ

The closed-form expressions (10) and (11)
capture the central message of this paper. On the
one hand, a rise in λ describes the effect of credit
market deepening in this model: When firms are
able to pledge more of their assets as collateral, the
share of credit in total output expands as shown
in expression (10). In tandem with the credit
expansion comes a higher firm volatility, as evidenced by equation (11). Relaxed credit limits spur
leverage, widening the gap between firm growth
–
rates, β 共R̃ – R 兲. On the other hand, a positive
technology shock triggers a rise in credit and in
firm volatility. The increase of A (relative to B)
raises ϕ, which unambiguously increases D/Y and
σ (which is again an implication of inequality (9)).
Intuitively, a positive productivity shock boosts
the value of collateral and thus the volume of
credit. Notably, credit rises more than one-for-one
with output, so the share of credit in output also
increases. Additionally, the positive technology
shock stimulates leverage, which enlarges the
spread between firm growth rates, increasing firm
volatility.

QUANTITATIVE ANALYSIS
This section explores the quantitative properties of the qualitative results obtained in the previous section: How well does this model explain
the observed dynamics of output, business credit,
and firm volatility? To calibrate the steady state,
I first choose the following five parameters: the
capital share, α ; the discount factor, β ; the collateral share, λ ; the mean spread between technologies, ϕ–; and the share of productive entrepreneurs,
–
π. The technology level A (and thus B) merely
shifts the level of aggregate output and capital
but has no impact on the capital-to-output ratio

or on any other relevant economic variables.
–
Therefore, I normalize A = 1.
Because there is no depreciation in this model,
I adjust the capital share to include the value of
the undepreciated capital stock. In the following,
the term “wealth” refers to GDP plus undepreciated capital, Y = GDP + 共1 − δ 兲K. With an annual
capital-to-GDP ratio of K/GDP = 2.7 and a 5 percent depreciation rate, the wealth-to-GDP ratio is
3.57. With capital income in GDP at one-third, it
follows that the capital share in wealth is α =
[0.33 + 共0.95 . 2.7兲]/3.57 ≈ 0.81. Further, in steady
state, αβ = K/Y = 2.7/3.57, which yields β = 0.938.
I choose the collateral share, λ , to match a share
of business credit in GDP of around 0.55, the
average over the period 1955-2000. As equation
(10) gives the credit-to-wealth ratio, the righthand side of this equation must be equalized to
0.55/3.57. Given the above choices for α and β ,
and for any choice of ϕ– and π, λ is chosen to satisfy
this equation. The remaining parameters π and ϕ–
are chosen to match the following two targets: a
–
3 percent real interest rate (R = 1.03) and a value
of firm volatility (measured by the SD of firm
growth) of around 0.14, the average of median firm
volatility during 1955-2000. This yields ϕ– = 1.13
and π = 0.08, which in turn implies that λ = 0.51.
At these parameter values, assumption (9) is satisfied by a wide enough margin. On the other hand,
if λ would exceed α 共1 − π 兲/ϕ– ≈ 0.66, assumption
(9) would be violated, in which case all capital
would be used at the technology frontier. Although
productive entrepreneurs may still be credit constrained,6 the model behaves like a standard real
business cycle model and the value of λ has no
effect on aggregate output.
In the stochastic model of this section, I do not
compute firm volatility defined over an infinite
time horizon—which, in steady state, gives rise
to equation (11) for every firm. Instead, I follow
the procedure of Comin and Philippon (2005) to
calculate rolling SDs of firm growth rates over
10-year time windows. Specifically, at each point
6

An entrepreneur with equity E borrows D = λϕ E/共α – λϕ 兲 and
invests K A = α E/共α – λϕ 兲 to earn profit π = A共kA 兲α –1K A – RD –
wK A/kA = α A共kA 兲α –1K A – λA共kA 兲α –1K A = R̃E.

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

Precisely, when λ < α 共1 − π 兲 ≈ 0.75, the steady-state interest rate
stays below the marginal product of capital of productive entrepreneurs. Although the economy would be production efficient, it is
consumption inefficient because idiosyncratic volatility still matters.
First-best allocations are attained only when λ > α 共1 − π 兲.

MARCH/APRIL

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Figure 3
Response to a 5 Percent Permanent Increase in the Collateral Share λ in Period t = 5
Output

Credit
0.040

0.608

0.039
0.038
0.037

0.604

0.036
0.035
0.600

0.034
0.033

0.596

0.032

Capital Misallocation

Volatility
0.158

0.715
0.154
0.705
0.150
0.695

0.146

0.685

0.142
0.138

in time t, I bootstrap the distribution of these SDs
from 10,000 firms drawing their growth rates from
共β Rt +τ , β R̃t +τ 兲τ5= –4. Then I use the median of this
distribution as the volatility measure.
Figure 3 shows the model’s response to a
permanent increase in the collateral share λ by
about 5 percent. Output increases on impact by
1.3 percent, converging to the new steady state,
which is more than 2 percent higher. Credit
increases by about 23 percent, and volatility
increases by 15 percent. The response of volatility
is sluggish; also, the response begins four periods
before the shock because volatility is constructed
using rolling windows that are four periods backward looking and five periods forward looking.
The largest adjustment of volatility occurs three
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0.675

periods after the shock. The lower-right graph
shows the “capital misallocation,” defined as the
share of capital used by unproductive entrepreneurs. Note that only 8 percent of entrepreneurs
have access to the technology frontier, but they
still use 28 percent of capital when λ =0.51. As λ
increases to 0.535, 32 percent of capital is used
at the technology frontier.
Whereas this experiment shows the effect of
a permanent rise in collateral value, it also is illuminating to investigate the impact of a temporary
decline in collateral value as a result of a severe
financial crisis. To this end, suppose that the
collateral share drops by 20 percent for a period
of three years before it returns to its original value.
I find that the impact of such a shock is a decline
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

Kaas

Figure 4
Response to a 1 Percent Permanent Increase in Productivity A in Period t = 5
Output

Credit
0.348

0.608

0.344
0.340

0.604
0.336
0.332

0.600

0.328
0.596

0.324

Capital Misallocation

Volatility
0.158

0.719
0.154
0.717
0.150
0.715

0.146

0.713

0.142
0.138

of GDP by 3 to 3.5 percent in the three years of
the crisis, the largest occurring in the third year.
Because the model has little amplification, output
returns to 0.5 percent below its steady-state level
in the first year after the crisis. During the three
crisis years, credit collapses dramatically: It falls
by more than 40 percent, which implies that only
20 percent of capital is used at the frontier technology. Note again that these macroeconomic
effects of a decline of λ are due to the misallocation of capital; they would disappear if λ exceeded
the threshold level implied by assumption (9).
Public policy may attempt to prevent the adverse
effects of the credit collapse to some extent, either
by restoring collateral value or by the injection of
liquidity—for example, by providing unsecured
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

0.711

credit lines. Without analyzing such policies formally, it is clear that they must be of a large scale,
given the substantial decline of the credit market.
Figure 4 shows the impulse response to a
permanent increase of productivity at the technology frontier by 1 percent. As the value of pledgeable assets rises, credit expands by 6 percent, and
the higher leverage leads to an increase of firm
volatility by about 15 percent. Output increases
by 2 percent, which comes about through two
effects: The first is higher productivity at the technology frontier; the second is that capital is now
more efficiently allocated as capital misallocation
falls from 0.72 to 0.711.
To explore the stochastic model with autocorrelated shocks,
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series properties of the mean and the SD of the
cross-sectional productivity distribution, which
is beyond the scope of this paper.

Table 2
Simulation Results with Stochastic
Productivity for 10,000 Model Periods
Output

Credit

Volatility

Standard deviation

0.022

0.061

0.130

Annual autocorrelation

0.534

0.542

0.643

0.980

0.177

Correlation matrix
Output
Credit

—

0.183

Volatility

—

NOTE: All variables are reported in logs as deviations from an
H-P trend with smoothing parameter 100.

ln At = ρ ln At – 1 + σεt , εt  1 ( 0,1),
I choose the two parameters ρ and σ to target the
SD and autocorrelation of the cyclical component of the model-generated GDP time series. As
explained previously, GDP in period t is the difference between Yt and the undepreciated capital
stock, which is 0.95 Kt = 0.95 αβYt −1. All time
series again are detrended with an H-P filter with
smoothing parameter 100, and the cyclical components are the log deviations from trend. The
result of this exercise is that ρ = 0.95 and σ = 0.014
match the first two moments in Table 1 reasonably well. These and all other model-generated
moments from a simulation with 105 periods are
listed in Table 2. Relative to the data, the amplification of credit is matched reasonably well,
whereas the SD of firm volatility is more than
twice as large as in the data. Although all contemporaneous correlations have the right sign,
the one between output and credit is larger than
in the data, whereas the cross-correlations with
volatility are too low.
Volatility is strongly amplified because productivity of the inferior technology stays constant.
–
If B were to fluctuate with A according to Bt /B =
– γ
共At /A 兲 , the SD of firm volatility would halve in
value for γ = 0.5, and it would (counterfactually)
become smaller than the SD of output for γ = 1.
Proper calibration of the stochastic dynamics of
both At and Bt would require matching the time104

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CONCLUSION
This paper has developed a tractable real
business cycle model with idiosyncratic productivity shocks and collateral-based credit constraints. Important features of the model are that
output is below the efficient level because not all
capital is used at the technological frontier and
that firm growth rates are volatile. The model
allows derivation of closed-form expressions for
the dynamics of output and capital, for the volume of credit, and the SD of firm growth rates. It
accounts qualitatively for the observed simultaneous long-term increase of the credit-to-output
ratio and of firm volatility. Quantitatively, the
model is able to generate the correct comovement
among output, credit, and firm volatility, although
firm volatility is too strongly amplified.

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APPENDIX
This appendix characterizes the solutions to the workers’ and entrepreneurs’ utility maximization
problems. Consider entrepreneurs first, and suppose that productive entrepreneurs are debt constrained,
which requires that
(A1)

(1−α ) α

Rt < α At1 α (1 − α ) w t 

for all t ≥ 0. All entrepreneurs hire labor to equalize marginal product to the wage; hence,
1α

Lit = K ti  Ati (1 − α ) w t 

Consider first productive entrepreneurs 共Ati = At 兲. They borrow up to their debt limit because the marginal product of capital exceeds the interest rate because of equation (A1); hence,

Dti =

λAt K ti
(1−α ) α
 At (1 − α ) w t 
.
Rt

Let Sti = Kti – Dti denote equity (savings) of the entrepreneur. Wealth at the end of period t is proportional
to the borrower’s capital investment and also proportional to equity:
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Kaas

i 1−α
t

( ) (L )

At Kti

− w t Lit − Rt Dti
(1−α ) α

= (α − λ ) At  At (1 − α ) w t 
K ti
Rt (α − λ )
Sti
=
(1−α ) α
−1 α
w t (1 − α )
−λ
Rt At
= R S i .
t

Here R̃t is the return on equity for an entrepreneur who is productive in period t. Consequently, the
i
i
budget constraint in period t +1 reads as C t+1
+ St+1
= R̃t Sti. Consider next an unproductive entrepreneur
i
in period t; that is, At = B. There are two possibilities. First, either the interest rate exceeds the marginal
product of capital of these entrepreneurs—in which case they do not produce and their return on
savings is simply Rt—or, as is assumed in the main text, the interest rate equals their marginal product
of capital,7 which requires that
(1−α ) α

Rt = α B 1 α (1 − α ) w t 

Again, Sti = Kti – Dti is savings and –Dti > 0 are financial assets of unproductive entrepreneur i. Wealth
at the end of period t is again proportional to savings:
α

i 1−α
t

( ) (L ) − w L − R D
= R (K − D ) = R S .

B K ti
t

i
t

i
t t

i
t

i 1−α
t

( ) (L )

= α B Kti

− Rt Dti

i
t

i
i
+ St+1
= RtiSti, where Rti = Rt
Therefore, any entrepreneur’s budget constraint in period t +1 reads as C t+1
if the entrepreneur is unproductive in period t and Rti = R̃t if the entrepreneur is productive in t. The
Euler equation for entrepreneur i’s utility maximization problem is then

1
1
= β Rti Et i .
i
Ct
C t +1
i
i
= 共1 – β 兲RtiSti and St+1
= β RtiSti are the only solution
Clearly, constant consumption/saving shares C t+1
to this equation that satisfy the transversality condition.
For workers, the Euler equations for their problem specified in (ii) of the equilibrium definition is

1
1
≥ β Rt E t w , Dtw ≤ 0,
w
Ct
Ct +1
with complementary slackness. In the main text, it is shown that Rt β < 1 holds in the neighborhood of
the steady state. Further, in the neighborhood of the steady state (i.e., small-enough productivity shocks),
– and E 共1/w 兲 ≈ 1/w
– hold, where w
– is the steady-state wage level. Therefore, it follows from the
wt ≈ w
t
t +1
complementary slackness condition that Dtw = 0 and Ctw = wt for all t ≥ 0.

The third case—that the interest rate is below the marginal product of capital of all entrepreneurs—is incompatible with equilibrium; then
all entrepreneurs would be lenders, whereas workers do not save (as shown below). Hence, the capital market cannot be in equilibrium.

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Full text of Review (Federal Reserve Bank of St. Louis) : March/April 2009, Vol. 91, No. 2

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