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Economic
Review
Federal Reserve Bank
of San Francisco
SUIIllller 1990
Number 3
Randall J. Pozdena
Do Interest Rates Still Affect Housing?
John P. Judd and
Bharat Trehan
What Does Unemployment Tell Us
About Future Inflation?
William C. Gruben,
Jonathan A. Neuberger
and Ronald H. Schmidt
Imperfect Information
and the Community Reinvestment Act
Table of Contents
Do Interest Rates Still Affect Housing? 999<,»999». 99»99e 9999„9999„9«,9909„9999 3
Randal! J. Pozdeea
What Does Unemployment Tell Us About Future Inflation? .. 09. 0„.». „ 0a.. 0. . . . 15
John Po Jadd and Bharat Tfrehan
Imperfect Information and the Community Reinvestment Act . . . . . . . . . . . . . . . . . 27
William C. Gruben, Jonathan A. Neuberger, and Ronald H. Schmidt
Federal Reserve Bank of San Francisco
1
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2
E conom ic R eview / Sum m er 1990
Do Interest Rates Still Affect Housing?
Randall 1. Pozdena
Vice President, Federal Reserve Bank of San Francisco.
The author wishes to thank Rachel Long and Deborah
Martin for their skilled and patient research assistance.
Editorial committee members were Carolyn SherwoodCall, Jonathan Neuberger, and Adrian Throop.
Activity in the housing market traditionally has been
very sensitive to changes in interest rates. This sensitivity
has had important implications bothfor participants in the
housing industry and monetary policy. Theory suggests,
however, that financial innovation and deregulation in
recent years may have altered the link between housing
and interest rates. In this paper, the theoretical linkages
are discussed and studied empirically for the periods
before and after 1983. A significant difference in the
strength and nature of the linkages is revealed.
Federal Reserve Bank of San Francisco
The housing market historically has displayed pronounced cycles in investment activity. In the last 30 years,
for example, the variation in the volume of new housing
starts has been Biz times greater than the variation in GNP
over the same period. 1 Economists and central bankers
long have been interested in understanding these fluctuations for several reasons. First, the cycles in housing
activity empirically have been useful leading indicators of
the general business cycle. In most recessions, residential
fixed investment appears to have led both declines in
business investment and GNP. 2 Its perceived value as a
leading indicator has made understanding housing cycles
important to economic forecasters.
Second, understanding investment behavior in the economy is important for understanding aggregate economic
volatility. Investment spending is the most volatile component of aggregate demand, and spending on new home and
apartment. construction (residential fixed investment) is
the most volatile component oftotal investment spending. 3
Thus, although residential investment is a smaller proportion of GNP than business fixed investment, its volatility
has a particularly important influence on the volatility in
national income over time.
Finally, because housing activity apparently has been
sensitive to changes in interest rates, the housing sector
historically has been an important channel through which
monetary policy has influenced economic activity. In fact,
there is some evidence that the economy may react more
quickly to shocks that make their way through the housing
component of aggregate demand than through the business
fixed investment component. 4 Thus, when monetary authorities have decided to slow the national economy to
bring inflation down, they typically have used monetary
restraint to raise interest rates, which tended to contract the
housing sector, and in this way, they were able to effect the
desired cooling of the overall economy. 5
A key linkage in this process, of course, has been the
relationship between housing activity and the level of
interest rates. Historically there does appear, indeed, to
have been a strong, inverse relationship between disturbances to interest rates and changes in housing starts. In
3
recent years, however, the relationship between housing
and disturbances in interest rates appears to have become
less regular. (See Chart 1.)
This article explores the changes in the relationship
between interest rates and housing, and tries to examine
the potential causes of this changed relationship. The
extensive financial innovation and reform that occurred in
banking and mortgage markets in the early 1980s changed
the way in which housing lenders raised their funds, and
changed the types of mortgage instruments that were made
available to homeowners. The empirical evidence pre
sented in this paper suggests that the relationship between
housing starts and interest rates changed significantly in
the period after deregulation.
The remainder of this paper is structured as follows.
In Section I, the various theoretical links between in
terest rates and housing are presented, and in Section II,
the influence of financial reform on these links is hy
pothesized. As we shall see, there are numerous potential
channels by which housing may have been affected by
financial innovation and regulatory reform. In Section III,
the relationships between interest rates and housing and
between funds flows and interest rates are examined em
pirically. The data reveal that, in fact, a significant change
in these relationships has occurred.
The article concludes (in Section IV) with a discussion
of the policy implications of these findings. These implica
tions relate both to the effects of the changes on monetary
policy transmission and the likely effects on housing
investment.
Chart 1
H ousing S tarts and Interest H ates
(000’s)
3 .0 0 0
Interest Rate
(Detrended) ^
2 .5 0 0
2.000
1 .50 0
1,000
1967
1973
1979
1985
5 00
L Interest Mates ami Housing: Ctiammds of Influence
Because of the intimacy of the relationship between
housing and national income, it is important to understand
the behavior of housing cycles, particularly as they relate
to movements in interest rates, since the level of interest
rates generally has been the control variable for monetary
policy. In this section, I discuss the various linkages
between housing investment demand and the interest rate
that likely operated during the period prior to the recent
financial reforms. To do so, I posit a simple model of
housing investment.
4
A User Cost Model off Housing Investment
In this model, housing investment is a function of
housing demand and a (lagged) supply process. Housing
demand, or the desired stock of housing (//*), is deter
mined by the periodic costs of owning a unit of housing,
that is, the user cost of housing, and demographic factors:
H *= H *(U ,W ,D )
(1)
where
Economic Review / Summer 1990
v =
w
D
user cost
= household wealth
= various demographic factors, such as population,
household formation behavior, etc.
The user cost of housing capital (or, sometimes more
ambiguously, the rental price) represents all current, outof-pocket costs and net foregone income that are associated
with owning a home. Amajor component ofthe user cost is
the interest cost associated with an investment in housing.
In addition, costs are affected by (economic) depreciation
of the structure, maintenance expenditures, and expected
changes in the market price of the housing unit. Tnis latter
component, of course, can reduce or increase user costs
depending on whether inflation or deflation in the market
price of the unit is expected. Tax policy also affects user
costs through the treatment of both interest expenses and
capital gains in the tax code.
The relationship between the user cost, V, of a unit of
housing, the real interest rate, r, and the other components
of the user cost can be stated more precisely as:
V
= P [(1- t) (i) - (1- c) (h)
+ d]
(2)
where
P
t
c
d
i
h
r
e
=
=
=
=
=
=
=
=
market price of the housing unit
marginal tax rate on normal income
marginal tax rate on capital gains
rate of economic depreciation ofthe unit per period
the nominal interest rate = (r + e)
expected house price inflation
real interest rate
rate of inflation expectations
or, equivalently, if expected house price inflation, h, equals
the expected rate of general price inflation, e,
U
= P[(l-t) (r+e) - (l-c) (e)
= P[(l-t)r - (t-c)e + d].
+ d]
(3)
From Equation (3), it is clear that user costs increase
with the after-tax real interest rate, (1- t)r, and the rate of
depreciation, d. User costs decline with increases in
inflation expectations, e, as long as the tax treatment of
capital gains is favored (that is, as long as c < t).
If the desired stock of housing equals the actual existing
stock at the prevailing user cost (that is, if H* = H), then
no investment in housing will occur. More likely, however,
the desired stock is less than or greater than the actual, and
investment (I) will occur as:
I
=
s(H* - H),
Federal Reserve Bank of San Francisco
(4)
where
s
an adjustment weight or function
and the actual housing stock will adjust toward the desired
stock at a speed that depends upon the nature of the supply
adjustment process, s. In markets in which the supply
process is elastic, the adjustment in the housing stock will
take place primarily through investment or disinvestment;
less elastic supply conditions will result primarily in price
adjustments to bring the desired and actual stocks into
balance.
The Effects of Interest Rate Changes
We can now discuss the ways that interest rates affect
housing investment. We begin first by discussing the
channels of influence revealed by the simple user cost
model described above. As we will see, however, in the
period prior to recent financial market reforms, institu'tional factors created additional "channels" of influence.
Channell: Simple
U~er
Cost Effects
In the simple user cost model presented above, the
interest rate is the key component of user costs, revealing a
direct channel of influence of interest rates on housing. The
precise effects of a change in interest rates depends,
however, on whether the changes in interest changes occur
because of changes in the underlying real rate or changes in
inflation expectations.
Specifically, the effect on housing is unambiguous when
a rise in the real interest rate occurs. As the rate, r, in
Equation (3) rises, the user cost rises and depresses stock
demand. This, in tum, results in depressed net new investment (manifested in reduced housing starts, for example),
and possibly depressed real housing prices, depending on
the elasticity of the housing supply response.
On the other hand, the effect of an increase in interest
rates associated solely with an increase in inflation expectations is less clear. Equation (3) implies that ifthe tax rates
on normal income and capital gains are the same, an equal
increase in general and housing price inflation expectations would have no effect on housing demand. If, however,
the capital gains tax rate is effectively lower than the
normal tax rate (the case in the U. S.6 ), then an increase in
inflation expectations can actually lower the user cost of
housing capital because the higher interest costs are more
than offset by the expected after-tax gain in the value of the
housing assets. If the user cost is lower, then the demand
for the housing stock increases, and with it, the price of
housing and/or investment.
5
In summary, the demand for housing is a function of
interest rates through their effect on the user cost of
housing. The link between housing and interest rates is a
negative one when the real interest rate changes and a
positive one when inflation expectations change (assuming
that capital gains receive preferential tax treatment, as is
the case currently).
Channel 2: Credit Scoring and Affordability
A second channel by which interest rates potentially
have influenced housing is the so-called affordability constraint, which arises out of the loan qualification process.
This channel was a particular source of concern in the midto late-1970s.Because state laws limit lenders' ability
to secure mortgage loans via the non-housing net worth
and/or future income of households, the current home
value and current income of the household play an important role in credit scoring or loan qualification standards.
The standards usually are stated as limits on the ratio of
mortgage payment size to household income, among other
variables. To the extent that these standards do not change
(because of constraints on mortgage design, or sluggish
adjustment of the standard due to regulation or convention)
they can become an additional source of influence for interest rate shocks. If interest rates rise abruptly, for example,
the effective supply of mortgage credit to borrowersunder a fixed set of standards-can change abruptly
as well.7
The affordability effect can be viewed in the context of
the user cost model presented above as an additional factor
that implicitly augments the interest rate component of
user costs. To the extent that affordability constraints are
binding, therefore, affordability constraints have the effect
of depressing housing demand and lowering either housing
investment activity or prices, or both.
To summarize, affordability considerations reinforce the
depressing effect of higher real interest rates on housing
investment and prices. Affordability considerations also
will offset, at least partially, any stimulative effects of
higher inflation expectations on housing investment. The
extent to which affordability considerations depress housing investment and prices will depend upon the availability
of ameliorative mortgage designs.
Channel 3: Interest Rates and Disintermediation
A third channel through which interest rates may have
influenced housing investment is the phenomenon known
as "disintermediation." Disintermediation refers to the
tendency of funds to flow away from conventional housing
6
lenders (such as thrifts and banks) when interest rates rise
suddenly. Disintermediation occurred historically because
the conventional mortgage intermediaries faced restrictions on their ability to pay deposit rates that were competitive with open-market investment opportunities. Faced
with higher-yield opportunities elsewhere, consumers are
said to have moved their deposits out of financial intermediaries, thereby reducing the funding available to conventional housing lenders. To the extent that other sources
of mortgage funding were imperfect substitutes for financial intermediaries, the result was an increase in the cost of
mortgage funds.
It is unlikely that the effects of disintermediation could
have persisted for long periods of time, however. After the
initial effects of an increase in interest rates, investment in
mortgage debt by other lenders should have provided an
offsetting supply of mortgage credit. For example, lending
by non-depository intermediaries (such as insurance companies), issuance and sale of mortgage-backed securities
by banks and thrifts, and financing by home sellers most
likely increased to offset the decline in traditional mortgage intermediation.
In addition, even if banks and thrifts have been restricted
in their ability to compete via higher deposit rates, in the
long run, they were able to attract funds by increasing the
services offered their depositors. This non-pecuniary form
of competition eventually would have drawn some funds
back to the affected banks and thrifts.
This argument suggests that disintermediation, to the
extent it was influential, had primarily transient effects
related to sudden changes in the level of interest rates and
not to the level itself. The extent to which disintermediation
affected the supply of mortgage funds depends on a
number of factors, including the breadth and sophistication of the mortgage-backed securities market and the
speed with which the deposit rate regulations could be
circumvented by banks and thrifts. Disintermediation is
cited as a significant contributor to short-term housing
cycles in the 1960s and 1970s not only because deposit
regulations were binding at times during this period, but
also because the mortgage-backed securities market was
not yet highly developed.
From a user-cost perspective, the disintermediation phenomenon would be manifested in price- or non-price
rationing ofmortgage funds that effectively would raise the
interest cost component of housing user costs. The expected effect of this channel of influence, therefore, would
be for higher interest rates (transiently, at least) to depress
housing demand, housing investment, and housing prices.
Economic Review / Summer 1990
II. The Effects of Financial Change
In the early 1980s, major changes in the financial system
secondary markets have strongly influenced the types of
mortgages that lenders have issued ever since the 1930s,
occurred that may have affected the functioning of these
various linkages. Legislative reforms and financial innovathis change in regulation means that prior to 1981 it is likely
tion affected mortgage instrumentation, mortgage interthat well over 95 percent of all residential mortgages
issued were conventional, fixed-rate, self-amortizing inmediaries, and household mortgage demand.
struments, although accurate statistics to support this
A Changing Marketplace
observation unfortunately are·not available.
In addition, the technology of the mortgage marketplace
There were both legislative and market changes in
was
changing during the period of the early 1980s. As a
the early 1980s that may have influenced the interest
result
of the continued development of the secondary
rate/housing link. Two key pieces of legislation affectmortgage
market, in particular, newly-originated morting mortgage markets that were enacted in the early
gages no longer needed to be funded within the bank or
1980s were particularly important. The first, the Deposithrift
portfolio. Instead, mortgages could be used to create
tory Institutions Deregulation and Monetary Control Act
mortgage-backed
securities which could then be sold to a
(DIDMCA), was passed in 1980. Title II of this Act
variety
of
institutional
and private investors. This process,
provided for interest rate ceilings on time and saving
known as securitization, was facilitated by govemmentdeposits at banks and thrifts to be phased out over a six year
backed mortgage agencies which provided credit enhanceperiod. Title III provided nationwide authorization of
ment in the form of principal and interest guarantees to
interest-bearing transactions accounts as of January 1,
investors
in the securities. Development of the secondary
1981. These accounts were negotiated order of withdrawal,
mortgage market was particularly rapid in the early 1980s.
or NOW, accounts with a regulated maximum rate.
The
volume of contracted mortgage commitments of the
Because depository institutions were believed to still be
Federal
Home Loan Mortgage Corporation (FHLMC), for
at a disadvantage vis avis the continued, intense competiexample,
grew from about $7 billion in 1981 to almost $33
tion from (non depository) money market mutual funds, a
billion in 1983.
second piece of legislation was passed in 1982. The GarnSt. Germain Depository Institutions Act of 1982 authorEffects on the Housing Market
ized (in its Title III) the money market deposit account
(MMDA). The MMDA required a minimum balance and
These legislative reforms and market developments had
had restricted transactions capability, but offered an unregthe effect of facilitating better matching of the needs of
ulated deposit rate. It was widely available by the end of
demanders and suppliers of mortgage credit over the
1982. On January 5, 1983, so-called Super Now accounts,
interest rate cycle, and as a result, affected most of the
with unregulated deposit rates, were permitted. Thus,
interest rate/housing channels discussed earlier. First, the
effective deregulation of retail transactions deposit rates
deregulation of deposit rates removed the primary cause of
occurred sometime between 1980 and 1983, although full
financial disintermediation. Deposit rate flexibility enaremoval of rate ceilings and account minimums on all
bled banks and thrifts to price their deposits more competitypes of retail accounts did not occur until 1986.
tively with non-deposit investments. Thus, when general
These Acts had features that also affected the mortgage
interest rates rise in the current regulatory environment,
markets. Title V ofDIDMCA, for example, authorized an
there need be no tendency for depositor funds to flow out of
override of state usury provisions on loans secured by liens
financial intermediaries into investments in the primary
on eligible residential real estate and made after March 31,
securities markets. 10 This presumably has had the effect of
1980. Title II of the Garn-St. Germain Act, also preempted
making mortgage supply less cyclically-sensitive.
state-imposed restrictions on the execution of the due-onSecond, the continued development of secondary mortsale clause in mortgage contracts. 8
gage markets also helped to make mortgage supply less
In addition to legislative changes, several important
cyclical. A mortgage lender having difficulty attracting
regulatory changes broadened the types of mortgage infunds can now originate a qualified mortgage, and sell it
struments that could be offered by banks and thrifts. First,
into a very liquid secondary market.
in 1981 the Federal Home Loan Bank Board permitted
Third, the availability of the adjustable rate mortgage
thrifts to offer adjustable rate mortgages on a wideafter April 1981 likely affected the channel relating to the
spread basis. 9 Since regulation and the conventions of the
affordability constraint. The ARM generally has initial
Federal Reserve Bank of San Francisco
7
payments that are lower than those of fixed rate mortgages,
making any given payment-to-income test less binding. In
addition, the flexibility of the instrument’s payment struc
ture (allowing such things as low buy-in or “teaser” rates,
negative amortization, and so on) can be used to tailor the
instrument to borrower needs over the business cycle.
This, too, should have the effect of better insulating
mortgage supply conditions from interest rate cycles.
The adjustable rate mortgage may be influential in
another way, as well. It can be shown that borrowers may
prefer ARMs over fixed rate instruments when they believe
that their own income is likely to fluctuate with future
interest rate movements. Elimination in 1981 of restric
tions on ARMs therefore likely made the mortgage market
more “complete” ; that is, it may now be better able to
efficiently match borrowers’ and lenders’ needs as they
vary over the business cycle, reducing the cyclical linkage
among interest rates, mortgage credit, and housing in
vestment.11
As Chart 2 illustrates, the share of ARMs in new
mortgages varies with the interest rate cycle. The chart
plots the deviations in interest rates from a simple linear
time trend, and the share of new mortgages issued as
adjustable rate instruments. When interest rates rise above
their trend, the ARM share also rises, consistent v/ith the
notion that the ARM instrument does, indeed, help to
“buffer” somewhat the effects of interest rate spikes.
%
C h a rt 2
A R M s and In te re s t R ates
In summary, there are a number of reasons to expect a
weakening of the linkage between interest rates and hous
ing investment activity at some point in the early 1980s.
The linkage likely has weakened along with the weakening
of the secondary channels of influence— affordability and
credit scoring constraints, financial disintermediation ef
fects, and other mortgage instrumentation constraints.
III. The Interest Rate Link: The Empirical Record
In this section, the available data are examined to
determine whether the changes in the early 1980s actually
diminished the strength of the relationship between inter
est rates and housing. The empirical approach employs
simple, time-series models estimated using data from the
period from 1960 to 1989. In this section, I test for changes
in the effect of interest rates on housing starts and for
changes in the effect of interest rates on fund flows to insti
tutional housing lenders (thrifts and banks). The model
presented above permits analysis of the effect on housing
of one-time disturbances or “ shocks” to interest rates and
comparison of the size of this effect in the pre- and post
deregulation periods. My interest in testing the effects on
housing starts follows directly from the hypothesis that
positive disturbances to interest rates typically have de
pressed housing demand and, thereby, housing invest
ment. My interest in studying the effect of interest rates on
8
fund flows is to determine whether mortgage-supply phe
nomena were, in fact, a channel of influence.
The Basic Model
The models estimated in this section use simple, vector
autoregression (VAR) systems. These VAR models em
ploy generalized time-series equations to identify dynamic
relationships among the variables of interest. Such models
are particularly appropriate in this application because
they permit exploration of shocks and other dynamic inter
actions among the variables. In addition, their atheoretical
structure is desirable in this context because we are inter
ested in changes in linkages across periods, rather than
testing a particular model specification.
The estimated VAR equation systems involve the cur
rent value of each variable of interest regressed on lagged
values of itself and every other variable in the system. In a
E conom ic R eview / Sum m er 1990
two variable (X and Y) system, for example, the estimated
equations would be:
n
n
Xt =
C1
+ i~laliXt-l + i~lbli Yt - 1 +
Yt =
C2
+ i~la2i X t - 1 + i~lb2i Yt - 1 + e 2t
n
e lt
(5)
n
(6)
where a, b, and C are estimated coefficients and n is the lag
length employed.
In the empirical work below, equations similar to those
in (5) and (6) are estimated using monthly data on interest
rates and various housing-related variables. A comparison
of the relationships estimated for the period prior to
deregulation with those for the period afterward can detect
changes in the interest rate/housing linkage. For the purposes of the analysis below, the pre-deregulation period is
assumed to span from 1960 to 1982, and the post-deregulation period extends from 1983 to 1989,12
The linkages between the interest rate variables on the
one hand, and housing starts or funds flows, on the other,
are explored in a series of simple VARs, rather than in one
large VAR system, which would take into account all the
interrelationships among these variables. As a practical
matter, the paucity of data in the post-deregulation period
constrains the size of the VARs that may be employed.
Thus, housing starts and funds flows are studied one at a
time, paired with the interest rate variable(s).13
Several statistical tests are presented to demonstrate the
changes in the interest rate/housing linkage. First, a Chow
test is used to compare the VAR systems for the prederegulation period with those estimated over the subsequent period to determine whether the estimated equations
differ significantly between the two estimation periods .14
Second, the share of the total observed variation in
housing starts "explained" by interest rate variation is
examined for the two periods. While such "variance decomposition" exercises cannot reveal changes in statistical
"causality" with great precision, changes in the contribution of interest rates to the variance in statts between the
two periods is suggestive of a change in the underlying
structure of the housing market. 15
Finally, impulse response functions are estimated and
presented for both the pre- and post-deregulation periods.
These relationships project the effects into future periods
of an hypothetical, one standard deviation shock in interest
rates. Unlike a simple comparison of coefficients, the
impulse response functions incorporate all direct and
feedback effects. They provide a graphical summary of
interest rate effects before and after deregulation.
Federal Reserve Bank of San Francisco
The Data
The models reported in this paper are all two- or threevariable VARs that use monthly data and a 12-period lag
structure on all variables. The interest rate (TBILLS)
variable employed is the short-term interest rate, measured
by the 90-day Treasury bill yield. In addition, in some of
the VARs reported below, the difference between the shortand long-term interest rate (LNGMSHRT) is also included as a proxy for the effects on the yield curve that
would accompany a change in long-term inflation expectations. As discussed in Section II, whether an increase in
interest rates is due to the real rate or inflation expectations
may have different effects. The long rate used is the AAA
corporate bond yield. 16
Housing starts data (rather than data on housing investment) are employed in this study to permit a monthly time
frame for analysis and to avoid the arbitrary valuation
assumptions that must be made to calculate housing investment flows. The housing starts variable (STARTS) is
seasonally adjusted. The aggregate of funds flows to thrifts
and commercial banks (FUNDTOT) is measured as net
changes in total share balances and total deposits.
Empirical Results
The results presented first shed light on the hypothesis
that changes in mortgage instrumentation and other factors
have relaxed the "affordability" constraint, thereby reducing the "direct" effect of interest rate cycles on housing starts.
Housing Starts and Interest Rates
Housing start relationships are studied using two simple
VAR systems, compared over two periods. In the first
VAR, the only interest rate variable is the Treasury
bill rate. In the second, both the Treasury bill rate and
the difference between the long rate and the short rate
are used.
Chow tests suggest that in both VARs, the results from
the two periods are significantly different at a confidence
level of over 90 percent. In addition, the pattern of coefficients (for brevity, not shown here) in both models suggests
that the relationship between interest rates and housing
starts has changed significantly since 1983.
Table 1 presents the variance decomposition obtained
from the two models for both time periods. As would be
expected if the interest rate channel had weakened in the
later period, the contribution of interest rates to the total
variation in housing starts has declined.
9
15
o
5
246
10
24
Economic .. ~.,,'~.., / Summer
Federal Reserve Bank of San Francisco
are consistent with the hypothesis that disintermediation
has declined in the sense that fund flows are less sensitive
to interest rate shocks in the post-82 period. This is
confirmed more formally by a Chow test which finds the
estimated relationship for the two periods to be significantly different at better than the 90 percent level.
The impulse response functions graphed in Chart 4
depict the effects of these changes. Prior to 1983, a one
standard deviation increase in the Treasury bill rate resulted in a decline in net fund flows to banks and thrifts that
began aboutthree months after the shock, and extended for
seven or eight months. In the period after 1982, an effect of
this scale appears to be absent.
In the third and fourth columns of Table 2, the variance
decomposition results from the VARs linking housing
starts to fund flows and interest rates are reported. In this
case, the impact on housing starts of a shock to interest
rates declines as expected. The impact of fund flows increases, suggesting that traditional intermediaries, if anything, playa more important role in the post-82 period.
However, this may simply be a result of higher variance in
fund flows after 1982. For this reason, it is important to
inspect the impulse response function. The change in the
coefficients estimated in the two periods is significant here
as well, as confirmed by a Chow test.
In panels A and B of Chart 5, the effects of positive
shocks to fund flows and Treasury bills are depicted for the
pre-1983 and post-1982 periods, respectively. As in the
simpler VARs discussed above, .a depressing effect ·on
housing starts of shocks to the Treasury bill rate is observed in the pre-1983 period. A one-standard deviation
shock results in a 70 thousand unit decline in housing
starts. In this model, the additional funds flow variable
also has an effect on starts; a shock to fund flows does
appear to stimulate starts, suggesting that during this
period housing was linked to the funding capability ofthe
traditional housing lenders.
Panel B of Chart 5 suggests that both effects are much
less pronounced in the post-1983 period. This finding is
consistent with the notion that not only is housing less
sensitive to interest rates directly, but also that the supply
of funds to housing from other sources (via the mortgage
securities market, for example) has increased.
Chart 5A
Impulse Response of Housing
Starts to Shocks in Treasury
Bills & Net Fund Flows
Chart 5B
Impulse Response of Housing
Starts to Shocks in Treasury
Bills & Net Fund Flows
(Pre 1983)
Housing Starts
(000'5)
30
20
10
30
20
10
O~----.......;;....-------
-10
-20
-30
-40
-50
-60
-70
-80
12
Shock in
Treasury Bills
-+--r-"T""T"""""""""""""""""''''''''''''''T""T''"T""T''"..-r""T'-r-T'''''T'""T''""T"'''1
2
4
6
8 10 12 14 16 18 20 22 24
Months Since Shock
(Post 1982)
Housing Starts
(000'5)
Shock in
Net Fund Flows
"
O-r-JC:"'"-r--T:'-r::!lL-'R:t7t;;;;;;;::;;;;""-e:;/~
-10
-20
~
-30
Shock in
Treasury Bills
-40
-50
-60
-70
-80 +-r-T"'T"""rT'""I...,.-,.""T""T'.,.-r-T"'T"""rT'""I.........,....,...."T""'T'O
2
4
6
8 10 12 14 16 18 20 22 24
Months Since Shock
Economic Review / Summer 1990
IV. Conclusions and Policy Implications
The potency of the interest rate/honsing linkage appears
to have changed significantly in the period following
extensive financial deregulation in the early 1980s. In this
paper, simple time series statistical models were used to
measure the changes in the strength of this linkage, and to
explore the possible causes of the changes.
The available data allow demonstration of a strong
association in time between the changes in this linkage and
changes in the regulation of mortgage lending institutions.
The data also allow testing ofthe independent causal linkage between housing starts and fund flows into traditional
mortgage lenders. The results, therefore, are consistent
with linkages associated with disintermediation processes,
affordability constraints, mortgage instrumentation restrictions, and growth of secondary markets.
Less important than the precise linkage, however, is the
fact that the strength of the link appears to have weakened
considerably in the post-82 period. This change has the
greatest import for investors, builders and owners of
housing in the United States, since it means that the
housing sector is less likely to be buffeted severely during
periods of economic policy manipulation.
Federal Reserve Bank of San Francisco
The housing market appears to be functioning at a level
of housing production of about 1.6 million units per year;
this puts the market in a steadier environment that is below
the peaks of earlier cycles, but is also well above the
troughs. In such an environment, participants in the housing market can direct their resources to responding to other
planning parameters, such as local economic and demographic conditions.
The weakening of the interest rate link to the housing
cycle also may be important from the standpoint of the
conduct of national economic policy. With a weaker link
between interest rates and housing, national output levels
become less sensitive to interest rate disturbances, at
least on a cyclical basis. This is a desirable prospect, of
course, to those economists who would prefer to see the
economy buffered against most macroeconomic disturbances, which they view as originating from the mismanagement of monetary aggregates and interest rates. If, on
the other hand, manipulation of aggregate real output
levels is a key element of effective national economic
policy, the increased insulation of the housing sector may
make such management more difficult.
13
NOTES
1. For example, the standard deviation of housing starts
from its trend from 1962 to the present has been one-fifth
of its mean level, versus only one-twentieth for real GNP.
2. R. E. Hall and J. B. Taylor, Macroeconomics (New York:
W. W. Norton & Company), 1986, p. 203.
3. The other two components are nonresidential fixed investment (purchases of new plant and equipment by businesses) and inventory investment (changes in stocks of
goods produced but not yet purchased).
4. See P. K. Clark, "Investment in the 1970s: Theory,
Performance and Prediction," Brookings Papers on Economic Activity, Washington, D.C., 1979, pp. 73-113.
5. The role of residential investment in business cycles
is discussed along these lines in Dornbusch and Fischer, Macroeconomics, New York: McGraw-Hili, 1987,
pp.317-326.
6. There are several aspects of U.S. tax policy that make
the capital gains tax rate less than the tax rate on "ordinary" income. First, the statutory rate on realized, longterm capital gains historically has been lower than the rate
on ordinary income. Thus, although the tax reforms of
1986 made these rates the same, over most of the period
covered in this paper, there was a significantly lower longterm capital gains rate. Second, capital gains generally
have been taxed in the U.S. only as they are realized
(rather than on an "accrual." basis). This ability to time and
delay capital gains tax burdens (but not ordinary income
tax burdens) is an additional source of preferential treatment of capital gains. Finally, housing capital gains have
enjoyed an additional advantage in that the tax burden
can be sheltered beyond the date of realization if the
proceeds from the sale of one primary residence are
rolled over into another home within a specified time
(presently, 2 years).
7. The size and significance of the disintermediation phenomenon was the subject of considerable discussion.
See, for example, F. Arcelus and A. Meltzer, "The Markets
for Housing and Housing Services," Journal of Money,
Credit and Banking (1973), pp. 78-99, and D. Jaffee and
K. Rosen, "Estimates of the Effectiveness of Stabilization
Policies for the Mortgage and Housing Markets," Journal
of Finance (1978), pp. 933-46.
8. The "due-on-sale" clause gives the lender the option
to terminate the loan secured by a home when the home
is sold.
9. The Federal Home Loan Bank Board in April 1981
allowed thrifts under its supervision to offer ARMs. This
power was extended to other institutions as the result of a
provision of the Garn-St. Germain Depository Institutions
Act, passed in 1982.
10. Whether the relationship between interest rates and
deposit flows disappears altogether, however, is less
certain. Depending upon the deposit pricing strategy of
banks and thrifts, and how rapidly and completely openmarket rates are matched, there still may be some reac-
14
tion of deposit flows to interest rate changes. See M. J.
Flannery, "Retail Bank Deposits as Quasi-Fixed Factors
of Production," American Economic Review, June 1982,
pp. 527-536, for a discussion of the process that might
cause banks to make less-than-complete adjustments to
open-market rates.
11. See, for example, H. R. Varian, "Divergence of Opinion in Complete Markets: A Note," Journal of Finance
(1985), pp. 309-317.
12. The selection of the date that constitutes the break
between the pre- and post-deregulation periods necessarily is somewhat arbitrary. Conceptually, it should be
possible to find a breakpoint that maximizes the differences between the pre- and post-period VAR estimates.
As a practical matter, the results are relatively insensitive
to a range of breakpoints a year or so on either side of the
chosen date.
13. The alternative of estimating the VARs with exogenous period dummy variables, and interactions of those
dummies with the interest rate variable(s), also was explored. This permits a much larger model, but that structure complicates testing of the significance of changes in
the model's coefficients. In addition, sample size limitations do not permit incorporating the full number of interaction terms in the larger model. Qualitatively, however,
the findings are the same in either modelling context.
The simpler methodology facilitates presentation of the
findings.
14. The Chow test employs residual sum of squares (RSS)
information from a regression spanning the entire data
sample (RSS1), the first subperiod (RSS2), and the second
subperiod (RSS3). An F test is then constructed as:
F = [(RSS1-RSS2-RSS3)/k] / [(RSS2+RSS3)/(N1 +N2-2k)]
with degrees of freedom = {k,N1 + N2 - 2k}whereN1 is
the sample size of the first subperiod, N2 is the sample
size of the second subperiod, and k is the number of
estimated parameters.
15. The use of the variance decomposition in this manner
has two potential problems. First, a problem in interpretation of the variance decomposition can occur if the variance of interest rates changes significantly between the
two periods. In such a case, the contribution of interest
rates to the variance of housing starts may appear to have
changed, butthe measured effect is caused simply by the
change in the variance of interest rates. Second, the
"ordering" of the variables (which affects the precedence
of shocks) can affect the results. In our case, however, we
are interested only in comparisons across periods (not the
levels of variance contributions per se). This is less affected by ordering considerations.
16. The mortgage rate is not used specifically because of
the potential problems interpreting this series, as mortgage instrumentation and other features of the mortgage
market change over the time frame of the analysis.
Economic Review / Summer 1990
What Does Unemployment Tell Us
About Future Inflation?
John P. Judd and Bharat Trehan
Vice President and Associate Director of Research, and
Senior Economist, Federal Reserve Bank of San Francisco. The authors would like to thank Jack H. Beebe and
the members of the editorial committee, Chan G. Huh,
Brian Motley, and Carl Walsh, for helpful comments.
The unemployment rate commonly is used as an indicator offuture inflation, with a low unemployment rate,for
example, assumed to imply higher inflation. This negative
correlation between current unemployment and future
inflation assumes that aggregate demandfactors primarily
are responsible for movements in these variables. However, as discussed in this paper, changes in aggregate
supply conditions, such as technology and labor supply,
also cause movements in unemployment and inflation.
Thesefactors lead to a positive relationship betweenfuture
unemployment and current inflation. Consequently, a
given rate of unemployment could be associated with
almost any rate of inflation, depending on the source of
the shock. In this paper, we attempt to disentangle demand and supply shocks, and analyze their influence on
unemployment and inflation in the post-World War II
U.S. economy.
Federal Reserve Bank of San Francisco
The level of the unemployment rate commonly is used as
an indicator of future inflation. When unemployment is
judged to be below (above) its long-run, or "natural" rate,
inflation is projected to rise (fall) in the future. This
negative correlation between unemployment and inflation
is fundamental to the Keynesian, expectations-augmented
Phillips curve, which expresses inflation as a function of
the unemployment rate relative to its long-run level, expected inflation, and changes in certain relative prices such
as those of oil and the dollar.
This interpretation of the relationship between unemployment and inflation focuses primarily on the effects of
demand factors, such as monetary and fiscal policies. In
recent years, however, macroeconomic research increasingly has incorporated such aggregate supply factors as
changes in technology and the supply of labor in models
of the behavior of the economy. "Real business cycle"
models, in particular, attempt systematically to incorporate the effects of supply factors. As discussed below, this
real business cycle approach l suggests a positive correlation between unemployment and inflation.
Conceptually, the correlations between inflation and
unemployment implied by both the Phillips-curve and real
business cycle models may coexist. The observed relationship in any given period thus depends on whether demand
or supply factors were the more influential during that
period. Accordingly, in this paper we estimate a model that
treats unemployment and inflation as endogenous variables
that respond to both aggregate demand and aggregate
supply factors.
We find that both kinds of shocks are important in
explaining movements in inflation and unemployment, and
that both produce the well-known clockwise temporal
loops observed when the actual inflation rate is plotted
against the actual unemployment rate. Thus these loops,
which commonly are presented in macroecono~ic textbooks as arising from demand shocks in the context of the
Phillips-curve relationship, also are consistent with supply
shocks playing an important role. In addition, we find that
while the effects of demand shocks on the unemployment
15
rate reverse themselves in one to two years, the effects of
supply shocks last much longer, and appear to have been
responsible for large, persistent movements in the unemployment rate. Finally, the fact that both demand and
supply shocks play significant roles diminishes the usefulness of the unemployment rate as an indicator of future
inflation, since policy makers must be able to identify the
source of a change in the unemployment rate before that
variable can be used to make a forecast of future inflation.
The remainder of the paper is organized as follows.
Section I spells out the kinds of correlations between
inflation and unemployment that may be expected on a
priori grounds in response to demand and supply shocks.
Section II discusses the econometric method we use to
estimate demand and supply shocks, and presents some
evidence on the characteristics of these shocks. In Section III we present empirical estimates of how inflation and
unemployment react to these shocks, and also the role
played by the shocks in generating the observed correlation
between inflation and unemployment over the past 25
years. Finally, Section IV discusses some policy implications.
I. Inflation-Unemployment Correlations in Theory
Keynesian theory stresses the role of aggregate demand
factors in causing business cycles, and focuses on capacity
bottlenecks caused by excess demand as the catalyst for
inflation. In this view, prices rise to relieve shortages of
labor and capital, and when monetary policy accommodates these price pressures, inflation results. The expectations-augmented Phillips curve embodies this hypothesis;
in this case, for a given level of expected inflation, the
difference between the prevailing rate of unemployment
and the bench-mark rate (the so-called "natural" rate)
provides a measure of aggregate-demand pressures on
inflation. 2
The inflation process can be illustrated with the following example. A positive demand shock induces firms to
hire more workers. As the unemployment rate falls below
the natural rate, labor markets become increasingly tight,
and firms push wages up as they bid for labor. Faced with
rising labor costs, firms raise product prices to maintain
their mark-up over cost. 3 Thus, a decrease in the unemployment rate is followed by higher inflation. Ultimately,
however, the unemployment rate returns to its original
(long-run) level. 4 When the unemployment rate is graphed
against the inflation rate over time, this sequence of events
leads to clockwise loops similar to those shown in Chart 1.
Current research on the Phillips curve relationship also
allows some kinds of relative prices to affect the inflation
rate, such as changes in the relative price of oil and the real
foreign-exchange value of the dollar. However, the Phillips
curve captures only the direct price effects of a change in
relative prices. By construction, it excludes possible effects on the unemployment rate of supply shocks associated with changes in relative prices. For example, a rise in
the price of oil not only can be expected to raise the
aggregate price index, but also may raise the unemployment rate. 5 Moreover, the Phillips curve omits by construc-
16
tion a broad range of other types of supply shocks, the most
significant of which may be changes in technology and in
the labor-leisure decisions of households. Attempts to
incorporate aggregate supply factors into the Phillips curve
model have been ad hoc, and do not represent a comprehensive and systematic treatment of this aspect of
economic behavior. 6
By contrast, real business cycle models attempt to
explain business cycles entirely on the basis of real developments, such as shocks to labor supply and technology. 7
These models de-emphasize demand factors in much the
same way that Keynesian models de-emphasize supply
factors. The real business cycle approach received considerable impetus from the observation that the levels
of many real variables, including real GNP, contain
permanent, random-walk-like components. 8 Given that
Chart 1
Inflation and Unemployment
1965·1989
Inflation
(Percent)
10
9
8
7
6
5
4
3
'69
'83
'86
2-t-----,r----r---.----r--.--...------,.---,
2
3
4
5
6
7
8
9
10
Unemployment
(Percent)
Economic Review / Summer 1990
economic theory suggests that demand factors cannot
permanently affect the levels of real variables, supply
shocks, which can have permanent effects, must playa role
in explaining fluctuations in real GNP.
The simple model of aggregate demand and supply
commonly used in macroeconomic textbooks can be used
to illustrate how a supply shock would affect the correlation between inflation and output. A positive technology
shock, for instance, leads to an increase in aggregate
supply (that is, a rightward shift in the aggregate supply
curve), implying an increase in equilibrium output and a
fall in the price level. In a dynamic context, a rise in
aggregate supply would translate into lower inflation and
higher real GNP growth.
Rigorously-derived real business cycle models that alIowa role for money also predict such a negative correlation between inflation and output. 9 Moreover, a positive
(negative) technology shock will have sustained negative (positive) effects on the unemployment rate in these
models as long as searching for labor is costly.lO For example, a higher marginal product of labor (positive technology shock) raises the marginal net benefit to searching
for labor, and thus lowers the unemployment rate.
Putting these elements together implies a positive rela-
tionship between inflation and the unemployment rate.
Whether the predicted co-movements are consistent with
the clockwise temporal loops shown in Chart I depends
upon the dynamic properties of the responses of inflation
and unemployment to supply shocks. For instance, clockwise loops likely would result if the inflation rate responded first to supply shocks, and the unemployment rate
responded afterwards. Theory does not predict the exact
dynamic pattern that will occur, so the question must be
resolved empirically.
Real business cycle and Phillips curve models both
imply extreme views of the source of observed co-movements in the inflation and unemployment rate data. Theory
does not rule out the possibility that both demand and
supply factors operate simultaneously, and combine to
produce the data we observe. The magnitude of each
factor's independent influence, then, is an empirical issue.
A balanced approach, in which neither demand nor supply
factors are excluded, appears to be the most fruitful
strategy for research. In the next section, we use an
approach that is theoretically agnostic about the relative
importance of demand and supply factors, and instead uses
the data to estimate the magnitudes of each of those
influences.
II. Estimates of Demand and Supply Shocks
In assessing the major forces determining the inflationunemployment relationship, economic time series that
directly measure aggregate demand and supply shocks
would be most helpful. However, this is not possible in
most cases.
Demand shocks can arise from a number of sources
including changes in monetary policy, fiscal policy, inflation expectations, and consumer tastes, among others.
Deregulation of the financial system has made the money
supply (historically a good source of information on demand shocks emanating from Federal Reserve policy) a
poor measure of these shocks. ll Interest rates might provide an alternative measure since they are influenced by
Federal Reserve actions. But because they also are influenced by other factors such as fiscal policy, inflation
expectations, and aggregate supply, they are likely to be
poor measures of monetary policy shocks as well.
With respect to variables representing fiscal policy,
there are major problems in the national income accounts
that make it difficult to obtain conceptually appropriate
measures of government activity, including the inability to
Federal Reserve Bank of San Francisco
distinguish between capital and current expenditures and
the exclusion of the "revenues" generated by the inflation
"tax",1 2 Other factors that can induce demand shockssuch as changes in the public's expectations of inflation
or consumer confidence-also are difficult to measure
directly.
Similar problems exist in attempting to measure supply
shocks. These shocks originate from a variety of sources,
including the development of new products (for example,
computers), new ways to combine labor and capital more
efficiently, changes in individuals' willingness to work,
changes in tax laws, as well as sudden changes in the
relative prices of important inputs to production such as
oil. While certain taxes and relative prices can be measured directly, the other potential sources of supply shocks
do not have direct empirical counterparts.J3
Econometric Method
An alternative approach to direct measurement is to
estimate econometrically the demand and supply shocks
that have influenced the aggregate macroeconomic time
17
nterest Rates
5
20
tl'pf1p""i'l1
Reserve Bank of San Francisco
Table 1 presents the associated variance decomposi
tions, which show the relative importance of demand and
supply shocks in explaining the unpredictable movements
in real GNP and the nominal interest rate. Demand shocks
account for slightly more than one half of the unpredictable
variation in output one quarter ahead, and about one third
of that variation four quarters ahead. The remainder of the
variation is accounted for by supply shocks. Thus, both
demand and supply shocks play important roles in causing
short-run fluctuations in real output. However, by con
struction, the long-run movements in the level of real GNP
are the result only of supply shocks.
With respect to movements in interest rates, in contrast,
demand shocks are much more important, accounting for
about three fourths of the unpredictable interest rate varia
tion one quarter ahead, and nearly all the variation at
horizons of one year and beyond.
Chart 3 shows the estimated quarter-by-quarter effects
of demand and supply shocks on real GNP over the period
from 1960:Q1 to 1989.Q3.15 These effects seem broadly
consistent with the conventional interpretation of the ma
jor events in the period covered. As shown in the top panel,
supply shocks were responsible for much of the above
average economic growth during the 1960s, coinciding
with the well-known productivity surge in that period.
They also played a role in the 1973-75 and 1980—82
recessions, and may therefore be associated with the large
oil shocks in those periods. Consistent with the recent
history of monetary policy, the estimates shown in the
bottom panel suggest that contractionary aggregate de
mand shocks played substantial roles in both the 1973-75
and the 1980-82 recessions, and that an expansionary
demand shock was important in the late 1970s, when
inflation accelerated.
C ha rt 3
H is to ric a l D e c o m p o s itio n
o f Real QMP G row th
A) Effect of Supply Shocks
(Percent)
B) Effect of Demand Shocks
(Percent)
III. Explaining Unemployment and Inflation
Having obtained measures of the supply and demand
shocks during the 1960-89 period, our objective is to
assess the relative importance of each of these shocks in
explaining movements in inflation and unemployment. For
this purpose, we estimated separate equations for unem
ployment and inflation as functions of current and lagged
values of the estimated demand and supply shocks.
The equations are:
16
=
.
8
| 0a i St~ i +
8
7
'tn
H'
om
II
s
4
20
(1)
M r-/ +
+
1
(2 )
where u r and ut denote the rates of inflation and unemploy
ment, respectively, and d t and st are the (zero mean)
demand and supply shocks. The inflation equation con
tains 16 lags of the supply shock variable and eight lags of
the demand shock variable. These lag lengths were se
lected by doing F-tests on the relevant variables, four lags
at a time. rht denotes the average rate of M2 growth over the
prior five years. It is included to allow the trend of inflation
to move over the sample.16 The demand and supply shock
terms, then, explain deviations of inflation from the trend
rate. Inclusion of m reduces the available sample size
(compared with the sample used for the VAR above)
because data for M2 begin only in 1959. Taking into
E conom ic R eview / Sum m er 1990
consideration the lags in the model, 1965 is the earliest
date at which we could begin the sample for the inflation
equation.
The unemployment equation contains four lags of the
supply shock, eight of the demand shock, and a lagged
dependent variable. Without the latter variable, the signifi
cant lags on supply shocks in the unemployment equation
were extremely long— at least 50 quarters. Thus, the
lagged dependent variable was used to save degrees of
freedom.17
In addition, we estimated
8
m
<
=
4
3
+ ,.|04>,4-i + ,5,P /»!,_,■
(3)
where m t denotes the rate of growth of M2. The M2
equation is required for dynamic simulations of the infla
tion equation, since the latter contains the 5-year average
growth rate of M2 as a regressor. Equation 3 also contains
constant dummy variables to eliminate the following ob
servations from our sample: 1980:Q2 and 1980:Q3, be
cause of the imposition and removal, respectively, of the
Carter credit control program; and 1982:Q4 and 1983:Q1,
because of the introduction of MMDAs. Finally, we also
allowed the intercept term of the equation to change
following the introduction of MMDAs.
Table 2 presents summary statistics on these equations.
Both the estimated demand and supply shocks are highly
significant in all three equations. The errors from the
ordinary-least-squares estimates of the inflation equation
show evidence of first-order serial correlation, and we
applied a correction for this. The first-order autocorrelation
coefficient (AR(1)) estimate of 0.41 in the inflation equa
tion compares to the AR(1) estimate of 0.75 in the raw
inflation data, so our explanatory variables account for
some, but not all, of the serial correlation in inflation.
To provide a better idea of the fit of these specifications,
Chart 4 shows the actual values of inflation and the
unemployment rate as well as dynamic simulations from
our estimated equations. The equations do a good job
of capturing the major swings in unemployment and
inflation.
Chart 4
Dynamic Simulations
A) Inflation
(Percent)
''TT;T-;vy:T
Summary S
From Regn
Dependent Variable
Statistics
Unemployment
Rate
Marginal Significance
Levels of:
T A T •. 'V
.01
F,
Inflation
M2 Growth
.0 1
.0 1
B) Unemployment Rate
f2
.0 1
.01
.01
«.
—
.01
—
Adj. R2
SEE
AR(1)
(t-statistic)
.99
.18
* *
—
—
.67
.40
.41
(3.8)
(Percent)
*, S||r \
.79
.40
—
—
F! is F statistic for null hypothesis that supply shocks have no im
pact on relevant variable.
F2 is F statistic for null hypothesis that demand shocks have no
impact on relevant variable.
tj is t-statistic for null hypothesis that M2 growth has no impact
on inflation.
Federal R eserve Bank o f San Francisco
21
Chart 5
Dynamic Responses
B) To a Demand Shock
A) To a Supply Shock
(Percent)
(Percent)
Chart 5 presents the estimated responses of inflation and
unemployment to (one-standard-deviation) positive de
mand and supply shocks.18 These dynamic responses have
the signs predicted by theory. A positive demand shock re
duces unemployment and raises inflation, while a positive
supply shock reduces both unemployment and inflation.
Clockwise Loops
Chart 6 plots these dynamic responses in inflationunemployment space. For illustrative purposes, we assume
that the unemployment rate initially is 5.5 percent and the
rate of inflation is 5.0 percent. The left panel shows the
effects of a positive supply shock. The immediate response
is a reduction in the inflation rate, after which unemploy
ment gradually declines. The inflation rate moves back to
its original level in two to four years after the shock, but
the unemployment rate takes much longer to get back to
its original level. Thus, even supply shocks lead to clock
wise loops.
As shown in the right-hand panel, a demand shock
initially has a larger impact on the unemployment rate.
Unemployment reaches its minimum in less than a year,
but by the end of the second year has risen back to its
original level. The inflation rate rises as the unemployment
Chart 6
Dynami© Effects ©f Steaks ®n
Unemployment and Inflation
Inflation
(Percent)
22
Inflation
(Percent)
B) Demand Shock
E conom ic R eview / Sum m er 1990
rate declines, and remains high for nearly a year after the
unemployment rate has returned to its original level. Thus,
demand shocks produce the temporary trade-off predicted
by the Phillips curve. Note that the effects of supply shocks
evolve more slowly and take longer to be completed than
those generated by demand shocks.
The loops in Chart 6 demonstrate why it is not possible
to develop simple rules of thumb to judge future inflation
based upon current observations of the level of unemployment. Any given rate of unemployment could be followed
by almost any rate of inflation depending on the source of
the shock. Further, since the loops ultimately go back to
their starting points, a particular rate of unemployment
will be associated with different rates of inflation at
different points in time.
For similar reasons, changes in the unemployment rate
are unlikely to provide accurate information about future
changes in inflation. Consider, for instance, the left-hand
panel of Chart 6. A falling rate of unemployment may be
followed either by rising inflation (as inflation moves back
to its original level between the second and fourth years
after the shock), or by no,change in inflation (as unemployment gradually adjusts back to its original level after the
fourth year). Thus, Chart 6 provides an illustration of the
general principle that using one endogenous variable to
draw inferences about another endogenous variable can be
a tricky enterprise.
Simulating Inflation-Unemployment Loops
Chart 7 presents dynamic simulations of unemployment
and inflation over the 1965-89 period, using the historical
values of the estimated demand and supply shocks. The
first panel shows the effects of both kinds of shocks over
this period. The shape of our simulated loops is quite close
to the actual data shown in Chart 1.
The second panel shows how unemployment and inflation would have evolved if there had been no supply shocks
over this period. As expected, we obtain negatively sloped
loops, with the number of loops attesting to the relatively
short period over which the effects of a demand shock
dissipate.
The third panel shows what would have happened if
there had been no demand shocks over this period. The
plot shows little tendency to loop around and come back to
its original position, reflecting the long-lived effects of
supply shocks.
Supply shocks have moved the unemployment rate and
inflation over a much wider range than have demand
shocks. Thus, they account for more long-run volatility in
Inflation
(Percent)
A) Demand and Supply Shocks
10
9
8
7
6
5
4
3
'74
'83
24----,.-----y--~---.----.---r-----..--,
2
3
4
5
6
7
8
9
10
Unemployment
(Percent)
Inflation
(Percent)
10
9
8
7
6
5
4
B) Demand Shocks Only
'79
~
'71
3
2-+--r----,..--r------,.-----y--~----,.-.....,
2
345
6
7
Unemployment
(Percent)
8
9
10
C) Supply Shocks Only
'83
2
Federal Reserve Bank of San Francisco
Chart 7
Dynamic Simulations
9
10
23
these variables. Supply shocks are estimated to have
caused inflation and unemployment to move within ranges
that are 5.3 and 5.1 percentage points wide, respectively.
The comparable figures for demand shocks are 4.3 and 2.2
percentage points.
In Section II, we discussed how our decomposition of
movements in output into those caused by demand and
supply shocks compared with conventional wisdom regarding the events over our sample period. Using Chart 7,
we can now repeat this exercise in terms of combinations
of inflation and unemployment. The largest movements
that are estimated to have been caused by demand shocks
occurred in 1977-79, and in 1980-83. In the earlier period,
widely recognized as one of excessively expansionary
monetary policy, the estimates suggest that demand shocks
raised inflation by about 3Yz percentage points and lowered
the unemployment rate by about one percentage point. In
the latter period, the Federal Reserve adopted reservesoriented monetary policy procedures to reduce inflation.
We estimate that this negative demand shock reduced
inflation by about 4Y2 percentage points and raised the
unemployment rate by nearly two percentage points in
this period.
The largest supply shocks occurred in 1973-74, 197980, and 1983-86. The positive shock in the 1960s, presumably related to the large persistent productivity surge in
those years, is mostly excluded by our 1965-89 sample
period. 19 The 1973-75 and 1979-81 periods are associated
with well known oil price shocks. According to our
estimates, negative supply shocks raised inflation by about
·1Y2 and two percentage points in these two periods, respectively, and raised unemployment by 2Y2 and lY4 percentage points.
A large positive supply shock shows up in 1983-86.
Any hypothesis concerning the source of this shock would
be especially speculative. However, the period roughly
corresponds with the cut in marginal tax rates in the early
1980s, which some have suggested was a supply-side
source of rapid investment and increased work effort. In
addition, rapid technological change in personal computing appears to have begun in the early 1980s, and this factor
could be related to the estimated positive supply shock.
IV. Policy Issues
A major long-run goal of U.S. monetary policy is to
eliminate inflation. 20 One way to attempt to meet this goal
is to use (formal or informal) forecasts of future inflation to
judge the appropriateness of the current stance of monetary
policy. For example, given the current stance of policy, a
forecast of inflation for any period in the future that exceeds
the inflation goal would indicate that policy should be
tightened. Our results suggest that the Phillips curve
model of inflation could provide misleading signals under
this forecast-oriented approach to policy.
The empirical importance of supply shocks as well as
the long duration of their effects means that the unemployment rate can remain above or below its steady state value
for long periods. 21 Consequently, to determine what a
given rate of unemployment implies for future inflation,
it is necessary first to determine the factors that are
responsible for the prevailing unemployment rate. When
analyzed in terms of the Phillips curve, supply-induced
movements in the unemployment rate can lead to inappropriate policy actions. For example, a relatively low
level of unemployment resulting from supply shocks offers
little or no reason for concern about the potential for an
acceleration of inflation. However, when viewed through
the Phillips curve, such a change in the unemployment rate
would suggest that policy should be tightened.
24
The preceding discussion is not meant to suggest that the
Phillips curve model is inferior to other models of inflation
that are currently available. On the contrary, the Phillips
curve models appear to be at least as accurate at forecasting
as the other available demand-side models. Stockton and
Struckmeyer (1989), for example, support this conclusion
with tests of forecasts from Phillips curve, monetarist, and
monetary-misperceptions models. We have focused on the
Phillips curve in this paper simply because it is incorporated into the large Keynesian-style "structural" models
that are most widely used in macroeconomic forecasting.
Our major point is that there is good evidence that
aggregate supply factors, in addition to aggregate demand
factors, affect inflation dynamics in complex ways. Models
that ignore part or all of these supply factors run the risk of
making large errors in episodes when these supply shocks
are important.
One response to this potential problem is to use an
unrestricted vector autoregression for forecasting. VARs
can capture both demand and supply factors, at least
insofar as the average behavior of these shocks over the
estimation period applies to the forecast period. Thus, this
approach may provide more accurate forecasts on average;
however, it appears susceptible to large errors in episodes
involving large, atypical shocks.
Economic Review / Summer 1990
Another response would be to develop a forecasting
model along the lines of the approach used in this paper.
Whether this approach would be fruitful is uncertain, since
we are not aware that any such model has been built. In any
event, given our finding that both demand and supply
factors have been important in determining short- to intermediate-run macroeconomic developments over the past
three decades, it would seem worthwhile to explore ways
to disentangle the effects of these shocks in the context of
forecasting future economic developments.
NOTES
1. Plosser (1989) questions the usefulness of distinguishing between demand and supply shocks, as well as the
identification of real business cycle models with supply
factors. Instead, he prefers to make a distinction between
real and nominal factors.
2. For a discussion of the traditional Phillips curve, see
Gordon (1982). Ball, Mankiw and Romer (1988) discuss
the "new" Keynesian approach. Finally, for alternative
theories concerning unemployment and inflation, see
Lucas (1973) and Taylor (1980).
3. See Brayton and Mauskopf (1985) and Gordon (1982).
4. For analysis of the theoretical basis for the natural rate
of unemployment, seePhelps (1970).
5. Within the context of a full Keynesian-style model, an oil
shock can have an effect on the unemployment rate. At
given nominal interest rates, for example, an adverse oil
price shock could reduce real GNP by lowering business
fixed investment and thus raise unemployment (via the IS
and Okun's law relationships.) Note, however, that the
increase in unemployment would feed into the Phillips
curve like a demand shock: i.e., it would reduce inflation,
tending to offset the direct upward pressure on prices
from the oil shock.
6, For example, the inclusion of the relative price of oil
occurred when the Phillips curve relationship became
unstable in the mid 1970s following the oil embargo.
7. For discussions of real business cycle models and
further references, see Plosser (1989) and Mankiw (1989).
8. Nelson and Plosser (1982).
9. See Huh (1990) and Cooley and Hansen (1989).
10. For unemployment to exist in equilibrium business
cycle models, we need to allow for heterogeneity of firms
or workers, necessitating job search. For a discussion,
see Blanchard and Fischer (1989), pp. 346-350.
11. For a discussion of financial deregulation and its
adverse effects on the stability of the monetary aggregates, see Simpson (1984). These developments do not
imply, however, that there necessarily has been a change
in the long-run relationship between M2 and inflation.
Federal Reserve Bank of San Francisco
12. For discussion of issues in measuring the budget
deficit and further references, see Gramlich (1989), Barro
(1989), Bernheim (1989), and Eisner (1989).
13. Boschen and Mills (1988) have attempted to relate
real shocks to various economic time series.
14. In an earlier paper, Judd and Trehan (1989), we used
a five variable VAR to analyze unemployment rate dynamics. Using real GNP, the unemployment rate, a shortterm nominal interest rate, the ratio of U.S. real exports to
imports, and working-age U.S. population, we allowed for
four different kinds of shocks-domestic technology, labor supply, (two different) demand shocks, and a foreign
shock. That paper focused on relationships between
these shocks and the unemployment rate, and did not
explicitly analyze the inflation rate within the model.
15. These effects are obtained by multiplying the coefficients in the impulse response functions by the appropriate historical shocks as measured by the model. We use a
forecast horizon of 40 quarters for this purpose, which
moves the starting date of our sample to 1960:01.
16. As noted earlier, financial deregulation has made the
relationship between M2 and inflation more susceptible
to short-run disturbances. However, such disturbances
can be expected to be internalized within the five-yearaverage observations used in equation (1).
17. Inclusion of the lagged dependent variable does not
lead to demand shocks having long-lived effects on the
unemployment rate because the later lags on the demand
shocks have negative coefficients.
18. The estimated impulse response functions for inflation
are noticeably jagged. Consequently, for the purposes of
Charts 5 and 6, but not elsewhere in the paper, both the
inflation and unemployment equations were re-estimated
after imposing smoothness priors. For a discussion of
these priors see Shiller (1973).
19. As discussed above, the inclusion of M2 forces us to
shorten our sample period.
20. See Greenspan (1990) and Parry (1990).
21. When interpreted within the context of a Phillips curve
equation, these supply-induced movements in the unemployment rate could appear to be changes in the socalled natural rate of unemployment.
25
REFERENCES
Ball, Lawrence, N. Gregory Mankiw, and David Romer.
"The New Keynesian Economics and the OutputInflation Trade-off," Brookings Papers on Economic
Activity, 1988.1.
Barro, Robert J. "The Ricardian Approach to Budget
Deficits," The Journal of Economic Perspectives, Volume 3, Number 2, pp. 37-54.
Bernheim, Douglas B. "A Neoclassical Perspective on
Budget Deficits," The Journal of Economic Perspectives, Volume 3, Number 2, pp. 55-72.
Blanchard, Olivier J. and Stanley Fischer. Lectures
on Macroeconomics. Cambridge, Mass.: The MIT
Press. 1989.
Blanchard, Olivier J. and Stanley Fischer. Lectures on
Macroeconomics. Cambridge, Mass.: The MIT Press.
1989, pp. 520-23.
Boschen, John F. and Leonard O. Mills.· "Tests of the
Relation Between Money and Output in the Real Business Cycle Model," Journal of Monetary Economics,
22,1988.
Brayton, Flint and Eileen Mauskopf. "The Federal Reserve
Board MPS Quarterly Econometric Model of the U.S.
Economy," Economic Modeling, July 1985.
Cooley, T.F., and GD. Hansen. "The Inflation Tax in a Real
Business Cycle Model," American Economic Review,
Summer 1989, pp. 733-48.
Eisner, Robert. "Budget Deficits: Rhetoric and Reality,"
The Journal of Economic Perspectives, Volume 3,
Number 2, pp.73-93.
Gordon, Robert J. "Inflation, Flexible Exchange Rates,
and the Natural Rate of Unemployment," in M. Bailey,
ed., Workers, Jobs and Inflation. Washington, D.C.:
The Brookings Institution, 1982, pp. 89-158.
Gramlich, Edward M. "Budget Deficits and National Saving: Are Politicians Exogenous?," The Journal of Economic Perspectives, Volume 3, Number 2, pp. 23-35.
Greenspan, Alan. Testimony Before the Subcommittee
on Domestic Monetary Policy, House Committee on
Banking, Finance and Urban Affairs, U.S. House of
Representatives, February 20, 1990.
Huh, Chan G. "Output, Money and Price Correlations in a
Real Business Cycle Model," Working Paper 90-02,
Federal Reserve Bank of San Francisco, May 1990.
26
Judd, John P. and Bharat Trehan. "Unemployment Rate
Dynamics: Aggregate-Demand and -Supply Interactions," Economic Review, Federal Reserve Bank of
San Francisco, Fall 1989, pp. 20-38.
Kydland, F.E. and E.C. Prescott. "Time to Build and
Aggregate Fluctuations," Econometrica, 50, 1982,
pp. 1345-1370.
Lucas, Robert E. "Some International Evidence on Output-Inflation Tradeoffs," American Economic Review,
63,1973.
Mankiw, N. Gregory. "Real Business Cycles: A New
Keynesian Perspective," The Journal of Economic
Perspectives, Volume 3, Number 3, Spring 1989,
pp.79-90.
Motley, Brian. "Has There Been a Change in the Natural
Rate of Unemployment?," Economic Review, Federal
Reserve Bankof San Francisco, Winter 1990, pp. 3-16.
Nelson, Charles R. and Charles I. Plosser. "Trends and
Random Walks in Macroeconomic Time Series: Some
Evidence and Implications," Journal of Monetary Economics, 10, 1982.
Parry, Robert 1. "Price Level Stability," FRBSF Weekly
Letter, Federal Reserve Bank of San Francisco, March
2,1990.
Phelps, Edmund S. Microeconomic Foundations of Employment and Inflation. New York: w.w. Norton, 1970.
Plosser, Charles I. "Understanding Real Business Cycles," The Journal of Economic Perspectives, Volume
3,1989, Number 3, pp. 51-77.
Shapiro, Matthew D. and Mark W. Watson. "Sources of
Business Cycle Fluctuations," NBER Macroeconomics Annual 1988, Cambridge, Mass.: M.IT Press.
Shiller, Robert J. "A Distributed. Lag Estimator Derived from Smoothness Priors," Econometrica, 1973,
pp. 775-788.
Simpson, Thomas D. "Changes in the Financial System:
Implications for Monetary Policy," Brookings Papers
on Economic Activity, 1, 1984.
Stockton, David J. and Charles S. Struckmeyer. "Tests of
the Specification and Predictive Accuracy of Nonnested Models of Inflation," The Review of Economics
and Statistics, 1989, pp. 275-283.
Taylor, John B. "Aggregate Dynamics and Staggered
Contracts," Journal of Political Economy, February
1980, pp. 1-23.
Economic Review / Summer 1990
Imperfect Information
and the Community Reinvestment Act
William C. Gruben, Jonathan A.
Neuberger, and Ronald H. Schmidt
The authors are, respectively, Senior Economist and
Policy Advisor, Federal Reserve Bank of Dallas; Economist, Federal Reserve Bank of San Francisco; and Senior
Economist, Federal Reserve Bank of San Francisco. The
editorial committee members were Reuven Glick, Chan
Huh, and Elizabeth Laderman.
The Community Reinvestment Act has been used as a
vehicle to increase lending to low-income neighborhoods.
In this article, a conceptual framework is developed to
evaluate the effect of CRA on bank portfolios. Results
suggest that CRA will boost lending to low-income neighborhoods, with the cost ofachieving the social goal ofmore
even lending borne by bank customers and owners. The
increase in lending to low-income neighborhoods is reinforced by an information effect: as banks expend greater
effort searching for high-quality, low-income borrowers,
this increased knowledge about the area reduces risks in
that area.
Federal Reserve Bank of San Francisco
Over the last two decades, community groups and
Congress have expressed concern about "inadequate"
lending to disadvantaged neighborhoods. These groups
have argued that restrictive lending practices have led to
decay and blight in some neighborhoods because qualified
borrowers who would have made improvements could not
get loans.
The arguments have centered around "redlining," a
practice whereby a financial institution indiscriminately
limits loans for the purchase of property in certain "undesirable" neighborhoods within its market area. According
to this practice, lenders are alleged to deny loan applications for purchases in those geographic areas, regardless of
the credit worthiness ofthe individual borrower. A number
of statistically-based studies that purported to show evidence of redlining were influential in securing passage of
the Community Reinvestment Act (CRA) as part of the
Housing and Community Development Act of 1977.
Since 1977, redlining, or the absence of redlining, has
occupied much of the attention of those investigating
CRA-related issues. In practice, however, protests by community groups based on CRA grounds have delayed or
prevented bank mergers and acquisitions even without
specific proof that a particular bank has engaged in redlining. Moreover, the implementation of CRA has tended
to encourage banks to make more loans in certain neighborhoods, regardless of whether a given bank has been
shown to have engaged in redlining. Clearly, then, CRA
has implications for banks beyond its anti-redlining provisions. Consequently, this article seeks to evaluate the
effects of CRA within this broader context, leaving aside
the questions whether CRA is necessary or whether redlining occurs. We develop a model to explain, first, why a
bank might have different lending policies for different
neighborhoods, and second, how the current approach
to CRA's enforcement affects a bank's decisions in this
regard.
Differential neighborhood lending patterns can be
shown to be a rational response to an environment in which
27
the costs of acquiring information are high and neighborhoods differ widely in their average default risks. The
existence of CRA suggests that society views these differential lending patterns as "suboptimal," and CRA enforcement essentially requires financial institutions to bear
the social cost of providing low-income borrowers greater
access to funding. Specifically, banks are encouraged
under CRA to increase lending in low-income neighborhoods. To do so, they may incur higher costs investigating
the credit worthiness of potential borrowers in these areas
than would be optimal from the perspective of profit
maximization. CRA trades off bank profits for the social
benefits derived from greater access by borrowers in
disadvantaged neighborhoods.
This view of CRA, as a mechanism to induce banks to
increase lending in low-income neighborhoods, is consis-
tent with a variety of institutional responses to CRA. These
responses can be interpreted as efforts to reduce the costs
that kept banks from making loans prior to CRA. Among
these responses are pooling agreements by banks and
cooperative efforts between banks and community groups.
We present an imperfect information model in Section I
to demonstrate conditions under which banks would
choose to allocate credit across neighborhoods on the basis
of average neighborhood characteristics. The effects of
changes in information on the allocation of funds across
neighborhoods are explored in Section II. The role of CRA
in the lending decision is highlighted in Section III,
where it is introduced as an. additional constraint on the
bank's choice. We discuss institutional arrangements that
have emerged to minimize the cost burden of CRA in
Section IV, and draw conclusions in Section V.
I. An Imperfect Information Model
The operations of a bank are based on a broad spectrum
of factors and motivations, including maintaining the
goodwill of customers, serving the needs of the community, and providing returns to investors. A central feature
of commercial banks is their role as credit intermediaries.
Banks develop expertise in evaluating the credit worthiness of borrowers and enjoy economies of scale in monitoring loans to ensure prudent behavior on the part of
borrowers. The extent to which this monitoring activity is
not performed easily or as efficiently by other participants
in the credit markets determines the market share of
banking relative to direct placement activity. 1
Portfolio diversification is another factor in bank lending
decisions. Every loan faces some default risk associated
with the particular characteristics of the borrower or the
project as well as overall economic conditions. A bank can
reduce these risks, however, by diversifying its portfolio
since the specific risks of every project are not perfectly
correlated, and these risks tend to offset one another. As a
result, the total risk of a diversified portfolio is generally
less than that of an undiversified one.
Diversification can occur along many different dimensions, such as across industries (agriculture, manufacturing, services, etc.) and size categories (large corporations
or single proprietorships), and across general classifications of customers (residential, industrial, commercial,
etc.). Diversification also can be accomplished geographically, by lending to similar customers in different markets
or neighborhoods.
As commonly expressed, the problem of "socially inad-
28
equate" lending to particular neighborhoods may arise
because the costs of identifying good loans in certain areas
outweigh the advantages that would be gained through
greater geographic diversification. This form of. credit
rationing, sometimes referred to as "rational redlining,"2
occurs-when banks restrict lending or are less aggressive in
marketing loan products in certain neighborhoods because
the costs of identifying the qualified loans are too high
to be profitable. Thus, the lack of readily available, complete information can· affect the allocation of credit across
neighborhoods.
In this model, we assume a bank operates in a geographic lending market comprising two neighborhoods,
which we denote by the subscriptsR (for "rich") andP (for
"poor"). The bank divides its portfolio of loans between
the two neighborhoods, with proportion 6 allocated to
neighborhood P, and (1- 6) to neighborhood R.
We define ip as the contractual interest rate on neighborhood P loans and iR as the contractual interest rate on loans
to residents of neighborhood R. 3 We assume that loan
markets are competitive and that interest rates on loans are
determined in these markets. Loan interest rates may be
affected by the underlying risks of projects in the two
neighborhoods, although they may not correct for risk
differentials exactly. We assume that the risk of a loan
project in neighborhood P exceeds that in neighborhood R.
Consequently, the loan rate in neighborhood P may be
higher than that in neighborhood R.
The limit on banks' ability to tailor rates to reflect fully
the differences in neighborhood risks may arise for a
Economic Review / Summer 1990
variety of reasons, including transaction costs or pressures
from social or regulatory groups. 4 Moreover, problems of
adverse selection, where higher rates may attract less
credit worthy borrowers, can prevent banks from adjusting
interest rates to compensate fully for risk. 5 ,6
Finally, because much of the attention in the application
of CRA is focused on home mortgage lending, the model
reflects some of the characteristics of that market. In
particular, while lenders can in principle charge differential rates across areas, in practice they tend to have only
slight variations in mortgage terms at any given point in
time. In large part, this leveling of rates and terms results
from the desire of lenders to create homogeneous mortgage contracts that can be resold in secondary markets.
Because of these factors restricting interest rate differentials, we assume that individual banks are price takers
and that rates are set exogenously. Thus, in this model, ip
and iR are not viewed as explicit choice variables by
the bank.?
In the absence of defaults, total dollar returns for the
bank on neighborhood P loans are ipOL where L is the total
dollar volume ofloans in the bank's portfolio. Similarly, the
income on neighborhood R loans is iR (1- O)L. To simplify
the analysis, we assume that the volume of loans is given.
We define units such that L = 1and thus eliminate it from
the two expressions above. 8
Banks are assumed to maximize an objective function
that trades off risk and return. The bank's perception of a
loan's riskiness depends, first, on the actual distribution of
potential rates of return to that loan project. This distribution depends on the interaction between specific characteristics of the project and the realization of future random
events. (This distribution likely will change when the
interest rate changes.) Even with full information about
current conditions, the bank still faces risks from future
events.
Although the bank cannot observe this distribution and
therefore derive atrue measure of the loan's actual riskiness, it can estimate a project's riskiness by obtaining
information about the details of the individual project,
details that are observable at some cost to the bank. Thus, a
bank's estimate of a project's riskiness depends on the
amount of information gathered. Essentially, as the bank
invests in more information, its ability to distinguish
among borrowers and projects rises, allowing it to restrict
its portfolio to the lowest risk projects seeking loans at the
given contractual interest rate.
Risk can be expected to differ across neighborhoods. We
assume that, for a given interest rate, the variance of
Federal Reserve Bank of San Francisco
returns to loans in neighborhood P is higher than in
neighborhood R. This effect could be expected if income
streams in the poor neighborhood were more volatile.
Moreover, if banks operate less in low income areas, as is
alleged by CRA advocates, they can be expected to have
less information about neighborhood P.
The bank's estimate of risk to loans in the two neighborhoods can be written as:
+ 'Ap(Ip )
= (J"k + 'AR(IR )
VAR(r p ) =
VAR(rR )
(J"~
(1)
(2)
where r p and r R are actual returns on loans that would be
expected at the prevailing interest rates. (J"~ and (J"k represent the variances of loan returns in neighborhoods P and
R, respectively, that result from unobservable factors. We
can think of these measures as the full-information minimum variances of returns of the portfolio the bank would
choose if it had all the information available about possible
projects. For a given interest rate, these components of the
variance are assumed to be fixed. The 'A terms in equations
(1) and (2) are the result ofthe component of risk caused by
imperfect information, with 'Ap > 'AR . 9 These terms are
dependent on the information the bank obtains about the
two neighborhoods, I p and I R . Our assumption that information reduces this component of risk suggests that 'A~ < 0
and 'A~ < O. We assume that 'Ap and 'AR are unaffected by
information about the other neighborhood. Thus, 'Ap is independent of IR and 'AR is independent of Ip.l°
Banks, therefore, can reduce loan risk by acquiring
more information about projects and borrowers in the two
neighborhoods so that they can weed out the higher-risk
projects. If information gathering were costless, they
would seek information about both neighborhoods until
'Ai = O.
But information gathering is not costless. Banks typically must set up an on-site branch or loan origination
office, conduct local surveys regarding the values of neighborhood properties, and solicit and evaluate loan applications from neighborhood residents-all functions that
entail significant expenditures by the bank.
We characterize these information gathering costs by the
average cost functions, Cp(Ip) and CR(IR). Total information costs are equal to Cp(Ip )0 for neighborhood P and
CR (IR )(1- 0) for neighborhood R. Typically, there are
large initial fixed costs associated with the investment in
information (such as setting up a branch), which lead to
declining average costs over some range. We assume,
however, that the marginal cost of obtaining information
29
30
EC()Do]mic Review / Surnmler
1;'1"111"1'1>11
Reserve Bank of San Francisco
31
eventually rises as the desired type or quality of information becomes more difficult to obtain or evaluate. This
produces V-shaped average and marginal cost curves.
We abstract from the deposit-taking activities of the
bank, even though this activity may affect the bank's cost
of funds and, thus, its profits. In effect, we assume a
perfectly elastic supply of deposits at a risk-free rate of
return to depositors, rd. ll As a result, we separate the
bank's deposit-taking function from the business of making loans.
With the components described above, it is possible to
state the bank's objective function as
Max'TI' =
ipS
+
iR(I-
S) -
~
var[rpS
+ rR (1- S))
- Cp (Ip )8 - CR (IR )(1-S)-rd
(3)
where 'TI' is the bank's adjusted return. 'TI' must be positive
for the bank to operate. The bank chooses values of S, I p ,
and I R that maximize this expression.
The objective function in (3) asserts that the bank seeks
a balance between a portfolio's interest income, information costs, and variance. In this case, we assume that the
adjusted return depends negatively on portfolio variance.
This effect could arise for a variety of reasons, including
risk aversion on the part of banks. 12 In addition, bankruptcy costs resulting from failed projects can be expected
to make portfolio risk a negative factor to the bank. The
third term, therefore, reflects a reduction in the bank's
income from expected loan losses to its portfolio, which for
simplicity is assumed to be a constant multiple, ~, of the
bank's portfolio variance. 13
This formulation differs from other models of credit
allocation. For example, as discussed in the box, "Imperfect Information vs. Credit Rationing, " the standard credit
rationing model focuses on the effects of asymmetric
information on the determination of loan rates and the
decision to exclude or ration credit to various borrower
groups. The current work, which should be viewed as
complementary to this credit rationing model, focuses on
the process by which information gathering changes credit
allotments. Moreover, the structure of this model is designed explicitly to model the effect of eRA, which is
difficult to incorporate directly into the credit rationing
framework. Nevertheless, many of the implications of the
credit rationing model can be expected to carry over into
this analysis as well.
The solution of (3) yields the following optimal conditions for a bank's portfolio allocation and information
gathering:
S*
32
=
ip -
iR
+
CR
-
Cp
+ 213[var(rR )]
-=-----~_=_=_----:.':-:---.:..----:--'--:_::__----'.:..213[var(rp )
var(rR )]
+
(4)
(5)
C~(l~) =
- ~(1- S)A~(I~)
(6)
Equations (4) to (6) represent equilibrium first-order
conditions for the three choice variables, which are simultaneously determined and clearly interdependent. By totally differentiating equations (4) to (6), it is possible to
solve for reduced form expressions that calculate the effect
of changes in exogenous variables and model parameters
on the equilibrium values of the choice variables. We
present these comparative statics results in the Appendix.
The solution to the model suggests several factors
that influence a bank's allocation of loans across neighborhoods:
• The bank lends a larger proportion of its loan portfolio
in the poor neighborhood when the contractual interest rate
on neighborhood P loans rises relative to that on neighborhood R loans.
• When the variance of neighborhood P returns falls
relative to that in neighborhood R, the proportion of loans
in neighborhood P rises. Assuming that the risk-adjusted
return to lending in the rich neighborhood is higher before
Var(rp ) declines, the relative advantage of the wealthier
neighborhood is eroded. 14 Similarly, factors that reduce
the cost of obtaining information about neighborhood P
relative to that for neighborhood R increase the proportion
of loans to neighborhood P. Clearly, if information is less
costly to obtain in one area, more information is acquired,
thereby reducing the relative variance of returns to that
neighborhood .
• The effect of an increase in risk aversion (or the
expected default rate) is less clear and depends, among
other things, on the spread between contractual interest
rates and differences in variances of the two neighborhood
returns. As ~ rises, the value of reducing the portfolio's
variance rises, pushing the solution toward the minimum
variance portfolio. For low initial levels of S, the effect of
an increase in 13 is to shift the portfolio toward neighborhood P loans to capture the advantages of portfolio diversification. At high values of S, similar diversification
incentives shift the loan portfolio toward neighborhood R
loans.
The solution to the model is depicted graphically in
Figure 1. The figure shows how different allocations across
neighborhoods affect profits, holding constant the optimal
quantities of information, It andII. The curve labelled 'TI'p
represents the portion of adjusted returns attributable to
lending in neighborhood P. The 'TI'R curve is the equivalent
measure for neighborhood R loans. The curve marked 'TI' is
the vertical sum of the 'TI' p and 'TI'R curves, representing the
Economic Review / Summer 1990
bank's total profits as a function of e. At e = 0, the entire
bank portfolio is allocated to neighborhoodR loans and the
total adjusted return is thus equal to 'ITR . Conversely, at
e = 1, the bank's portfolio consists entirely of loans to
neighborhood P projects and total returns are derived from
'IT p . The twofunctions, 'ITp and 'ITR are concave in e.l 5 Their
curvature creates the total return function that, in the
current figure, rises over some portion of values of e, and
then falls. The profit-maximizing bank chooses the highest
point on the total return curve, with an optimal credit
allocation equal to e*.
Factors that raise the marginal profit of neighborhood P
loans relative to that of neighborhood R loans will increase
e*. For example, an increase in ip relative to iR , or a decrease in the variance of r p relative to that of r R will rotate
71'p upward, and tend to move e* to the right. An increase
in 13 will increase the concavity of both profit functions,
and e* will increase if it was very low initially and if the
increased concavity raised the marginal profit of neighborhood P loans more than that for neighborhood R loans.
In the solution shown in Figure 1, neighborhood P is not
redlined, that is, the optimal credit allocation implies
1> e>0. It is possible, however, to derive aredlined solution
in the current framework. Redlining will occur if the
marginal profit from lending to the poor neighborhood,
represented by the slope of the 71'p function, is less than the
absolute value of the slope of the 'ITR function at low levels
of e. In such a case, the total return function slopes
downward over its entire length, with a maximum value
occurring at e= O. In this case, the profit-maximizing bank
would allocate all of its loans to neighborhood R projects
and would redline neighborhood P.
II. The Effect of Information
The equilibrium lending pattern across neighborhoods,
shown in Figure 1, is directly affected by the information
gathering process. As we demonstrate in this section, the
equilibrium values of all three choice variables are highly
interdependent, with optimal investment in information
about both neighborhoods determined simultaneously with
the decision about portfolio shares.
The optimal investment in information about the two
neighborhoods is closely related to the portfolio allocation
decision. The first-order conditions for I p and I R' equations
Figure 1
Optimal Credit Allocation in the
Imperfect Information Model
Federal Reserve Bank of San Francisco
33
(5) and (6), suggest that the bank should invest in informa
tion until the marginal cost of the last units acquired (the
left-hand sides) just equals the value of the reduced port
folio risk (the right-hand sides). (Note in equations (5) and
(6) that < 0 and Q > 0).
Comparative statics results for the information choice
variables, derived in the Appendix, show several factors
that affect the optimal information acquisition:
0 The amount of information acquired is positively
related to the share of loans allocated to that neighborhood.
Thus, 0 and I P move together. Whenever the bank allocates
more of its loan portfolio to the poor neighborhood, it also
is in the bank’s interest to acquire more information about
neighborhood P borrowers and projects. Because more of
the portfolio is at risk in the neighborhood, the marginal
benefit of information about that neighborhood rises. Any
factor that raises the optimal value of 0, such as a relative
increase in contractual interest rates on neighborhood P
loans or a decrease in the risk of neighborhood P projects,
also will induce the firm to obtain more information about
the poor neighborhood.16
0 The amount of information purchased also depends on
the degree to which more information reduces portfolio
variance. If additional information about neighborhood P
becomes less valuable because some exogenous factor
negatively affects the bank’s perception about the neigh
borhood’s risk, the marginal benefit falls. The bank then
reduces the amount of information it obtains about the poor
neighborhood, and allocates less of its portfolio to neigh
borhood P loans. The opposite effect occurs if the marginal
benefit of I R falls; that is, the bank responds by increasing
its allocation of loans to the poor neighborhood and pur
chasing more information about neighborhood P. These
results suggest that information investment in the two
neighborhoods is a choice between substitutes: factors that
raise the value of information in one neighborhood also
reduce the relative value of information about the other
neighborhood. This result is dependent on our assumption
that information about one neighborhood does not affect
the variance of projects in the other neighborhood.
9 Factors that reduce the marginal cost of information
for one neighborhood will increase investment in informa
tion in that neighborhood. As discussed in Section IV,
pooling arrangements and collaboration with community
groups can reduce the marginal cost of information to an
individual bank. Banks will then increase information to
balance marginal costs and benefits.
9 Finally, the solution to the model depends on the
relationship between defaults and portfolio variance. Ob
viously, if there were no defaults, (that is, (3 = 0) the bank
Figure 2
Effect of Positive information
Shock to Neighborhood P
34
E conom ic R eview / Sum m er 1990
would not invest in information at all. Information is only
valuable for its variance-reducing content. As the sensitivity of adjusted returns to portfolio variance increases, that
is, as J1 rises, the value of information rises, and the bank
invests in more information about both neighborhoods.
The role of information gathering in our model can be
seen in Figure 2. The black curves represent the initial
equilibrium depicted in Figure 1. We suppose that a
positive shock occurs to neighborhood P that raises the
return to information. For example, a firm announces its
intention to build a manufacturing plant in neighborhood
P, with plans to hire many local workers. This announcement should lead to better income prospects for neighborhood P residents, and raise the credit quality of the pool of
applicants in that neighborhood. The assumed shock to
neighborhood P increases the bank's perception of the
marginal benefits of additional information. (This implies
that A~ increases in absolute value as a result of the
announcement. )
The higher marginal benefit of information about neighborhood P induces more investment in that information.
As a result, 'ITp shifts upward. The higher profit schedule,
therefore, boosts the optimal e. The rise in ealso boosts the
marginal benefit of information in neighborhood P, while
reducing the marginal benefit of information in neighborhood R, thereby reinforcing the initial information shock.
The bank responds by increasing the information investment in the poor neighborhood even more, further shifting
the 'ITp curve in Figure 2 up to the green line. At the same
time, the marginal benefit to neighborhood R information
falls relative to its marginal cost. The bank reduces its in-
formation investment in the rich neighborhood, resulting
in a downward shift of the 'ITR curve in Figure 2. The new
equilibrium implies that the bank responds to the positive
shock in the poor neighborhood by raising the portion of its
portfolio allocated to neighborhood P loans, increasing
the amount of information purchased about neighborhood
P, and reducing the information investment in neighborhoodRY
This imperfect information framework may shed light on
empirical studies claiming to find evidence of neighborhood redlining. Given the cost of obtaining information, it
would not be surprising to observe banks using general
neighborhood characteristics to evaluate return functions,
as well as to assess information costs. This type of information is widely available at relatively low cost. To the
extent that racial and other social characteristics are correlated with overall economic variability, returns can appear
to be a direct function. of these characteristics. Moreover,
as the costs of finding the lowest risk loans rise, the
potential for credit rationing increases in neighborhoods
with characteristics correlated with higher risks. Use of
these characteristics as a screening device may therefore
represent a first guess by lenders as to default risk in
different neighborhoods. Once banks choose (or are induced) to make more substantial investments in information, however, the relevance of general neighborhood
characteristics may give way to more costly borrower- or
project-specific data that carry more information content.
In the context of our model, CRA represents one such
inducement.
III. The Role of eRA
CRA can be considered an additional regulatory constraint imposed on banks, thereby affecting their optimal
portfolio allocation across neighborhoods. As we show in
this section, the basic model presented in Section I can be
easily modified to capture the essential features of CRA.
Congress passed the Community Reinvestment Act
partially in response to community groups' claims that
previous anti-discrimination laws had failed to keep banks
from redlining. A financial institution is said to redline if it
indiscriminately denies loans for the purchase of property
in certain "undesirable" neighborhoods within its market
area. In hearings prior to the drafting of what became the
CRA, statistically-based studies were presented (New
York Public Interest Research Group, 1977; National Peoples Action, 1976) that claimed to confirm the existence of
redlining, despite the earlier passage of the Equal Credit
Federal Reserve Bank of San Francisco
Opportunity Act (1974) and the Home Mortgage Disclosure Act (1975).
It is true that those earlier laws may not provide effective
sanctions against redlining. While the Equal Credit Opportunity Act prohibits discrimination in credit transactions
on the basis of race, color, religion, national origin, sex,
marital status, and age, it does not outlaw geographic
discrimination. The Home Mortgage Disclosure Act requires financial institutions to disclose data on the volume
of mortgage loans by census tract or zip code, but does not
proscribe geographically discriminatory loan policies.
CRA requires federal regulators to motivate commercial
banks and thrift institutions to meet community credit
needs by considering a financial institution's record of
community lending when they evaluate its applications for
mergers or acquisitions. Members of the public also may
35
formally protest an application if they think that the institution's record with regard to lending in certain neighborhoods is unsatisfactory.
The primary purpose of CRA, which is expressed in
purposefully vague language, is subject to debate. An
often-used, narrow interpretation is that CRA is an antiredlining bill. In this view, the critical issue becomes one
of identifying clear evidence that banks engage in irrational redlining. Otherwise, enforcement of CRA is not
needed.
The evidence in redlining studies is inconclusive. Several studies have found average neighborhood racial and
other social characteristics to be significantly correlated
with lending activity even after controlling for a variety of
other influences. However, these studies have been criticized for excluding important variables or using incorrect
data-factors that can lead to overestimates of the importance of race or other social factors in neighborhood
lending. (For a discussion of empirical studies of redlining, see the box entitled "Evidence of Redlining.")
CRA is viewed more broadly in this study, however.
Rather than an anti-redlining law, CRA is viewed here as a
mechanism to increase disadvantaged neighborhoods' access to credit whether or not redlining was actually occurring. This broader view of CRA is consistent with two
recent developments. In February 1989, the Federal Reserve Board denied on CRA grounds an application by
Continental Illinois to acquire another institution, even
though Continental Illinois was not believed to be engaged
in redlining per se.
Also, in 1989, the federal regulatory agencies 18 revised
the guidelines for compliance with the CRA, and established more stringent and specific standards. However,
because CRA requires that lending be consistent with
"safety and soundness" considerations, even the new
guidelines do not delineate an acceptable geographic pattern of lending. In the initial statement of the CRA, twelve
criteria were to be used in evaluating a lender's record ·of
compliance. One of the criteria states that regulators are to
consider "the geographic distribution of the bank's credit
extensions, credit applications, and credit denials." The
1989 amendment refers to "unwarranted geographic differences in lending patterns," and to "disparities in
lending. that do not appear to be attributable to safety
and soundness considerations or to factors beyond an institution's controL" What would make these geographic
differences unwarranted or unattributable to safety and
soundness considerations is not stated.
In light of this broader perspective onCRA, two alternative interpretations of the application of CRA have
36
emerged. The regulatory mandate requires that financial
institutions search harder for good loans in disadvantaged
neighborhoods, but does not outlaw the rationing of credit
or require banks to make riskier loans. The law imposes on
banks and thrifts the costs associated with expending the
effort to seek out high-quality borrowers in areas that are
perceived as riskier.
In this "effort-oriented" approach, a bank is penalized
for noncompliance with CRA if it demonstrates insufficient efforts to meet the credit needs of the community it
serves. The penalties take the form of delays in processing,
or even denial of, applications for mergers and acquisitions. CRA examination ratings consider the extent to
which the bank conducts outreach programs, educates
the public on its policies, and aggressively markets its
products in low-income neighborhoods.
Effort, however, may not translate into a greater amount
of funds lent to poorer neighborhoods. Recent CRA protests, therefore, have focused more on results than on
effort. Challenges to bank mergers and acquisitions on
CRA grounds have been raised when community groups
have claimed that those institutions failed to meet a
"socially acceptable" minimum level of lending in lowerincome neighborhoods. In order to avoid the eRA "penalty," banks have responded with specific commitments of
loan funds to those neighborhoods.
Modelling eRA
In modelling the effect of CRA, it is necessary to choose
between the regulatory interpretation and the more recent
results-oriented application ofCRA. An "effort-oriented"
approach would focus on the amount of information the
bank acquires. In contrast, a "results-oriented" approach
emphasizes 8, the proportion of the portfolio allocated to
the low-income neighborhood. We have chosen to model
the latter interpretation.
In the context of our imperfect information model, CRA
has the effect of establishing a minimum proportion of the
bank loan portfolio allocated to the poor neighborhood.
The value of this minimum allotment is determined by a
social welfare function that is exogenous to our model. We
refer to the socially acceptable minimum level of credit
allocated to the poor neighborhood as e. We assume that
CRA imposes a penalty on the bank. (delays in processing
applications, negative publicity, etc.) if it fails to allocate
at least this proportion ofits loan portfolio to neighborhood
Ploans. We characterize this penalty by the function:
(7)
d(e - 8)
whered(.»Owhen8<e,andd(.) =
owhen 8 ?
e.
Economic Review / Summer 1990
Federal Reserve Bank. of
Francisco
37
The post-CRA net return function for the bank, therefore, becomes:
'IT
= ipO
+ iR(l-O)
- [3var[rpO + rR(l-O)]
- Cp(Ip)O - CR(IR)(l-O) - d(e-O) - r d (8)
and the optimal portfolio share in neighborhood P loans
becomes:
o
_. ip -
eRA -
iR
+ CR -
Cp + 2[3[var(rR)]
2[3[var(rp ) + var(rR)]
+d
(9)
The only difference between (4) and (9) is that d now
appears as an argument in the numerator. As the penalty for
allocating ~oo little credit to neighborhood P increases, the
bank:s optl~al sh~e of lending to P rises accordingly.
WIth the ImposItIon of the CRA penalty, where binding,
the post-CRA value of 0 exceeds the value obtained in
Section I by the ratio of the penalty to the weighted sum of
the return variances, thus increasing the bank's lending in
the poor neighborhood. The bank now treats the CRA
penalty as an additional cost of doing business and, in
effect, chooses the optimal penalty.
The influence of CRA on the model's solution is depicted graphically in Figure 3. Again, the solid curves
represent an initial equilibrium, with 0* the pre-CRA
optimal portfolio allocation. In the presence of the CRA
penalty, the returns to neighborhood R loans are reduced
for all portfolio allocations below "6. The bank must pay the
CRA penalty for not allocating a sufficient amount of its
portfolio to neighborhood P loans. This is shown in Figure
3 by the do~nward shift of the 'ITR function for all values of
oless than 0. Our assumption that the penalty increases the
further 0* is from the social optimum is presented by the
increasing distance between the black and green curves as
oapproaches zero.
As the CRA penalty shifts down a portion of the 'IT
function, it als~ shifts the total return function for all value~
of 0 less than O. The profit-maximizing bank chooses the
highest point on the total return function, in this case
corresponding to the value 0CRA. This portfolio allocation
is clo.ser to the socially optimal value of 0 than the original
solutlo~. CRA thus has the desired impact of raising the
proportIOn of the bank's portfolio allocated to neighborhood P loans. Moreover, the larger the penalty, the larger is
the resulting shift in the portfolio allocation.
The achievement of this goal, however, comes at a cost.
Total returns for the bank are smaller after the imposition
of CRA (as long as the CRA constraint is binding and the
actual, as opposed to perceived, risks oflending in neigh?orhood P are higher than those in neighborhood R). CRA
Imposes an additional cost on the bank and induces it to
increase its lending to the neighborhood with the higher
expected return variance. Total returns decline because this
Figure 3
Effect of CRA on Optimal
Credit Allocation
8* 8eRA 8
38
1
8
Economic Review / Summer 1990
higher variance is associated with a greater probability of
default. From the bank's standpoint, CRA has an undesirable impact. In essence, CRA forces the bank to pay
the social cost of increased lending to the poor neighborhood. 19
One beneficial side-effect of CRA is its impact on
information gathering. Figure 3 does not show the separate
information effects that augment the impact of the penalty.
Banks seek to reduce the penalty by raising e, which in
turn raises the marginal benefit of information in neighborhood P. Banks, therefore, invest more in Ip and less in IR'
The change in information investment shifts the '1Tp and '1TR
curves as in Figure 2, reinforcing the increase in 6CRA ' and
moving it closer to a. Thus, the ability to invest ininformation moves the equilibrium credit allocation even closer to
the socially desired value than is shown in Figure 3.
This informational effect of CRA potentially can mitigate some of the cost of complying with the law. If the
bank's initial perception ofthe low-income neighborhood's
risk was too high, CRA's incentive to gather more information can lead the bank to discover that there are far more
high-quality loans that can be made in the area than it
initially believed. Of course, the increased information
also may confirm the bank's initial characterization of the
neighborhood's risk. And, in fact, if credit quality is too
low, the bank may choose to redline and pay the regulatory
penalty.
CRA's effect on information, as modeled here, also
achieves the "effort-oriented" enforcement of CRA.
Banks are encouraged to aggressively seek loans to boost
their portfolio of low-income neighborhood loans, thus
satisfying the regulatory interpretation of the law.
IV. Implications and Institutional Developments
loans. 21 This approach lowers the costs of information for
One particularly attractive feature ofthe imperfect inforthe lending institution by shifting part of the search and
mation model is its potential to explain the emergence of
post-CRA institutional arrangements. The model suggests
monitoring costs to the community groups. This approach
that socially suboptimal lending occurs in part because the
also may reduce default risks since the community group,
by placing its "reputational capital" on the line, has an
costs of finding good loans are too high, not necessarily
because good loans cannot be made in a particular neighinterest in encouraging the borrower to follow the terms of
borhood.
the loan. It also increases community group sensitivity to
the credit-risk problems faced by institutions when lending
A predictable response of banks to this new regulatory
constraint is to seek ways to minimize the cost and risks of
in certain areas.
complying with CRA regulations. Several arrangements
Third, some banks form separate corporations for CRA
activity which allow banks to take equity positions in the
have emerged in the financial community to reduce the cost
of CRA compliance. First, as an explicit response to CRA,
borrower as well as debt positions. 22 Joint loan-equity
financial institutions in a number of states have formed
positions, when they are possible, have been shown to
increase the monitoring and information gathering camulti-institution consortia20 which not only lower the perpability of the lender. 23,24
institution cost of information, but allow participants to
share credit risks. A prime example is the California
Two points are particularly interesting with regard to all
of these arrangements. First, these strategies are explicitly
Community Reinvestment Corporation, in which major
targeted at CRA and are not widely applied to other
lenders in the state have pooled funds in a separate entity
whose sole directive is to find and make loans in disadvanlending problems. Second, all ofthese strategies are aimed
at reducing the costs of obtaining neighborhood informataged neighborhoods. Since these same individual institution and possibly at spreading risk.
tions perform many other types of loan functions in-house,
it is clear (and is sometimes explicitly stated) that the
The model provides an explanation for these arrangements and an interpretation of their effects on lending to
establishment of such consortia serves the purposes of
lowering per-institution costs of information and of spreaddisadvantaged neighborhoods. Consider, first, a post-CRA
ing risk in a lending process where such costs and risks are
arrangement in which a number of banks pool their resources to obtain and share information about the poor
relatively high.
Second, some banks allow non-profit community groups
neighborhood. If we assume thatNbanks participate in the
to perform the initial applicant screening for CRA-related
consortium (each as an equal partner), then for each unit of
Federal Reserve Bank of San Francisco
39
information the individual bank purchases, it receives
N - I units through the consortium sharing agreement. In
effect, for a given quantity of information, the cost to the
individual bank is split among N institutions. The neighborhood P cost function thus becomes Cp(Ip)/N. Maximizing the modified adjusted return function yields the
following solution for 8: 25
ip-iR+C r
8POOL =
-
C
if
+ 2~[var(rR)] + d
2~[var(rp) + var(rR)]
(10)
For a given quantity of I p , eis unambiguously larger than
in the previous case where each bank obtains neighborhood P information on its own. Clearly, if information
costs are lower, the optimal perceived return function for
the bank is higher. (In fact, if N becomes so large that perinstitution costs become very small, the return function
may approach the full-information returns function, and
problems caused by imperfect information may be fully
mitigated.)
Referring back to the diagrammatic treatment, a decline
in information costs acts the same way as that portrayed in
Figure 2. Because the marginal cost of a given amount of
information falls with pooling, the optimal amount of
information gathered rises and the marginal profit function
for neighborhood P loans shifts outward, generating an
increase in lending to that neighborhood.
Pooling arrangements increase the total amount of information gathered. To see this, consider the first-order
condition for neighborhood P information and the resulting
partial equilibrium solution for marginal cost:
(11)
For a given value of neighborhood P information, the
marginal cost is lower than in the previous case, and
probably lower than the marginal benefit of investing in
information. Each bank in the consortium faces a private
incentive to invest in more information since they share the
costs. The net result is a quantity of I p that is greater
than the case without the consortium. The cost-pooling
arrangement thus yields a greater investment in information than the case where all banks operate alone. Such
pooled arrangements appear to be particularly cost-effective mechanisms for overcoming problems of imperfect
information in lending markets.
Although such methods may minimize the costs of CRA
compliance, it is important to emphasize that participating
40
banks still can be expected to be worse off compared to the
no-CRA case. If pooling arrangements yielded profits
similar to those in the wealthier areas, banks would have
had an incentive to form joint ventures before CRA was
adopted.
That consortia form under CRA and not without CRA
suggests several properties of the cost function. There are
economies of scale in information that were not exploited
previously. Thus, a bank's costs can be reduced by sharing
information, increasing total information while cutting
individual information gathering. Moreover, the minimum
efficient scale of lending necessary to satisfy CRA may be
too high for one bank to enter separately and make normal
profits. The consortium, in contrast, may be able to attain a
scale of lending activity sufficient to make CRA-related
lending profitable. Finally, the costs of forming and maintaining a lending consortium may have prevented pre-CRA
arrangements of this type. The benefits of reducing the
CRA penalty, however, act to offset these costs.
This result suggests that even with pooling arrangements, profits are lower under CRA. Otherwise, (a) it
would not be necessary to form consortia, or (b) if the
expected return to lending in the neighborhood is sufficiently high, such consortia would have formed withoutCRA.
The other arrangements, that is, the involvement of
community groups and the use of greater equity control,
offer similar advantages in reducing information costs.
Community groups may have lower costs of finding good
borrowers because of their familiarity with the neighborhood and the potential borrowers. Greater equity control
offers lower monitoring costs to the bank, although it does
not reduce the initial information cost of finding the loans.
The two most prominent methods, the use of community
groups and bank-pooling arrangements differ in their distribution of costs. The use of community groups is attractive to banks since the information costs are passed along
to the community and not borne directly by the bank.
However, to the extent that banks have a comparative
advantage in identifying good loans, that approach may be
less efficient. The costs of bank pooling operations are
directly borne by the stockholders or customers of the
banks, but they have greater control over the lending
process.
Other potential arrangements also can be envisioned
within this framework. If the costs of complying with social goals put banks at a competitive disadvantage, it might
be appropriate to use government funds to subsidize the
Economic Review / Summer 1990
cost of gathering information, rather than effectively taxing banks as occurs at present. Government agencies could
assist community group efforts in screening, or they could
subsidize information costs or risks through tax credits. In
such ways, the costs ofsocial policy can be directly transferred to society, rather than indirectly through the effect
on bank costs, which are borne by bank customers and
owners.
v. Summary and Conclusions
In this article, we incorporate CRA policies explicitly in
a microeconomic model of bank behavior. We demonstrate
that CRA can be viewed as an additional cost or tax on
banks when they fail to achieve some socially desirable
balance of lending across neighborhoods. Moreover, part
of the effectiveness of CRA derives from its inducements
to banks to increase lending in disadvantaged neighborhoods-costs that it would not otherwise undertake if
CRA were not imposed.
Previous studies have not explicitly modeled the linkage
between bank behavior and CRA. Instead, for the most
part, they have dealt with the empirical question whether
neighborhoods are rationed on the basis of non-economic
factors. These studies have been concerned not with how
CRA affects lending activity, but with whether CRA was
needed to correct some systematic bias in lending patterns.
In the context of our model, differences in neighborhood
lending patterns arise in response to differences in the
perceived risks oflending in certain areas. Thus, given the
costs involved in obtaining information about neighborhoods, these lending patterns may be optimal from the
standpoint of a private, profit-maximizing bank. However,
our interpretation of the CRA suggests that it has been
invoked to overcome what is viewed as socially suboptimal
lending in disadvantaged neighborhoods.
The current study provides a better understanding of the
relationship between bank behavior and the application of
the CRA. Results from this study lead to several conclusions. First, CRA places the social cost of more geographically even lending directly on banks. Banks are, in
effect, taxed in such a way as to force them to achieve social
goals, with bank customers or shareholders paying the cost
of the policy.
Second, by imposing a penalty, CRA will increase
Federal Reserve Bank of San Francisco
lending to disadvantaged neighborhoods-an effect that is
reinforced in the model by the assumption of imperfect
information. When banks are induced by CRA to increase
lending in the poor neighborhood, the value of information
about that area rises. The induced investment in information increases the bank's knowledge about the poor neighborhood and may reveal additional low-risk loan projects.
Information effects thus raise the proportion of the portfolio allocated to poor neighborhood loans over and above
the direct effect of the CRA penalty.
An important policy question arises: if lending patterns
are suboptimal from society's standpoint, is it efficient and
equitable to place the cost of that social policy on banks?
Other mechanisms can be found to lower the cost of
information about some neighborhoods, and banks could
be subsidized intheir information costs rather than taxed.
The policy question raised by this article is whether
CRA is the most efficient way to achieve this social goal.
Future researchers may wish to shift their focus from
whether lending to various neighborhoods is sufficient, to
comparing the relative advantages of other mechanisms
that can remove the informational inefficiencies that inhibit the desired investing activity.
Moreover, the "penalty function" implicit in CRA
offers only one incentive structure for banks to increase
their search activity. This approach, which offers vague
regulatory penalties on mergers and acquisitions, may not
offer the most efficient incentives to banks to increase their
lending to disadvantaged neighborhoods. By starting from
a clear understanding of the cause of the suboptimal
lending-namely, differential risks, exacerbated by costly
information-the incentive structure to achieve that goal
can be crafted more efficiently.
41
NOTES
1. See, for example, James (1987).
2. Sullivan and Pozdena (1982) make the distinction between rational red lining, where differential lending occurs
as a result of differences in future prospects of borrowers
or projects, and irrational redlining. The latter is arbitrary
and discriminatory. In our model, only rational redlining
occurs.
3. This return includes the explicit interest charged on
loans as well as other fees and payments. that may be
required by the lender. These fees include such items
as closing costs, origination fees, prepaid interest, .etc.
Booth (1990) finds that loan fees play an important role in
the pricing of bank commercial loans and that loan fees
assume an extensive variety of forms.
4. Although banks have considerable latitude to vary
interest rates, collateral requirements, and various fees,
some flexibility may be sacrificed to gain advantages of
scale through standardization. Moreover, recent work by
Jaffee and Russell (1990) suggests that lenders may be
limited in their ability to differentiate loan terms because of
social pressures regarding "fairness," as well as legal
limits associated with discrimination.
5. According to the notion of adverse selection, increases
in interest rates may discourage safer borrowers and
attract riskier ones who have a lower probability of repaying the loan. The increase in interest rates has an adverse
effect on the quality of loan applicants and may actually
lead to lower expected returns for lenders (after accounting for defaults). This adverse selection effect limits the
extent to which interest rates can reflect loan risk. See the
box on Imperfect Information vs. Credit Rationing.
6. In the credit rationing literature, Stiglitz and Weiss
(1987) implicitly argue that banks choose to allocate
credit sequentially to different borrower classes. The bank
chooses a loan rate to each class that maximizes the
expected utility (return) from loans to that group, taking into account the adverse selection problem. Consequently, rates differ to different groups, but the differences
in rates are not necessarily constructed to yield the same
expected return.
7. Although this assumption may appear quite restrictive,
relaxing it does not affect the general nature of the results.
As long as rates do not fully reflect underlying risks,
changes in risk will affect expected returns to the bank. In
the model discussed here, changes in variance induced
by information do not affect loan rates. This can be generalized easily by making loan rates a direct function of risk,
in which case there would be some partially offsetting
effect on loan rates. This would reduce the magnitude of
the effect on portfolio allocation resulting from a change in
risk, but it would not change the direction of the effect.
8. In practice, the volume of loans is an endogenous
variable that may be at least partially determined by the
bank's deposit-taking activities in the two neighborhoods.
42
For purposes of this discussion, however, the assumption
of an exogenous total loan volume is not crucial.
9: Information problems may be more acute in the poor
neighborhood if banks have fewer branches in those
areas. A smaller deposit base makes branching in poor
neighborhoods less profitable. In this way, deposit-taking
activity can exacerbate information asymmetries across
neighborhoods and impinge on the lending decisions.
10. Although this assumption simplifies the ensuing analysis,it is somewhat restrictive. At the very least, we believe
that any covariance between these errors is likely to be
positive, a relationship that mitigates somewhat, but does
not change, the predictions of the model presented below. Negative cross correlations between neighborhood
information sets seem unlikely.
11. This assumption is not unreasonable given that deposit insurance in U.S. banking markets has covered
virtually 100 percent of deposits.
12. An alternative reason for the negative relationship
between returns and variance has to do with the nature of
the debt contract. The probability of default rises with
variance, as does the probability of a high payoff to the
project owner or borrower. Since lenders cannot receive
more than the loan rate when favorable outcomes occur,
they are not compensated for the increased probability of
default. Thus, lenders' returns have a truncated distribution, the mean of which falls as the variance of returns to
project owners rises. This is true even if the rising variance
is mean preserving.
13. Clearly, the expected loss parameter ~ could be an
increasing function of the portfolio's variance. In that case,
the loss associated with having greater variance would be
higher than in the case derived here, further encouraging
the movement away from the riskier neighborhood.
14. The share of loans made in neighborhood P also
increases as the full-information variance of returns in R
rises: as (J~ - ) 00, e --> 1. An interesting case arises when
the two neighborhoods are identical. In this case, variances of returns in the two areas are the same, as are the
information cost functions and the interest rates on loans.
In this setting, the bank allocates half of its loan portfolio to
each neighborhood. Since there are neither greater loan
risks in one neighborhood relative to the other nor greater
costs of obtaining information, the bank treats both areas
the same in its lending activity.
15. The concavity of these return functions can be shown
using the full solution to the model presented in the Appendix. We assume, for simplicity, that the two functions
are monotonic. Thus, 1Tp rises continuously as eincreases
while 1TR falls as e rises. It is possible that these two
functions might be sufficiently concave to slope downward at their ends, a possibility that only reinforces the
results presented here.
Economic Review / Summer 1990
16. We assume that the economies of scale in information
gathering drop off rapidly, in the sense that the negatively
sloped portion of the marginal cost schedule occurs only
at very low levels of Ip . In practice, banks would tend to
operate on the positively sloped portion of the marginal
cost curve, such that an increase in e increases the
amount of information acquired.
17. As long as the marginal benefit of information regarding a particular neighborhood exceeds its marginal cost,
additional information will shift the return function from
that neighborhood upward. Once information investment
reaches the optimum, however, any additional investment
in information will reduce returns and the 'Tl' function will
shift downward.
18. These regulators include the Board of Governors of
the Federal Reserve System, the Federal Deposit Insurance Corporation, the Office of the Comptroller of the
Currency, and the Office of Thrift Supervision (formerly the
Federal Home Loan Bank Board).
19. Banks may be able to pass some of these costs on to
Federal Reserve Bank of San Francisco
their customers in the form of reduced services, higher
fees, etc. If costs are too high, in fact, a bank may choose
to drop the neighborhood as part of its market area, thus
passing the costs on to the community.
20. See Mannion and Faber (1989) p. 26.
21. See U.S. News & World Report (1989), pp. 26-27.
22. See Mannion and Faber (1989), p. 26.
23. See Kim (1989).
24. An alternative strategic response of banks could be to
close branches and limit their service area. Someevidence of this effect is presented for the Phoenix metropolitan area by Booth and Smith (1984), where CRA had a
negative impact on branching. Limits are imposed on this
ability, however, with community groups seeking regulatory prohibitions to such closures.
25. To the extent that pooling also spreads risks and
reduces the variance of low-income neighborhood loans
to pool participants, Var(rp) also may fall in expression
(10), further increasing e.
43
APPENDIX
The three first-order conditions from the model yield a
system of three equations in three variables, e, I p, and I R'
We can totally differentiate this 3-equation system and
then solve it in terms of the exogenous variables and
parameters of the model. The results of this exercise
represent the "complete" solutions to the model in that
they take account of all interactions among the variables.
In matrix notation, the system of three equations can be
represented (after total differentiation) as:
Ax = y
where
[C~ + 21)(1-e)A~)
A=
]
(0)
[ - I)(l- e)A~ - C~)
y=
The solution for the vector, x, requires inverting matrix A,
i.e. ,
x
=
A-ly.
The inversion process includes evaluating the determinant
of A. In order to ascertain the sign of this determinant, it is
necessary to place certain restrictions on the magnitudes of
the second order derivatives of the C (.) and A(.) functions
in the model. These restrictions entail requiring the
second-order own derivatives of these functions (with
respect to each neighborhood) to dominate second-order
cross effects (i.e., between neighborhoods). In addition,
we assume that first-order effects generally dominate second-order effects. These restrictions are reasonable and
not likely to be violated.
With the above-imposed restrictions, we obtain the
following general form:
x
44
=
A-ly =
[
(-) (-) (+)]
(-) (-) (-)
This equation system leads to the following set of results:
ile
ilip
>0
ilIp
ilip
>0
ilIR
ilip
<0
ile
iliR
<0
ilIp
iliR
<0
ilIR
iliR
>0
?O
ilIp
ill)
>0
ilIR
ill)
>0
ile
ill)
ile
il(J"~
ile
il(J"k
<0
>0
ilIp
il(J"~
<0
ilIp
>0
il(J"k
ilIR
il(J"~
>0
ilIR
<0
il(J"k
[y).
(+) (-) (-)
Economic Review / Summer 1990
We have also considered the impact of parameters that shift
the costs entailed in gathering information (a j ), the underlying return variance ('Y j), and the eRA penalty function (8).
ae
aap
ae
aaR
-
ae
a'Yp
-
ae
a'YR
ae
aB
<0
alp
<0
aap
aIR
>0
aap
>0
alp
>0
aaR
aIR
<0
aaR
<0
alp
<0
a'Yp
aIR
>0
a'Yp
>0
alp
>0
a'YR
aIR
<0
a'YR
>0
alp
>0
aB
aIR
<0
aB
Federal Reserve Bank of San Francisco
45
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@FedFRASER