Full text of Economic Review (Federal Reserve Bank of Cleveland) : 1994 Quarter 4, Vol. 30, No. 4

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Vol. 30, No. 4

ECONOMIC REVIEW

1994 Quarter 4
Tax Structure, Optimal Fiscal
Policy, and the Business Cycle

2

by Jang-Ting Guo and Kevin J. Lansing

Cross-Lender Variation in
Home Mortgage Lending

15

by Robert B. Avery, Patricia E. Beeson,
and Mark S. Sniderman

The Efficiency and Welfare Effects
of Tax Reform: Are Fewer Tax
Brackets Better than More?
by David Altig and Charles T. Carlstrom




FEDERAL RESERVE BANK
OF CLEVELAND

30

■
ECONOMI C

REVIEW

1994 Quarter 4
Vol. 30, No. 4

Tax Structure, Optimal
Fiscal Policy, and the
Business Cycle

2

by Jang-Ting Guo and Kevin J. Lansing
The real business cycle (RBC) approach to the study of aggregate fluctua­
tions is now a well-established paradigm in macroeconomics. Most RBC
models abstract from government fiscal policy altogether or treat it as some
exogenous stochastic process. This article develops an RBC model in
which government fiscal variables such as tax rates and public expendi­
tures are endogenous. The authors characterize the "optimal” behavior of
fiscal policy over the business cycle for two different tax structures and re­
late this behavior to movements in private-sector variables like output, con­
sumption, labor hours, and Investment. As a benchmark, they also provide
a comparison between the model and U.S. data.

Cross-Lender Variation in
Home Mortgage Lending

15

by Robert B. Avery, Patricia E. Beeson,
and M arkS . Sniderman
This study evaluates the feasibility of using information collected under the
Home Mortgage Disclosure Act (HMDA) to form quantitative measures of
lender activity for use in enforcement. By evaluating three firm-level meas­
ures— loan application, approval, and origination rates— the authors find
that cross-lender variation in minority and low-income originations primar­
ily reflects differences in home mortgage application rates, not in approval
rates. The authors also compare gross measures of lender performance
with indices controlling for property location and loan applicant charac­
teristics and determine that they perform similarly. This suggests that most
of the variation in lender behavior is idiosyncratic and cannot be attributed
to variance in applicant characteristics reported in the HMDA data or to dif­
ferences in the geographic markets served by the lenders.

The Efficiency and Welfare Effects
of Tax Reform: Are Fewer Tax
Brackets Better than More?

30

by David Altig and Charles T. Carlstrom
On the wish list of many members of the new Congress is an income tax system
characterized by constant marginal tax rates, typically referred to as a flat-tax
system. In reality, what we are likely to see Is a continuation of the worldwide
trend toward replacing systems with high marginal-rate progressive with
those that have a smaller number of rates that are flat over relatively broad in­
come ranges. In this article, the authors compare a simple two-bracket tax
code with an approximation to traditional structures that entail steeply rising
marginal tax rates. Their conclusion — that the simpler rate structures are not
necessarily more efficient than alternatives with numerous, highly progressive
brackets — serves as a cautionary note to potential reformers.




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2

Tax Structure, Optimal
Fiscal Policy, and the
Business Cycle
by Jang-Ting Guo and Kevin J. Lansing

Introduction
The real business cycle (RBC) approach to the
study of aggregate fluctuations is now a wellestablished paradigm in macroeconomics. The
early groundbreaking articles in this area
(Kydland and Prescott [1980a, 1982] and Long
and Plosser 119831) completely abstracted from
government behavior, yet were reasonably suc­
cessful in capturing the broad comovements
and relative variabilities of the economic aggre­
gates that characterize the business cycle.
More recently, researchers have introduced
elements of government fiscal policy into these
models to help match various business cycle
facts. For example, Christiano and Eichenbaum
(1992) include stochastic government spending
in the household utility function to help explain
the low observed correlation between labor
hours and real wages (as measured by average
labor productivity) in postwar U.S. data. This
works in their model because shocks to gov­
ernment spending impact the marginal utility
of private consumption and thereby induce
shifts in the household labor supply. These
interact with labor demand shifts (caused by
technology shocks) to produce a low correlation

between wages and hours. Braun (1994) and


Jang-Ting guo is an assistant profes­
sor of economics at the University of
California, Riverside, and Kevin J.
Lansing is an economist at the Fed­
eral Reserve Bank of Cleveland. For
helpful comments and suggestions,
the authors thank David Altig,
Charles T. Carlstrom, Jagadeesh
Gokhale, Joseph G.Haubrich,
Finn Kydland, Peter Rupert, and
an anonymous referee.

McGrattan (1994) show that a similar result can
be obtained by introducing stochastic distortionary taxes to shift the labor supply curve. A
common feature of these studies is that govern­
ment policy is viewed as exogenous.
In this paper, we develop an RBC model in
which government fiscal variables such as tax
rates and public expenditures are endogenous.
Our objective is to characterize the “optimal”
behavior of these policy variables over the
business cycle and to relate this behavior to
movements in private-sector variables like out­
put, consumption, labor hours, and investment.
As a benchmark, we also provide a comparison
between the model and U.S. data.
We build on the recent work of Chari, Chris­
tiano, and Kehoe (1994), who develop a com­
petitive RBC model in which a government
policymaker chooses an optimal sequence of distortionary taxes on labor and capital income in a
dynamic version of the Ramsey (1927) optimal
tax problem. Our model differs from theirs in
three main respects. First, we introduce monopoly
profits into the production sector of the economy
such that the optimal steady-state tax on capital is
positive, consistent with U.S. observations. In a
competitive model, this tax rate is zero (see Judd
[19851 and Chamley [19861). Second, our model

3

incorporates the "indivisible labor” specification
of Rogerson (1988) and Hansen (1985). In
standard RBC models (which abstract from
government), the indivisible labor specification
serves to increase the variability of hours rela­
tive to the real wage to a value that is more in
line with U.S. data. Third, we endogenize the
time series of government spending by includ­
ing in household preferences a separable term
that represents the utility provided by public
goods. In the Chari, Christiano, and Kehoe
model, government spending follows an exoge­
nous stochastic process.
We compare simulations from our model to
post-WWII, annual U.S. data and an otherwise
similar model with nondistortionary lump-sum
taxes. Our results can be summarized as follows:
For a given stochastic process of the technology
shock, we find that optimal distortionary taxes
reduce the variability of output and labor hours,
but increase the relative variability of household
investment, compared to the model with lump­
sum taxes. This result can be traced to the behav­
ior of the optimal distortionary tax rates on labor
and capital income. The optimal labor tax in the
model is procyclical, which reduces the variability
of hours (and output) by providing households
with an implicit insurance mechanism against
variations in their after-tax wage. The optimal
capital tax in the model is countercyclical and dis­
plays a high standard deviation relative to the
labor tax. This tends to increase the variability of
household investment relative to output, but pro­
vides an efficient means of absorbing shocks to
the government’s budget (which are caused by
changes in the size of the tax base over the busi­
ness cycle).
In addition, we find that the distortionary tax
model underpredicts the variability of hours
worked relative to the real wage in U.S. data, de­
spite our specification of indivisible labor. This
result is due to the procyclical optimal labor tax,
which tends to reduce the variability of hours
worked in comparison to a standard RBC model
with indivisible labor. Finally, both mcxlel versions
capture the procyclical behavior of government
spending in annual U.S. data, but underpredict
its variability over the business cycle. We find that
this comparison, as well as comparisons along
some other dimensions, are substantially improved
if we exclude U.S. data prior to 1954 to avoid the
influence of the Korean War. However, a few
comparisons, such as the correlation between gov­
ernment spending and output, become worse.
The remainder of the paper is organized as
follows: Sections I and II describe the model and
the solution method. The choice of parameter


values is discussed in section III. Section IV
examines the business cycle characteristics of
the two tax structures and compares them to
U.S. data. Concluding remarks are presented in
section V.

I. The Model
The model economy consists of three types of
agents: households, firms, and the govern­
ment. Households obtain direct utility from
government-provided public goods, which are
financed by taxes on households and firms.
Following Benhabib and Farmer (1994), we
postulate that firms w hich produce intermedi­
ate goods exhibit some degree of monopoly
power such that they realize positive economic
profits even though the final-goods sector of
the economy is perfectly competitive. The prof­
its are equal to the difference between the
value of output and the payments made to in­
puts. The reason for introducing profits is to
obtain a positive optimal tax rate on capital un­
der the distortionary tax structure, consistent
with U.S. observations.1
As owners of the firms, households receive
net profits in the form of dividends. It is as­
sumed that profits are initially taxed at the firm
level, then distributed as dividends and taxed
again at the household level. This formulation
is intended to capture the double taxation of
corporate dividends in the U.S. economy. Further­
more, under the distortionary tax structure, we
assume that the government can distinguish
between labor and capital income, but cannot
distinguish between the various categories of
capital income, such as profits, dividends, bond
interest, and capital rental income. Therefore,
this version of the model includes only two
types of distortionary taxes: a labor tax and a
capital tax.

■ 1 Jones, Manuelli, and Rossi (1993) show that the existence of
profits and a restriction on the menu of available tax instruments (the ab­
sence of a separate profits tax) is one method of obtaining a positive opti­
mal tax rate on capital in the steady state. Without profits, the optimal
steady-state tax on capital is zero.

The Household’s
Problem
There is a continuum of identical, infinitely
lived households, each of which maximizes a
stream of discounted utilities over sequences
of consumption and leisure:
(1)

max
•fi’o X ^
cr br
-h,+■ t= o

^nct ~ A bt +B\ngt)

0 < |3< 1, A, B > 0 .

(3)

In this utility function, (3 is the household dis­
count factor and ct represents private consump­
tion goods. The symbol Et is the expectation
operator conditional on information available at
time t. Each household is endowed with one
unit of time each period and works ht hours dur­
ing period t. The fact that utility is linear in hours
worked draws on the formulation of indivisible
labor described by Rogerson (1988) and Hansen
(1985). This means that all fluctuations in labor
hours are due to changes in the number of work­
ers employed, as opposed to variations in hours
per worker.2 Household preferences also include
a term representing the utility provided by aggre­
gate public consumption goods gt. The separabil­
ity in ct and gt implies that public consumption
does not affect the marginal utility of private con­
sumption, a specification supported by parameter
estimates in McGrattan, Rogerson, and Wright
(1993). Households view gt as outside their con­
trol. Examples of public consumption goods that
might affect household utility are national de­
fense, police protection, and government provi­
sion of food and shelter during natural disasters.
Public goods are assumed to be noncongestable
and free of specific user charges.
The representative household faces the fol­
lowing within-period budget constraint:
(2)

kt+1 = (1 - 5) kt+ x t ,

0 < 8 <1 .

Households view tax rates, wages, interest
rates, and dividends as determined outside
their control.

Household
Optimality
The household first-order conditions with respect
to the indicated variables and the associated
transversality conditions (TVC) are

(4a)

c ■X = —
'
c,

(4b)

b,:

(4 0

kt+, :

X,(\-\b,)W = A

x, = p £ , x (+1
[(1 - T 41+ i ) ( ri+1 - 8) + 1]

(4d)

b
X =M
BE
u t + i •■ 'W
^ t ^X t + 1
~ 1 k t+ 1 ) r b t+ 1 +

(4e)

TVC: lim E 0
t—

kt+1 = 0,

lim E 0 $ fX tbt+1 = 0 ,
t—

c t+ x t + b t+1< ( l -\ht)w t ht
+ (1-T kt)(rtk,+

the firm’s net profits, Kt (which are distributed
to households as dividends), and the interest
earned on government bonds, rhtbt. Dividends
and interest are taxed at the same rate as capital
rental income, rtkt. The term Tktdkt represents
the depreciation allowance built into the U.S. tax
code, and Tt is a lump-sum tax.
The following equation describes the law of
motion for the capital stock, given a constant
rate of depreciation 8:

Kt + rbtbt)

+ Tktdkt + bt- Tt,

where X, is the Lagrange multiplier associated
with the budget constraint (2) in period t. The
interpretation of X t is that it represents the

k 0 ,b 0 given,
w'here xt is investment, kt is the stock of physi­
cal capital, and bt+l represents one-period, real
government bonds carried into period t + 1 by
the household. Households derive income by
supplying labor and capital services to firms at
rental rates u\ and rr and pay taxes on labor and
capital income at rates xht and xkt, respectively.
Two additional sources of household income are




■ 2 The linearity of (1) in h t implies that the effective labor-supply elas­
ticity of the representative household is infinite. In a decentralized economy,
both Rogerson and Hansen show that this utility function can be supported
by a lottery that randomly assigns workers to employment or unemployment
each period, with the firm providing full unemployment insurance. Wage
contracts call for households to be paid based on their expected (rather than
actual) number of hours worked. RBC models with indivisible labor are better
able to match some key characteristics of aggregate labor market data. Spe­
cifically, U.S. data display a large variability of hours worked relative to the
real wage, and a weak correlation between hours and the real wage (see
Christiano and Eichenbaum [1992]).

5

marginal utility of an additional unit of after-tax in­
come received in period t. The transversality con­
ditions ensure that the household’s within-period
budget constraint (2) can be transformed into an
infinite-horizon, present-value budget constraint.

The Firm’s Problem
This section closely follows the model devel­
oped by Benhabib and Farmer (1994). Suppose
there exists a continuum of intermediate goods
yit, i e [0,11 and a unique final good yt that is
produced using the following constant-returnsto-scale technology:

(8c)
Due to their monopoly power, intermediategoods producers earn an economic profit that
is taxed at rate xkt. The firm’s after-tax profits,
distributed to households in the form of divi­
dends, are
(9a)

nt= ( l - x b )(yt- rt k t - w t ht).

(9b)

7t,= (1 - xkt) (1 - 01 - 02 )yt.

The Government’s
Problem
(5 )

yt =

y ^di

We assume that the final-goods sector is per­
fectly competitive, but that intermediate-goods
producers exert a degree of monopoly powrer
that is captured by the parameter x In the spe­
cial case when x = 1, all intermediate goods are
perfect substitutes in the production of the final
good, and the intermediate sector becomes per­
fectly competitive.
Each intermediate good is produced using the
same technology, with labor and capital as inputs:
(6)

yit = e x p (zt) k ? h ° 2,
0 < a . < 1, a 2 + a , = 1

(7)

zt+i - Pzzt +Et+v 0 < Q Z< 1 ,
Et ~ i.i.d. (0, Oe2), zQ given,

where (7) is the law of motion for aggregate tech­
nology shocks zt, which are revealed to agents
at the beginning of period t and which generate
business cycle fluctuations in the model. Under
the assumptions that firms maximize profits and
factor markets are competitive, Benhabib and
Farmer show that in a symmetric equilibrium
(kit = kt and hit= ht for all /), the aggregate pro­
duction function, the rental rate on capital, and
the real wage are
(8a)

yf = exp (zt) kta\
htaz,

(8b)

r/=ei j ’ 9i =%a i -and




yt

The government chooses an optimal program
of taxes, borrowing, and public expenditures
in order to maximize the discounted utility of
the household. This is a dynamic version of the
Ramsey (1927) optimal tax problem, where Tht,
xkt, rht, gt , and Tt summarize government pol­
icy implemented at time t. To set up this prob­
lem, we begin by spelling out some important
assumptions. First, we assume that the govern­
ment can com m it to a set of time-invariant de­
cision rules that specify policy variables as a
function of state variables. This is done to avoid
the complicating issue of time inconsistency,
which arises in policy design problems when
the tax base includes fixed assets (such as capi­
tal or bonds) that cannot be quickly adjusted
in response to a change in the level of the tax.
In these situations, the government has an in­
centive to deviate from its originally announced,
optimal policy by implementing surprise in­
creases in asset taxes in order to obtain nondistortionary tax revenue. Because households
understand that the original policy is time incon­
sistent, it cannot be supported as an equilibrium
unless the government can commit itself (and all
successor governments) to carrying out the plan.3
Second, given that the initial stocks of capital
and bonds are fixed, we rule out any confisca­
tory taxes on assets at t = 0 that might be used
to finance all future expenditures. This case is
not very interesting because no taxes beyond the
initial period are required. With these assump­
tions, the government’s problem is

■ 3 The time inconsistency problem does not arise under the lump­
sum tax structure because taxes are nondistortionary. See Chari (1994)
for a summary of the issues and a review of the literature dealing with
time inconsistency problems and optimal policy design.

6

(10)

max

£ 0 X P' {\nct - A h t +B\ngt)

8,’ h n h ,

1=0

subject to
(i)

household first-order conditions and the
budget constraint,

(11)

firm profit-maximization conditions,

(iii)

g t = b t + l - b t(l + rht)
+ x hlw tb t + x kt[(rt- S ) k t+ r htb t]

+[1 —(1 — x kt) 2] (1 —0j —02)j^-i- Tt,

(iv)

7’ = 0 for the distortionary tax structure,

(y )

xht = xkt = 0 for the lump-sum tax structure,

(vi)

lim —------------------ = 0.

bt

n n + (i
/■
=i

)ri«-i i

As a condition for equilibrium, government
policy must take into account the rational re­
sponses of households and firms, as summarized
by constraints (i) and (ii). The chosen policy
must also satisfy the government’s within-period
budget constraint (iii), where the squared term
on the right-hand side reflects the double taxa­
tion of firm dividends. Constraints (iv) and (v)
impose the restrictions associated with the two
tax structures wre intend to analyze. For the dis­
tortionary tax structure, we rule out the possi­
bility of lump-sum taxes. For the lump-sum tax
structure, we set xht and X kt equal to zero. Fi­
nally, (vi) is a transversality condition ensuring
that the government budget constraint is satis­
fied in present-value temis. The summation of
the household budget constraint and the gov­
ernment budget constraint yields the following
resource constraint for the economy:
(11)

yt = c t + xt + gr

Because the resource constraint and the govern­
ment budget constraint are not independent
equations, equation (11) will be used in place of
(iii) in solving the government’s problem.




II. Solving
the Model
Our approach to solving the government’s prob­
lem is to find the allocations ct, ht, kt +v and
bt+l that maximize household utility subject to
the constraints, where allocations are ex­
pressed as functions of the economy’s state
variables. The appropriate set of prices rt and
wt and the policy variables x ht, X kt, rht, gt , and
Tt that decentralize the optimal allocations can
be computed using the profit-maximization
conditions (8), the household first-order condi­
tions (4), the household budget constraint (2),
and the resource constraint ( l l ) . 4 For example,
the optimal allocations uniquely determine X,
and wt through equations (4a) and (8c). Given
Xt and wt, the household’s first-order condition
for ht, equation (4b), uniquely determines the
government’s optimal choice for x ht. The gov­
ernment has much more flexibility, however, in
choosing the optimal capital tax and the optimal
interest rate on government debt. The expecta­
tion operators in the household’s first-order
conditions for kt+1 and bt+1, equations (4c) and
(4d), imply that the after-tax returns on capital
and bonds (weighted by marginal utility) must
be the same “on average.” In response to a se­
ries of shocks, the government can satisfy this
ex ante arbitrage condition and implement the
optimal allocations using many different combi­
nations for the period-by-period values of x kt
and rht. Consequently, the stochastic version
of the model does not uniquely pin down the
time-series behavior of these policy variables
(see Zhu [1992] and Chari, Christiano, and Kehoe [1994] for a more complete description).
To facilitate a comparison with U.S. data,
w7e make a particular assumption about the
way in which the government picks x kt and rht
to decentralize a set of allocations. Specifically,
we employ the certainty versions of (4c) and
(4d) to identify xkt and rht each period. Requiring
the government to satisfy the certainty versions
of these constraints guarantees that the uncer­
tainty versions will also be satisfied. Essentially,
we are restricting the policy instruments available
to the government by ruling out fully flexible,
state-contingent capital taxes and bond interest
rates. This might be interpreted as reflecting the
political infeasibility of some types of policy re­
gimes. The restriction we impose has an impact
on the behavior of the allocations in response to
stochastic shocks, as does any other restriction

■ 4 This method of solving the government’s problem is described
as the “primal" approach by Atkinson and Stiglitz (1980), chapter 12.

on the set of available policy instalments (such as
ailing out lump-sum taxes). Consequently, the allo­
cations we compute in response to shocks are dif­
ferent from the “Ramsey allocations” that could be
supported in an unrestricted environment.^ In the
restricted case, the government’s decision rules
for Tkt and rht are identical to those for an econ­
omy with no uncertainty. It is important to note
that this result follows from a particular decentral­
ization scheme. However, our solution method
also employs a linear-quadratic approximation of
the problem. Thus, the decision rules governing
household allocations also display the property
of certainty equivalence.6
Given these assumptions, the government’s
problem with distortionary taxes can be solved
using a recursive algorithm developed by Kydland and Prescott (1980b). The problem with
lump-sum taxes can be solved by adopting the
view of a social planner for an appropriately
defined “pseudo-economy” in which the plan­
ner cannot exploit the monopoly power of
firnis. The government’s problem under lum p­
sum taxes is not equivalent to a standard social
planning problem because when X < b the decentralized equilibrium is not Pareto optimal.
The pseudo-economy approach is an indirect
method of obtaining the equilibrium allocations
(see Stokey and Lucas [19891, chapter 18). Gov­
ernment debt does not appear in the pseudo­
planner’s problem. This reflects the wellknown “Ricardian proposition,” which states
that government debt policy is irrelevant to the
determination of equilibrium allocations in an
economy with lump-sum taxes (see Sargent
[19871, chapter 3). Since debt doesn't matter in
this case, we arbitrarily set it equal to zero
each period such that g t = Tr The pseudo­
planner’s problem is recursive and can be
solved using standard methods.

III. Calibrating
the Model to the
U.S. Economy
To explore the quantitative predictions of the
model, we assign parameter values based on
empirically observed features of post-WWII
U.S. data. The time period in the model is
taken to be one year, which is consistent with
both the time frame of most government fiscal
decisions and the frequency of available data
on average marginal tax rates. The discount
factor P (= 0.962) implies an annual rate of
time preference of 4 percent. The parameter A
in the household utility function is chosen such



that the fraction of time spent working is close
to 0.3 in the steady state for each tax structure.
This coincides with time-use studies, such as
Juster and Stafford (1991), which indicate that
households spend approximately one-third of
their discretionary time in market work. The
value of B is chosen to yield a steady-state
value of g/y near 0.22 for each tax staicture,
the average ratio of government spending to
GNP for the U.S. economy from 1947 to 1992.8
The steady-state level of government debt is
chosen to yield a steady-state ratio of b/y
equal to 0.45. This is the average value of U.S.
federal debt held by the public as a fraction of
GNP from 1947 to 1992.9
The exponents in the Cobb-Douglas pro­
duction function are chosen on the basis of
two criteria. First, the selected values of 0,
(= 0.31) and 0, (= 0.60) are in the range of the
estimated shares of GNP received by capital
and labor in the U.S. economy (see Christiano
[1988]). Second, the model’s share of output
devoted to monopoly profits (= 1 - 0 ( —0, ) is
chosen to yield a reasonable value for the
steady-state tax on capital (Tk) under the distor­
tionary tax structure. Because a separate profits
tax is not available in this case, the government
uses the tax on private capital to recapture a
portion of the profits. In the model, the steadystate ratio of profits to output is 0.09, and the

■ 5 See Chari, Christiano, and Kehoe (1994) for examples of decentrali­
zations that support the Ramsey allocations. See Cassou (forthcoming) for a
case where policy instruments are restricted to follow a univariate Markov
process in response to government spending shocks.

■

6 The approximate version of the problem involves the maximiza­
tion of a quadratic objective function subject to linear constraints. Since
the first-order conditions are linear in all variables, the expectation opera­
tor can be passed through the expressions, dropping out stochastic
terms associated with the technology shock innovation e /+1 in equation
(7). See Sargent (1987), p. 36.
■ 7 A technical appendix to this paper, available from the authors
upon request, describes the details of our solution procedure.
■ 8 The specific parameter values used in the computations are
A = 2.50, B = 0.350 for the distortionary tax structure, and A = 3.48,
0=0.381 for the lump-sum tax structure.

■ 9 The model does not pin down a unique value for the steady-state
level of government debt (see Chamley [1985]). Rather, steady-state debt
is a function of the initial level of debt, b Q, and the entire transition path
of taxes and spending from t= 0 until the steady state is reached. As an
alternative to performing this difficult computation, we follow the ap­
proach of Lucas (1990) and simply choose the level of steady-state debt
to reflect a debt-to-GNP ratio consistent with the data. We assume that b Q
and the transition path are set such that the government budget constraint
is satisfied in present-value terms. Data on U.S. federal debt held by the
public are from Federal Debt and Interest Costs, Congressional Budget
Office, 1993, table A-2.

8

resulting steady-state tax on capital is 0.31. This
value of xkapproximates the average effective
corporate tax rate in the United States from
1947 to 1980, as estimated by Jorgenson and
Sullivan (1981).10 The steady-state tax on labor
(xh) turns out to be 0.25. This is close to the
average marginal tax rate on labor income
from 1947 to 1983, as estimated by Barro and
Sahasakul (1986). The U.S. tax rate estimates
can be viewed as summarizing the various ele­
ments of the tax code that impact the behavior
of agents. These include not only the statutory
rate, but also the many types of exemptions,
deductions, credits, and allowances.
The monopoly power parameter % is chosen
such that the aggregate production technology
demonstrates constant returns to scale. Given
the values chosen for 0j and 0 ,, a value of
X = 0.91 yields yt = exp (z t) kt 0i4 ht 066. The
capital depreciation rate 8 (= 0.07) is consistent
with values commonly used in the RBC litera­
ture. Together with the values of (3 and 0,, this
depreciation rate implies a steady-state ratio of
capital to output ranging from 2.4 (under the
distortionary tax structure) to 2.8 (under the
lump-sum tax structure), and a ratio of invest­
ment to output ranging from 0.17 to 0.20. The
corresponding average ratios for the U.S. econ­
omy from 1947 to 1992 are 2.58 and 0.21. The
process governing technology shocks is esti­
mated using annual data from 1947 to 1992. The
series for zt was constructed by computing the
changes in output not accounted for by changes
in the productive inputs.11 The parameter esti­
mates, p„= 0.85 and cre = 0.015, are close to
those estimated by other studies using annual
data, such as Benhabib and Jovanovic (1991).

IV. Simulation
Results
In this section, we describe the model’s predic­
tions for the behavior of fiscal policy over the
business cycle and provide a comparison with
U.S. data. The simulation results are shown in

■ 10 Higher prolit levels imply a higher steady-state tax on capital in
our model. When profits are zero (01 + 0 2 = 1), the optimal steady-state
tax on capital is zero. If a separate profits tax were available, the govern­
ment would choose to tax profits at 100 percent and other capital income
at 0 percent in the steady state (see footnote 1).
■ 11 The production function residual was measured as zt = InGNPt0.34ln/r?-0.66ln/7r The private capital stock k, is defined as fixed private
capital + stock of consumer durables + residential capital from Fixed Repro­
ducible Tangible Wealth in the United States, U.S. Department of Commerce,
1993. Real GNP and the labor input (ht = LH0URS) are from Citibase.




tables 1-2 and figures 1-5. Note that the distor­
tionary tax structure makes predictions for a
larger set of variables than does the lump-sum
tax structure. The additional variables are the
stock of real government debt, bt, and the
average marginal tax rates on labor and capital
income, xht and xkru
In comparison to the full sample of U.S. data
from 1947 to 1992, both tax structures underpredict the standard deviation of output ( y t ) ,
consumption (<;,), government expenditures
(g t), and hours (b t), but overpredict the stan­
dard deviation of investment (xt). Since we
employ a general-equilibrium framework, the
behavior of one variable cannot be viewed in
isolation, because it is linked by the equilib­
rium conditions to the behavior of other vari­
ables in the model. For example, the low
variability of output is linked to the low vari­
ability of hours, because the production tech­
nology is labor intensive.13 Likewise, the low
variability of consumption is linked to the high
variability of investment, because changes in
household saving (which correspond to changes
in investment) act as a buffer against earnings
shocks, thereby allowing households to smooth
their consumption over the business cycle. Con­
sistent with standard RBC models (see Kydland
and Prescott [1982]), both model versions cap­
ture the fact that output is more variable than
consumption, but less variable than investment,
over the U.S. business cycle.
In comparison to the lump-sum tax structure,
the distortionary tax structure displays a lower
standard deviation of output and hours and a
higher variability of investment relative to out­
put. This behavior can be traced to the move­
ment of the optimal distortionary tax rates on
labor and capital income. Specifically, the opti­
mal labor tax is procyclical (positively corre­
lated with output), while the optimal capital tax
is countercyclical. The procyclical labor tax oper­
ates to smooth households’ after-tax income from
labor. For example, a positive technology shock
(which shifts the production frontier outward
and raises the real wage) is accompanied by an
increase in xht. The higher tax rate tends to offset
the higher real wage and thus provides households
with an implicit insurance mechanism against

■ 12 In all figures, model variables are the realizations from a single
simulation (based on randomly drawn shocks) to compare volatility and
persistence properties with the corresponding U.S. variables. There is no
intention to predict the actual time path of U.S. variables.

■ 13 This can be readily observed from the aggregate production
function (equation [8a]), where the coefficient on the labor input, a 2 =
0.66, is nearly double the coefficient on the capital input, a 1= 0.34.

9

TABLE

1

Business Cycle Statistics for
Models and the U.S. Economy
Standard Deviation (percent)

Variables

Distortionary
Tax
Structure“1

Lump-Sum
Tax
Structure3

U.S. Economy*5
1947-92

1954-92
2.16

2.11

2.39

2.46

ct

0.69

0.96

1.14

1.19

s,

1.66

1.00

6.45

3.04

y,

k.

1.05

1.03

0.75

0.74

xt

9.10

9.00

5.96

6.14

h,
yt /h,

1.19

1.60

1.76

1.86

1.09

0.96

1.45

0.90

b,

2.72

—

4.54

4.80

T ax rates

xb,

1.71

—

6.42

4.08

xkt

13.91

—

17.76

19.28

3.61

1.62

2.65

1.88

Rev/yt

Contemporaneous Correlation with Output

Variables

Distortionary
Tax
Structure“1

U.S. Economy15

Lump-Sum
Tax
Structure“1

1947-92

1954-92
0.87

0.67

0.89

0.71

st

0.98

0.85

0.62

0.40

k.

0.03

- 0 .0 1

0.62

0.63

xt

0.97

0.97

0.69

0.89

bt
yt /ht

0.93

0.96

0.81

0.91

0.92

0.89

0.71

0.52

bt

0.03

—

0.23

0.36

0.97

—

0.39

- 0 .1 0

—

0.08

- 0 .1 5

0.39

0.11

T ax rates

*bt

*kt
Rev/yt

- 0 .9 3
- 0 .9 1

- 0 .9 5

a. Model statistics are means over 100 simulations, each 46 periods long, after
dropping the first 50 periods. The symbol Rev/yt is the economywide average
tax rate, defined as total tax revenue as a fraction of output.
b. The following quarterly series from Citibase were annualized before computing
the statistics: y, = GNPQ, c, = GCN Q + GCSQ (nondurables + services), g, = GGEQ,
h,= LHOURS (household survey), and } ’i /h,= GNPQ/LI IOURS. The series for x,
is business fixed investment + consumer durable expenditures + residential invest­
ment. The series for kt is fixed private capital + stock of consumer durables + resi­
dential capital. Both x, and k, are annual series from Fixed Reproducible Tangible

Wealth in the United States, U.S. Department of Commerce, 1993- The series for
bt is federal debt held by the public from Federal Debt and Interest Costs, Congres­
sional Budget Office, 1993, table A-2, where nominal debt has been converted
into real debt by dividing by the GNP deflator for each year. Rev/y, is total gov­
ernment receipts (federal, state, and local) as a fraction of GNP from Economic

Report o f the President, 1991, 1994, table B-80. Data on average marginal tax rates
do not extend over the full sample: xht is from Barro and Sahasakul (1986) for
1947-83, and x^ is from Jorgenson and Sullivan (1981), table 11. for 1947- 80.
NOTE: Before computing the statistics, all series were logged and detrended using
the Hodrick-Prescott filter (see Prescott [1986]). The smoothing parameter for the
filter was set at 100, since all data are at annual frequency.
SOURCE: Authors’ calculations.




variability in the after-tax wage (1 - zht) u\.
Since labor supply decisions depend on the
quantity (1 - Tht) wt (see equation [4b]), a
lower variability in the after-tax wage leads to
a lower variability in hours worked. With a
labor-intensive production technology, this
also leads to lower variability in output.
Zhu (1992) shows theoretically that the cycli­
cal behavior of the optimal labor tax depends
on the degree of risk aversion (or curvature)
exhibited by the household utility function. The
optimal labor tax is procyclical for low-riskaversion (less curved) utility functions, such as
the logarithmic case used here, but counter­
cyclical for high-risk-aversion (more curved)
functions. Chari, Christiano, and Kehoe (1994)
provide a quantitative demonstration of this re­
sult. In general, the level of risk aversion deter­
mines the amount by which households are
willing to adjust their labor supply in response
to a change in the real wage. With low risk
aversion, the substitution effect of an increase
in wt (caused by a positive technology shock)
results in a relatively large increase in labor
hours. The government takes advantage of this
greater willingness to work by raising the tax
on labor, thereby collecting additional reve­
nue, but still allowing an increase in labor to
spur output during this period of high labor
productivity. With high risk aversion, however,
the substitution effect is much smaller; that is,
households are less willing to increase their
labor supply in response to the higher real
wage. The government’s optimal response now
is to lower the tax rate on labor. This stimulates
labor supply in order to boost output while
labor productivity is high. Our results are con­
sistent with the findings of these researchers.
The capital tax in the model moves counter­
cyclical^ and displays high variability relative to
the labor tax (see table 1 and figures 1-2). This
serves to increase the variability of household in­
vestment relative to output under the distortionary tax structure. Ordinarily, a positive technology
shock raises the real rate of interest and motivates
an increase in investment because the rate of
return becomes more attractive. However,
when a positive technology shock is accompa­
nied by a decrease in x kt, the after-tax return
on investment becomes even more appealing,
leading to a larger rise in investment. From the
government’s perspective, a countercyclical
capital tax is optimal because it serves as an
efficient means of absorbing shocks to the gov­
ernment’s budget constraint. These shocks are
caused by changes in the size of the tax base
over the the business cycle. For example, a
positive technology shock generates more tax

10

FIGURE

1

Capital Tax Rates
Percent

Year
a. Distortionary tax structure.
SOURCES: Jorgenson and Sullivan (1981); and authors’ calculations.

F I G U R E

2

Labor Tax Rates
Percent

Year
a. Distortionary tax structure.
SOURCES: Barro and Sahasakul (1986); and authors’ calculations.

FIGURE

3

Government Expenditures as a
Fraction of GNP

revenue because GNP and household incomes
(the tax base) increase. This motivates a reduc­
tion in xkt because government spending require­
ments can be met using a lower tax rate. A similar
argument holds in reverse for the case of a nega­
tive technology shock. Absorbing shocks mainly
by changes in xkt, as opposed to changes in xht,
is efficient because the capital stock cannot be
quickly adjusted in response to a change in the
capital tax. In contrast, the household can instan­
taneously adjust labor supply in response to a
change in the labor tax. The shock-absorbing
feature of Xkt allows the government to maintain
a very smooth time series for gt/ yt, as compared
to the lump-sum tax structure (see figure 3).14
We experimented with varying the level of
monopoly profits by adjusting the values of
the parameters 0, , 0 „ and % . In general, we
found that as profits declined, the standard de­
viation of xkt i ncreased. The intuition for this
result is straightforward. Recall that dividends
(equal to after-tax profits) do not distort house­
hold decisions because profits are determined
outside households’ control. A lower level of
profits implies a smaller and more elastic tax
base for the capital tax. Consequently, larger
changes in the tax rate are needed to produce
the same revenue effect when responding to
technology shocks.
The model’s prediction that the capital tax
should display more variability than the labor
tax is consistent with the U.S. tax-rate estimates
we have chosen for comparison.1^ Note, how­
ever, that the correlation coefficients between
U.S. tax rates and real GNP display a change
in sign, depending on the sample period. The
labor tax and the capital tax are weakly procy­
clical using data on average marginal tax rates
that begin in 1947, but weakly countercyclical
for data that begin in 1954. The model, on the
other hand, predicts a strongly procyclical labor
tax and a strongly countercyclical capital tax.
Thus, there is a sharp negative correlation

Percent

■ 14 The optimality of using a state-contingent capital tax to absorb
budget shocks has been shown previously by Judd (1989) and Chari,
Christiano, and Kehoe (1994). Our quantitative results are not directly
comparable because Judd does not explicitly model household behavior,
and Chari, Christiano, and Kehoe employ a different decentralization
scheme for

and rbt.

■ 15 The figures display the tax-rate series before detrending. For
quantitative comparisons (table 1), detrending is necessary because the U.S.
labor tax displays a distinct upward trend, while the U.S. capital tax displays
a downward trend. These trends have no counterpart in the model. The trend
a. Distortionary tax structure.
b. Lump-sum tax structure.
SOURCES: Citibase; and authors' calculations.




in xht is possibly linked to the phenomenon of “bracket creep,” which ex­
isted before tax schedules were indexed for inflation in 1985. Auerbach and
Poterba (1988) argue that the downward trend in x w is due to increasingly
generous investment tax credits and accelerated depreciation schedules.

n
FIGURE

4

Total Tax Revenue as a
Fraction of GNP
Percent

Year
a. Distortionary tax structure.
b. Lump-sum tax structure.
SOURCES: Economic Report o f the President, 1991, 1994; and authors’
calculations.

FIGURE

5

Government Debt as a
Fraction of GNP
Percent

SOURCES: Congressional Budget Office, Federal Debt and Interest Costs, 1993;
and authors’ calculations.

between Xkt and xht in the model, while the
corresponding correlation in the data is weakly
positive.16 Figure 4 displays the economywide
average tax rate, defined as total tax revenue
as a fraction of output. This rate is countercycli­
cal in both versions of the model, but weakly
procyclical in the U.S. data. Thus, the model
does not capture some important features of
U.S. tax-rate movements. This highlights the dif­
ficulty of summarizing the entire U.S. tax code
using only one or two broadly defined rates.
The predicted standard deviations for gt are
substantially lower than the U.S. value of 6.45
percent computed using the full sample. Start­
ing the sample in 1954 to avoid the influence of
the Korean War reduces the standard deviation
 of gt in the data by half, to a value of 3.04 per­


cent, which is much closer to model predic­
tions. Although we have no theoretical justifica­
tion for excluding the Korean War years (since
we include the Vietnam War), the fact that our
model contains only one type of shock limits
its ability to explain large movements associ­
ated with a war. Incorporating an additional
shock to households’ preference for public
goods to simulate high demand during wars
would increase the variability of gt in the model
(see Lansing [1994]). Both model versions capture
the procyclical behavior of government spending
in annual U.S. data, but the correlations from the
model are much stronger than observed in the
data. When the years prior to 1954 are excluded,
the correlation between government spending
and real output in the U.S. data drops from 0.62
to 0.40, worsening the comparison with the model.
In the distortionary tax structure, government
debt is essentially acyclical (it behaves similarly
to capital in this respect), but is less variable
than U.S. government debt (see figure 5). We
experimented with an alternate version of this
model in which the government is required to
balance its budget each period. For this experi­
ment, we retained the decentralization scheme
described in section II, whereby the govern­
ment is required to satisfy the certainty version
of equation (4c). Qualitatively, the results are
similar to those reported in table 1. However,
the variability of the labor tax goes up, since
government debt is no longer available to help
cushion budget shocks. The insurance effect of
the procyclical labor tax thus becomes more
significant, leading to lower variability in hours
and output. Interestingly, our model implies
that a balanced-budget amendment can help
smooth business cycle fluctuations, provided
the government sets tax rates in the manner
we have described.
The lump-sum tax structure does a reason­
ably good job of matching the relative standard
deviations of hours and the real wage, where
the real wage is measured by average labor
productivity yt/ ht (see table 2). This behavior
is typical of standard RBC models with indivis­
ible labor (see Hansen [1985]). In the distortion­
ary tax structure, however, the standard devia­
tion of hours relative to the real wage is too low,
despite the specification of indivisible labor.
The insurance effect of the procyclical labor tax

■ 16 In the U.S. data, the correlation coefficient between (logged and
detrended) xh l and x kt equals 0.36 from 1947 to 1980, the period for
which estimates of both tax rates are available. For the years 1954 to 1980,
the correlation coefficient is 0.34. In the model, the correlation coefficient
is -0 .9 7 .

T A B L E

2

Comparison of Labor Market Statistics

Variables

Distortionary7
Tax
Structure1*

Lump-Sum
Tax
Structure*1

U.S. Economy
1947-92

1954-92

a h / a v/h

1.09

1.67

1.22
2.10

2.43

corr (b, y /h )

0.72

0.72

0.16

0.13

-

0.02

2.07

-

this one to explore the welfare effects of vari­
ous tax structures and find that these effects
can be quite dramatic. In this paper, our
model meets with varying degrees of success
in matching the observed behavior of tax rates,
government spending, and aggregate eco­
nomic variables in the U.S. economy. Nonethe­
less, this exercise is useful in that it provides
information on how models of government fis­
cal policy might be improved.

0.21

a. Model statistics are means over 100 simulations, each 46 periods long, after
dropping the first 50 periods.
b. The first num ber denotes hours worked from the household survey in
Citibase (LHOURS), and the second denotes hours worked from the estab­
lishment survey (LPMHU).
NOTE: Before com puting the statistics, all series were logged and detrended
using the Hodrick-Prescott filter (see Prescott [1986]). The smoothing parame­
ter for the filter was set at 100, since all data are at annual frequency.
SOURCE: Authors’ calculations.

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V. Conclusion
We have constructed a model that combines
elements from the theory of optimal public fi­
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tions. Our aim is to develop a framework that
is useful for carrying out realistic policy experi­
ments with regard to both the structure of the
U.S. tax system and the composition and fi­
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[1994a, 1994b]), we employ models similar to

■ 17 See Chari, Christiano, and Kehoe (1994) for a more extensive
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15

Cross-Lender Variation in
Home Mortgage Lending
by Robert B. Avery,
Patricia E. Beeson,
and Mark S. Sniderman

Introduction
Federal fair housing and credit legislation ad­
dresses two major requirements. First, depository
institutions must help meet the credit needs of
their communities in a manner consistent with
safe and sound lending practices (Community
Reinvestment Act of 1977 [CRA]). Second, lenders
must not discriminate against individual appli­
cants on the basis of race, ethnic origin, gender,
or religion (Equal Credit Opportunity Act of 1974
[ECOA]) and Fair Housing Act of 1968 [as amend­
ed in 1988]). Government agencies charged with
regulating depository' institutions are responsible
for monitoring individual lenders’ compliance
with these statutes.
Historically, enforcement of the CRA and fair
lending statutes has relied on qualitative, nonstatistical methods. CRA examinations, for ex­
ample, have focused primarily on procedural
issues. With rare exception, regulators have
considered the actions of individual complain­
ants to enforce the other fair lending statutes.
In the past year, both community activists and
lenders have called for strategies to move to­
ward more quantitative, outcome-based en­
forcement procedures. These calls stem, in part,

from a belief that CRA and fair lending policy


Robert B. Avery is an associate
professor in the Department of
Consumer Economics and Hous­
ing, Cornell University, and Patricia
E. Beeson is an associate professor
of economics at the University of
Pittsburgh; both are visiting schol­
ars at the Federal Reserve Bank of
Cleveland. Mark S. Sniderman is
senior vice president and director
of research at the Federal Reserve
Bank of Cleveland. The authors
thank Glenn Canner, Charles
Carlstrom, John Duca, Stuart
Gabriel, Jagadeesh Gokhale,
John Flam, Joseph Haubrich,
Stuart Rosenthal, Peter Rupert,
and Peter Zorn for helpful com ­
ments and suggestions.

guidelines are unclear and often counterpro­
ductive, and perhaps more likely to generate
paperwork than loans and services.
A recent change in the reporting require­
ments of the Home Mortgage Disclosure Act
(HMDA) makes the move toward outcomebased enforcement procedures seem much
more feasible. Since 1990, lenders in urban
mortgage markets have been required to re­
port to regulators the neighborhood (census
tract) and a limited number of other character­
istics (such as loan size, applicant race and
income, and government guarantee) of all ap­
plications for mortgage credit during each cal­
endar year. These data permit the quantitative
comparison of a number of lending activities
across lenders. Indeed, recent proposals by the
bank regulatory agencies call for the use of
HMDA data in evaluating CRA and fair lending
compliance for lenders.1
The objective of this study is to evaluate the
feasibility of using HMDA data to form quanti­
tative measures of lender activity for use in
enforcement. We consider three potential meas­
ures of firm-level mortgage lending activity:

■ 1 See “Community Reinvestment Act Regulations," Federal Regis­
ter, O clobeH , W 4 (59 FR 51232).

16

loan application rates, loan approval rates, and
loan origination rates. We examine the extent
to which the three measures can differentiate
among hanks with respect to how they serve
four subpopulations cited in the fair lending
laws: minority loan applicants, applicants for
loans in minority neighborhoods, low-income
loan applicants, and applicants for loans in
low-income neighborhoods. Using national fil­
ings for the first year of the new7HMDA regula­
tions, 1990, we compare the performance of
measures adjusted and unadjusted for local
conditions and borrower characteristics.
Several conclusions emerge. We find that
variation across lenders in loan originations to
each of the four subpopulations is driven primar­
ily by variation in application rates, not by vari­
ation in lender approval rates. This finding holds
when both unadjusted and adjusted measures are
examined and for a wide variety of lender groups
sorted by size and type of institution. Further­
more, we find virtually no correlation between
application rates and approval rates, so using in­
dices based only on approval rates can be poten­
tially misleading when evaluating individual
lenders' compliance with the CRA. Indeed, varia­
tion in application rates appears to play a much
more significant role in explaining variation in
credit flows. Furthermore, focusing on approval
rates may lead to outcomes that are counter to
the intent of the legislation: To improve their
minority-to-white approval rates, some lenders
may discourage applications from all but the
most creditworthy minority applicants, thereby
reducing credit originations to minority and lowincome communities.
One objection that has been raised to the
use of application rates in evaluating lender
compliance is that these rates are determined
primarily by the neighborhoods that lenders
serve. Our evidence suggests that this is not
the case. Most of the variation in application
rates stems from differences in the applicants
that lenders attract w ithin neighborhoods and
not from the general racial characteristics of
the neighborhoods as a whole. Finally, we also
find that controlling for the economic character­
istics and neighborhoods of the loan applicants
provides relatively little powrer in explaining
cross-lender differences. This suggests that gross
application and approval-rate measures may give
relatively good rankings of bank performance.




I. Background of
Fair Housing
Legislation
In response to community concerns about the
flow of housing credit to minority and lowincome communities and about the extent to
wrhich individual lenders were meeting the
credit needs of their communities, Congress
passed a series of laws during the 1970s. The
ECOA of 1974 and the Fair Housing Act of 1968
(as amended in 1988) mandate that lenders do
not discriminate against individual applicants
on the basis of race, ethnic origin, gender, or
religion. Two other laws were enacted primar­
ily to fight geographic discrimination. HMDA,
enacted in 1975, requires certain lenders to re­
port annually the number and dollar value of
mortgage loans they make in their communities
according to census tract. Under the terms of
the CRA, enacted in 1977, depository institutions
must help meet the credit needs of their com­
munities, including low- and moderate-income
neighborhoods, in a manner consistent with
safe and sound lending practices.
Monitoring individual lenders for compliance
with these fair lending statutes is problematic.
The standard for compliance with the ECOA is
relatively well defined— other things equal,
lenders cannot discriminate on the basis of
race or property location. This implies that
lenders must treat “comparable” applications
from members of different racial groups and
neighborhoods equally. Problems arise, how­
ever, in determining what types of behavior
are considered discriminatory and in measuring
whether two applications are the same except
for the applicant’s race and the property loca­
tion.2 Moreover, focus on the treatment of for­
mal applications sidesteps the issue of indirect
screening, whereby applicants are screened out
before they formally apply. These concerns
have shifted much of the focus in current en­
forcement of ECOA from procedures to out­
comes. If the outcome of the process differs
across racial groups or neighborhoods, then
the burden of proof is on the lender to demon­
strate that its procedures are not biased. For
example, the lender can show that the differ­
ences arise from variables other than race and
that the use of these variables in loan screening
can be justified by their relationship to costs or
loan performance. If differential outcomes in
origination rates create the prima facie case for

■ 2 See Wienk (1992) for a discussion of conceptual and measure­
ment problems related to assessing the degree of discrimination in credit
markets.

a

bias, the lender could face an examination of
its application and approval rates, as both af­
fect originations.
CRA is concerned with the extent to which
individual lenders extend credit to various
groups within their market areas. While Con­
gress did not articulate the standards for com­
pliance beyond "meeting the credit needs of
the community,” the bank regulatory agencies
responsible for enforcement issued joint policy
statements in 1980 and 1989 reflecting their
procedures. Apart from periodic examinations
for compliance, regulators are required to take
account of an institution’s CRA record in assess­
ing applications for regulatory actions such as
mergers. Since 1990, lenders have also been re­
quired to give the public access to their exami­
nation assessments. Enforcement of CRA has
generally focused on procedures rather than
outcomes. Regulators have given significant
weight to evidence of affirmative action— for
instance, the location of loan offices, number
of minority loan officers, methods of advertis­
ing, participation in community development
banks, and availability of special low- to
moderate-income housing programs.
O n the surface, ECOA and CRA appear to
address different aspects of the lending process.
ECOA is concerned primarily with individuals,
equal treatment, and race; CRA involves neigh­
borhoods, credit flows, and income. More re­
cently, though, enforcement of both acts has
begun to evolve along quite similar lines. Regu­
lators consider fair lending practices a critical
factor in assigning CRA ratings. Moreover, as a
practical matter, CRA enforcement has begun to
place more weight on racial issues rather than
focusing exclusively on income.
HMDA was instituted to provide regulators
and the public with information on how lenders
were serving low-income areas. Data reported
under HMDA are now integral to enforcement
efforts for both ECOA and CRA. Initially, deposi­
tory institutions were required to report mortgage
lending totals by census tract with no disaggrega­
tion by race, but concerns arose about the dearth
of data available to analyze the reasons for differ­
ential mortgage credit flows and individual dis­
crimination in mortgage lending. Amendments to
HMDA in 1989 now require most mortgage lend­
ers to collect and report information on all indi­
vidual loan applications taken, whether approved
or not. In addition, some applicant information is
now recorded, most notably income, loan amount
requested, property location, gender, and race.
Many informative HMDA-based studies ad­
dressing issues concerning both ECOA and CRA




have appeared during the past 15 years. Because
the pre-1990 HMDA data contain no information
about the individual applicants or about applica­
tions that were not approved, most of the early
studies focus on the flow of credit to various
neighborhoods (CRA), as opposed to a considera­
tion of discrimination against particular loan
applicants (ECOA). These studies ask whether
mortgage lenders in an area, taken collectively,
provided mortgage credit in predominantly mi­
nority or low-income neighborhoods at dimin­
ished rates relative to predominantly white or
higher-income neighborhoods. Although re­
searchers generally find disparate lending patterns
between white and minority (or low-income)
neighborhoods, they do not consider differences
in lending patterns across individual lenders: Are
these neighborhoods receiving less credit be­
cause each lender originates only a few loans in
these areas, or because there are only a few lend­
ers operating in these areas?3 In addition, the
data do not allow a clean investigation of the
roles of credit supply and credit demand: Are
these neighborhoods receiving less credit because
of lender bias, or because lenders are not receiv­
ing comparable numbers of qualified applications
from the various neighborhoods examined?
The expanded HMDA data set has spawned
a number of new analyses of individual and
neighborhood discrimination. Using informa­
tion from a special survey that supplemented
HMDA data for Boston, Munnell et al. (1992)
examine the role of individual characteristics,
particularly race, in loan approval. Avery,
Beeson, and Sniderman (1993) discuss similar
issues using 1990 and 1991 HMDA data drawn
from the whole country. The role of neighbor­
hood racial composition in generating applica­
tions and approving loans is explored in
Avery, Beeson, and Sniderman (1994).
Many questions remain as to the appropriate
methods of CRA and ECOA enforcement and
the nature of the data collected to support this
effort. Critics of the CRA, in particular, have
argued that enforcement efforts need to focus

■ 3 Using pre-1990 HMDA data, Canner (1981), Avery and Buynak
(1981), Avery and Canner (1983), and Bradbury, Case, and Dunham
(1989) contrast the differences in mortgage credit originations between
predominantly white and predominantly minority neighborhoods in vari­
ous metropolitan statistical areas (MSAs). One of the few studies to look
at lenders is Calem (1993). He contrasts the experiences of individual
lenders participating in a Philadelphia area mortgage-lending plan with
those who did not participate. However, his paper does not document the
existence of lender differences in the penetration of minority communi­
ties; his primary focus is on the characteristics of the voluntary mortgage
plan operated by a group o f lenders. Avery (1989) notes the differences
between studies based on lending in a neighborhood and the procedures
adopted by individual lenders.

18

B O X I

HMDA Data and Methodology
Overall, HMDA reported information on 6,595,089 loan applica­
tions and purchases in 1990. O f these, 1,137,741 were purchased
from other institutions and 1,523,429 were applications received
for properties outside an MSA. Excluding these left 3,933,919
applications (59.6 percent) to reporting institutions for properties
within an MSA in which the lender had an office. O f these appli­
cations, 787,952 were for home improvement loans, 716,595
were for refinancing of one- to four-family home loans, and
32,176 were for multifamily home loans. An additional 241,295
applications were never acted on because they were either with­
drawn by the applicant or closed due to incompleteness. Elimi­
nating these from our sample left a total of 1,984,688 loan
applications that met the saidy criteria.
Not surprisingly, the initial HMDA filings contained many er­
rors and inconsistencies that required extensive editing by the re­
ceiving federal agencies. Unfortunately, these procedures do not
appear to have been unifonnly applied, requiring additional
cleaning and editing for this study. In addition, smaller institu­
tions were not required to report race, income, and gender for
loan applicants. We decided to deal with missing data using a
“hot deck” imputation procedure similar to that used by the U.S.
Census Bureau. Applications with missing data were statistically
matched to applications in the same census tract that came clos­
est to them in reported characteristics (race, loan action, income,
and loan amount). Missing values were filled in using the vari­
able value of the matched observation. Applications with implau­
sible reported values were treated as missing and imputed in the
same way. Overall, income was imputed for 4.9 percent, loan
amount for 1.5 percent, gender for 4.0 percent, and race for 5.6
percent of the study sample applications.

more on performance and less on process. In
this spirit, the bank regulatory agencies have
recently called for comments on a comprehen­
sive reform of CRA regulations and enforce­
ment procedures. The proposed reforms would
institute a new system of evaluation based pri­
marily on performance. The data reported un­
der HMDA are critical to the success of such
an effort, both for quantifying an institution’s
own performance and for providing a bench­
mark of what other institutions are doing.
Because the new regulations encompass an
expanded role for HMDA data, it is natural to
ask how capable the data are for meeting this
task. The new regulations call for only a mild
expansion of HMDA, so the current data are
representative of what would be available in
the future. In this paper, we use the existing
 data to examine their effectiveness in provid­


ing the quantitative measures of institutional
performance called for by the proposed new
regulations. We examine three potential out­
come measures: loan origination rates, loan
application rates, and application approval
rates. These are used to compare institutions’
performance in serving four subpopulations
cited by CRA: minority individuals, minority
neighborhoods, low-income individuals, and
low-income neighborhoods. In each case, we
compare the rankings implied by gross out­
come measures with those adjusted for neigh­
borhood and applicant characteristics.

II. Data Description
Amendments to HMDA in 1989 now require
most depository institutions (and certain other
mortgage lenders) to collect and report infor­
mation on all individual loan applications taken
for home purchase, mortgage refinance, and
home improvements, whether approved or
not. This study makes use of the HMDA data
for 1990 — the first release of the new data —
which represent the most comprehensive sur­
vey of mortgage lending in the United States.4
All commercial banks, savings and loan asso­
ciations, credit unions, and other mortgage
lending institutions (primarily mortgage bank­
ers) that have assets of more than $10 million,
make one or more one- to four-family home
purchase loans, and have an office in a metro­
politan statistical area (MSA) are required to
meet HMDA reporting requirements.
For each mortgage application received or
mortgage loan purchased from another institu­
tion during the calendar year, the lender must
report the loan amount; the location of the prop­
erty (state, county, and 1980 census tract num ­
ber); whether the property is owner-occupied;
the loan purpose (home purchase, home
improvement, or refinancing for one- to fourfamily or multifamily unit); the type of loan
(conventional, FHA, VA, guaranteed by Farmers
Horne Administration [FmHA]); the action taken
by the lender (loan approved and originated, ap­
plication approved but withdrawn, application
denied, application withdrawn before lender
action, file closed for incompleteness, loan pur­
chased from another institution); the race and
gender of the loan applicant (and co-applicant, if

■

4 At the time this paper was published, 1991 and 1992 HMDA data
were also available. Although not reported here, analysis of data from these
later years suggests similar conclusions to those presented here.

19

TABLE

1

Characteristics of Home Mortgage
Applications, 1990 HMDA
Percent
of Sample

Percent
of Loan
Dollars

Approval
Rate

Race of Applicant
Native American
Asian (or Pacific Islander)
Black
Hispanic
White
Other

0.6
4.6
6.2
6.6
81.4
0.7

0.6
6.8
4.8
6.4
80.5
1.0

80.7
85.6
70.6
77.9
86.9
80.2

Race of Co-applicant
No co-applicant
Same race as applicant
Different race than applicant

28.4
69.4
2.2

24.1
73-4
2.5

82.7
86.2
84.4

Loan Type
Conventional
FHA
VA
FmHA

75.1
20.4
4.5
0.0

82.9
13.7
3.5
0.0

85.1
85.5
84.2
98.0

14.8
2.9
82.3
44.9
14.5
10.5
9.0
21.1

13.1
3.5
83.4
47.7
14.4
7.6
9.1
21.2

Lender Action
Loan denied
Loan accepted and withdrawn
Loan originated
Loan kept by originator2
Loan sold to FNMAa
Loan sold to GNMAa
Loan sold to FHLMC3
Loan sold elsewhere3
Memo Items
Median income
Median loan request
Number of loans

$48,000
$77,000
1,984,688

a. Percent o f originations.
SOURCE: Authors’ calculations.

any); and the income relied on by the lending
institution in making the loan decision.^
In total, 9,333 financial institutions filed
HMDA reports in 1990 on more than 6 million
loan applications and loan purchases. Our
analysis focuses on a subset of these filings: ap­
plications for one- to four-family home pur­
chase loans that were acted upon (approved
or denied) by the lender. This sample includes
1,984,688 loan applications made to 8,745 sepa­
rate lenders operating in 40,008 census tracts
in all 340 of the U.S. MSAs defined as of 1990
(see box 1 for details).
The study sample has a substantial degree
of representation from applicants of different
races and income levels (table 1). Overall,
however, applicants for home purchase mort­
 gages are a select sample of American house­


holds. Applicants’ median income ($48,000) is
substantially higher than the median income of
families in MSAs ($37,918) as reported in the
1990 decennial census.6 The racial composition
of the study sample also appears to differ
somewhat from that of all U.S. families. Blacks
filed 6.2 percent of the HMDA housing loan ap­
plications, yet were 7.7 percent of the home­
owners and headed 11.4 percent of the MSA
households. Asian loan applicants (4.6 per­
cent), however, were overrepresented com­
pared with their numbers in the census (2.5
percent of MSA household heads and 2.2 per­
cent of homeowners). The share of white (81.4
percent) or Hispanic (6.6 percent) applicants is
approximately representative of their numbers
(78.1 percent of household heads and 84.8 per­
cent of homeowners for whites and 7.5 percent
of household heads and 5.0 percent of home­
owners for Hispanics).7
Also worth noting is the substantial pres­
ence of the federal government in mortgage
lending. One-quarter of the mortgages issued
were directly guaranteed by the federal govern­
ment (FHA, VA, or FmHA), with an additional
quarter purchased in the secondary market by
one of the federal housing credit agencies
(FNMA and FHLMC).8 Indeed, 55 percent of
all mortgages issued were sold in the second­
ary market, suggesting that the study of mort­
gage lending patterns is more an analysis of a
brokered industry than one where participants
buy for their own portfolios.
Sample characteristics are broken down by
type of lender and applicant in table 2. Lender
here is defined at the MSA level. Thus, a lender
reporting loans for two different MSAs is
treated as two different lenders.9 Lenders,
shown in the rows, are grouped by size and
■ 5 See Canner and Smith (1991,1992) for a full description of the
HMDA data. Information on income, race, and sex of the applicant does
not have to be supplied by reporting institutions with assets less than
$30 million or for purchased loans.

■

6 In the HMDA data, household income may be slightly under­
stated because it reflects only the portion of an applicant’s income
needed for mortgage qualification.

■ 7 The percent Hispanic in the HMDA sample is slightly higher than
the share for the overall U.S. population, due in part to the inclusion of
Puerto Rico.

■

8 These acronymns represent, respectively, the Federal Housing
Administration, Veterans Administration, Farmers Home Administration,
Federal National Mortgage Association, and Federal Home Loan Mort­
gage Corporation.

■ 9 The 8,745 financial institutions with loans in the study sample
operated in an average of 2.4 MSAs. This translated into 20,695 study
lenders when lenders were defined at the MSA level.

20

T A B L E

2

Minority and Low-lncome Individuals
and Tracts Relative to Total Mortgage
Lending, 1990 HMDA
Minority“
Overall
Approval
Rate
Type of Institution
Commercial banks
Thrift institutions
Credit unions
Bank subsidiaries
Thrift subsidiaries
Other mortgage banks
Size of Institution
> 500 applications
100-500 applications
<100 applications
Market Share of Institution
> 5 percent
1-5 percent
< 1 percent
Size of M S A
> 25,000 applications
< 25,000 applications
Percent Minority Applications
>22 percent
< 22 percent
Total

Percent
Appli­
cations1

Low-Incomeb

Percent
Relative
Origi­ Approval Approval
nations1
Rate
Rate

Percent
Applicationsc

Percent
Relative
OrigiApproval Approval
nationsc
Rate
Rate

0.82
0.87
0.89
0.84
0.86
0.87

11.2
13.9
9.0
12.7
14.2
15.9

9.1
12.5
7.7
11.1
12.0
14.3

0.67
0.78
0.77
0.73
0.72
0.79

0.81
0.90
0.86
0.87
0.84
0.90

20.5
11.0
15.6
17.9
14.5
12.0

17.4
9.6
13.4
14.5
12.6
11.1

0.69
0.76
0.77
0.68
0.74
0.81

0.85
0.87
0.86
0.81
0.87
0.92

0.86
0.85
0.84

17.1
10.9
9.5

15.3
9.2
8.1

0.77
0.72
0.71

0.90
0.85
0.85

12.1
17.0
17.6

10.4
14.5
14.7

0.74
0.73
0.70

0.86
0.85
0.83

0.86
0.85
0.84

14.2
13.2
11.6

12.3
11.7
10.1

0.74
0.76
0.73

0.87
0.89
0.87

16.9
14.2
12.4

14.5
12.0
10.4

0.73
0.72
0.70

0.86
0.85
0.84

0.86
0.85

18.1
10.9

16.5
9.2

0.78
0.72

0.91
0.85

8.6
18.2

7.4
15.4

0.74
0.72

0.86
0.85

0.80
0.86

31.8
10.3
13.3

29.5
8.9
11.7

0.75
0.75
0.75

0.93
0.87
0.88

12.8
15.5
15.0

9.6
13.2
12.7

0.66
0.73
0.72

0.82
0.85
0.85

0.85

Minority' Census Tracts d
Overall
Approval
Rate

Percent
Appli­
cations*^

Percent
Origi­
nations*^

Low-lncome Census Tracts1

Relative Percent
Approval Approval Appli­
Rate
Rate
cations0

Percent
Relative
Origi- Approval Approval
nationsc
Rate
Rate

Ty pe of Institution
Commercial banks
Thrift institutions
Credit unions
Bank subsidiaries
Thrift subsidiaries
Other mortgage banks

0.82
0.87
0.89
0.84
0.86
0.87

11.0
13.2
8.5
11.7
13.3
14.9

9.3
12.1
7.7
10.2
11.3
13.6

0.69
0.80
0.80
0.73
0.73
0.80

0.85
0.92
0.90
0.87
0.85
0.91

22.5
10.4
18.0
17.7
17.0
12.7

20.1
9.4
16.5
15.3
14.9
11.9

0.76
0.79
0.82
0.72
0.75
0.82

0.93
0.90
0.92
0.86
0.88
0.94

Size of Institution
> 500 applications
100 - 500 applications
<100 applications

0.86
0.85
0.84

16.7
9.8
8.9

15.2
8.4
7.8

0.78
0.73
0.74

0.91
0.86
0.88

10.8
18.8
19.8

9.4
17.1
18.0

0.75
0.77
0.76

0.88
0.91
0.90

Market Share of Institution
> 5 percent
1-5 percent
< 1 percent

0.86
0.85
0.84

13.1
12.5
11.8

11.5
11.3
10.5

0.76
0.77
0.75

0.88
0.90
0.89

18.7
14.4
11.0

16.7
12.9
9.9

0.77
0.76
0.75

0.90
0.90
0.89

0.86
0.85

18.8
9.5

17.3
8.2

0.79
0.73

0.92
0.86

5.7
20.4

5.1
18.4

0.77
0.76

0.90
0.90

0.80
0.86

40.2
8.0
12.6

38.2
7.1
11.2

0.77
0.75
0.76

0.88
0.95
0.89

12.5
16.0

10.7
14.4

15.5

13.9

0.69
0.77
0.76

0.86
0.90
0.90

Size of M S A
> 25,000 applications
< 25,000 applications
Percent Minority Applications
> 22 percent
< 22 percent
Total

0.85

a. Native Americans, blacks, and Hispanics.
b. Applicant income below $25,000.
c. Percent of applications received (loans originated) by each class o f lender from minority applicants or low-income tracts.
d. Census tracts with more than 30 percent o f loan applications from minority applicants.
e. Census tracts with more than 30 percent o f loan applications from low-income applicants.
SOURCE:
Authors' calculations.



21

type of institution and by the size and minority
population of their MSA as shown in the rows
of the table. Applicants are grouped into five
categories shown in the columns: 1) overall; 2)
minority (native American, black, and Hispanic,
about 13 percent of applicants); 3) low-income
(family income of $25,000 or less, roughly the
bottom 15 percent of applicants); 4) residents
of minority census tracts (those with more than
30 percent of loan applications from minority
applicants, roughly 13 percent of applicants);
and 5) residents of low-income census tracts
(those with more than 30 percent of loan appli­
cations from low-income applicants, again
roughly 15 percent of applicants).10 For each
applicant category, we show the percent of the
lender-type’s loan applications or originations
made to members of the category.11 We also
present the category approval rate (the portion
of all loan applications from members of the
category that are approved) and the relative ap­
proval rate (the ratio of the category approval
rate to the overall approval rate for all appli­
cants), shown in column 1.
There is little evidence that specific types of
lenders, such as commercial banks or thrifts,
specialize in minority lending. O n the other
hand, at least superficially, it would appear
that there is specialization by size of lender.
About 17 percent of the applicants to lenders
receiving more than 500 home purchase loan
applications were minorities, with a similar per­
centage from minority tracts. Smaller lenders
(those with less than 100 applicants) took in
only 9 percent of their applications from these
categories. However, much of this difference
may simply reflect the concentration of large
lenders in large MSAs, where there is also a
high concentration of minority applicants and
minority tracts. Within MSAs, the difference in
minority share between the larger institutions
(those with market shares exceeding 5 percent)
and small institutions is much less.
The picture looks somewhat different for
low-income applicants. Commercial banks and

■ 10 The decision to treat Asians and ‘‘other race” applicants as non­
minorities was somewhat arbitrary. As shown in table 1, the overall accep­
tance rate tor Asian home purchase loan applicants is much closer to the
white acceptance rate than to acceptance rates for blacks, Hispanics, or
native Americans. We note, though, that the acceptance rates for Asian re­
finance and home improvement loan applicants are closer to those of His­
panic applicants than to those of whites.

■ 11 We count all applications approved by the lender as “origina­
tions.” In fact, some applications (2.9 percent) are approved by the lender

 but are subsequently withdrawn by the borrower. In these cases, the loan
will not actually be made.


their subsidiaries receive a disproportionately
large share of low-income applications; on the
other hand, a disproportionately small percent­
age of thrift business comes from low-income
borrowers or tracts. Larger lenders also receive
disproportionately fewer low-income loan ap­
plications. Again, though, this appears to be a
result of the betw?een-MSA distribution of appli­
cants. Within MSAs, the largest lenders tend to
receive more low-income applications.
Finally, we note that the specific measure
used to compare minority and nonminority
lending or low-income and high-income lend­
ing has little impact on the distribution across
lenders. The same patterns are found when
minority lending is measured by the number
of minority applications, the number of applica­
tions from minority census tracts, the dollar
value of minority applications (not showTi), or
the dollar value of applications from minority
tracts (not showrn). Similarly, for low-income
lending, the cross-lender distribution is the
same whether lending is measured by the num ­
ber or dollar value of loans or whether income
is measured by the applicant or tract.

III. Variance in
Lending Patterns
The sample statistics reported in the previous
section reflect the average percentage of loan
applications from minority and low-income in­
dividuals (or tracts) and the average approval
rate on those applications by various types of
lending institutions. These statistics could be
thought of as describing the prototypical lender
in the mortgage market, not the actions of any
individual lender operating in that market, and
as ignoring the variation across these individ­
ual lenders. In this section, we compare three
measures of individual lender performance: 1)
minority and low-income origination rates (the
share of loans originated going to minorities or
low-income individuals or tracts), 2) application
rates (the share of applications received from
minorities or low-income individuals or tracts),
and 3) relative approval rates (differences in
the actions taken on applications).
We first address the relationship among
these three measures. Because origination rates
are equal to the product of application rates
and relative approval rates, we would like to
know the extent to which credit origination
differences among lenders stem from the for­
mer factor versus the latter. That is, if we are
concerned about credit flows to minority and

22

TABLE

3

Analysis of Variance in Origination
Rates across Lenders, 1990 HMDA
Origination
Rate

Percent Attributable
to Variance in:b

N u m b e r of
Lenders

N u m b e r of
Applications

Mean

Standard
Deviation2

Regression
R-Squareda

Minority
Number
Dollar value
Center city

11,598
11,598
8,548

1,867,211
1,867,211
745,161

0.16
0.14
0.23

0.18
0.18
0.22

0.92
0.91
0.93

86.7-90.7
87.4-91.1
82.5-88.5

9.3-13.3
8.9-12.6
11.5-17.5

Minority Tracts
Number
Dollar value

8,846
8,846

1,624,207
1,624,207

0.20
0.17

0.19
0.19

0.91
0.91

88.7-91.9
89.7-92.2

8.1-11.3
7.8-10.3

Low-income Applicants
Number
Dollar value
Center city

13,651
13,651
9,668

1,918,018
1,918,018
764,423

0.21
0.16
0.26

0.19
0.19
0.23

0.91
0.92
0.93

85.4-87.8
88.4-90.7
81.7-85.8

12.2-14.6
9.3-11.6
14.2-18.3

Low-income Tracts
Number
Dollar value

11,024
11,024

1,566,699
1,566,699

0.32
0.27

0.24
0.23

0.94
0.94

90.2-92.6
93-3-95.3

7.4-9.8
4.7-6.7

Minority/Low-Income
Relative
Application Rate
Approval Rate

a. Expressed as deviation around MSA means.
b. M inim um and m axim um contributions to variance based on deviations around MSA means.
SOURCE: Authors’ calculations.

low-income applicants and neighborhoods,
does variation across lenders arise primarily
from differences in treatment or in application
rates?
An approximate answer to this question can
be obtained by estimating the following equation:
(1)

O rigination rateL = $1MSAL
+ (3, application rateL
+ P3 relative approval rateL + eD

where the origination rate for lender L equals
minority (or low-income) originations as a por­
tion of total originations, MSAL is a vector of
dummy variables indicating the metropolitan
area in which lender L operates, application
rate is minority (or low-income) applications
as a share of total applications, and relative
approval rate is the minority (or low-income)
approval rate divided by the overall approval
rate. The MSA fixed effects control for differ­
ences in the mortgage lending market that are
common to all lenders in that market but may
vary across markets, such as the size of the mi­
nority population or lending practices.
Fitting equation (1) provides an estimate of
the relative importance of application rates and

approval rates in explaining variation in origi­


nation rates. Unfortunately, as with any regres­
sion, because application rates and relative ap­
proval rates are likely to be correlated, we
cannot compute a precise estimate of the con­
tribution of each component to the variation in
origination rates. However, several approxi­
mate estimates are possible. We determine a
lower bound on the contribution of each com­
ponent by estimating its marginal contribution;
that is, the additional variation in origination
rates explained by adding the component to a
model containing the other component. We
compute an upper bound on the contribution
of each component from its univariate fit —
the proportion of the variation in origination
rates that it explains by itself. The difference in
the lower and upper bound estimates derives
from how the impact of the covariance be­
tween the two components is assigned. The
lower bound estimate assigns the covariance
to the other component, and the upper bound
assigns the full effect of the covariance to the
variable in question.
Table 3 reports the allocation of variance
for estimates of equation (1) for several differ­
ent origination rates. The variance associated
with MSAs is removed from the total before we
measure the contributions of the application

23

and relative approval rates. Thus, we are de­
composing the variance in the deviations about
MSA means. Rowr 1 shows the variance in de­
composition across lenders for the origination
rate of minority individuals. Row 4 shows the
decomposition for originations in minority
tracts. Rows 6 and 9 show the decomposition
for low-income individuals and tracts, respec­
tively. Rows 2, 5, 7, and 10 report decomposi­
tions for origination rates weighted by dollars.
Finally, decompositions for minority and lowincome individuals applying in central cities
are shown in rows 3 and 8.
For each decomposition estimated, the sam­
ple includes all lenders for which the origina­
tion rate, application rate, and relative approval
rate are defined. We note that this reduces the
sample of lenders substantially from the full
sample reported in tables 1 and 2. For example,
the sample used for minority individuals in­
cludes only 11,598 of the 20,695 HMDA-reporting
lenders (40 percent were dropped because
they had no minority applicants and 3 percent
because they had no originations of any type).
However, these lenders received 1,867,211 of
the 1,984,688 full sample applications (94 per­
cent). Moreover, the percentage of applications
made by minorities in the decomposition sam­
ple (14.1 percent) is only slightly higher than
in the full sample (13-3 percent).
For each decomposition, we present several
statistics. In columns 3 and 4, we show the
mean and standard deviation of the origination
rate across lenders. Note that the mean origina­
tion rate across lenders is generally higher than
the sample average, indicating that smaller
lenders make more of their loans to minorities
or low-income individuals. In column 5, we
show the R-squared of the estimated equation
(1). Both the R-squared and standard deviations
are adjusted for deviations about MSA means.
Finally, in columns 6 and 7, we show the per­
centage of the total variation of the origination
rate that can be attributed to the application
rate or relative approval rate, adjusted for MSA
fixed effects.
We find that the overwhelming majority of
the cross-lender variance in minority origina­
tions is attributable to differences in minority
application rates. Differential approval rates by
race account for a relatively small portion of
the variance. For example, after controlling for
MSA differences, 87 to 90 percent of the vari­
ance in originations to minority individuals is
captured by lender-specific differences in mi­
nority application rates; only 10 to 13 percent
 stems from different approval rates for these


applications. This narrow range suggests that
the contribution of the covariance is quite
small, which greatly enhances our ability to
identify the importance of the application rates.
Our results concerning low-income lending
are much the same as those for minority lend­
ing. The only difference is that the ranges for
low-income lending are somewhat larger than
those for minority lending, indicating that the
covariance between application rates and rela­
tive approval rates contributes more to the
cross-lender variance in low-income origina­
tions than it does to the cross-lender variance
in minority origination rates. The results are vir­
tually identical when dollar values are used or
when census tracts rather than individual appli­
cant characteristics are examined. Restriction of
the sample to central cities does little to alter
the results, other than showing a slight increase
in the variance that may be attributable to rela­
tive approval rates.
To examine the robustness of these results
further, table 4 reports the allocation of the
variance across lenders in minority originations
for lenders grouped by type, size, and market
share of institution, and by MSA size and per­
cent minority. The dominance of differences in
application rates as the source of lender differ­
ences in minority origination rates holds across
all types of lenders, all sizes of lenders (meas­
ured in terms of both the volume of applica­
tions received by the lender and the lender’s
market share), and types of MSAs. Even for
mortgage banks (subsidiaries of depository in­
stitutions as well as independents), where the
contribution is smallest, cross-lender differences
in application rates account for at least threequarters, and may account for as much as 90
percent, of the variance in minority originations.
The contribution of minority application
rates to the variance in originations is smallest
among small lenders, regardless of the type of
lender. For the largest lenders (those with 500
or more applications), differences in application
rates account for 93 to 99 percent; for lenders
with less than 100 applications, they account
for 85 to 89 percent. This is also true when
size is measured by market share. Differences in
lender minority application rates account for 96
to 97 percent of the variance across those with
5 percent or more of the market, and for 84 to
89 percent across lenders with less than 1 percent
of the market. Although not presented here, simi­
lar conclusions hold for the decomposition of
minority tracts and low-income individuals and
tracts by lender types and size.

24

T A B L E

4

Allocation of Variance in Minority
Origination Rates by Type and
Size of Lender, 1990 HMDA
Origination Rate

Percent Attributable to Variance in:b

Mean

Standard Deviation3

Regression
R-Squareda

Minority/Low-Income
Application Rate

Relative
Approval Rat

Type of Institution
Commercial banks
Thrift institutions
Credit unions
Bank subsidiaries
Thrift subsidiaries
Other mortgage banks

0.13
0.11
0.18
0.13
0.13
0.16

0.19
0.14
0.29
0.15
0.18
0.18

0.91
0.93
0.97
0.88
0.90
0.94

86.5-91.1
92.0-93-9
85.2-93.1
80.4-83-4
74.2-81.7
86.5-90.2

8.9-13.5
6.1-8.0
6.9-14.8
16.6—19.6
18.3-25.8
9.8-13.5

Size of Institution
More than 500 applications
100 to 500 applications
Less than 100 applications

0.13
0.09
0.15

0.09
0.08
0.21

0.99
0.96
0.92

92.8-98.8
96.5-98.0
85.0-89.3

1.2-7.2
2.0-3.5
10.7-15.0

Market Share of Institution
More than 5 percent
1 to 5 percent
Less than 1 percent

0.10
0.11
0.20

0.07
0.09
0.22

0.95
0.93
0.92

95.7-97.3
92.8-94.1
84.0-88.7

2.7-4.3
5.9-7.2
11.3-16.0

Size of MSA
More than 25,000 applications
Less than 25,000 applications

0.15
0.18

0 20
0.17

0.94
0.91

86.4-91.0
86.6-90.4

9.0-13.6
9.6-13-4

Percent Minority Applications
More than 22 percent
Less than 22 percent

0.36
0.13

0.24
0.17

0.94
0.92

76.6-86.8
87.7-91.0

13.2-23.4
9.0-12.2

Total

0.16

0.18

0.92

86.7-90.7

9.3-13.3

a. Expressed as deviation around MSA means.
b. M inim um and m axim um contributions to variance based on deviations around MSA means.
SOURCE: Authors’ calculations.

We conclude that differences in the relative
approval rates of minority and low-income loans
account for only a small portion of the variance
across institutions in the portion of originations
going to minority and low-income applicants. In
the following section, we examine various factors
that may be contributing to the cross-lender vari­
ance in application and approval rates.

IV. Sources
of Cross-Lender
Variance in
Lending Patterns
The outcome measures presented in the previous
section are gross measures of lender perform­
ance. As such, they do not control for exogenous
market factors that affect lender performance but
 that are beyond the lender’s control. The effects


of any such exogenous factors should be re­
moved before constructing measures of lender
performance to be used in CRA and fair lend­
ing evaluation. Although it by no means con­
tains an exhaustive list, HMDA includes infor­
mation on a number of applicant characteristics
that arguably should be controlled for: loan
size, applicant income, loan type (FHA/VA or
conventional), and property location. To the
extent that these factors are correlated with
race, this specialization will contribute to the
observed cross-lender variance in minority appli­
cation rates. Similarly, to the extent that they are
correlated with creditworthiness, these applicant
characteristics may also be contributing to the
observed differences in relative approval rates.
In this section, we examine the effect of remov­
ing these factors on our assessment of various
measures of lender performance. We focus on
individual minority application rates and relative

25

approval rates, although our results hold for lowineome and neighborhood taxonomies as well.
We compute adjusted indices as the lender
average for each variable after the effects of prop­
erty location and applicant characteristics are re­
moved. For the application and overall approval
rate, this is estimated directly from a fixed-effects
linear probability model, where the fixed effects
are, by construction, the average of the depend­
ent variable after the effects of other variables are
removed. The fixed-effects linear probability
models used to compute the adjusted indices
were estimated with the full 1,984,688 loan sam­
ple, and have the following form:
(2)

APPLICATIONiMn = fiAAC] + $m MSAm
+ fijTRACT^+ Pi LENDERi +

nonminorities. Thus, the adjusted lender indi­
ces were taken either as the direct LENDER
fixed effects estimated in equations (2) and (3)
or computed as lender residuals averaged over
the minority and nonminority subgroups. Final­
ly, we were also interested in computing the
average lender “quality” of applicants as meas­
ured by their average AC and TRACT effects.
The exact construction of each of the variables
used in this portion of the analysis is
1) the average economic characteristic effects
of the Zth lender’s applicants,

A C apr. minority

"

AAC/

NJ •

fo r

al1

minority applicants /'
^ ^ a p r . nonminority ~ ^‘ k e L ^ A ^ ^ ' k ^ ^ k '

(3)

APPROVALiMTL = r AACi + V RRACEt
+ Tm MSAm + T,TRACTt + TlLENDERl

+

2) the average census tract effects of the
lender’s applicants,

UiMTL ’

where APPLICATION is coded one if the zth
applicant using the Ith lender in the M th MSA
and rth census tract is a minority (native Amer­
ican, black, or Hispanic) and zero otherwise;
and APPROVAL is coded one if the /th appli­
cant loan using the Zth lender in the M th MSA
and Tth census tract is approved and zero
otherwise. AC is a vector of application charac­
teristics reported in the HMDA data, including
gender, marital status, occupancy, income,
loan amount, income-to-loan ratio, loan type,
and interactions among these variables. RACE
includes dummy variables for six applicant and
two co-applicant racial categories. The racial
dummies are also interacted with FHA and VA
loan dummies. MSA, TRACT and LENDER are
dummy variables indicating which of the 340
MSAs, 40,008 census tracts, and 20,695 lenders
the application relates to, and u and v are re­
siduals. By construction, the MSA effects are
normalized to have an overall mean of zero,
and within each MSA, the lender and tract ef­
fects are normalized to have means of zero.12
Adjusted indices for the minority and relative
approval rates are more complicated to estimate
because they involve the ratio of predictions
for two groups. For these calculations, we
used variants of the fixed effects, computed by
averaging lender residuals from the overall ap­
proval rate model separately for minorities and

■

nonminority applicants k\

12 Estimates of these regressions are available from the authors

upon request.


TRACTapp='Ll t $ TTRACTlIN,

TRACTa^r minority = ^/e ¡T -¡TRACTj/Nj,
for all minority applicants j,
TRACTapr nonminority =
for all nonminority applicants k;

^kr

3) and the adjusted lender indices, estimated
directly as fixed effects or averaged separately
for minorities and nonminorities,
LENDER
L E N D E R ^ - T„
LENDER^ minority

MINORITY'APPROVAL RATE
— ACapr, minority — TRACTapr, minority
—Hjei rR RACE./N- - r M, for all minority
applicants j,
LENDERapr, nonminority
NONMINORITY APPROVAL RATE
—ACapr, nonminority — TRACTapr, nonminority
~ ZkeLrR RACEkNk - r ip for all nonminority7applicants k,
where N, N , and Nk are, respectively, the total,
minority, and nonminority number of applicants
to the lender and M is the MSA of the lender.
Four different measures of lender loan activ­
ity were regressed against these constructs,
and a variance decomposition similar to that

26

T A B L E

5

Allocation of Institutional Differences,
Percent Deviations around MSA
Means, 1990 HMDA

Applicant economic characteristics
Census tract
Overall lender effect
Unexplained lender effect

iMinority
Application Rate

Relative
Approval Rate

Minority
Approval Rate

Overall
Approval Rate

0 8 2.6

2.4-4.6
4.0-5.9

70.7-74.8

91.0-92.7

2.5-5.7
3.Ó-4.2
26.4-38.3
53-8-65.9

3.5-10.9

21.9-28.9

.

-

2 . 0 - 3.2

88.7-91.1

SOURCE: Authors’ calculations.

performed in the previous section was under­
taken. The four measures were
1) the minority application rate, which was
regressed against A C app and T R A C T app,
2) the relative approval rate, which was re­
gressed against A C apr minorny, A C apr nonminority>
T R A C T apr minority ’ 1 'K A d a p r ; nonminority ’
L E N D E R apr minority >

Z iïT V D Æ / ? ^ nonminority ’

3) the minority approval rate, which was
regressed against A C apr minorny, A C ap r nonminority >
^ ^ ^ ^ a p r minority ’ ^ ^ ^ ^ a p r , nonminority ’
L E N ,D F
•
l Rxapr, nonminority >

4) the overall approval rate, which was re­
gressed against A C apr minoritv, A C apr nonminontv,
T R A C T apr minority ’ and T R A C T apr nonminority ’
Each regression was run with MSA dummies;
thus, we analyze within-MSA variation. The
contribution of each component to the overall
variance in minority application rates is identi­
fied using the same variance decomposition
procedure as in the previous section. Again,
because we are looking at a decomposition of
variance, the amount attributable to each source
can only be approximated. As in the previous
section, lenders used in these regressions were
limited to the 11,598 lenders for whom all de­
pendent variables were defined (at least one
minority applicant and one approved loan).
The A C and T R A C T components can be
thought of as exogenous factors, potentially be­
yond the lender’s control. The adjusted lender
effects in minority application and approval rates
constructed above ( L E N D E R a p p , L E N D E R apr,
L E N D E R apr milloritv, and L E N D E R apr nonminority)




can be interpreted as lender-specific differences
in application and approval rates controlling
for applicant characteristics and property loca­
tion. The variance decomposition allows us to
compare the unadjusted measures of lender
performance, as represented by the gross mi­
nority application and relative approval rates,
with the adjusted indices, as measured by the
L E N D E R variables. If the L E N D E R variables
account for most of the variation in the gross
measures, then regulators may be able to use
gross performance measures without serious
cost. If, on the other hand, A C and T R A C T ac­
count for a substantial portion of the variation
in the gross measures, this may be an inappro­
priate decision.
Table 5, column 1 shows the decomposition
of the cross-lender variance in minority applica­
tion rates. Differences in application character­
istics account for 1 to 3 percent of the withinMSA variance across lenders. Much more sur­
prisingly, differences in the census tracts from
which lenders receive applications account for
only 22 to 29 percent of the variation, with 71
to 75 percent of the variation across lenders
attributable to the unexplained pure L E N D E R
effect. This means that most of the variation
across lenders in the number of minority appli­
cations they receive does not stem from the fact
that they serve different neighborhoods, but
from how they draiv applicants w ithin neigh­
borhoods. This result is robust to a number of
variations, such as ignoring MSA effects or
weighting the regression by the number of
applications received by the lender, and runs
counter to the conventional wisdom that vari­
ation in the racial composition of the neighbor­
hoods served by lenders is the major source of

27

cross-lender variation in the proportion of mi­
nority applications received.13
Column 2 of table 5 shows the decomposi­
tion of the within-MSA variance in relative ap­
proval rates. Between 2 and 5 percent of the
difference across lenders can be attributed to
variation in the application characteristics, and
between 4 and 6 percent can be attributed to
census tract location. The overwhelming major­
ity of variation (91 to 93 percent) cannot be ex­
plained by these factors and is attributable to
the pure lender effect.
Similar conclusions are reached when we
use the same methodology to examine sources
of cross-lender variation in minority approval
rates (table 5, column 3). Applicant economic
and census tract effects are small. The overall
standard of the institution, measured by the non­
minority lender effect, explains about one-third
of the within-MSA variation (that is, minorities
who apply to institutions with low approval rates
for all applicants tend to be approved at lower
rates, ceteris paribus). However, more than half
of the variation in minority approval rates cannot
be explained by any of these factors. These re­
maining differences may reflect differential treat­
ment of minority applications or differences in
the unobserved characteristics of the loan appli­
cation; without additional information, it is impos­
sible to make a determination.
It appears that this large component of unex­
plained variation is consistent with evidence of
significant idiosyncratic lender behavior. Column
4 of table 5 reports the decomposition of the
cross-lender variance in overall approval rates
(minority and nonminority) based on the same
methodology7used above. About 90 percent of the
within-MSA variation in overall lender approval
rates cannot be explained either by applicant char­
acteristics (as we measure them) or by census tract.
These results suggest that the adjusted meas­
ures of lender performance account for the vast
majority of variation in the gross measures.
This finding is further examined in table 6,
which reports the differences in gross and ad­
justed performance measures across various
lender groups arranged by type, size, and mar-

■ 13 The potential contribution of census tracts is larger when the re­
gression is weighted by the number of applications each lender received.
Since this decomposition focuses on within-MSA variation and gives most
weight to the largest lenders within the MSA, it is difficult to separate the
lender effect from the census tract effect. As a result of the covariance be­
tween the two, the range of the contribution of each is quite large (27 to 69
percent for census tracts and 30 to 63 percent for lender effects). We note
that even in this decomposition— the most favorable case for census tract ef­
fects— at least 30 percent of the variance across lenders cannot be explained
 by loan application characteristics or by the racial composition of the neigh­
borhood from which the lender draws applications.
http://fraser.stlouisfed.org/

Federal Reserve Bank of St. Louis

ket share, and by size and percent minority in
the MSA. The difference between the gross
and adjusted standard deviations for each
group reflects the importance of the control
factors, AC and TRACT.
The first column of table 6 is the cross­
lender variance in minority application rates; the
second column is the variance in the pure lender
effect on the application rate. For the full sample
of lenders, cross-lender variance before controll­
ing for the applicant characteristics and property
location is 0.20; after controlling for these factors,
the variance is 0.14. Thus, about 30 percent of
the cross-lender variance in minority application
rates is explained by control factors. These fac­
tors account for a larger portion of the variance
across commercial banks than for other types of
lenders. They also account for more of the vari­
ance across lenders with large market shares,
and those in MSAs with large numbers of minor­
ity applicants.
The control factors explain relatively little of
the cross-lender variance in overall approval
rates (columns 5 and 6) or in minority approval
rates (columns 7 and 8). However, they do ex­
plain a sizable portion of the cross-lender
variance in relative approval rates (minority ap­
proval rate/overall approval rate). Before con­
trolling for the factors in our model, the cross­
lender variance in relative approval rates is
0.37; after controlling for them, the variance is
0.26 — almost 30 percent lower. As was the
case with application rates, control factors ac­
count for relatively more of the variation in ap­
proval rates for commercial banks and their
mortgage subsidiaries, for lenders with large
market shares, and for lenders in MSAs with
larger numbers of minority applicants than
other institutions.
It is also interesting to examine the relation­
ship between the pure lender effect on minor­
ity application rates and the pure lender effects
on absolute and relative minority approval
rates. Overall, those lenders with higher-thanexpected minority application rates (positive
lender effects) are associated with slightly
higher-than-expected minority approval rates,
both absolute and relative. However, the corre­
lations are surprisingly small (0.001 and 0.024,
respectively), suggesting that minority appli­
cants do not seem to be applying to lenders
where their probability of approval is higher.

28

T A B L E

6

Standard Deviation of Minority Lending
across Lenders Controlling for Applicant
Characteristics and Property Location
Minority
Application
Rate

Minority
Origination
Rate

Overall
Approval
Rate

Minority
Approval
Rate

Relative
Approval
Rate

Gross2 Adj.b

Grossa Adj.b

Gross'1 Adj.b

Gross2 Adj b

Gross3 Adj b

Type of Institution
Commercial banks
Thrift institutions
Credit unions
Bank subsidiaries
Thrift subsidiaries
Other mortgage banks

0.23
0.18
0.28
0.16
0.19
0.19

0.14
0.11
0.26
0.12
0.15
0.15

0.18
0.15
0.19
0.14
0.14
0.17

0.15
0.11
0.26
0.12
0.15
0.15

0.17
0.12
0.16
0.20
0.19
0.17

0.16
0.11
0.16
0.18
0.18
0.16

0.34
0.27
0.32
0.32
0.30
0.28

0.32
0.25
0.31
0.30
0.28
0.27

0.41
0.29
0.38
0.40
0.38
0.33

0.28
0.23
0.27
0.27
0.27
0.23

Size of Institution
More than 500 applications
100 to 500 applications
Less than 100 applications

0.13
0.12
0.23

0.05
0.05
0.17

0.13
0.11
0.19

0.05
0.05
0.17

0.11
0.13
0.19

0.09
0.11
0.18

0.16
0.21
0.35

0.13
0.20
0.34

0.12
0.21
0.43

0.07
0.16
0.31

Market Share of Institution
More than 5 percent
1 to 5 percent
Less than 1 percent

0.16
0.14
0.23

0.05
0.06
0.18

0.16
0.14
0.25

0.05
0.06
0.19

0.12
0.15
0.19

0.10
0.13
0.18

0.23
0.27
0.35

0.10
0.13
0.18

0.24
0.30
0.43

0.18
0.22
0.30

Size of MSA
More than 25,000 applications
Less than 25,000 applications

0.20
0.20

0.14
0.14

0.21
0.21

0.14
0.15

0.17
0.17

0.16
0.16

0.31
0.29

0.27
0.29

0.38
0.32

0.24
0.27

Percent Minority Applications
More than 22 percent
Less than 22 percent

0.28
0.17

0.18
0.14

0.30
0.18

0.18
0.14

0.19
0.16

0.19
0.15

0.28
0.31

0.27
0.30

0.32
0.37

0.21
0.27

Total

0.20

0.14

0.21

0.15

0.17

0.16

0.31

0.29

0.37

0.26

a. Gross cross-lender variation not controlling for applicant characteristics or property location.
b. Adjusted cross-lender variation controlling for applicant characteristics and property location.
SOURCE: Authors’ calculations.

V. Conclusion
This paper uses recently released HMDA data
to examine differences in minority and lowincome lending patterns across lending institu­
tions. The new data allow us to identify both
the application and the action taken on that ap­
plication by the lender, thus enabling us to
son out lender behavior from applicant behav­
ior to a greater extent than allowed by pre­
vious data. We therefore can determine the
extent to which the differences across lenders
in minority (low-income) originations found in
earlier studies reflect differences in minority
(low-income) application rates across lenders
as opposed to differences across institutions in
their minority (low-income) approval rates rela­
tive to their overall approval rates.
Our examination of the HMDA data reveals the
following patterns related to lender differences in

minority lending. First, lender differences in mi­


nority approval rates account for only about 10
percent of lender differences in minority loan
originations: Differences across lenders in mi­
nority application rates account for the remain­
ing 90 percent. Second, wre find that very little
of the lender variation in either minority appli­
cation rates or approval rates can be attributed
to applicant characteristics. Third, somewhat
surprisingly, we detemiine that while property
location explains a nontrivial portion of the
cross-lender variance in application rates, most
variation stems from differences in the applicants
that lenders attract within the neighborhoods
they serve. Finally, the correlation across lenders
between minority application rates and minority
approval rates is quite small. Minorities do tend
to apply to lenders with low overall approval
rates, but within this class of lenders, minority
application rates are highest at those lenders
with relatively large minority approval rates.

29

These results suggest that gross measures of
lender performance may work fairly well in
implementing a more quantitative regulatory
evaluation system. They also suggest that appli­
cation rate measures should play a particularly
important role if increased credit flow's to se­
lected groups are the desired objective. Inter­
estingly, even here, gross application rate
measures may work fairly w^ell in differentiat­
ing among lenders. We caution, however, that
even though our research indicates that lenders
vary enormously in terms of their relationships
with minority and low-income applicants, we
can say little about the reasons for this varia­
tion. Differences may result from illegal prac­
tices, or simply from economic factors on both
sides of the market. Furthermore, because a
number of financial institutions have initiated
new lending practices during the last few years,
the observed variation among lenders may be
narrowing. Regulators and the public should
attain a better understanding of the variation in
lenders’ practices before reaching definitive
conclusions about how to use measures of
such variation in enforcement of the CRA or
fair lending laws.

References
Avery, Robert B. “Making Judgments about
Mortgage Lending Patterns,” Federal Re­
serve Bank of Cleveland, Economic Com­
mentary, December 15, 1989.
________ , and Thomas M. Buynak. “Mortgage
Redlining: Some New Evidence,” Federal Re­
serve Bank of Cleveland, Economic Review,
Summer 1981, pp. 18-32.
________ , and Glenn B. Canner. “Mortgage Red­
lining: A Multicity Cross-Section Analysis,”
Board of Governors of the Federal Reserve
System, unpublished wrorking paper, 1983________ , Patricia E. Beeson, and Mark S. Sniderman. “Accounting for Racial Differences in
Housing Credit Markets,” Federal Reserve
Bank of Cleveland, Working Paper 9310, De­
cember 1993- Also forthcoming in Proceed­
ings o f a Conference on D iscrim ination a n d
Mortgage Lending, U.S. Department of
Housing and Urban Development.




________ , _________ , a n d _________ . “Under­
served Mortgage Markets: Evidence from
HMD A,” Federal Reserve Bank of Cleve­
land, working paper, December 1994 (forth­
coming).
Bradbury, Katharine L., Karl E. Case, and Con­
stance R. Dunham. “Geographic Patterns of
Mortgage Lending in Boston, 1982-1987,”
Federal Reserve Bank of Boston, New Eng­
lan d Economic Review, September/October
1989, pp. 3-30.
Calem, Paul S. “The Delaware Valley Mortgage
Plan: Extending the Reach of Mortgage
Lenders,” Jo u rn a l o f Housing Research, vol.
4, no. 2 (1993), pp. 337-38.
Canner, Glenn B. "Redlining and Mortgage
Lending Patterns,” in J. Vernon Henderson,
ed., Research in Urban Economics. Green­
wich, Conn.: JAI Press, 1981, pp. 67-101.
________ , and Dolores S. Smith. "Home Mortgage
Disclosure Act: Expanded Data on Residential
Lending,” Federal Reserve Bulletin, vol. 77,
no. 11 (November 1991), pp. 859-81.
________ , a n d _________ . “Expanded HMDA
Data on Residential Lending: One Year
Later,” Federal Reserve Bulletin, vol. 78, no.
11 (November 1992), pp. 801-24.
Munnell, Alicia H., Lynne E. Browne, James
McEneaney, and Geoffrey M.B. Tootell.
“Mortgage Lending in Boston: Interpreting
HMDA Data,” Federal Reserve Bank of Bos­
ton, Working Paper No. 92-7, October 1992.
Wienk, Ronald E. “Discrimination in Urban
Credit Markets: What We D on’t Know and
Why We Don't Know It,” Housing Policy
Debate, vol. 3, no. 2 (1992), pp. 217-40.

30

The Efficiency and Welfare
Effects of Tax Reform:
Are Fewer Tax Brackets
Better than More?
by David Altig and Charles T. Carlstrom

Introduction
The 1980s was the decade of tax reform. The
American economy experienced two major
changes in federal personal income-tax legisla­
tion, the Economic Recovery Tax Act of 1981
(ERTA) and the Tax Refomi Act of 1986 (TRA86).
But significant change was not limited to the
United States. By 1989, tax legislation had been
passed in Australia, Canada, Denmark, New
Zealand, Japan, Sweden, and the United King­
dom, with proposals for reform pending in
many other nations (see Tanzi [1987], Boskin and
McLure [1990], and Whalley [1990b]).
Although actual and proposed tax legisla­
tion within each of these countries wyas multi­
faceted, sometimes with substantial variance in
details, the reform proposals shared certain
broad characteristics across countries. Most
striking among these was the uniform tendency
toward lower top marginal tax rates, fewer rate
brackets, and "base broadening.” For example,
in the latest rounds of reform, top statutory
marginal rates in the federal personal tax codes
fell from 34 to 29 percent in Canada, 83 to 40
percent in the United Kingdom, and 50 to 31
 percent in the United States.1 Corresponding
http://fraser.stlouisfed.org/
to these changes were reductions in the num ­
Federal Reserve Bank of St. Louis

David Aitig is an assistant vice
president and economist and
Charles T. Carlstrom is an econo­
mist at the Federal Reserve Bank of
Cleveland. For helpful comments,
the authors thank Zsolt Besci,
Finn Kydland, Eric Rasmussen,
and seminar participants at Indi­
ana University and the Federal
Reserve Banks of Cleveland,
Minneapolis, and St. Louis.
Susan Byrne provided valuable
research assistance.

ber of rate brackets from 10 to 3 (Canada), 11
to 2 (United Kingdom), and 15 to 3 (United
States). These examples and others are summa­
rized in table 1.
A major motivation for these changes was the
growing perception that the distortionary effects
of high marginal tax rates had resulted in sub­
stantial inefficiencies.2 Consequently, an es­
sential impulse for tax reform was — and is —
the desire to create more efficient income tax sys­
tems by substituting base-broadening measures
for high marginal tax rates. Reductions in the

■ 1 Effective marginal tax rates can differ from statutory rates due to
special treatment of credits, deductions, and exemptions at certain thresh­
old income levels. An obvious example is the TRA86 provision for phas­
ing out personal exemptions for high-income taxpayers.

■ 2 In its 1984 report on early tax proposals, the Joint Committee on
Taxation identified three major objectives of comprehensive reform: equity,
efficiency, and simplicity. With respect to efficiency, the Committee wrote
that “ ... a widely accepted goal of tax policy is that taxes should interfere
as little as possible with the incentives to engage in specific types of eco­
nomic activity, except to the extent that Congress intends such effects...
[A] major goal of tax policy is to reduce [inefficiencies] to as low a level
as possible.” Furthermore, they indicated that “ ... in all [pending] pro­
posals, marginal tax rates are substantially reduced. This reduction ap­
pears to be motivated by efficiency and equity considerations.” See Joint
Committee on Taxation (1984).

31

T A B L E

1

Specific Elements
of World Tax Reform

Country7

Top Marginal
Tax Rate,
Pre-Reform

Pre-Reform
Year(s)

Number of
Pre-Reform
Brackets

Top Marginal
Tax Rate,
Post-Reform

Post-Reform
Year(s)

Number of
Post-Reform
Brackets

Australia

60%

1980-86

5

49%
47

1987-88
1992

4
5

Austria

62

1982-88a

10b

50

1989

5

Belgium

72

1983-88

13b

50

1989-92

7

Canada

34

1987a

10

29

1988-92

3

Italy

65

1983-87

9

56
51

1988
1992

8
7

Japan

70

1984-86

15

60
50

1987
1988-92

12

Netherlands

72

1982-86a

9

66
60

1987-88
1990-92

5
4

New Zealand

66

1979-85

5

48
33

1986
1988-92

3
2

5

Sweden

80

1985a

11

72
50

1986
1991-92c

4
4

United Kingdom

83

1978a

11

60
40

1979
1988-92

6
2

United States

50

1983-85

15

33
31

1986
1992

3
3

a. Rate may have been in effect prior to earliest date indicated.
b. Figures refer to num ber o f rate brackets in 1988.
c. From 0 to 186,600 kronor (SEK), the national tax is a flat SEK 100. For incomes in excess o f SEK 186,600, the tax is SEK 100 plus 20 percent
of the excess.
SOURCES: Platt (1985); Tanzi (1987); Boskin and McLure (1990); Whalley (1990a, 1990b); various issues of the Organisation for Economic
Co-operation and Development’s Economic Survey; and the 1982 and 1992 editions of Price Waterhouse’s Individual Taxes: A Worldunde Summary.

number of rate brackets are presumably meant to
reinforce this goal by simplifying the tax code and
minimizing distortions through the creation of
broad classes of income over which marginal tax
rates are essentially flat. Although often implicit,
this motivation for reducing the number of rate
brackets is sometimes explicit in discussions of
specific tax reform proposals. For example, in dis­
cussing the Takeshita reforms in Japan, Noguchi
(1990, p. 118) describes the U.K. and U.S. changes
in rate structures as “developments ... toward flatrate income taxes,” while Ishi (1989) refers to the
rate structure implemented in Japan as a “modified
flat-tax” system.
However, a brief glance at figure 1, which
depicts various vintages of Canadian, Japanese,
and U.S. personal income-tax rate structures,
 reveals the problematic nature of concluding


that a smaller number of rate brackets is less
distortionary than a larger number. Although
recent rate structures have wider bands of in­
come over which the marginal tax rate is flat,
jumps in the marginal rate are much more sig­
nificant for some taxpayers. It is unclear, a
priori, which structure will most significantly
distort household consumption and work-effort
decisions on net. Given the almost universal
tendency toward reforms that simultaneously
reduce the number of brackets and increase the
distance between them, it is surprising that these
issues have not been given more attention.
That, then, is the goal of this paper. Using
the well-knowTi dynamic fiscal policy frame­
work pioneered by Auerbach and Kotlikoff
(1987), we examine the welfare and efficiency
implications of shifting from linear to discrete

32

F I G U R E

1

Marginal Tax Rates
Percent
40
CANADA

1987

j= £

20
30
40
Income (thousands of 1989 Canadian dollars)

10

50

60

Percent

marginal tax-rate structures. In other words, we
consider the pure distortionary effects of replacing
a tax structure with many (infinitely small) steps
between marginal tax rates with one defined by
two large bands of flat tax rates connected by a
single, large discrete jump.
We find that when our model is calibrated
to match the main features of the U.S. econ­
omy, a hypothetical two-bracket code (roughly
patterned after the rate structure in the 1989
U.S. personal income tax code) is less efficient
than alternative linear-rate codes with similar
average-tax progressivity and present-value
revenue implications. By less efficient, we
mean that there is no sequence of lump-sum
transfers the government could feasibly imple­
ment that would make the shift from the linear
to the discrete rate structure Pareto-improving.3
This finding is generally robust to parameter as­
sumptions and to the chosen method for equal­
izing revenues. This central message should
serve as a cautionary note in the midst of grow­
ing political sentiment for further changes in
the U.S. income tax code; Without disputing
the merits of completely flat marginal tax rates,
our results do not support the position that a
modified flat-tax system is necessarily superior
to all alternatives with steeply sloped marginal
rate structures.

I. The Simulation
Model

2,000

1,000

3,000
4,000
Income (thousands of 1989 yen)

5,000

Percent

10

15

20
25
30
35
Income (thousands of 1989 dollars)

NOTE: Figures are scaled to a m axim um o f S50,000 equivalent U.S. dollars.
SOURCES: W halley (1990b); Ishi (1989); Boskin and McClure (1990); Internal


Revenue
Service, Statistics o f Income. Individual Tax Returns, 1965-89; and
http://fraser.stlouisfed.org/
International Monetary Fund, International Financial Statistics, J u ly 1992.
Federal Reserve Bank of St. Louis

The model specification includes mathematical
representations of the preferences and constraints
of utility-maximizing households, the produc­
tion technology available to profit-maximizing
firms, a government budget constraint, and a
specification for the income tax code, all of
which are described in this section. In combi­
nation with labor-, capital-, and goods-marketclearing conditions, a competitive equilibrium
is constructed by finding aggregate quantities
and prices that are, given the government’s be­
havior, consistent with the decentralized deci­
sions of individual households and firms.

■ 3 We argue only that a rate structure with revenue and progressivity
properties similar to TRA86 is less efficient than the specific alternative we
consider — not that all discrete marginal-rate schemes are less efficient.
Although we believe that requiring the same revenue collections and averagerate progressivity is a sensible constraint on the alternative tax codes, our
results should be interpreted in light of these particular restrictions.

33

Households and
Preferences

where
(3b)

Our model economy is populated by a sequence
of distinct cohorts (individuals born on the same
date) that are, with the exception of size, identical
in every respect. Each generation lives, with per­
fect certainty, for 55 periods (interpreted as adult
years) and is 1 + n times larger than its predeces­
sor. One can think of life as beginning at age 21
and ending at age 75.
Individuals “born” at calendar date b choose
perfect-foresight consumption ( c) and leisure
(/) paths to maximize a time-separable utility
function of the form
55

(1)

£4 = I
t=

1

where u,/ > 0,7 u„Z/ < 0,7 lim 1— / = °°,7 and u,Z is the
partial derivative of the function u(-) with re­
spect to argument i. The preference parameter (3
is the individual’s subjective time-discount factor.
We assume that (3 > 0, but do not strictly require
that (3 < 1.
Letting ats equal the sum of capital and
government debt holdings for age t individuals
at time s = b + t- 1, maximization of equation
(1) is subject to a sequence of budget constraints
given, at each time 5, by
(2 )

a t s = ( l + rs) * , _ 1>s_ i

+ e, ws( 1 - lt s) + v, s - T (y*s) - cl s,
where ws is the real pre-tax market wage at time
5, rs is the real return to assets held from time
s- 1 to s, e, is an exogenous labor-efficiency
endowment in the t period of life, and vt s re­
fers to lump-sum transfers received by age t
individuals at time s.4
The function T(y* s) defines the amount of
income tax paid, which depends on the tax base
given by yt s = rsat_ Xs_ , + e, w5( 1 - ltt5) - d .
The constant d represents a fixed level of deduc­
tions and exemptions used to convert gross in­
come to taxable income. In the linear marginalrate case, the function T(•) is defined as

(3a)

I GO = a + byt s, a, b > 0

defines the marginal tax rate as a linear function
of taxable income. In the discrete tax case, the
function is defined as

(4)

TDlsM. J xLy'.s
s
[ t 'y+ x H(y*s -y)

if y* >y

Note that at any time s, there are three dis­
tinct possibilities with respect to the budget
constraint in the discrete tax case, correspond­
ing to the cases where y* < y, y* > y, and
y* s = y The latter applies when individuals
are at the kink in the budget constraint.
In addition to equation (2), we impose the
initial condition that all individuals are born
with zero wealth and the terminal condition
that the present value of lifetime consumption
plus tax payments cannot exceed the present
value of lifetime resources. In the absence of a
bequest motive and lifetime uncertainty, this
wealth constraint implies that a 55 v= 0.

The Government
The government in our model raises revenue
through a combination of distortionary income
taxes, debt issues, and lump-sum taxes. Gov­
ernment purchases of output equal zero at all
times, and all government revenue is eventually
redistributed to households in the form of
lump-sum transfers. We specifically require
that revenue raised from the income tax be re­
bated in the form of lump-sum payments to the
individuals from whom it is collected. This al­
lows us to isolate the efficiency losses due to
the distortionary nature of marginal tax-rate
changes.
Initially, we assume that D0, the amount of
government debt at the beginning of time, is
zero, and that the individual transfer payments,
vt s, equal the amount of income tax revenue
collected for all individuals age t at all times s.
These assumptions, which we relax to calcu­
late efficiency measures in section V, imply
that debt issues are zero for all 5.

>’*s
jLinear_ f x{y )d y ,
y= d

■ 4 Capital and government debt are assumed to be perfect substi­


tutes in households’ portfolios.


Firms and
Technology
Output in the model is produced by competitive
firms that combine capital (K ) and labor (Z)
using a neoclassical, constant-returns-to-scale

34

production technology. Aggregate capital and
labor supplies (in per capita terms) are ob­
tained from individual supplies as
55

(5)

KS= Z

7. 5- 1
(1 +

Ds-i
l-l- n

and
55

(6)

i s= X
t= 1

(1 + 77)'-55

Note that the capital stock at time 5 is given
by private and public saving decisions at time
5 — 1. Also, recall that we initially assume Ds = 0
for all 5.
The production function is wTitten in terms
of the capital-labor ratio k as
(7)

scale steady-state cohort incomes to values con­
sistent with average household income in 1989,
the year for which the tax code is calibrated.
We discuss this choice in more detail below.
In the benchmark model, we assume that the
depreciation rate of physical capital is 10 percent
per period, a choice that, again, is motivated by
the arguments in Kydland and Prescott. The pop­
ulation growth rate is set to the postwar U.S.
average of 1.3 percent per year, and the life-cycle
labor efficiency profile {e/1^ 1 is calculated by
interpolating estimates in Hansen (1986).

Preferences
We assume that preferences are isoelastic, spe­
cializing equation (1) to

q - f ( k , ),

where qs is per capita output and / (• ) is de­
fined such that / ' > 0, f " < 0, l i m ^ ^ / ' = 0,
and l i m ^ o / ' =
The competitive wage rate
and (gross) interest rate are given by

1_J_
°c

( 11)

' t, b + t - 1

1——
I

°1

t, b + t - 1

--- -— + a£ 4 = X P '- ‘
i - i
1a,

where the preference parameters o c , <5l , and
(8)

ws = qs - kf'(- )

a represent the intertemporal elasticities of sub­
stitution in consumption and leisure and the
utility' weight of leisure, respectively. In our

rs.= / '( • ) - 5,

benchmark model, we assume o t. = 1, so that
equation (11) becomes

and
(9)

where 8 is the depreciation rate on physical
capital.

ln(c, b+t. l ) + CL

II. Model Calibration
t= 1

In order to quantify the model, it is necessary
to choose particular values for the model’s
parameters. In this section, we describe the
choices that result in our benchmark model
and discuss their rationale.

Technology
The simulation exercises reported in section IV
assume an aggregate production technology
given by
( 10)

q - A k ®,

where 0 is capital’s share in production and
A is an arbitrary scale factor. Our benchmark
value for 0 is 0.36, following Kydland and
 Prescott (1982). The value of A is chosen to


t, b+ t - 1

i- l

This form has the special property, not gener­
ally exhibited by specification (11), that the
capital-labor ratio is invariant to the scale fac­
tor A in equation (10).5 Also, evidence from
state-level data reported by Beaudry and van
Wincoop (1992) suggests preferences that are
logarithmic in consumption.6
■ 5 Scale invariance follows from the fact that changes in the level of
wages have offsetting wealth and substitution effects on individual labor
supply decisions. Since scale invariance also implies that average hours
worked will not change with growth, preferences similar in form to those
in equation (11") often appear in the real business cycle literature (see
King, Plosser, and Rebelo [1988]).

■

6 Further, Beaudry and van Wincoop find no evidence supporting
either nonseparabilities between consumption and leisure or the absence
of time separability in consumption, results that generally support the
specification in equation (11). However, it should be noted that their em­
pirical findings are based on a different model of aggregate consumption
behavior than the one presented here.

35

We base the choice of C/, the intertemporal
elasticity of substitution of leisure, on the exten­
sive empirical literature devoted to estimating the
wage elasticity of the labor supply. This elastic­
ity, which we denote r^ , is related to <5t by

(12)

n =

The Tax Code
The benchmark tax code is patterned after the
statutory U.S. personal tax code for 1989.
Over the income region that is relevant in our
simulations, the 1989 schedule was given by

20,
( 13)

MaCurdy’s (1981) study of men’s labor supply
suggests values for r|7 in the range of 0.1 to
0.45, a result that is largely confirmed in re­
lated studies (see Pencavel [1986]). However,
Rogerson and Rupert (1991) argue that, be­
cause of corner conditions, estimates of the
degree of intertemporal substitution obtained
from conventional analyses of male labor sup­
ply are likely to be understated. Furthermore,
despite greater disparity in estimates obtained
from studies of female labor supply, there is
broad agreement that the elasticity is higher for
women (see Killingsworth and Heckman [1986]).
Based on this evidence, in our benchmark model
we set <51= 0.25 and choose the parameter a so
that steady-state hours worked by an individual
at peak productivity are slightly greater than onethird of total time endowment, which we take to
be 16 hours per day.
Most empirical studies find values for the
subjective discount factor (3 at annual frequen­
cies to be in the neighborhood of 1.0 — some­
times slightly lower (Hansen and Singleton
[1982]), sometimes slightly higher (Eichenbaum
and Hansen [1990]). We choose a benchmark
value of 0.99. Together with the other parame­
ter choices, this value results in a steady-state
real pre-tax interest rate of about 3.7 percent
(which corresponds closely to the [apparent]
historical average of real pre-tax returns on
long-maturity riskless bonds in the United
States") and in a steady-state capital output
ratio of 2.63 (which corresponds closely to the
ratio of total capital to GDP in the United States
over the 1959-90 period8).

TDiscrete —

0.15

if y*t s< $30,950,

0.28

if y* s> $30,950.

We refer to this tax code as the “tax-reform” case.
The income levels obtained from the model
are scaled to match those in the 1989 tax code
as follows: The scale parameter A in the pro­
duction function of equation (10) is chosen so
that the highest income in the model matches
the average income level for the highest-paid
age group found in 1988 Census Bureau data.9
We calculate the average for this group, which
consists of persons aged 45-54, to be $44,217
in 1989 dollars.10 This value of A is then used
in all subsequent simulations. To obtain tax­
able income, we subtract exemptions and de­
ductions of $11,206.

III. Welfare Effects
In this section, we examine the effects of shift­
ing to the tax-reform code from an alternative
linear-rate code, under the maintained assump­
tion of revenue neutrality. Holding the struc­
ture of the discrete code constant, two natural
approaches to achieving revenue neutrality are
1) choosing the intercept of the linear-rate
code to equalize revenues, and 2) adjusting de­
ductions to equalize revenues.
In each of our experiments, we consider an
initial steady state under the linear-rate regime
and examine the transition to a new steady
state under the tax-reform regime.11 Thus, un­
der an intercept-adjusted approach, we para­
meterize the function x(y) in equation (3b) as

■ 9 Recall from our previous discussion that household utility func­
tions are chosen so that real outcomes are unaffected by the choice of

■ 7 See Siegel (1992), which reports average rates for the 1800—
1990 period. We note, for the record, that average real rates appear to dif­
fer significantly across particular subperiods. Specifically, real returns to
long-term bonds averaged 1.46 percent between 1889 and 1978, but are
5.76 percent outside that interval.

■

8 The measure used to construct the U.S. capital stock is the
constant-cost net stock of fixed reproducible tangible wealth reported in
 the January 1992 Surveyof Current Business, compiled by the U.S. De­
partment of Commerce. This measure includes consumer durables and
http://fraser.stlouisfed.org/
Federal Reserve Bankgovernment
of St. Louis
capital.

A.

■ 10 The data used in constructing this variable were taken from the
Bureau of Labor Statistics’ Current Population Reports, series P-60, no.
166. The cohort mean is obtained by multiplying the median income of
families with household heads aged 45-54 by the ratio of average to me­
dian family income for the entire population. All money values in this pa­
per are quoted in 1989 dollars.
■ 11 The experiments we report involve unanticipated changes in the
tax regime. We have also conducted analyses (not reported) with antici­
pated regime shifts and found that our conclusions are robust.

36

F I G U R E

2

Marginal Tax Rates
(Benchmark Parameters)
Marginal tax rate (percent)

0.30
Tax reform

0.28 0.26
0.24
0.22

Linear-deduction adjusted

0.20
Linear-intercept
adjusted

0.18
0.16
0.14

0.12

-

/
... J .........

27

I _______1...... ... _ L _ _ 1 _____ _ L _

33

39

45

51

57

~1—

i

63

69

.

75

Age of population
SOURCE: Authors’ calculations.

TABLE

2

Average Tax-Rate Comparisons:
Steady-State, Benchmark Parameters
(percent)
Low
Income

Median
Income

High
Income

Tax reform code

4.1

10.9

11.8

Linear-rate code, intercept
adjusted to equalize
revenues

3.3

10.8

11.9

Linear-rate code, deductions
adjusted to equalize
revenues

0.1

10.7

12.1

SOURCE: Authors' calculations.

(14)
and choose the intercept \
|/ so that the present
value of income tax revenues generated by the
linear-rate code is acceptably close to the present
value of revenues generated by the tax-reform
 transition path and steady state.12 Under the
http://fraser.stlouisfed.org/
alternative deduction-adjusted approach, we set
Federal Reserve Bank of St. Louis

\
j/ = 0.146 and choose the deduction to match
the revenue levels.13 For the benchmark model,
this approach yields deductions of $14,561 in the
initial steady state.
Figure 2 shows the steady-state, life-cycle
path of marginal tax rates for the tax-reform
and two linear-rate regimes. For the interceptadjusted linear-rate code, approximately 55
percent of the population, accounting for an
equal amount of steady-state income, face
lower marginal tax rates than they would under
the tax-reform system. The highest marginal
tax rate in the linear-rate case is approximately
20 percent, as opposed to 28 percent in the
tax-reform regime. For the deduction-adjusted
linear-rate code, things are slightly different:
Approximately 35 percent of the population,
accounting for 42 percent of steady-state in­
come, face lower marginal tax rates than they
would in the tax-reform case. Furthermore,
the rate reductions are concentrated — and es­
pecially pronounced — at high income levels.
The highest marginal tax rate in the deductionadjusted linear-rate scenario is approximately
22 percent.
In addition to the revenue implications, the
progressivity of each tax structure is a key ele­
ment in considering the comparability of the
different tax codes. Information on average taxrate progressivity, provided in table 2, is one
convenient way of examining progressivity.
Although no more than an informal summary of
the nature of a particular tax code, this meas­
ure does provide a sense of how average tax
liabilities are related to income, highlighting
the sort of comparisons often invoked in dis­
cussions of alternative tax regimes. As claimed
above, the results in table 2 do suggest that in
the long mn, the tax-reform and linear-rate codes
(especially the intercept-adjusted variant) exhibit

■ 12 By “close,” we specifically mean within 0.001 percent. The
slope of the function in equation (14) is obtained by fitting a linear regres­
sion to the 1965 statutory tax code. The 1965 schedule was chosen as
representative of the marginal rate structure in place over much of the
1964-78 period. Over the income range $0—$54,000, which covers the
incomes generated by our model, a linear function is a reasonably good
approximation of this statutory schedule.
Present values are calculated as the Interest rates realized under tax re­
form, that is, along the transition path and in the new steady state. Meas­
uring revenue neutrality under a fixed assumption about interest rates,
while not strictly consistent with ex post neutrality, seems consistent with
the fashion in which tax legislation is actually contemplated. Further­
more, because the final, tax-reform steady state is the same in all simula­
tions conducted under a particular parameterization of the model, our
choice delivers a common discount factor across like experiments.

■ 13 The choice of 0.146 is motivated by the same regressions used
to determine the slope of the linear code. See footnote 12.

37

F I G U R E

3

Welfare Loss Due to Tax
Reform: Basic Results
Percent of wealth

Generation
NOTE: Each x on the horizontal axis corresponds to the oldest generation
alive jc periods after the tax regime change.
SOURCE: Authors’ calculations.

similar degrees of progressivity, subject of
course to the usual caveats about the validity
of the average tax measure.
Armed with these observations, we turn next
to examining the welfare implications of shift­
ing from a linear-rate regime to the tax-reform
regime. Throughout, we calculate welfare
losses as the percentage increase in full wealth
that must be given to an individual in the taxreform regime in order to compensate him for
the switch to the linear code.14 Negative num ­
bers therefore represent welfare gains associ­
ated with tax reform.
Figure 3 illustrates welfare losses for differ­
ent age cohorts arising from an unanticipated
change from the intercept-adjusted linear-rate
regime to the tax-reform regime. Cohorts in fig­
ure 3 are identified by year of death. Thus, the
welfare number for period 1 of the transition
path represents the loss by an individual age 75
(fifty-fifth year of life) at the time the tax-reform
regime becomes effective. All cohorts alive in
the initial (linear-rate) steady state have died
by period 55 of the transition path. The three
sets of losses shown in figure 3 are calculated
from the benchmark model and from two alter­

native parameterizations with different choices
http://fraser.stlouisfed.org/
for
intertemporal elasticity of substitution
Federal Reserve Bank of the
St. Louis
in leisure.

In the long run, tax reform generates wel­
fare losses, with the magnitude of the loss posi­
tively related to individuals’ willingness to shift
leisure intertemporally. The intuition for this re­
lationship between welfare costs and GI can be
appreciated by recalling that, because heteroge­
neity in the steady state is due strictly to life­
cycle characteristics, the highest incomes in the
model are earned by individuals who are at
their peak levels of labor productivity. As
shown in figure 2, this is exactly the period of
the life cycle for which tax reform implies
higher marginal tax rates relative to the linearrate regime. The distortions on labor supply
created by this fact are magnified for higher de­
grees of willingness to substitute leisure across
periods of life. Thus, an apparently important
factor in the relative efficiency of the linearrate structure is that, for roughly the same de­
gree of progressivity, the marginal tax rate
faced by the highest-income individuals is
lower than in the tax-reform case.
The welfare effects apparent in figure 3 arise
primarily from the direct distortions of the taxreform code vis-à-vis the hypothesized linearrate code, not from general equilibrium effects
associated with changes in interest rates and
wages.H In figure 4, we compare the welfare
effects for the benchmark model with the effects
obtained when the entire path of interest rates
and wages is held fixed at the initial steady-state
values. Although general equilibrium effects
mitigate the welfare losses, the picture that
emerges is little changed by the partial equilib­
rium assumption, especially in the long run.
Note, however, that general equilibrium effects
have a significantly greater impact on older co­
horts alive at the time of the regime change.
Finally, we consider the welfare consequences
when the linear-rate structure is chosen accord­
ing to the deduction-based method for equal­
izing revenues. Figure 5 shows the results of
welfare calculations for these experiments.
Relative to the intercept-adjusted experiments,
the long-run welfare losses of tax reform are

■ 14 Full wealth, O , is defined as the present value of wage income
when the entire time endowment is allocated to labor. Thus,

i

£twb+t-1

'=2n a + w i )
/=2
■ 15 Recall that for the simulations in this section, we assume that
lump-sum taxes and transfers maintain zero net tax payments for every
cohort at every point in time. Therefore, wealth effects arise only as a re­
sult of changes in the aggregate levels of capital and labor, which are in
turn reflected In interest rates and wages.

38

F I G U R E

4

Welfare Loss Due to Tax Reform:
Partial versus General Equilibrium
Percent of wealth

Generation

F I G U R E

5

Welfare Loss Due to Tax Reform:
Deduction-Adjusted Results
Percent of wealth

FI GURE

6

Welfare Loss Due to Tax Reform:
Alternative Consumption Elasticities
Percent of wealth

Generation

NOTE: Each x on the horizontal axis corresponds to the oldest generation
alive x periods after the tax regime change.

SOURCE:
Authors' calculations.



somewhat lower when revenues are equalized
in the linear-rate code by adjusting deductions.
However, as reported in table 2, equalizing
revenues by deduction adjustments results in
greater average-tax progressivity than does
either the intercept-adjusted linear code or the
tax-reform code. Essentially, the increase in
marginal rates on high-productivity/high-asset
cohorts associated with tax reform is smaller
when taxes are equalized by increasing deduc­
tions in the linear code, resulting in smaller
long-run welfare losses.
This last observation underscores a critical
point that bears reemphasizing. The relative
welfare effects of each of the tax structures we
consider are dependent on the relative levels
of marginal tax rates necessary to preserve
revenue neutrality. The discrete code examined
here generates welfare losses because a linearrate code with similar average-tax progressivity
(or less progressivity, for that matter) allows the
application of lower rates to the critical highincome cohorts.
Finally, figure 6 presents the same experi­
ments for different degrees of intertemporal
elasticity of substitution for consumption.16
Note especially that as consumers become less
willing to substitute consumption across time,
tax reform actually generates long-run welfare
gains. However, welfare losses persist for the
early years following the introduction of tax
reform. This observation raises the interesting
question of whether, for certain parameter choices,
long-run welfare gains are large enough to offset
short-run losses. We turn to this issue next.

IV. Efficiency Effects
The pattern of welfare effects in figures 3-5
clearly indicates that the contemplated shifts
from the tax-reform regime result in efficiency
losses. However, the welfare calculations pre­
sented do not provide a simple measure that
summarizes the economic cost of such changes.
Furthermore, as shown in figure 6, there are
long-run welfare gains for some plausible al­
ternatives to the benchmark model. For these
cases, the question is open regarding whether
the shift to the tax-reform regime can be con-

■ 16 Recall that, given the preference specification in equation (11),
equilibrium outcomes in the model are not invariant to the scale of the
model when c c * 1. There are, however, other utility functions that allow
more flexibility in the choice of the intertemporal consumption elasticity
while preserving scale invariance, albeit at the cost of less flexibility in
choosing intertemporal leisure elasticity.

39

T A B L E

3

Efficiency Losses Due to Tax Reform
(percent of wealth)
Revenues Equalized
by Adjusting
Intercept in the
Linear-Rate Code

Revenues Equalized
by Adjusting
Deductions in the
Linear-Rate Code

Benchmark

0.139

0.058

o, =0.17
= 0.50

0.065
0.235

0.027
0.103

p

0.080
0.211

0.030
0.088

= 1.005
= 0.976

o c = 0.20

0.162

0.074

= 0.33

0.151

0.069

= 0.07

0.160

0.066

0.362
0.362
0.362

0.165
0.165
0.165

5

0 7 = 0.20
(3 = 0.971
Ô = 0.07
SOURCE: Authors’ calculations.

structed to maintain positive long-run welfare
gains for some generations without diminish­
ing the lifetime utility of any other.
In this section, we develop a measure of
the efficiency costs of shifting from the hy­
pothesized linear-rate codes. Furthermore, for
cases that generate gains for some generations,
we ask whether there exists a set of transfers
that preserves positive long-run gains while
eliminating all welfare losses of cohorts alive
along the post-reform transition path.
To these ends, we calculate an efficiency
measure in the spirit of the one introduced in
Auerbach, Kotlikoff, and Skinner (1983). Spe­
cifically, let 5=1 be the time at which tax re­
form is introduced. To obtain our efficiency
measure, we ask how much wealth can be
taken away from cohorts born on or after 5=1
following the implementation of a fiscal policy
with the following characteristics:17
(a)
The government first introduces lum p­
sum taxes and transfers so that the lifetime util­
ity of all generations is maintained at the
steady-state level realized in the initial, linearrate regime. For instance, in figure 6, cohorts
experiencing welfare losses would receive

■

17 Auerbach, Kotlikoff, and Skinner refer to the hypothetical gov­

 ernment agency that implements these policies as the “Lump Sum Redis­
tribution Authority.”


transfers while those enjoying welfare gains
would be taxed.
(b)
Following the policy in (a), the govern­
ment’s long-run budget will be in surplus if the
present value of taxes exceeds the present
value of transfers, or in deficit if the converse
is true. Because the long-run budget must bal­
ance, the government must choose a sequence
of other transfers (for the surplus case) or taxes
(for the deficit case) so that the present value
of taxes less transfers equals zero. For the pur­
pose of constructing our efficiency measure,
we assume that the budget is balanced by im­
posing lump-sum taxes, or by granting lum p­
sum transfers, that are a constant fraction of
the full wealth of all generations born after the
tax reform.
If, after policy steps (a) and (b), generations
along the transition path and in the new steady
state are worse off, our efficiency measure is
negative and equal to the percentage wealth loss
suffered by each. A more detailed sketch of our
procedure is offered in the appendix.
Table 3 reports the results of efficiency cal­
culations for alternative parameterizations of
the model. Losses are associated with all of the
cases considered, even those in which there is
a long-run welfare gain from shifting to tax re­
form. Thus, the short-run losses that occur in
figure 6 dominate the long-run gains.
For the benchmark model, the shift to the taxreform code results in an efficiency loss of 0.14
percent of full wealth when revenues are equal­
ized by adjusting the intercept of the linear-rate
schedule. More generally, calculated losses
range from 0.08 to 0.36 percent, depending on
the chosen parameters. W hen revenues are
equalized by adjusting deductions, the efficiency
losses are uniformly smaller, but still range
from 0.03 to 0.17 percent of full wealth. As
shown, losses increase with individuals’ willing­
ness to shift resources intertemporally, again
reflecting the fact that high-tax periods corre­
spond to periods of high relative saving rates
and high labor productivity.
To put some perspective on the magnitude of
the efficiency losses, full wealth for each cohort
in the tax-reform steady state is about 63 percent
of total output. Thus, a reduction in full wealth
of 0.14 percent represents an annual loss equal
to about 0.09 percent of output in the model.
Converting full wealth in the model to 1989 dol­
lars implies an efficiency loss equivalent to
roughly $1,418 per person bom (or reaching
working age) after the regime change.

40

V. Concluding
Remarks
Significant reductions in the number of mar­
ginal tax-rate brackets — that is, a trend to­
ward structuring systems of personal income
taxation such that there exist wide bands of in­
come over which marginal tax rates are flat —
have been a striking characteristic of world­
wide tax reform over the past decade. In this
paper, we argue that this trend is not obviously
accounted for by appealing to the efficiency
gains inherent in tax codes with just a few
brackets separated by discrete-rate jumps. Rela­
tive to revenue-neutral linear-rate structures,
changing to a simple two-bracket discrete-rate
structure creates efficiency losses in all of the
numerical experiments we conduct. Further­
more, in most cases welfare gains are uniformly
negative, even in the long mn.
Two explanations come immediately to
mind for the discrepancy between the reality
of recent tax reforms and the results of our
analysis. First, our analysis is conducted in a
purely life-cycle framework. Hence, in steadystate equilibria, all cohorts face exactly the
same life-cycle profile of relatively high taxes
during periods of peak productivity and sav­
ing. The inefficiency of the discrete code that
we consider follows in important ways from
the fact that, holding average-tax progressivity
constant, shifting from an equal-revenue linear
code requires marginal tax-rate increases dur­
ing this phase of the life cycle.
It is reasonable to conjecture that these ef­
fects would be mitigated in a more general
framework that included intracohort heteroge­
neity. For instance, suppose that there existed
two types of agents, “rich folks” and “poor
folks.” It is conceivable that the two-bracket
tax code could be structured so that the shift
from the linear tax would result in poor folks
facing only the lower rate and rich folks facing
only the higher rate over their entire lives. In
this event, the discrete tax code would be
equivalent to a flat-tax regime, which would al­
most certainly create welfare and efficiency
gains. In a slightly less extreme case, some por­
tion of each cohort would face the life-cycle
pattern of rates on which we have focused,
while for others, the poor-folk/rich-folk sce­
nario would be relevant.
We have, however, conducted experiments
in which we relax the representative life-cycle
agent characteristic of the model presented in
this article. In particular, we have replicated
 several of our welfare experiments in a frame­


work that includes 13 distinct life-cycle agent
types with varying degrees of lifetime wealth
and income. The qualitative aspects of our re­
sults are unchanged by this extension.
A second explanation for the widespread
adoption of rate-bracket reductions is that, per­
haps for administrative or political reasons,
they are a necessary concomitant to lowering
the level of tax rates and to the various basebroadening measures that also characterized
tax reform in the 1980s. In this case, the ap­
proach advocated by Slemrod (1990), which
emphasizes the broad institutional framework
in which tax policy is chosen, may ultimately be
necessary to fully understand the consequences
of the income tax systems that have undeniably
come to dominate industrialized economies.

Appendix
Notes on Calculating
Efficiency Gains
Our efficiency calculations require extending
the government sector so that an individual’s
budget constraint becomes
(Al)

a t s = (1 + rs) a t_ l s_ x+ z , ws{1 - lt ,)

+vt,s~ T(y*.s) +Z,. s-c,'SThe only difference between the above
equation and equation (2) in the text is the ad­
dition of zt s , which represents the net lum p­
sum transfers (negative numbers represent
taxes) in excess of those necessary to offset
income tax collections. Given this definition,
the per capita level of debt evolves according
to the relationship

(A2)

D s -

1

Z> = (1 + r ) —-—- —Z ,
5 1+ n
5

where
55

(A3)

z s= ^ ( 1 + n )55~ 'z, s.

t=i
Letting 5 = 1 be the first period of the transi­
tion path and normalizing the population at
5 =1 to unity, intertemporal budget balance for
the government requires that

41

5=2 n o * ' - )
1= 2

The algorithm for obtaining our efficiency
measure proceeds in the following steps:
(i) Conjecture a sequence of interest rates for
the transition path and the new (tax-reform)
steady state.
(ii) Calculate the present value of lump-sum
taxes, net of lump-sum transfers, that would be
needed to maintain all cohorts at the initial
steady-state level of utility. Refer to the resulting
number as the “utility-compensation surplus,” or
UCS. If positive, the UCS determines the present
value of transfers that can redistributed by the
government while maintaining long-run budget
balance. If negative, the UCS determines the pres­
ent value of taxes that must be raised to maintain
budget balance.
(iii) Maintain the utility level of all cohorts
alive at the time of the tax regime change, so
that the government budget balance is satisfied
by solving for the constant tax or transfer (as a
percentage of each cohort’s full wealth) that
can be applied to all subsequent cohorts while
just exhausting the UCS.
(iv) Use the path of taxes and transfers from
steps (ii) and (iii), along with the associated
path of government debt implied by equation
(A2), to recalculate the entire problem, as de­
scribed in section II.
(v) Update interest rates and the UCS until
the procedures converge to an equilibrium that
satisfies public and private budget constraints,
all market-clearing conditions, and the firstorder conditions governing individual con­
sumption and leisure choices. Once the problem
has converged, the efficiency gain is the per­
centage of full wealth that is redistributed to
(or taken from) all cohorts bom after the change
in tax regime, as calculated in step (iii).

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Francisco: ICS Press, 1990b, pp. 73-91.




43

Fourth Quarter
Working Papers
Current Working Papers of the
Cleveland Federal Reserve Bank
are listed in each quarterly issue
of the Economic Review. Copies
of specific papers may be re­
quested by completing and
mailing the attached form below.

Single copies of individual pa­
pers will be sent free of charge
to those who request them. A
mailing list service for personal
subscribers, however, is not
available.

Institutional subscribers, such
as libraries and other organiza­
tions, will be placed on a mail­
ing list upon request and will
automatically receive Working
Papers as they are published.

■ 9411
Similarities and
Dissimilarities in the
Collapses of Three
State-Chartered Private
Deposit Insurance Funds

■ 9413
The Annuitization of
Americans’ Resources:
A Cohort Analysis

■ 9415
Bankruptcy Rules and
Debt Contracting: On
the Relative Efficiency
of Absolute Priority,
Proportionate Priority,
and First-Come, FirstServed Rules

by Walker F. Todd

■ 9412
The Burden of German
Unification:
A Generational
Accounting Approach
byJagadeesh Gokhale,
Bernd Raffelhuschen, and
Jan Walliser

by Alan J. Auerbach,
Jagadeesh Gokhale,
Laurence J. Kotllkoff,
John Sabelhaus, and
David N. Weil

■ 9414
Loan Sales: Pacific
Rim Trade in
Nontradable Assets
by Joseph G. Haubrich and
James B. Thomson

by Stanley D. Longhofer

■ 9416
Executive Compensation:
A Calibration Approach
by Joseph G. Haubrich and
Ivilina Popova

Please complete and detach the form below and mail to:
Research Department
Federal Reserve Bank of Cleveland
P.O. Box 6387
Cleveland, Ohio 44101




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requested

Please send the following Working Paper(s):

□ 9411

□ 9413

□ 9415

□ 9412

□ 9414

□ 9416

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44

The Federal Reserve Bank of Cleveland
and the Journal of Money, Credit and Banking
Announce:

Derivatives and Intermediation
November 2-3, 1995
Cleveland, Ohio

The Federal Reserve Bank of Cleveland and
the Journal of Money, Credit and Banking
are jointly sponsoring a conference on
Derivatives and Intermediation:
Theory and Evidence.




The growing derivatives market poses several chal­
lenges for policymakers. The first is to understand
the sources of financial innovation resulting in the
proliferation of these products. What economic
forces make derivatives viable instruments? What
gains do rational participants obtain from these con­
tracts, and why do they dominate transactions in
the cash securities markets? To what extent does
regulatory policy— bankruptcy rules, capital require­
ments, accounting rules, and deposit insurance—
affect the market? In other words, does derivativerelated financial innovation stem from changes in
the marketplace, or from changes in the regulatory
environment? The answer is crucial to understand­
ing both derivatives and intermediation. The second
challenge for policymakers is to understand how
derivatives impact regulatory concerns in the areas
of bank risk, payments system reform, and
intermediary powers.

Call for Papers
The conference proceedings will be published in the
and authors
will receive an honorarium. Prospective contribu­
tors are invited to send a completed paper or de­
tailed abstract by May 30,1995 to:

Journal of Money, Credit and Banking,

Joseph G. Haubrich
Research Department
Federal Reserve Bank of Cleveland
P.O. Box 6387
Cleveland, OH 44101-1387