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ESTIMATINGINTERTEMPORALELASTICITY
OF SUBSTITUTION:THE CASE OF
LOG-LINEARRESTRICTIONS
C/&g-Sheng Mao *

Introduction

The modern theory of consumer behavior is concerned with how consumption adjusts to changing
prices over time. When time is not involved, the demand for a normal consumer good declines as its
relative price rises. Similarly, consumption at different
points in time can be regarded as different goods,
in which case the price that determines consumer
behavior is the cost of today’s consumption in terms
of tomorrow’s, or, equivalently, the cost of borrowing against the future. This price is called the real
interest rate. When the expected real interest rate
rises, consumers will attempt to defer current consumption by saving. Economists refer to the substitution between consumption at different points in time
in response to changes in the real interest rate as
intertemporal substitution in consumption.
The mechanism of intertemporal substitution plays
an important role in the theory of consumption and
macroeconomics in general. For instance, it implies
that consumers will smooth their consumption given
the expected time profile of real interest rates and
lifetime wealth. Thus, consumers respond to an increase in current income by raising both current and
future consumption. This effect has been widely used
in analyzing a number of important issues. These include the behavior of aggregate consumption over
time, the volatility of stock prices, and the burden
of government deficits and social security. Because
the smoothing of consumption tends to propagate
current shocks into the future, this mechanism also
helps explain persistence of business cycles. Furthermore, the willingness of consumers to substitute
intertemporally is a key determinant of the effectiveness of many government policies. Consider the
recent debate over the reduction of capital gains tax
rates. Proponents of the tax cut argue that it would
* The author received helpful comments from Michael Dotsey,
Marvin Goodfriend, Robert Hetzel, Thomas Humphrey, and
Yash Mehra.
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encourage saving by making current consumption
more expensive relative to future consumption, i.e.,
by raising the after-tax real return to saving. In fact,
however, the influence of the tax cut on saving and
investment depends crucially on the response of consumption to the corresponding changes in the intertemporal terms of trade. Thus, to evaluate the
empirical effect of the tax cut, or in fact any policy
that is meant to promote saving and economic
growth, one must know the intertemporal elasticity
of substitution.
While many authors have attempted to use actual
data to estimate the intertemporal
elasticity of
substitution, their results are widely different. For
example, using time series data in the United States,
Hall (1988) concluded that there is no strong
evidence that the elasticity is positive. By contrast,
other studies have suggested a much stronger tendency of intertemporal substitution. The estimate
obtained by Hansen and Singleton (1982, 1983), for
instance, lies between 0.5 and 2, while the estimate
obtained by Eichenbaum, Hansen, and Singleton
(1986) can be as high as 10 depending on the data
set used. The estimation by Hansen and Singleton
(1988) even produces a negative elasticity estimate.
At the very least, this wide range of figures raises
questions regarding the reliability of the elasticity
estimates.
This paper explores the reliability of estimates of
the intertemporal substitution effect using Monte
Carlo simulation. A model economy is specified in
which the modeler himself selects the intertemporal
elasticity of substitution. Then, using conventional
statistical techniques, data generated from model
simulations are used to estimate the elasticity. Since
the elasticity’s true value is known, one can check
how closely the estimates conform to the value that
was chosen in constructing the data. This technique
allows one to evaluate the performance of the conventional strategies for estimating the intertemporal
elasticity of substitution. Since many of the empirical
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Figure 1

studies on intertemporal substitution ignore the potential wage effect on consumption, this paper also
examines the consequence of misspecification error
for a simulated model in which changes in the real
wage have effects on consumption behavior. It is
shown that ignoring the wage effect can cause a
substantial bias in the estimation of the elasticity of
substitution in consumption.
The next section outlines the notion of intertemporal substitution using a simple two-period model.
Section 3 introduces a formal maximization problem,
derives its first-order condition and discusses the
estimation method. Section 4 lays out a model
economy which serves a laboratory to generate
simulation data. Section 5 summarizes the estimation results and Section 6 discusses the misspecification bias.
2.

Intertemporal Substitution:
A Two-Period Model

To clarify the notion of intertemporal substitution,
consider a simple two-period consumer’s problem.
The consumer is assumed to be endowed with a fured
income yr in the first period and yz in the second
period. In period 1, there is a capital market where
the consumer may borrow or lend at a competitive
real interest rate rr. Let cl and c2 denote consumption in period 1 and period 2, respectively. Then the
budget constraint, expressed in present-value form,
is CI + cz/(l +rr) = yr + yz/(l +rr). That is, the
present value of current and future consumption must
exhaust but not exceed the present value of the consumer’s income stream. The consumer’s problem is
to choose cl and c2 in order to maximize his utility,
u(cr, cz), subject to the budget constraint. This is
a standard textbook problem. The consumer will adjust his borrowing or lending so as to equate the
marginal rate of substitution of cl for c2 with one plus
the real interest rate. l In equilibrium, the consumer
may be a net borrower or lender depending on his
initial endowment position.
Figure 1 depicts the consumer’s equilibrium in
which the horizontal and vertical axes measure cl and
cz, respectively. In equilibrium, the consumer will
choose to consume at point E at which the indifference curve is tangent to the budget line, which has
slope -(1 +ri). As depicted, this consumer is a net
lender and saving is equal to (yr -cl). Now, suppose
the real interest rate rises from rr to rr ‘, so that the
budget line rotates clockwise around the endowment
r In mathematical notation, this condition can be expressed as
ur/ua = (1 +rr), where ui (i = 1, 2) is the marginal utility of
consumption in period i.
4

ECONOMIC

REVIEW,

point (yr, ~2) and has a steeper slope. A key question is how the consumption ratio cz/ci will respond
to such a change. First, because consumption
becomes relatively more expensive in period 1, there
is a substitution effect that induces the consumer to
substitute cz for cl by making more loans in the bond
market. Because the consumer is lending, however,
there is also an income effect that tends to raise consumption in both periods. Whether or not the consumption ratio cz/cr will rise depends upon the
relative magnitude of these effects. For the purpose
seems
of this paper, the standard assumption
reasonable, namely, that on balance cz/cr increases
or that the income effect on cl is not strong enough
to outweigh the substitution effect and the income
effect on 122.2As a result, the new equilibrium will
be reached at point E ’ where the consumption ratio
cz/ci is higher. Because of the assumption of constant elasticity, the increase in cz/cr is proportional
to the increase in the real interest rate. The ratio
of the percentage change in the rate of growth of
consumption to the percentage change in the real
2 To be precise, the consumer’s utility function is taken to be
homothetic and constant elastic. This assumption implies that
the consumption good in each period is normal and that the slope
of the indifference curve is constant along a given ray from the
origin. Note that a utility function is called homothetic if the
marginal rate of substitution depends only on the consumption
ratio, and it is called constant elastic if the marginal rate of
substitution is proportional to the consumption ratio. An explicit
utility function will be specified in the next section.

NOVEMBER/DECEMBER

1989

interest rate is called the intertemporal elasticity of
substitution.
It is clear that the curvature (or the elasticity) of
the indifference curve will determine the extent to
which the consumer responds to changes in the real
interest rate. The more elastic or less curved is the
indifference curve, the greater the response will be.
Figure 2 depicts the difference in the intertemporal
substitution effect of two utility functions with different curvatures. For simplicity, assume that the
initial equilibrium is the same so that both indifference
curves UI and uz are tangent at the same point E to
the budget line. Note that the curve ur has flatter
curvature and is therefore more elastic. Suppose the
real interest rate rises from rr to rr ‘. Then the new
equilibrium will move from point E to point F in the
case of ur, and to point G in the case of u2. Comparing the consumption ratio CZ/CI at point F and G
reveals that consumption grows faster when the
indifference curve is more elastic. Thus, there is a
positive relationship between the intertemporal
elasticity of substitution and the elasticity of the
indifference curve.
Now, suppose an econometrician who observes
data on consumption and real interest rates over time
wishes

to estimate

the

intertemporal

elasticity

substitution. How would he go about doing this? The
preceding analysis suggests that a natural approach
is to think of each observation in time as represented

by the tangent point between the indifference curve
and the budget line. As one traces out these
equilibrium points over time, one essentially looks
at the change in these tangent points which are determined by the curvature of the indifference curve.
Thus, to estimate the elasticity one could simply
regress the rate of growth of consumption on the real
interest rate. This approach has been widely used
by many authors to study the dynamic behavior of
consumption [e.g., Hansen and Singleton (1983) and
Hall (1988)].
The foregoing discussion illustrates how equilibrium conditions can be used to interpret economic
data. Its implementation,
however, requires more
rigorous elaboration. For example, because of the
stochastic nature of the data one must consider
individual behavior under uncertainty. Also, in order
to account for the evolution of consumption over time
a fully dynamic model needs to be developed. Accordingly, the next section presents a formal maximization problem in which the equilibrium conditions
are explicitly used to construct the regression equation to be estimated.
3.

The Optimization Framework

To start with, the consumer is assumed to have
a time-separable utility function of the following
form:3

1
Uh)
Figure

1 -l/a

[Ctl-l’o-l],

I Ma),

if (T > 0 and
Of1
ifa=

This utility function, which has been widely used in
the literature, has the property that the elasticity of
substitution in consumption4 is constant and is equal
3 A utility function is called time-separable when the marginal
utility of consumption in a given period is independent of the
level of consumption in other periods. This assumption simplifies
the analysis.
4 The elasticity of substitution in consumption is defined as the
partial derivative of the rate of change in consumption with
respect to the marginal rate of substitution holding the level of
utility fixed. In notation, this can be expressed as:
a Met + h)
Ci In[u’(ct)/u’(ct+ r)] I u =;

’

where u ‘(.) denotes the marginal utility of consumption and ;
a constant utility level. Note that this quantity measures an
income-compensated
substitution of consumption along a given
indifference curve which is different from the uncompensated
notion of intertemooral substitution. The two notions. however,
turn out to be equivalent for two reasons. (1) The income
effect is proportional to changes in wealth due to the homotheticity of the utility function. (2) The real interest rate will
pin down the marginal rate of substitution in equilibrium.
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to the parameter (T. As will be seen shortly, this
parameter will control the interest rate effect on
consumption.
Now, let us consider the budget constraint. At the
beginning of time t, the consumer carries kt units of
capital from the last period. The capital is traded in
a competitive market and yields a stochzs~icrate of
return rt in units of consumption goods. At the end
of period t, the consumer collects interest income
rtkt and principal kt. This sum is the only income
that the consumer allocates between consumption
ct and new capital kt + 1 to be carried into the next
period. Thus, the consumer’s budget constraint for
period t is ct + kt + 1 = (1 +rt)kt.
The consumer’s problem is to choose a path of consumption and capital, contingent on the realization
of capital returns, that satisfies the budget constraint
each period and maximizes the expected present
value of lifetime utility over an infinite horizon.5
That is, given the initial capital stock ko, the consumer solves

max Eo[ F @u(ct)]
t=O
subject to ct + kt + 1 = (1 +rt)kt for all t
where /3 is the time preference discount factor that
lies between 0 and 1, and Eo is the expectation
operator conditional on information at time 0.
The first-order condition (or Euler equation) of this
problem is
u’(ct) = P Eb’(ct+l)

(l+rt+dl

It1

(1)

where It denotes the information set at time t.6 This
equation is precisely a stochastic version of the
equilibrium condition that the budget line must be
tangent to the indifference curve as depicted in
Figure 1.7 This equilibrium condition states that
the marginal cost of investing an extra unit of consumption good at time t (i.e., the foregone marginal
utility of consumption) should equal the marginal
benefit from investing - this return being com5 The assumption that the consumer lives forever is here
employed for analyticalconvenience only. The specificationof
a finite horizon problem will not alter the results of this paper.
6 The informationstructure is unspecifiedhere. Note, however,
that its specificationis necessary for computing the conditional
expectation.
’ Ignoringthe expectationoperator, equation(1) simply says that
the ratio of the marginal utilities (expressed in units at time t)
is equal to one plus ;he real interest r&e, which is the first-order
condition for the two-period model in Section 2.
6

ECONOMIC

REVIEW.

posed of the expected present value of the marginal
utility of consumption times the investment proceeds
at time t + 1 (principal plus interest). This condition
implies that a small deviation from the optimal consumption plan will leave lifetime utility unchanged.
From an empirical standpoint, the above first-order
condition is all that is needed to estimate the intertemporal elasticity of substitution. Obtaining the
estimate involves use of a simple procedure to derive
a regression equation from (1). First, given the
constant-elastic utility function specified at the beginning of this section, (1) takes the form
EN (ct + l/cd - 1’0 (1 +rt+l)

-l(It]

= 0.

(2)

This equation says that the residual (i.e., the term
defined in the bracket) has a zero mean conditional
on information available at time t. It implies that any
variable included in the information set should be
uncorrelated with the residual. These restrictions,
referred to as orthogonality conditions, admit a class
of instrumental variables procedures for estimating
the parameters p and n [e.g., Hansen (1982) and
Hansen and Singleton (1982)]. As can be seen, equation (2) is highly nonlinear and difficult to work with.
A common procedure is to make distributional
assumptions on certain variables at hand, and to
transform the equation into a linear representation.
This transformation renders the equation easy to
estimate but its tractability is obtained at the cost
of an extra assumption which may not be true.8
Specifically, assume that the measured growth of
consumption ct + l/c* as well as the real interest rate
(1 +rt + 1) has a lognormal distribution.9 This assumption implies
that ln(xt+ I), where
xt + 1 =
P(ct + lh)
- l’? 1 + rt + I), has a normal distribution
with a constant variance v and a mean pt conditional
on It. Using the lognormality assumption, we have
E[xt + 1[It] = exp[pt + v/Z]. Comparing with equation (2) yields exp[pt + v/2] = 1, which in turn
implies pt = -v/2. Since, by definition, pt =
E[ln xt + II&], it follows that
-v/2

= pt = In fi -

l/a E[ln(ct+ I/ct)lIt]

+ EM1 +rt+ djL1.
* It should be noted, however, that distributional-independent
methods such as the generalized method of moments proposed
by Hansen (1982) is available for dealing with nonlinear problems. The results pertaining to this procedure are beyond the
scope of this paper, and are presented in Mao (1989).
9 A random variable X is lognormally distributed if the natural
logarithm of X has a normal distribution. By definition, XY is
lognormally distributed if both X and Y are lognormally
distributed. If In(X) has a normal distribution with mean p and
variance Y, then the mean of X is exp[p+v/Z].

NOVEMBER/DECEMBER

1989

Multiplying both sides by 0 and arranging terms yields

EMct+dct)IItl

+ u E[ln(l +rt+l)lItl,

where /30 = a[ln P + v/21. Let Et+ 1 = ln(ct + l/et)

- Ellnkt + ht) lItI, then
Jn(ct+lW

+ ~Elln(l+r~+d~Ll

+ et+l.

(3)

Note that the expectational error Et+ 1 is uncorrelated
with the variables included in the information set,
and is normally distributed with a zero mean and a
constant variance. As can be seen, the parameter u
identifies exactly the intertemporal
elasticity of
substitution. This equation is used later to estimate
the parameter u.
Equation (3) implies that the mean of the rate of
growth of consumption is shifted only by the condotionai mean of the real interest rate. That is, information at time t is helpful in predicting the rate of
growth of consumption only to the extent that it
predicts the real interest rate. Since the expectedreal
interest rate is determined endogenously within the
model, an instrumental variables procedure will be
used to estimate the parameter u. This procedure
amounts to two-stage least squares in which the first
stage estimates the expected real rate using variables
(instruments) contained in the information set consisting of observations on past consumption growth
and real interest rates. The projected real interest
rates are then used in equation (3) to estimate u. This
procedure yields, a consistent estimate of the intertemporal elasticity of substitution.
As mentioned before, it has been difficult to pin
down the parameter u. The point estimates vary
widely, ranging from near 0 to 10. These results suggest that the linear regression equation (3) may not
be a proper model for estimating the intertemporal
elasticity of substitution. To examine this issue more
closely, consider the following question. Given that
the the true value of u is known, how accurately can
that value be recovered by using (3) and the
econometric procedure outlined above? A Monte
Carlo experiment
is carried out to answer this
question.
4.

The Data Generating Process

The first step of the Monte Carlo experiment is
to write down a model economy whose output will
be used to simulate the data. In particular, the
economy is represented by a general equilibrium
model in which the underlying production process

is explicitly specified. 10This approach allows quantities as well as prices to be endogenously determined within the model.
The economy is similar to that described in Section 3 with the exception that the consumer now also
plays the role of producer. In each period, the consumer carries from the previous period kt units of
capital which are used to produce output. Due to the
weather and other uncontrollable random factors,
however, the volume of output is uncertain. To capture such uncertainty, the technology is represented
by a production function of the form: yt = AIF
= XtktU, 0 < a < 1, where yt is output produced
at time t and Xt is a random shock with a known
probability distribution. The output may be consumed or invested. If invested, the capital will
depreciate at a constant rate 6 (0 < 6 < 1) so that
the investment at time t is defined to be it = kt + 1
- (1 - 6)kt. The agent is assumed to have a constantelastic utility function as specified above. His problem is to choose a contingent plan for consumption
and investment so as to maximize his expected
lifetime utility. That is, the agent solves

max Eo[ c” @u(ct)l
t=O
subject to ct + it = XtF(kt) for all t.
The solution of the above maximization problem consists of a sequence of consumption and investment
outcomes over time, contingent on the realization
of the random shock Xt. In this way the model
generates the consumption data for estimating the
intertemporal elasticity of substitution u in (3) above.
The model also generates an implied real interest rate
time series, needed to estimate (3). To see this, consider the first-order condition:

u’(ct) = P &(u ‘(ct + I) IA, + IF ‘(k + 1)
+ (1 - ml.

(4)

The intuition behind (4) goes as follows. Suppose
at time t the agent decides to carry one extra unit
of consumption good to the next period, which will
cost him, in utility terms, the marginal utility of consumption. The gain that results is the expected present value of the marginal utility of consumption times
the extra output that can be produced at time t + 1,
which is equal to the sum of the marginal product
lo Readers familiar with the literature on economic growth will
recognize that the model specified is a standard optimal growth
model as studied by Brock and Mirman (1972).

FEDERAL RESERVE BANK OF RICHMOND

of capital and the amount of capital that is left over
after depreciation. Equating the cost and benefit in
equilibrium yields equation (4). As can be seen, equation (4) is identical to the first-order condition of the
consumer’s problem [equation (l)] except that the
real interest rate is replaced by the rate of return on
investment, i.e., the marginal product of capital minus
the depreciation rate.
Because the optimization problem does not have
a closed-form solution, a numerical method will be
used to solve the problem. Specifically, a dynamic
programming algorithm is employed to approximate
the solution over a discrete state space.” It is
assumed that the production shock Xt can take 5
distinct values over the set [0.9, 1.11, i.e., 0.9, 0.95,
1 .O, 1.05, 1.1, and that it evolves over time according to the following Markov transition probability: l*
r

!0.50
0.25
0

0.25
0.50
0.30
0

0.25
0.20
0.50

0.25
0.30
0.50
0

0.25
0.50
0

This transition matrix implies that the random shock
will be, to some degree, persistent over time because
the probability of staying in the same state is higher
than that of switching to other states. The choice
of this transition matrix is motivated in part by the
fact that the actual production shocks in the United
States, as measured by the Solow residual,13 are
positively correlated over time. The estimation results
reported below do not appear to be sensitive to the
specification
of this transition
matrix. Other
parameters that are held constant throughout the
experiment are: 0 = 0.96, (Y = l/3 and 6 = 0.1.
These numbers are also chosen to reflect data actually generated from the United States economy.
For example, the value of /3 implies a real interest
rate of about 3 percent a year, which is close to what
is observed in the United States. The (Y value is
*I The algcrithm, known as the value successive approximation,
iterates on the problem’s value function over a discrete state
space. Technical details can be found in Bertsekas (1976).
r* The elements of this transition matrix assign the probability
of moving from one state to another. For example, if the value
of the production shock at time t is 1.0 (the third row), then
there is 25 percent chance that it will move to 0.95 or to 1.05
in the next period and 50 percent chance that it will stay in the
same state.
I3 Whether the Solow residuals, i.e., the residuals arising from
the regression of a production function, truly represent the
underlying shocks of the economy is a controversial matter. This
issue is ignored here.
8

ECONOMIC

REVIEW,

chosen to reflect the output elasticity of capital in
the United States-that elasticity figure being roughly
one-third and holding fairly steady over a long period
of time. Given these parameters’ values, the model
is solved for a set of four different values for u (0.1,
0.25, 1.0, and 2.5).
Since no interest attaches to the numerical solution per se, it is not reported. It is crucial, nevertheless, to have some idea about the accuracy of the
approximation procedure before the solution can be
used to generate random samples. This accuracy can
be assessed by checking whether the data generated
from the model satisfy the first-order condition, i.e.,
equation (2). Let ht + r = fl(ct + i/et) - “O( 1 +rt + 1)
- 1, then (2) can be rewritten as E[ht + rl~t] = 0.
As mentioned before, this condition implies a set of
orthogonality
conditions which require that the
residual ht + r be uncorrelated with any variable included in the information set. Let zt be a subset of
It; then these conditions imply that the first sample
moment of the cross product ht + rzt should be close
to zero for a sufficiently large sample. The vector
zt consists of a constant of ones plus the past observations on consumption growth ct + i/et and the real
interest rate (1 + rt + 1). The constant term is included
because the unconditional mean of ht + i must be
zero. Reported in Table I are, for each u value, the
sample means of the product ht+ rzt based on a
realization of 2000 observations. The number of lags
used for consumption growth and the real interest
rate is 2, so in total there are 5 variables in the
vector zt. The same set of variables will be used as
instruments in the econometric procedure of the next
section. As can be seen, the means are very small
and insignificantly different from zero (standard
deviations of the mean are reported in parentheses).
This result also holds for smaller sample sizes which
are not reported here. To conclude, the data
generated from the solution procedure fulfill the Euler
equation and have negligible approximation error.
5.

Estimation Results

This section pursues the second step of the Monte
Carlo experiment. The intertemporal elasticity of
substitution u is estimated using equation (3) and data
generated from the simulated economy discussed in
Section 4. The objective here is to see if this strategy
produces a reliable estimate of u.
A brief description of the simulation procedure
follows. First, for each of the four u values considered
in the experiment are generated a number of random
samples from the artificial economy. These observations are then employed to estimate the parameter
u. This process produces a sampling distribution of

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1989

Table

ORTHOGONALITY CONDITIONS

0.10

0.25

constant

(one)

2.50

Note:

means of the cross product

(ct + Jet) - 1

(ct+1’ct)-2

between

h,,,

and

(l+r,+J-,

(l+r,+,)-,

0.000048

0.000078

0.000052

0.000014

0.000026

(0.002415)

(0.002417)

(0.002416)

(0.002508)

(0.002507)

-0.000017
(0.001073)

1.00

Sample

- 0.000000

-0.000016

-0.000014

(0.001073)

- 0.000000

-0.000001

-0.000025
(0.001117)
- 0.000001

-0.000021
(0.001117)
- 0.000000

(0.000218)

(0.000227)

0.000003

(0.000004)

(0.000004)
.

(0.000004)

Calculation
is based on 2000 random observations.
Standard deviations of the mean are reported in parentheses.

the point estimate a’ for a given sample size. To
examine the convergence property of these estimates,
the experiment is repeated using four different
sample sizes, ranging from 50 to 500. As in Section
4, five variables are chosen as instruments, which
include two lags of the the consumption growth
ln(ct + r/c*) and two lags of the real interest rate
ln( 1 + rt + 1). The estimation results reported below
are not sensitive to the number of lags included in
these instruments.
Sampling Di.mhtion of the Point Estinzate a”. Consider Table II wherein are reported the means and
the standard deviations of the elasticity estimate a,
These statistics are calculated for each of the four
u values and each of the four sample sizes considered
in the experiment. At first glance, the sampling
distribution of the point estimate a” appears to have
a relatively small standard deviation and a mean that
is close to the true value of cr. Although the means
are slightly higher than the true value, the bias is not
significant and is probably due to the approximation
error of the solution procedure in Section 4. In fact,
as the sample size increases, the bias as well as the
standard deviation vanishes, a clear indication that
the estimate 6 is asymptotically unbiased and consistent. Notice that, even for a relatively small sample, one cannot reject the hypothesis that the mean
of the estimate a’ is equal to the true (Tvalue. Extensive simulations indicate that these results are robust
to the specification of the stochastic process of the
production shock Xt. For example, using an indeFEDERAL

RESERVE

pendently and identically distributed random shock
the sampling distribution of the elasticity estimates
is virtually identical to that reported in Table II.
The implication is clear: Equation (3) as an empirical model of consumption is capable of producing a reliable estimate of the intertemporal elasticity
of substitution, at least for the cases considered in
this paper. This result is somewhat puzzling because
the data used in the estimation procedure do not
necessarily satisfy the lognormal restriction that
renders the regression model linear. Violation of this
distributional assumption tends to cause the estimate
to be biased and inconsistent. This issue warrants
closer examination. Figure 3a-3d plots, respectively
for each of the u values, the frequency distribution
of the random variable ln(xt+ I), where xt+ 1 =
Pht + lh)
- 7
1 + rt + 1). As mentioned in Section 3,
this random variable should have a normal distribution if the lognormality assumption is correct. The
figures indicate that while such a distribution appears
to be the case when (T = 2.5, it is apparently violated
when u = 0.1, 0.25, and 1.0. How can we reconcile this finding with the simulation results? In particular, how does one explain the unbiasedness of
the estimates even if the distributional assumption
is violated? It turns out that the answer is quite
simple. What happens is that, under certain conditions, the Euler equation (2) can be approximated
by a linear regression model without directly invoking the lognormality assumption. Recall the following approximation: ln(xt + 1) = ln( 1 + ht + 1) E ht + 1
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Table

SAMPLING DISTRIBUTION

True (I

0.10

0.25

1.00

2.50

Number of
observations

OF THE POINT ESTIMATE 6 (a)
(I

Number of
simulations

Mean

780

0.257039

0.155508

150

520

0.172956

0.070608

300

480

0.142281

0.048254

500

400

0.129667

0.038071

780

0.414662

0.205668

150

520

0.321207

0.100773

300

480

0.286916

0.070803

500

400

0.273533

0.056699

780

1.126016

0.275207

150

520

1.044132

0.150668

300

480

1.017989

0.105218

500

400

1.009004

0.084706

780

2.504959

0.021614

150

520

2.503065

0.011713

300

480

2.502775

0.007199

500

400

2.502399

0.005670

ta) These results are based on assumed highly persistent shocks specified
and identically distributed
(iid) shocks yield similar results.

in the text. Experiments

for xt + 1 close to one or ht + 1 close to zero. Since
the condition that ht + 1 be close to zero is approximately true for our data (see Table I and Figure 3),
the linear regression equation (3) can be viewed as
an approximation to the Euler equation (2). It is worth
mentioning that in the United States the rate of
growth of consumption is about 2 percent a year and
the annual real rate of interest is about 3 percent,
suggesting that xt + 1 is close to one.
Hypothsk Testing Based on the regression model,
a number of hypotheses can be tested. This subsection focuses on the simple hypothesis that the
parameter u is equal to its true value. As usual, this
hypothesis can be tested using a conventional t
statistic. Since we know the true u value that is
used to generate the data, we are interested in the
Type I error for testing this hypothesis, that is, the
proportion of time that the null hypothesis is rejected
when it should have been accepted. The test results
are summarized in Table III. As can be seen, the
rejection frequency of the true model is higher than
expected. This is particularly clear when ~7is small.
10

s.d.

ECONOMIC

REVIEW,

with independently

For example,
at a 5
percent
significance
level, about 20 percent of
the time one will reject
u = 0.1 even though the
sample size is relatively
large (say, 500). At a
10 percent significance
level, the proportion rises
to above 30 percent.
Although the rejection
frequencies
are somewhat moderate for other
cases, it seems reasonable to conclude that the
risk of committing the
Type I error is still too
high. Again, this result
may appear
puzzling
because the point estimate is fairly close to the
true parameter value. A
moment’s
reflection
reveals that these errors
stem from the standard
error of the estimate’s
being so small that the
true parameter value lies
outside of the confidence
region.

Misspecification Bias with
Variable Labor Supply

Many of the empirical studies on intertemporal
substitution abstract from the interaction between
consumption and labor supply decisions and thereby
ignore the potential effect on consumption of changes
in the wage rate [for example, Hansen and Singleton
(1983) and Hall (1988)]. As noted before, such a
simplification implies that the growth of consumption is determined only by the expected real interest
rate. This section examines a more realistic model
in which an individual chooses both consumption and
labor supply at the same time. Such a model implies
that changes in the real wage can have important effects on consumption behavior. It will be shown that
failure to incorporate these effects can result in a
sizable bias in estimating the intertemporal
elasticity of substitution.
As in the previous case, the starting point is a simple two-period model. For comparison, refer to
Figure 1 in which the equilibrium moves from point
E to E’ when the real interest rate rises. What would

NOVEMBER/DECEMBER

1989

Figure

FREQUENCY DISTRIBUTION

OF THE TRUE RESIDUALS

(a): u = 0.10
141

8
F
t!
2

E8
8
b,

-0.2

-0.1

0.0

0.1

0.2

-0.016

(b): u = 0.25

-0.008

0.000

O.dO8

0.016

(d): u = 2.50

5’

-0.06

-0.02

0.02

0.06

0.10

happen if the consumer is allowed to supply work
effort in the labor market and earn wage income? In
general, the point E ’ will no longer be an equilibrium
because the labor supply decision, even if the wage
rate remains unchanged, is likely to alter the rate of
substitution
in consumption.
In this case, the
equilibrium point can go in either direction depending upon the extent to which labor supply affects the
marginal utility of consumption. In order to make a
specific prediction, one needs an explicit model.
The model considered below is similar to that
described in Section 3. First, the consumer’s utility
function is assumed to depend on consumption ct
and leisure time It and has the following form:
FEDERAL

RESERVE

- 0.0004

- 0.0002

0.0000

0.0002

0.0004

&$C’@ lt(l -~I~-:‘“,,~~~,
UWt)

z 1

f3 In ct + (l-0)

In It,

ifa

= 1

This utility function is similar to that specified before
and is constant elastic with respect to a “composite
good” defined as a Cobb-Douglas function of consumption and leisure. The parameter 8 lies between
0 and 1. As will be seen shortly, the parameter u
can still be identified as the intertemporal elasticity
of substitution.
But, more importantly,
the u
parameter controls the effect of leisure on the
marginal utility of consumption. Specifically, when
BANK

OF RICHMOND

Table III

(19SS)l. Since there is no direct evidence on whether
the utility function is separable, it is useful to check
how serious the misspecification bias could be.
To proceed, suppose the consumer solves the
following maximization problem:

REJECTION FREQUENCY OF THE
NULL HYPOTHESIS:

true da)

(Type I Error)

True 0

0.10

0.25

1.00

Number of
observations

Significance

level

5 Percent

10 Percent

26%

39%

150

21%

32%

300

18%

29%

500

19%

33%

23%

35%

150

16%

24%

300

12%

19%

500

11%

20%

19%

29%

150

13%

19%

300

14%

500

14%

max I%] c” P’u(ctJ41
t=O
s.t.

ct + kt + r = (1 +rJkt

+ wtnt for all t

where wt is the wage in terms of consumption goods
and nt = 1 - It is work effort. Following the same
derivation procedure as in Section 3 and assuming
lognormality, it can be shown that consumption now
obeys the following equation:

ln(ct+dct) =

+ u EM1 +rt+ d\Itl

+ ,&EMwt+dw)~Itl + Et+I (5)

r4 That is, uCr > 0 if u > 1, where uCris the partial derivative
of the marginal utility of consumption with respect to leisure time.

where fir = (1 - t9)(1 - a). Except for the additional term that captures the effect of wage growth
on consumption, this equation is similar to equation
(3) which abstracts from the labor supply decision.
As can be seen, the parameter u still measures the
interest rate effect on consumption. However, the
wage will have a positive effect (pr > 0) on consumption growth if u < 1, and negative effect (/3r < 0) if
u > 1. This is so because u < 1 implies ucr < 0,
so that when the real wage rate rises, leisure will
decline and the marginal utility of consumption will
rise. As a result, consumption must rise to restore
the equilibrium. Note that when u = 1, a change
in the real wage has no effect on consumption
because the utility function is additively separable in
this case.
What would happen if the true data were generated
from the above model, and yet the econometrician
erroneously ignored the wage effect and instead
used (3) to estimate a? This is a typical specification error in which an important variable is omitted
from the regression. Apparently, the estimate for u
will be biased, with the magnitude of the bias
measured by the true value of /I1 times the auxiliary
regression coefficient of the wage growth on the real
interest rate.r6 Thus, if the real interest rate and the
growth of real wages are positively (negatively)
correlated, then ignoring the wage effect leads to a
downward (upward) bias if u > 1, and an upward
(downward) bias if u < 1. Notice that, if the real
interest rate and the growth of real wages are un-

I5 A utility function u(x,y) is additively separable if it has the
form: m(x) + n(y). This class of utility functions is not limited
to the logarithmic case specified in the text.

I6 This is a standard result on specification
(1977).

2.50

11%

150

19%

300

10%

20%

500

12%

20%

19%

(a) These results are based on assumed highly persistent shocks specified in
the text. Experiments with iid shocks yield much higher rejection frequencies (more than 50 percent).

(I > 1, consumption and leisure are gross complements because an increase in leisure will raise the
marginal utility of consumption.14 The opposite is
true when u < 1. The value of u will dictate the
effect of the real wage on consumption.
It is important to note that the wage effect on consumption will depend on the form of the utility function. In particular, if the utility function is additively
separable,15 then the marginal utility of consumption
will be independent of the choice of leisure. In this
case, changes in the real wage have no effect on consumption. Consequently, equation (3) will still be the
correct specification for consumption. This assumption has been maintained by most authors [e.g., Hall

ECONOMIC

REVIEW,

NOVEMBER/DECEMBER

1989

bias. See Maddala

correlated, then the elasticity estimate using (3) will
be unbiased.
One way to evaluate the extent of the above misspecification bias is to conduct a Monte Carlo simulation. As in Section 4, the data are generated from
a model economy in which the production function
is assumed to be yt = Xtkt%t(’ - a), 0 < CY< 1.”
The production shock is generated in the same way
as before. Other parameters fixed in the experiment
are fl = 0.96, 6 = 0.1, cx = l/3, and 0 = 0.3.
Following the same procedure, u is estimated using
(3) as well as (5). Because of the difference in the
specification, the instruments used in estimating
equation (5) include lags of ln(ct + I/et), ln( 1 +rt + 1)
and ln(wt + l/wt). These instruments are used to
project the expected real interest rate as well as expected wage growth. Table IV summarizes the means
and the standard deviations of the estimated bias.
It is clear that when the model is correctly specified,
i.e., equation (S), the estimated bias is small and insignificant. However, the bias associated with equacion (3) is sizable. In particular, when (T = 0.25, the

point estimates are scattered around the value of 2,
and when u = 2.5, the point estimates are less than
one and in some cases close to zero. These results
show that ignoring a potential wage effect on consumption can introduce a substantial bias in the
estimation of the elasticity of substitution.
7.

Concluding Remarks

The results of this paper can be summarized succinctly. First, for a moderate sample size (perhaps
in the range of 100 to 150), the point estimate of
the intertemporal
elasticity of substitution produced by the linear model tends to be unbiased with
small standard errors. This result implies that the
loglinear model, despite its simplicity, is a useful and
convenient framework for estimating the intertemporal elasticity of substitution. Second, the conventional t test tends to over-reject the true model.
Therefore, one must be careful in drawing conclusions from this test. Third, if the estimated equation is erroneously specified and omits the effect of
the real wage on consumption, then the bias of the
elasticity estimate is sizable. One should not conclude, however, that it is always necessary to use the

I7 Specifically, the data are generated from a real business cycle
model:

extended

s.t.

ct + kt+l

= XtFhnt)

model

to estimate

+ (1 - 6)kt

where F(. , .) is the production function which depends on capital
and labor. As in Section 4, the equilibrium prices can be computed directly from the solution of the optimization problem.
In particular, the real interest rate is the marginal product of
capital minus the depreciation rate while the real wage is just
the marginal product of labor.

Table

0.25

2.50

Number of
observations

Number of
simulations

similar

BIAS
Bias: 0 -

True o

elasticity;

MISSPECIFICATION

Correct:

the

biases could arise in the extended model if it is also
misspmified.
In general, any econometric method founded on
an intertemporal
maximization problem and its
resulting Euler equation is bound to be sensitive to
measurement errors. Such errors are particularly
characteristic of consumption data, especially data
on durable goods consumption. They are perhaps

max &[ c” /3’u(ct, 1 -nt)]
t=O

Eq. (5)

Mean

Incorrect:
sd.

Mean

Eq. (3)
s.d.

600

0.119739

0.066889

1.958582

0.667838

150

400

0.053412

0.049080

1.732927

0.453833

300

400

0.030032

0.033670

1.692648

0.326624

500

300

0.022194

0.027314

1.670278

0.267501

600

0.433372

0.522541

- 1.770626

0.310914

150

400

0.174026

0.330437

- 1.657668

0.189137

300

400

0.080718

0.220140

- 1.607193

0.129013

500

300

0.057523

0.184815

- 1.596351

0.108533

FEDERAL

RESERVE

BANK

OF RICHMOND

the most important reason why empirical studies have
not been able to pinpoint the intertemporal elasticity of substitution. As shown above, however, even
if the data are properly measured, the econometrician still must choose a correct specification. Ironically, the data themselves are supposed to aid in this

task. There is no easy solution to this identification
problem. There are at present more sophisticated
test procedures,
such as tests of overidentifying
restrictions, that may be used to discriminate among
different models. However, the properties of such
test statistics under misspecification are not clear.

References
Bertsekas, Dimitri P. Dynamic Pmgramming and Stochastic Con&. New York: Academic Press, 1976.
Brock, W. J., and L. J. Mirman. “Optimal Economic Growth
and Uncertainty: The Discounted Case.” Jownaf of Lhomic
Theory 4 (June 1972): 479-513.
Eichenbaum, Martin S., Lars Peter Hansen, and Kenneth J.
Singleton. “A Time Series Analysis of Representative Agent
Models of Consumption and Leisure Choice Under Uncertainty.” Working Paper No. 1981. National Bureau of
Economic Research, July 1986.

Hansen, Lars Peter. “Large Sample Properties of Generalized
Method of Moments Estimators.” Economettica 50 (july
198.2): 1029-54.

ECONOMIC

REVIEW,

. “Stochastic Consumption,
Risk Aversion, and
the Temporal Behavior of Asset Returns.“Jounalof
Pofirical Economy 91 (April 1983): 249-65.
. “Efficient Estimation of Linear Asset Pricing
Models with Moving Average Errors.” Manuscript. University of Chicago, April 1988.
Maddala, G. S. Economerris. New York: McGraw-Hill,

Hall, Robert E. “Intertemporal Substitution in Consumption.”
humaf of Po.kicd Economic 96 (Apd 1988): 339-57.

Hansen, Lars Peter, and Kenneth J. Singleton. “Generalized
Instrumental Variables Estimation of Nonlinear Rational
Expectations Models.” Econotnetn~a 50 (September 1982):
1269-86.

1977.

Mao, Ching-Sheng. “Euler Equation Estimation: A Simulation
Study.” Manuscript, Federal Reserve Bank of Richmond,
August 1989.

NOVEMBER/DECEMBER

1989

LABORMARKETDATA
Roy H. Webb and WiL4’am Whe@‘q *

This art&e is part of a series that will be pubdished by this Bank under the title
Data: A User’s Guide. The book wil’l contain introductions to
important series of mac?veconomic data, including p&es, employment, pmduction,
and monq. The articles in the book are designed to he& the reader accurately inte?pret
economic data and thereby allow the numberx to be use&i analytical tools.

Macroeconomic

Aggregate data on jobs, unemployment and earnings are closely watched by millions of Americans.
The unemployment rate is probably the single most
widely followed economic indicator. Among financial market participants, the number of people
employed is perhaps the most closely followed
macroeconomic statistic that appears monthly. These
and other selected labor market indicators are
described in this article.

HISTORICAL DEVELOPMENT

Statistics describing the labor market were
estimated as early as 1820, based on questions from
the decennial Population Census. In the last decade
of the nineteenth century, the newly formed Bureau
of Labor-the
predecessor of the Bureau of Labor
Statistics (BLS)-began
to collect detailed data on
wages and earnings. In 19 1.5, the Bureau began a
monthly survey of employers to collect wage and
employment data. This survey is still conducted, and
data from it are reported on a monthly basis; it is
often referred to as the establishment survey, or also
as the pay& survq.
After a century of collecting data on labor markets,
there was surprisingly little systematic information
on the extent of unemployment.
When national
attention focused on unemployment during the Great
Depression, it was not immediately obvious how to
define or to gather relevant information. In 1940 a
monthly survey was designed, which is now known
as the Curt
Population Surwq. Information from the
survey allowed an unemployment rate to be calcuWebb is a vice president and economist at the Federal Reserve
Bank of Richmond; Whelpley is a principal of Whelpley
Associates Inc., and was an -as&tant economist at the Federal
Reserve Bank of Richmond when he contributed to this article.
The authors gratefully acknowledge helpful comments from Dan
M. Bechter, Timothy Q. Cook, William E. Cullison, Thomas
M. Humphrey, Janice Shack-Marquez, and employees of the
Bureau of Labor Statistics.

lated. By 1945 the questions were developed which
form the basis of the Survey used today, which is
usually referred to as the household sumq.
d

MAJOR DATA SERIES

Data From the Household Survey
Each month over fifty thousand households are
interviewed by the Census Bureau for the BLS as
part of the household survey. The BLS then analyzes
the survey results and reports its findings near the
beginning of the next month, usually on the first
Friday. Many statistics from this survey could be
discussed; the key concepts in this section are the
unemployment rate, the number of people employed,
and the labor force participation rate.
Unemployment rates are calculated for the entire
nation and also for more narrowly defined demographic groups and geographic areas. l An unemployment rate is defined as the number of people
unemployed as a percentage of the daborforce. The
size of the labor force, in turn, is defined as the
number of people empbyed plus those unempbyed, that
is, people without jobs who are willing and able to
work.
All three terms, employed, unemployed, and labor
force, have very specific definitions. A person is
counted as unemployed if he or she did not work
during the survey week and:
(a) made a specific effort (which can be anything from talking to friends to interviewing for
a specific opening) to find a job within the
previous four weeks, and was available for work
during the survey week; or
(b) was waiting to be called back to a job after
being laid off; or

FEDERAL

RESERVE

r Press reports often mention two unemployment rates. One is
calculated by removing military personnel from the calculations
and is slightly smaller than the overall rate.
BANK

OF RICHMOND

1.5

those who did not actually contact potential
employers as being out of the labor force.

if he

(a) did any work at all as a paid employee, as a
proprietor or farmer, or worked 15 hours or
more as an unpaid worker in an enterprise operated by a member of the family; or
(b) had a job but was not working during the
survey week due to a temporary absence resulting from illness, bad weather, vacation, labormanagement disputes, or personal reasons. Employment status is not affected by whether or
not pay is received during the absence, nor by
whether or not another job is being sought.
Finally, the labor force is simply the sum of persons who are employed plus those who are unemployed. The overallpa&$ation
rate is defined as the
labor force as a percentage of the population at least
sixteen years of age. Participation rates are also
calculated for smaller segments of the population,
again defined as the labor force as a percentage of
the relevant population segment.
There are many reasons why a person may not
be in the labor force, such as age, health, home
responsibilities, being in school, not wanting to be
employed, or not believing that job search would be
fruitful. The latter category is referred to as discouraged WOK&X;
they are counted as those who would
like a job but are not looking for work for one of the
following reasons listed in the household survey:
“thought no jobs were available in their line of
work or area.”
“previously tried unsuccessfully to find work.”
“lacked the necessary schooling, training, experience, or skills.”
“felt employers
considered
the person too
young or too old.”
“had some other personal handicap in finding
work.”
One’s intuitive definitions of employment
or
unemployment may be somewhat different from the
specific definitions given above. In particular,
people who are not working vary tremendously in
the amount of thought and effort spent on finding
work; it is inherently arbitrary to divide people
without jobs into only two categories, unemployed
or not in the labor force. Some analysts would add
discouraged workers to the unemployed,
thereby
boosting the reported unemployment
rate. Others
would lower the unemployment
rate by defining
16

ECONOMIC

REVIEW,

Behuvior Over Time Chart 1 shows the unemployment rate over the post-World War II period. One
notable feature is that sharp swings are associated
with the business cycle, the alternating periods of
expansion and recession in the whole economy.
Another feature is the general upward drift for much
of the chart after abstracting from business cycles.
Chart 2 shows the participation rate. Especially
notable is the substantial increase over the past
2.5 years. The major factor behind that increase can
be seen in the table, which contains the current
demographic composition of the labor force and contrasts it with the labor force in 1948 and 1969. The
rapidly growing fraction of adult women in the labor
force more than counteracts a decline in the fraction
of men in the labor force, resulting in a growing
participation rate for the whole population. The table
also reveals relatively high unemployment rates for
blacks and teenagers.

DATA FROM THE ESTABLISHMENT

SURVEY

The establishment survey covers the industry,
hours, and earnings of most employed members of
the labor force. State agencies send survey forms to
over 300,000 establishments, who then record the
requested information and return the forms to the
state agencies for processing. These agencies then
forward the tabulated information to the BLS in
Washington, D.C. Th e information is sent back and
forth between the collecting agencies and participating establishments
for one year; a written
record of the numbers can therefore be reviewed by
both the providers and collector of the information.
Employment and earnings figures are classified by
each worker’s characteristics, such as sex, industry,
and job category. A person is counted as empkyed
if he or she is on the payroll of an establishment for
the pay period which includes the 12th of the month.2
This measurement
excludes proprietors,
unpaid
volunteers, family workers, farmers and farm workers,
and domestic household workers. Salaried officers
of corporations, civilian government employees, and
part-time workers are included, however.3
Industry hours and earningsjgures also originate in
the establishment survey. Figures are presented in
2 Employees of the federal government are counted if they
occupy a position as of the last day of the calendar month.
3 Employees of the Central Intelligence Agency and the National
Security Agency are explicitly excluded from the survey.

NOVEMBER/DECEMBER

1989

Chart

UNEMPLOYMENT RATE
January 1948 - September 1989

Percent

1950

detail for Production
and Related Workers in
manufacturing and mining, Construction Workers,
and Nonsupervisory Employees in service industries.
The hours statistic reports the number of hours paid
for by the employer in the current reporting period,
not the number of hours actually worked. This figure
therefore includes items like holidays, vacations, and
sick leave. Overtime /wun includes that time for which
a premium is paid. Weekend and holiday hours are
included separately only if overtime premiums are
paid. Hours which have only incentive premiums
attached,
such as shift differential and hazard
premiums, are excluded from the overtime hours
measurement.
Average hourly and weekly earnings for nonsupervisory workers are estimated from data reported in
the establishment survey. Three features have led
some observers to question the relevance of that concept for studying certain problems. First, the data
do not include fringe benefits, which play a major
role in the compensation of most workers. Second,
the data do not cover executive, administrative, and
FEDERAL

RESERVE

managerial workers in private industry, nor do they
cover state and local government workers. And
finally, the data are affected by changes in the composition of employment.
To address those problems, the BLS also publishes
a quarterly employment cost index (ECI),4 which is
based on a special survey of employers. It is designed to cover all workers in private industry plus
state and local government. The EC1 adds the cost
of providing a wide range of fringe benefits to wage
and salary payments; some of the most expensive
benefits are social security and unemployment insurance taxes, paid vacation and sick leave, health and
disability insurance, and retirement plans. The EC1
is also based on a fixed industry and occupational
structure. Shifts between industries or occupations
do not directly affect the index.
4 A more accurate title might be employee compensation index,
however. Significant elements of labor cost that are not included are the costs of hiring, training, and strike activity.
BANK

OF RICHMOND

Chart 2

PARTICIPATION RATE
January 1948 - September 1989

Percent
70

54
1950

Chart 3 compares the EC1 and average hourly
earnings statistics. Both show a substantial decline
in the growth rate of compensation since the early
198Os, as general price inflation also declined substantially. The EC1 has grown faster than average
hourly earnings for much of the period, however,
reflecting the growing relative importance of fringe
benefits.
CAUTIONS

The data series described above provide a wealth
of timely, relevant information. The data can be
misinterpreted, however. The following cautions are
designed to help place data series in perspective. The
first two concern the exact meaning of widely used
terms.
Meaning of Terms
Unemplgyment Some observers tend to equate the
level of unemployment with an unambiguous measure of economic hardship. The unemployment
18

ECONOMIC

REVIEW.

rate, however, is a much more complex statistic. It
does not refer to an unchanging group totally composed of desperate individuals. It instead is a
snapshot-a
view at an instant of time-of
people
who are entering and leaving the labor force, and of
those who are starting and ending particular jobs.
Some unemployed persons find jobs quickly, others
more slowly, and some people move directly from
outside the labor force to employment.
Some job
changes are voluntary, others are involuntary.5
To help put unemployment rates in perspective,
note that it is often not in the best interest of an
unemployed person to take the first available job. It
may take time to achieve a good match between a
person’s interests, skills, and abilities on the one
hand, and a job’s skill requirements, working conditions, and promotion possibilities on the other.
5 In June 1989, for example, 42 percent of the unemployed had
lost their last job, 15.5 percent had quit their last job, and 42.5
percent were new entrants or reentrants into the labor force.
Half were unemployed less than six weeks, while 9.1 percent
were unemployed more than a half year.

NOVEMBER/DECEMBER

1989

DEMOGRAPHIC COMPOSITION OF THE LABOR FORCE
IN THE UNITED STATES
(Thousands

of persons unless otherwise

Characteristic

indicated)

1948

1969

1989

60,621

80,733

123,291

TOTAL
Civilian

Labor Force

Percent

of total population

Employed
Unemployed
Unemployment
MEN,

58.8

60.1

66.4

58,344

77,902

116,900

2,276

2,831

6,391

rate

3.8

3.5

5.2

AGE 20 & OVER

Civilian

Labor Force

Percent

40,687

of adult male population

Employed

39,382

Unemployed
Unemployment
WOMEN,

46,351

86.61

83.0
45,398

1,305

963

3.2

2.1

rate

63,468
78.1
60,642
2,827
4.5

AGE 20 & OVER

Civilian

Labor Force

Percent

15,500

of adult female

population

Employed
Unemployment

Civilian

41.5

51,890
57.6

26,397

49,514

564

1,016

2,376

3.6

3.7

4.6

14,936

Unemployed

TEENAGERS

27,413

31.3”

rate

(16-19)
Labor Force

Percent

of teenage

population

Employed
Unemployed
Unemployment

4,435

6,969

52.5

49.4

55.2

4,026

6,117

6,745

409

852

1,188

9.2

12.2

15.0

rate

7,933

WHITE
Civilian

Labor Force

Percent

of white

71,778
population

58.2b

Employed
Unemployed
Unemployment

rate

3.5

of black population

64.0b

59.9

105,964
66.7

69,518

101,338

2,260

4,626

3.1

4.5

13LACKc
Civilian

Labor Force

Percent

8,959

Employed
Unemployed
Unemployment
Note:

rate

5.9

13,444

62.1

64.4

8,384

11,898

570

1,561

6.4

11.2

Data represent the first quarter of 1989 and the full years of 1948 and 1969, and are taken
from the Month/y Labor Review and the Economic Report of the President, various issues.
Unless otherwise
indicated,
all population
figures exclude military and institutionalized
personnel, and young persons less than sixteen years old.

a Age 14 and over.

Recognizing the inevitability of
such search IMtemp/oymentimplies
a positive unemployment rate.
In short, a normally functioning economy will have some
unemployment,
and every
unemployed person does not experience substantial hardship.6
To provide a perspective
for
business cycle analysis, some
economists refer to a naturalrate
of unemployment, defined in one
textbook7 as “that rate of unemployment at which flows in and
out of unemployment
just
balance, and at which expectations of firms and workers as to
the behavior of prices and wages
are correct.” The natural rate is
neither constant nor precisely
known; at the present time many
economists believe that it is between five and six percent in the
United States. If actual unemployment were much higher, that
would be evidence of cyclical
slack in the economy: and if the
actual rate were much lower,
that would signal an overheated
economy.
The term “natural” is widely
used but may be misleading,
since
there
should
be no
presumption
that the current
natural rate is either optimal or
immutable. The natural rate is
affected by the incentives and
constraints facing persons and
firms; anything that affects the
average frequency or duration of
unemployment will also affect the
natural rate. Some important
factors affecting the natural rate
6 An individual’s hardship is also affected
by household wealth and by whether
transfer payments, such as severance
pay or unemployment
insurance, are
received. In addition, some unemployed
persons are on temporary layoff and will
almost certainly be recalled; others may
have accepted a job that begins in more
than a month.
7 Rudiger
Dornbusch
and Stanley
Fischer, Macroeconomics, 3rd ed. (New
York: McGraw-Hill) 1984, p. 466.

b Data are for 1954, not 1948.
c Nonwhite before 1972.
FEDERAL

RESERVE

BANK

OF RICHMOND

Chart 3

CHANGES IN EMPLOYMENT COSTS
3Q 1976-2Q 1989

Percent Change
fonm Year Ago

1977

are the unemployment insurance system, household
wealth, minimum wage legislation, the demographic
composition of the labor force, the mobility of labor,
and the dispersion of skill levels in the labor force.

The next caution involves one concept, employment, that is estimated from both the household and
20

ECONOMIC

REVIEW,

establishment surveys. The two should move together closely in the long run; however, in any month
they can diverge substantially.

Compensation of EmpZoyees
Many forms of compensation are ignored in the wage figures reported
each month, including some that are growing
especially rapidly. Fringe benefits are excluded, as
are contingent payments such as lump sum payments
in lieu of wage increases, bonuses, profit-sharing
payments, and stock options. In addition, some
benefits are not even included in the ECI. For example, medical benefits for retirees have been
promised by many employers with no provision
having been made for funding those costly benefits.
They are thus not included in the ECI.

Two Definitions of Employment

To see why employment totals can differ, note the
slightly different definitions of employment for each
survey. The establishment survey counts jobs, not
people; dual job holders are therefore doublecounted. The household survey only covers the
number of people employed, so that a person is never
double-counted. The household survey also counts
self-employed persons, agricultural workers, and
household workers, all of whom are omitted from
the establishment survey.
Many observers may prefer to ignore monthly
changes and focus on the longer run; for them it
probably does not matter which series they focus on.
But those with a short-run perspective often have to
choose one or the other when the two series give
conflicting signals. Many choose the establishment
series, since its growth is more closely correlated

NOVEMBER/DECEMBER

1989

with real GNP growth than is the other estimate.*
Also, the number of firms surveyed is much larger
than the number of households surveyed, which
could in principle result in a more accurate estimate
from the establishment survey. And finally, it is noted
below that some analysts question the accuracy of
survey responses from households.
Volatile Monthly Observations
Sampling Ermr-

A final set of cautions warns a user
not to overemphasize a single month’s data. A basic
reason is sampling error-that
is, statisticians are
attempting to esiima~e a statistic for a large population from a relatively small survey. It is especially
important as smaller segments of the labor force or
smaller geographic areas are studied. As Geoffrey
Moore put it:
A rise, say, from 5.0 to 5.3 percent in the unemployment
rate is statistically significant, whereas a rise from 9.7 to
10.4 percent in the unemployment rate for blacks is not.
The reason is that the population of whites is about ten
times that of blacks, so that the sample of whites is also
about ten times as large. Coupled with the fact that the
unemployment
rate for blacks is about twice that for
whites, this means that the sampling error of the unemployment rate for blacks is about four times as large as for
whites.9

The key concept is that of statist;cacsign%~cance,that
is, whether a result is likely to have resulted simply
from chance; a statistically significant result is not
likely to be due to sampling error. Moore uses a 0.2
percent change for the total unemployment rate, and
a 0.8 percent change for the black unemployment
rate, as thresholds for statistical significance.
One should therefore be cautious in attaching much
importance to a single month’s changes without
having some idea of how large a change must be to
be statistically significant. This caution applies more
forcefully as the size of the relevant population
becomes smaller. On the other hand, consistent

movements for several months considerably reduce
the likelihood of the fluctuations being due to chance.
Also, one’s confidence in a single month’s change can
be bolstered or reduced by movements in related
statistics. For example, suppose that employment
growth is reported to have been relatively strong but
also that average weekly hours were relatively soft.
In that case one could reasonably question the
economic importance of the employment figure.
Responses to Swwy Data Individuals responding
to the household survey may respond for themselves
and any other adults in the household without checking written records. Some observers have questioned the reliability of that information. It is, of
course, difficult to know the exact relevance of
answers to questions from any survey. One piece of
evidence is a test in 1977 that compared individual
responses with employer records.1° Relative to
employers’ records, household respondents overstated the number of hours worked and understated
both average hourly and weekly earnings.
Iregular Events All the monthly data series
described in this article are adjusted to remove predictable seasonal fluctuations such as the swell in
Christmas employment, or the effects of summer
vacations for students. Events that occur on an
irregular basis can be more difficult to take into
account. Strikes, for example, lower employment
estimates from the establishment survey but do not
directly lower employment (or raise unemployment)
estimates from the household survey. And while the
BLS may note an estimate for the direct effect of
a strike, the indirect effects may be substantial but
not estimated; an example of an indirect effect would
be layoffs of railway and port workers after a coal
strike reduced coal shipments. Extreme weather conditions can also affect the data, even after routine
seasonal adjustment.

SUGGESTIONS FOR FURTHER READING
a To check the validity of that common assertion, we regressed
real GNP growth on four own lags plus four lags of quarterly
employment growth, from 1948 to 1989. For the household
series, the R statistic was 0.36; for the payroll series it was 0.56.
Since both employment statistics are subject to sampling error,
it is possible that the average of the two might be better than
either one individually. We therefore substituted the average of
the two for the employment variable in the regression equation;
the R* statistic was 0.5 1. For monitoring the overall economy,
it therefore looks like the payroll series is the better choice, and
that averaging the two does not improve matters.
9 Geoffery H. Moore, Business Cycles, Inflation, and Forecasting
(Cambridge: Ballinger Publishing Co. for the National Bureau
of Economic Research, 1980) p. 111.
FEDERAL

RESERVE

Many books, professional journals and government
reports have been written about labor market data.
For an overview of labor markets and how they fit
into the larger economy, readers may wish to look
at a macroeconomics textbook such as Robert Barro,
Macmeconomics, John Wiley and Sons; or Dornbusch

10Accounts of this test are taken from Joseph R. Antos, “Analysis
of Labor Cost,” in Jack E. Triplett ed., Tfie Measurement of Labor
Cost, (University of Chicago Press for the National Bureau of
Economic Research, 1983) p. 162.
BANK

OF RICHMOND

&zmings summarizes current and historical statistics
collected from both the household and establishment
surveys. The Monthly Labor Review also summarizes
labor market statistics. It also contains articles that
discuss many aspects of labor markets, data concepts,
data collection procedures, and the series themselves;
several of the articles were helpful in preparing this
paper, such as an article contrasting the payroll and
household estimates of employment in the August
1989 issue. Finally, the BLS Handbook of Methods,
revised and published periodically, presents a discussion of the technical aspects of how the BLS collects,
transforms, estimates, and presents labor market
data.

and Fisher, op cit. For a more detailed analysis of
labor supply and demand and market institutions, see
a text on labor economics, such as Ronald G.
Ehrenberg and Robert S. Smith, Modern Labor
Economics, Scott Foresman and Co. A good discussion of problems in the data can be found in the report
of the 2979 NahnaG Commission on Employment and
Unemp.bymment
Statztics. The report contains a number
of background papers in addition to the summary of
recommendations.
The data series described in this article only hint
at the large quantity of statistics that describe the
labor market; many more series can be found in two
monthly publications of the BLS. Employment 63

Economic

Review

Index

Volume
Federal
January/February

Determinants
Monetary

March/April

Aggregates:

Banking
Lender

of the Federal

of Last Resort:
America’s

An Examination
May/June

The Future

Market
July/August

Precursors
The U.S.

September/October

Some

David

1970

Results

Fedwire

Michael

Data in the 1980s

An Analysis

Highest

Daylight

David

Overdrafts

Say

B. Humphrey

Thomas

M. Humphrey

William

E. Cullison

Roy H. Webb
and Rob Willemse
of Shift

in Ml

Demand

in the 1980s

Yash P. Mehra
Robert

Policy
Some

Provocative

Employment

William

Findings

in North Carolina

Counties,

1980-85

L. Hetzel
E. Cullison

Christine Chmura
and Jane lhrig

Ching-Sheng

Mao

Roy H. Webb and
William Whelpley

Data

Small

Dotsey

John R. Walter
and Donald L. Welker

in Decade

Estimating
Intertemporal
Elasticity of Substitution:
The Case of Log-Linear Restrictions

Top Performing

Heller

Anatoli Kuprianov
and David L. Mengle

of the Alternatives

What the Experts

on the Source

Labor Force:

M. Humphrey

H. Robert

on Assets:

Slowdown:

L. Mengle

Thomas

in History

Model

in Manufacturing

Labor Market

since

Price Indexes

M2 and Monetary

November/December

Return

to Pricing

Productivity

The Changing

The Fifth District

Trade

Insurance:

of the P-Star

Further

Changes

Rules:

Cook

John R. Walter

Competitiveness

Banks’

Macroeconomic

Timothy

1979-1982

Guide

of International

Responses

Bank of Richmond

Rate:

The Concept

of Deposit

Fifth District

Funds

A User’s

under Changing

Improving

Reserve

1989

Banks:

ECONOMIC

Making

REVIEW,

Money the Old-Fashioned

NOVEMBER/DECEMBER

1989

Way

Benton E. Gup and
John R. Walter

TOP PERFORMING SMALL BANKS:
MAKING MONEY THE OLD-FASHIONED WAY
Benton E. Gup and John R. Walter’

Introduction
Average profit rates of small banks (assets less than
$100 million) declined in the 1980s but about
2 percent had persistently high returns. Some have
attributed
persistent
profits to collusion, risktaking, or chance. In contrast, this study finds that
consistently profitable small banks were those that
stressed basic banking, in other words, acquiring lowcost funds and making high-quality investments.
Small bank average profitability declined in the
1980s for several reasons. Losses at many small
banks, especially at those located in regions of the
country beset with problems in the agricultural or oil
industries, accounted for much of the decline. Some
of the decline may have resulted from the increased
competition in the retail loan and deposits markets.
Federal legislation expanded the number of retail
deposit products banks and thrifts could offer and
deregulated interest rates on existing deposits while
allowing thrifts to compete more effectively with
banks for both deposits and loans. The specific acts
were the Depository Institutions Deregulation and
Monetary Control Act of 1980 (DIDMCA) and the
Garn-St. Germain Depository Institutions Act of
1982.
In this study we compare small banks having persistently high profits to all small banks over the period
1982 through 1987. We identify differences in portfolio structure, income, and expense between the two
groups of banks located throughout the country.
Moreover, to determine how the factors associated
with high performance may have differed from regionto-region, high performers and all small banks are
grouped by region and compared on a regional basis. *
Table I summarizes the significant differences

Gup holds the Chair of Banking at The University of Alabama;
Walter is an associate economist at the Federal Reserve Bank of
Richmond. The authors wish to acknowledge the unflagging
efforts of Richard K. Ko in the construction of the data base
for this article.
l

1 The regions are shown in Table II and are the same as those
used by the Federal Deposit Insurance Corporation (FDIC) in
its “Quarterly Banking Profile” (1989).
FEDERAL

RESERVE

between the average high-performance
and the average small bank.

small bank

Theories of Persistent Profits
Mueller (1986) observed that in the long run,
above- and below-average profits tend to converge
toward the industry norm. Competition
should
eliminate abnormally high profits over time. Where
persistent high profits occur, as they did at the 206
high-performance
banks in our study, economists
offer a variety of explanations, including the following four:
Co&&on It has been argued that firms can maintain high profits by agreeing explicitly or tacitly to
limit their competitive behavior. Collusion becomes
more difficult as the number of competitors in a
market increases; that is, as market concentration
declines. We would expect the number of competitors in banking markets to be larger in more
populated areas. Thus, if collusion is important to
profitability, high-profit banks should be found more
frequently in less populated areas. In our study, we
defined a populated area as any metropolitan
statistical area (MSA). While our data did show that
non-MSA small banks were likelier to be persistently profitable than were MSA small banks, the difference was not significant. Therefore we find no
evidence that collusion may have been responsible
for the strong performance of the high-profit small
banks. Using different proxies for market concentration, Kwast and Rose (1982) and Wall (1985) reached
the same conclusion.
The consistently
aboveGreater Risk- Taking
normal profits produced by the 206 high-performance
small banks identified in our study cannot be explained by greater risk-taking since these banks
operated in a less risky manner than average for all
small banks. They had fewer loan losses than their
peers, indicating that they were taking less credit risk.
They were less dependent on debt financing because
of stronger equity-to-assets
ratios. Finally, they
limited their credit and liquidity risks by holding more
securities than did their peer group.
BANK

OF RICHMOND

Table

SUMMARY OF MAJOR FINDINGS OF STUDY
SIGNIFICANT

DIFFERENCES

BETWEEN

HIGH-PERFORMANCE

SMALL

BANKS

AND ALL SMALL

BANKS:
High-Performance
Small Banks vs.
All Small Banks

Area of Difference

Interest

Higher

Income/Total
Assets
High-performance
small banks produced significantly
more interest
than the average for small banks while bearing less credit risk

income

relative

to assets

Loans/Total Assets
The high-performance
small banks had a significantly
lower ratio of loans to total assets than
the average small bank, meaning that they bore less credit risk since loans generally are more
risky than the other major category of assets held by banks-securities

Lower

Securities/Total
Assets
Higher ratio at high-performance

Higher
banks indicating

Municipal Securities/Total
Securities
High-performance
banks had more income
advantage of municipals
Earning
Interest

Assets/Total

lower credit

risk
Higher

to shelter

so they made greater

Higher

Assets

Expense/Total
Assets
High-performance
banks funded themselves at lower cost by emphasizing
structure and a conservative capital structure

Demand Deposit/Total
High-performance

Noninterest
Expense/Total
High-performance
resources
Assets/Employees
High-performance
Salaries/Employees
High-performance

use of the most traditional

liability

of funding

sources
Lower

retail deposits

to gather funds
Higher

banks had a stronger

or more conservative

Assets
banks held these expenses

capital

structure
Lower

to a lower level indicating

a more efficient

use of
Higher

banks required

fewer employees

per million

dollars

in assets
Higher

banks’

employees

Loan Loss Provisions/Total
Assets
High-performance
banks limited
restraining their credit risk
Loan Charge-Offs/Total
Loans
Lending to high-quality
borrowers
Nonperforming
Loans/Total Loans
Lending to high-quality
borrowers
their books
FACTORS NOT SHOWING
AND ALL SMALL BANKS:

Lower
a traditional

Higher

Liabilities
banks made greater

Interest Expense/Interest-Bearing
Liabilities
High-performance
banks made greater use of low-cost
Capital/Total
Assets
High-performance

use of the tax

SIGNIFICANT

were better

paid
Lower

their lending

and only lent to high-quality

borrowersLower

meant

fewer loan charge-offs

meant

high-performance

at high-performance

banks
Lower

DIFFERENCES

BETWEEN

banks carried

fewer bad loans on

HIGH-PERFORMANCE

SMALL

BANKS

Location in a Metropolitan
Area
Bank Holding Company Affiliation
Loan Income/Total
Loans
Securities Income/Total
Securities
Loan Portfolio Composition
Loan Maturity
Noninterest
Income/Total
Assets
High-performance
small banks placed
income than the average small bank
Fee Income/Total
Assets
Gains or Losses on Securities/Total
24

no more emphasis

on these

less traditional

Assets
ECONOMIC REVIEW, NOVEMBER/DECEMBER 1989

sources of

Table

SMALL BANKS BY GEOGRAPHIC REGION, 1987”
All Banks

Regionc

Northeast

Number

377

High-Performance

Number

As a Percent
of All
Small Banks

Bank@
As a Percent
of All HighPerformance
Banks

6.6

12.1

Southeast

1,196

4.5

26.2

Central

2,290

1.9

21.4

Midwest

2,841

1.2

16.5

Southwest

1,909

1.7

16.0

880

1.8

7.8

West
Total
Average

9,493

206

100.0

random.“2 According to this theory the highperformance banks in this study may have
selected, by chance, the management, investment, and lending policies that turned out to
be very profitable during the 1980s. To test if
this was so, the average ROA for the 206 highperformance small banks and all small banks
were calculated for each year between 1970 and
198 1. The average for the high-performers was
considerably above the average for all small
banks for each of the twelve years, indicating
that the high performers of the 1980s produced
supernormal profits during the 1970s as well.
Chance alone is an unlikely explanation of
almost two decades of persistently high profits.
Prior Empirical Research

2.2

Several other analysts have attempted to pinpoint factors associated with bank profitability.
a Small banks are those with end-of-year assets of $100 million or less that were
A study of bank profitability in the 1970s by
opened on or before December 31, 1982.
Kwast
and Rose (1982) included large banks
b High-performance
small banks have ROAs of 1.5 percent or more for all years,
1982-87.
from throughout the nation. The authors determined that neither pricing, operating costs,
c For regions, see map below.
market concentration,
or macroeconomic
effects were responsible for the higher earnings
of some banks. They hypothesized, instead,
that differences in regional factors, portfolio
make-up, or managerial abilities must explain
the better earnings of high-performance banks.
Wall (1985) examined small and mid-sized
banks over the period 1972 to 1981 to identify factors important to bank profits. Wall found
that consistently profitable banks had lower
interest and noninterest expenses than did their
less profitable counterparts because of more
capital, more demand deposits, slightly lower
rates paid on liabilities overall, greater holdings
of securities, and more efficient management.
Wall concluded that interest and noninterest
income at consistently profitable banks was no
Unique Quah2ie.c These include leadership in the
higher than at less profitable banks, and that asset
market, provision of services other firms cannot
size, number of branches, and market concentration
duplicate, having the dominant market share, or
did not explain higher earnings. Wall’s findings on
being first to arrive in the market. Perhaps one or
the factors associated with small and mid-sized bank
more of these apply to the high-performance banks.
profits in the 1972 through 1981 period differ little
from our findings for small banks in the 1980s.
S@&z.s~ Pmcess Persistent profits may result from
historical chance. The basic idea of the stochastic
process, as explained by Alchian, is that “where there
is uncertainty, people’s judgments and opinions, even
when based on the best available evidence, will
differ; no one of them may be making his choice by
tossing coins; yet the aggregate set of actions of the
entire group of participants may be indistinguishable
from a set of individual actions, each selected at

Methodology
Data for our study came from the Reports of Condition and Income (call report), a detailed financial
* Alchian (1950), p. 216. Alchian is an excellent background
source for understanding the issues involved in stochastic growth.
Also see Nelson and Winter (1982) and Steindl (1965).

FEDERAL RESERVE BANK OF RICHMOND

year and had been established in 1982 or before.3
The number of banks in this category declined each
year, from 12,353 in 1982 to 9,493 in 1987 as the
banks grew in asset size, merged, or failed. To be
included in the high-performance subset a bank must
have had no more than $100 million in assets and
must have produced a return on assets (ROA) greater
than 1.5 percent for each of the six years from 1982
through 1987. Banks with ROAs greater than 1.5
percent have very strong profits. Banks established
after 1982 could not have had high ROA in that year,
so are excluded from the high-performance group by
our convention that requires high ROA in every year.
There are 206 high-performance
banks. They are
listed in Table IA in the appendix.
The period 1982-87 is used in this study for two
reasons. First, it offers the most recent extended
period since the passage of DIDMCA and the GarnSt. Germain Act. Second, it provides an interval long
enough to be sure that luck or accounting choices
alone did not influence the selection of the highperformance small banks.

statement filed quarterly by banks with their regulators. A set of income, expense, and portfolio ratios
were calculated for all small U.S. banks established
in 1982 or before. Ratios were then averaged across
all small banks and all high-performance small banks
throughout the nation for each year from 1982
through 1987.
Because economic conditions varied from region
to region, ratios for both groups of banks were also
computed on a regional basis. For each of the six
years, the average ratios, regional and national, for
high-performance
small banks and all small banks
were compared using a standard t test to determine
statistically significant differences (see Table III).
A difference between the ratios of high-performance
small banks and all small banks is considered to be
due to factors other than chance if the t statistic is
significant at the 5 percent level. Regional patterns
in the ratios are identified and discussed.
The same banks are included in the highperformance group for each year of the study while
the number of banks in the all-small-banks category
varies. The all-small-banks category, for any given
year, includes all banks throughout the nation that
had assets less than $100 million at the end of that

3 Unless otherwise stated, the phrase al’lstnallbanks or average
smab’ bank should be assumed to include only those banks
meeting these two requirements.

Table III

COMPARISON OF SELECTED RATIOS: HIGH-PERFORMANCE
1982
NE

1983

CN MW SW

P
N

1
2N

W U.S.

PPPPP
NNNNNNN

P
N

1984

CN MW SW

W U.S.

NNN

CN MW SW

W U.S.

na na na na na na na
NNNNNNN
N

NNNNNNN

5NNNNNNN

N
N

6
7PPPPPPP
8
NNNNNN
9PPPPPPP
1OPPPPP

11NNNNN

1
2

Interest
Interest

3
4

Noninterest
Noninterest

Loan Loss Provision/Assets
Securities

Return

PPPPPPP
PPPPP

N
P

P
N

N
8
P
9
P 10

P
N

Income/Assets
Expense/Assets

6
PPPPPPP
NNNNNN

Gains/Assets

on Assets

Loans/Assets
Securities/Assets
Equity/Assets
Total Assets

that data were not available.

P indicates that the mean for the ratio for the high-performance
different at the 1 percent level.
P indicates

3N
4N

na indicates

BANKS VERSUS ALL SMALL BANKS

that the mean for the ratio for the h.p.s.b.

Blank space indicates

that there was no significant

small banks (h.p.s.b.)

exceeded

difference

exceeded

that for all small banks and was statistically

between

h.p.s.b.

significantly

different

at the 5 percent

level.

and all small banks for the ratio.

N indicates

that the mean for the ratio for all small banks exceeded

that for the h.p.s.b.

and was statistically

significantly

different

at the 1 percent

level.

N indicates

that the mean for the ratio for all small banks exceeded

that for the h.p.s.b.

and was statistically

significantly

different

at the 5 percent

level.

SEE TABLE IIA IN APPENDIX FOR RATIO AND T STATISTIC VALUES.

ECONOMIC

REVIEW,

NOVEMBER/DECEMBER

1989

Characteristics of High-Performance
Small Banks

compared for the nation. When tested by region and
across years, only in the Southwest were highperformance small banks significantly less likely to
be located in MSAs.
The asset size of the average high-performance
small bank was $40.8 million in 1987 compared with
$37.5 million for all small banks. Asset size of the
average high-performance small bank increased by
56 percent from 1982 through 1987, while the asset
size of the average small bank increased by only 20
percent. The percentage of high-performance and all
small banks that were subsidiaries of bank holding
companies (BHCs) increased through the period. In
1987, 46 percent of high-performance and 66 percent of all small banks were subsidiaries of BHCs.
A test was performed to determine if the difference
in BHC affiliation between the two groups of banks
was statistically significant across the years. For the
nation as a whole the difference was significant, but
statistically significant regional differences were not
found except in the Northeast and Southwest regions.
Firm conclusions about the relationship between
BHC ownership and profits based on these data are
difficult to draw.

Table II shows that high-performance small banks
were not distributed proportionately throughout the
country. The Northeast had the highest, and the
Midwest the lowest, proportion of high-performance
small banks relative to all small banks. During the
1982 through 1987 period, there were substantial
differences in regional economic performance which
likely caused some of the corresponding regional
differences in the proportion of high-performance
small banks. Slumping prices for energy, real estate,
and farm commodities had adverse effects on the
Southwest, Midwest, and Central regions, while
strong economic growth was occurring in the Northeast and Southeast through the period.
Although not shown in Table II, approximately 30
percent of high-performance small banks were headquartered in or near large population centers,
represented here by metropolitan statistical areas
(MSAs), while the figure averaged a slightly higher
33 percent for all small banks. Only in 1982 and 1983
were the differences statistically significant when
small banks, high-performance
versus total, were

1985
NE

1986

CN MW SW

W U.S.

1PPP
2NNNNNNN

1987

CN MW SW

W U.S.

CN MW SW

PPPPPPP

PPPPP

NNNNNNN

W U.S.

Pl
2

3
4N

3
N

5NNNNNNN
6
N
7PPPPPPP

NNN
N

8
NNNNNN
9PPPPPPP
1OPPPPP
11

N
N
NNNNNNN
N

NNN
N

N
N
NNNNNNN

4
5
6

PPPPPPP

NNNNN
PPPPPPP
PPPPPPP

NNNNN
PPPPPPP
PPPPPPPlO

7
N8
9
11

FEDERAL

RESERVE

BANK

OF RICHMOND

How The High Performers Did It

ROA OF SMALL BANKS

The high-performance small banks identified in this
study differed from the average small bank in several
ways. They depended more on low-cost demand
deposits, invested more in securities (especially
long-term and municipal securities), made more highquality loans, and were more highly capitalized. As
a result, the high-performance
small banks produced higher interest income, lower interest expense,
lower noninterest expenses, and lower provision for
loan losses than did the average small bank. The highperformance small banks did not differ significantly
from the average small bank in interest income from
loans and securities, in loan portfolio makeup, in
noninterest income, or in income from securities
gains. There was little variation among regions in how
the high-performance
small banks operated. As
shown in the chart, average ROA for the 206 high
performers exceeded 2 percent in every year and was
fairly stable, while average ROA for all small banks
declined in every year except 1987 and ended the
period at .51 percent.
In~emstIncome Except for one or two years’ observations for three regions, high-performance
small
banks produced significantly more tax-equivalent
interest income relative to assets than the average
for all small banks (see Table III, line l).4 Among
the major categories of income and expense, higher
interest income was second only to lower interest
expense as a contributor to the earnings differential
of the high-performance banks across the years and
regions of the study. Averaged for the six years of
the study, high-performance
small banks’ interest
income relative to assets was 58 basis points higher
than the average small banks. Wall (1985) found that
higher interest income was not associated with higher
profits for small and medium-sized banks between
1972 and 198 1. Greater pressure on interest expense
resulting from deregulation in the early 1980s of rates
paid on deposits may have made interest income
more important to profitability for our study period.
Interest income relative to assets depends on the
earnings per dollar of the various types of interest-

4 The interest income on most securities issued by local and state
governments
is exempt from federal income taxes. These
securities, therefore, pay lower rates of interest than taxable
securities of equivalent risk and maturity. To put the tax-exempt
income on a basis comparable to the pretax return on taxable
securities, or on a tax-equivalent basis, an adjustment is made
to income from state and local securities. For banks with positive
profits before taxes, income from state and local securities is
increased by t/( 1 -t) times the lesser of profits before taxes or
interest earned on state and local securities, where t is the bank’s
marginal federal tax rate.
28

ECONOMIC

REVIEW.

Net Income/Total Assets

Percent

High Performers
1.8
1.6
1.4
1.2

1982

8.5

earning assets, their proportions in the asset portfolio, and the proportion of nonearning assets to all
assets.
LOANS The
difference between loan income
relative to total loans at the high-performance small
banks and at the average small bank was not significant for most regions across years or for the national
average except in 1982 and 1983. As shown on line
8 of Table III, the ratio of total loans to total assets
was significantly lower for high performers than for
all small banks. In the Southwest and Midwest where
agriculture and oil industry problems were prevalent,
the high performers eschewed lending, especially in
the later years of the study. While at the national level
the high-performance small banks differed statistically
from the average of all small banks in terms of loan
composition, the regional data do not corroborate this
finding. The high performers in the West and
Midwest made fewer commercial and industrial loans
than average for small banks in those regions and
high-performance small banks in the Southeast made
more loans to individuals than average for small banks
in that region. Other regions show no consistent differences in portfolio makeup. There was no difference in the maturities of loans made by high performers and all small banks.
SECURITIES
High-performance small banks had a
much higher ratio of securities to total assets than
did all small banks (Table III, line 9). The difference
was statistically significant across all regions and all
years in the study. High-performance banks also had
more municipal securities than their counterparts,
accounting for most, but not all, of the higher

NOVEMBER/DECEMBER

1989

securities-to-assets ratios of high-performance banks.
Municipal securities are generally tax-exempt and pay
tax-adjusted rates comparable to other securities only
for those holders with high marginal tax rates. As a
bank’s net income increases, its ability to make use
of the tax-free income these securities generate increases. Accordingly, high-income banks would be
expected to hold more municipal securities than less
profitable banks.
At the national level the ratio of taxable securities
to total assets was higher at the high-performance
small banks than at the average small bank for the
years 1982 through 1984 only. On a regional basis,
the difference was consistently significant only for
the Southwest, probably because of the lack of good
lending opportunities in depressed oil industry areas
of the region.
On average the high-performance
banks generally had more securities with maturities greater than
one year than did their counterparts. The difference
was significant for the nation across all years but only
consistently different for three of the regions in all
the years.
High-performance small banks did not consistently
earn more on securities than did all small banks.
Securities income relative to total securities was
significantly greater at the high-performance
small
banks than at the average small bank in some years
but not in others at the national level and varied from
region to region across the years. In addition, there
was no significant difference between securities gains
and losses relative to assets between high-performance small banks and all small banks (Table III, line
6). Securities gains or losses are realized when a bank
sells a security, prior to the maturity of the security,
for a price different than that paid to purchase it5
EARNING ASSETS-TO-TOTAL ASSETS The national
average proportion of earning assets-to-total assets
at high-performance
small banks was 9 1.4 percent
in 1987 compared with 90.4 percent at the average
small bank. High-performance
small banks’ earning
assets-to-total assets ratio exceeded the average small
banks’ ratio significantly in every year from 1982
through 1987 at the national level and for most
regions across the years. This accounts for some of
the higher interest income relative to assets of the
high performers. Examples of nonearning assets are
cash, and foreclosed real
buildings, equipment,
estate.

5 For additional information on the relationship between market
rates of interest and securities prices see Gup, Fraser, and Kolari
(1989), Chapters 2 and 5.
FEDERAL

RESERVE

Interest lCq!mse Interest expense relative to assets
in 1987 was 3.9 percent for the average of all highperformance small banks in the nation and 4.6 percent for the average of all small banks. The difference
was significant across all regions and years with the
exception of the Southwest and West regions in 1982
(Table III, line 2). Among the major income and expense categories, interest expense was the largest
contributor to higher ROA at the high-performance
banks. Interest expense relative to assets depends
on the proportion of liabilities that are interestpaying, the rates paid on the interest-paying liabilities,
and the level of the capital-to-assets ratio.
DEMAND DEPOSITS TO TOTAL LIABILITIESThe
major liability not paying interest is demand deposits.
The high-performance small banks had a lower level
of interest expense relative to assets than the average
small bank, in part because they had more demand
deposits. The difference between the ratio of demand
deposits to total liabilities for high-performance small
banks and that of the average small bank was significant in all years for the nation and for varying regions
across the years.

RATES PAID ON INTEREST-BEARINGLIABILITIES
Interest expense relative to interest-paying liabilities
was lower at the high-performance small banks than
at the average small bank. The difference was significant across most regions and at the national level for
all six years and accounted for one-third to one-fourth
of the total difference in interest expense relative
to assets. For the national average, the highperformance banks were able to gather a higher proportion of their liabilities from passbook and statement savings, normally the least costly of the interestbearing liabilities, and were less dependent on expensive large certificates of deposit (CDs) than
average for all small banks throughout the nation.
Again, the regional data are not consistent in their
support of this finding. High performers made greater
use of savings only in the Northeast and Central
regions and lower use of large CDs in only the
Southwest and West regions. Other regions show no
consistent patterns.
CAPITAL-TO-ASSETSRATIO The average highperformance small bank had a significantly greater
equity-to-assets ratio than the average for all small
banks (Table III, line 10). That is, the highperformance banks had more capital than did their
counterparts. The difference was significant across
all regions in all years except for the West and was
significant at the national level for all years. Since
equity funds do not pay interest, they do not add
to interest expenses, so that higher ratios of equityBANK

OF RICHMOND

to-assets tended to lower interest expense-to-assets
ratios. Because one method of increasing equity is
to retain earnings, banks that maintain consistently
high-earnings can be expected to have more capital
than the average bank.
Nonihmst Income and Expetise With the exception
of the Northeast region in 1982 and 1983, noninterest income from fees and other sources was
never, in the period under study, significantly different at the high performers than at small banks in
general (Table III, line 3). High-performance
small
banks apparently did not make fee income a priority.
The high-performance banks had lower noninterest
expense relative to assets than did their counterparts
except in the Southeast and Midwest regions (Table
III, line 4). Relative to assets, the difference averaged 37 basis points for the 1982-87 period. Noninterest expense includes salaries expense, bank
premises and fixed asset expenses, and a category
reported on the call report as “other noninterest
expense, ” including legal fees, deposit insurance fees,
advertising expenses, management fees paid to parent
BHCs, and other expenses. Bank premises and
fixed assets expenses and other noninterest expenses
were significantly lower at high-performance
small
banks, though salaries expense was not. Assets per
employee also were higher at high-performance
banks. However, higher average salaries at those
banks made salaries relative to assets about the same
as at the typical small bank. A lower noninterest
expense-to-assets ratio could indicate more efficient
management. But it is difficult to tell simply from
call report data what, if anything, was being managed more efficiently.
As mentioned previously, a smaller percentage of
high-performance small banks were BHC subsidiaries
than was the case for all small banks. Since management fees paid to parent BHCs are an expense
faced only by BHC subsidiaries, banks not owned
by BHCs might tend to show up more frequently
in the high-performance group. Management fees are
included in other noninterest expenses on the call
report. Small BHC subsidiary banks had only a five
basis points higher other noninterest expense in 1987
than did small banks without a holding company
affiliation. This difference is so small it is not likely
to have biased the selection of high-performance
small banks in favor of non-BHC banks.
Ptiion&r
Loan Losses For every region in every
year and for the national averages for every year, provision for loan losses relative to assets was significantly lower at high-performance
small banks than
at the average small bank (Table III, line 5). Provision for loan losses relative to assets was, on average
30

ECONOMIC

REVIEW,

for the six years of the study, 49 basis points lower
at the high-performance banks. By substituting investments in securities for lending, that is, by holding
fewer loans relative to assets, the high-performance
banks decreased the proportion of the asset portfolio
subject to credit risk and therefore lowered their level
of loan losses relative to assets. In addition, the highperformance banks made higher quality loans. They
had significantly fewer charge-offs and nonperforming loans relative to total loans than other banks,
suggesting that the high performers lent to low-risk
borrowers. While many small banks in depressed
regions were having serious problems with their loan
portfolios, some banks in those same regions were
able to prosper. For example, 20 of the 206 highperformance small banks were located in Texas,
where many banks were having trouble producing
profits. As of 1987, there were 1,066 small banks
in Texas, so that 1.9 percent were high-performance,
close to the national average.
Conclusion
While the average small bank’s profits were fairly
low and falling for most of the 1982 through 1987
period, there were 206 banks, out of 9,493 small
banks (assets of $100 million or less) operating in
1987, that had a return on assets of 1.5 percent or
more in each of those six years. Although there were
fewer high-performance
small banks in geographic
regions that had economic
difficulties,
highperformance banks were found in all regions. Highperformance small banks seemed to choose similar
strategies in all regions.
The high-performance
banks did not engage in
exotic financial activities. Instead, they did a very
good job of basic banking-acquiring
funds at low
cost and making high-quality, profitable investments.
Wall (1985) found much the same for the 1972
through 1981 period. Our study provides evidence
that the deregulation of the early 1980s did not
change the methods for producing profits at small
banks.
The high-performance small banks earned abnormally high returns for long periods. On the contrary,
economic theory suggests that abnormally high
profits should be short-lived. Other banks, seeking
higher returns, will engage in similar activities and
drive down returns to the industry norms. The highperformance banks we studied were able to maintain persistent profits in the face of competition. Importantly, the high-performance banks were able to
acquire funds at lower cost than their competition
through demand and other low-cost deposits. How
they were able to attract these deposits in the face
of competition is a subject that deserves further
research.

NOVEMBER/DECEMBER

1989

References
Alchian, Armen A. “Uncertainty, Evolution, and Economic
Theory.” J&anal of Political Economy 58 (June 1950): 2 1 l-2 1.
Barry, Lynn M. “A Review of the Eighth District’s Banking
Economy in 1986.” Federal Reserve Bank of St. Louis
R~Y.&w 69 (April 1987): 16-21.
Clair, Robert T. “Financial Strategies of Top-Performance
Banks in the Eleventh District.” Federal Reserve Bank of
Dallas Economic Revim (January 1987), pp. 1-13.

. “Profitability Differences Among Large Commercial Banks During the 1970s.” Th Magazine of Bauk
Administration (September 1983), pp. 54, 56, 58, 62.
Mester, Loretta J. “Owners Versus Managers: Who Controls
the Bank?” Federal Reserve Bank of Philadelphia Business
Rev&~ (May/June 1989), pp. 13-22.
Mueller, Dennis C. Pn$ts in tke Lang Run. New York: Cambridge University Press, 1986, Chap. 2.

Cook, Timothy Q., and Timothy D. Rowe, eds. Zn.srruments
of tke Money Market, 6th ed. Richmond: Federal Reserve
Bank of Richmond, 1986.

Nelson, Richard R., and Sidney G. Winter. An Evohtionary
Tkeoty of Economic Chnge. Cambridge: Harvard University
Press, 1982.

Federal Deposit Insurance Corporation. “The FDIC Quarterly
Banking Profile.” First Quarter, 1989.

Scott, William L., and Gloria Shatto. “Social Efficiency in
Banking: A Stochastic Model of Bank Growth.” Quaflw&
Review of.&onomah andBusiness 14 (Autumn 1974): 85-93.

Fraser, Donald R., and James W. Kolari. Th Future of Small
Banks in a Deregulated Environment. Cambridge: Ballinger
Publishing Company, 1985.

Steindl, Josef. Random Pnxesses and The Ghwtk of Finns. New
York: Hafner Publishing Company, 1965.

Geroski, Paul A., and Alexis Jacquemin. “The Persistence of
Profits: A European Comparison.” Tke Economic Journal 98
(June 1988): 375-89.
Gup, Benton E., Donald R. Fraser, and James W. Kolari.
Commercial Bank Management, New York: John Wiley &
Sons, 1989, Chap. 2.

Wall, Larry. “Why Are Some Banks More Profitable Than
Others?” Journalof Bank Reseat& 15 (Winter 1985): 240-56.
Walter, John R., and David L. Mengle. “A Review of Bank
Performance in the Fifth District, 1986.” Federal Reserve
Bank of Richmond Economic Review 73 (July/August 1987):
24-36.

Gup, Benton E., and John R. Walter. “Profitable Large Banks:
The Key to their Success.” MidZand Corporate Finance
Journal 5 (Winter 1988): 24-29.

Watro, Paul R. “Have the Characteristics
of High-Earning
Banks Changed? Evidence from Ohio.” Federal Reserve
Bank of Cleveland Economic Commentary, September 1,
1989.

Kwast, Myron L., and John T. Rose. “Pricing, Operating Efficiency, and Profitability Among Large Commercial Banks.”
Journal of Banking and Finance 6 (June 1982): 233-54.

Whalen, Gary. “Concentration and Profitability in Non-MSA
Banking Markets.” Federal Reserve Bank of Cleveland
Economic Rewiew (First Quarter 1987), pp. 2-9.

FEDERAL

RESERVE

BANK

OF RICHMOND

APPENDIX
Table

HIGH-PERFORMANCE
City

Bank
Brunswick

Bank & Trust Co.

state

Manalapan

TWP

SMALL BANKS
Bank

City

state

First National

Sylacauga

Maywood

National

Trust Co. of Ft. Myers

Ft. Myers

Carmel

Peoples

Bank of Graceville

Graceville

Coxsackie

Peoples

State Bank

Groveland

Dryden

Springfield

Florida

Capital

Hermon

Wilcox County State Bank

Bank of Millbrook

Millbrook

Braselton

National

Stamford

Bank of Camilla

Community
Putnam

Bank of Bergen City

County

National

Bank of Carmel

Bank of Coxsackie

First National
National

Bank of Dryden

Bank of Florida

First National

Bank of Hermon

Bank of Stamford

Commercial

City Second
Banking

First National

Bank of Wyoming

Wyoming

First National

Bank of Tuckahoe

Tuckahoe

Merchants

Ashland

Commercial

Citizens

National

East Prospect
Citizens

Bank of Ashland

State

National

New Tripoli
Union

Bank

Bank of Lansford

National

Bank

Bank & Trust Co.

Summit

Hill Trust Co.

Guaranty
Harlan

Deposit
National

Bank

County

Bank

Jackson

First State Bank
Farmers
Baltic

& Trades

State

Bank

Custar State Bank Co.
Corn City State Bank
City Banking

Farmers

National

Farmers
Valley

Co.

Bank
National

Bank

Peoples

National

Capital

Centreville
Caroline

Bank of Rural Valley
Bank of Washington

National
County

Bank of Southern
New Windsor

Bank of Maryland

Bank
Maryland

State Bank

Co.

Bank of Polk County

& Farmers

Abbeville

Braselton

Camilla

Cedar-town

Comer

Crawford

Bank of Danielsville

Danielsville

Darien

New Tripoli

Fairburn

Banking

Fairburn

Pottsvi I le

Citizens

Bank

Folkston

Bank of Hazlehurst

Hazlehurst

Cumberland

Hinesville

Bank

Hinesville

Harlan

Wilkinson

County

Irwinton

La Fayette

Hill

Bank
Co.

Bank

McKee

Bank of La Fayette

Manchester

Farmers

& Merchants

Mt. Olivet

Security

State Bank

Baltic

Pembroke

Custar

First State

Bank

State Bank
Bank

Farmers & Merchants

Bank of Thomson

Plain City

West Union
Freeport

Bank

Lakeland

McRae

Pembroke

Stockbridge

Summerville

Darby Bank & Trust Co.

Thomson
Vidalia

GA
GA

First National

Bank of West Point

West Point

First National

Bank in Deridder

Deridder

Rural Valley

Bank of Sunset

Washington

Citizens

Centreville

Abingdon

Greensboro

First Trust & Savings

La Plata

Algonquin

City

& Trust Co.

Bank & Trust Co. of Grainger
Bank & Trust Co.

District

Irving Bank

Bank of Currituck

Moyock

National

Avery County

Newland

First National

Heath

First Bank & Trust Co.

Springs

Bank

State Bank

New Windsor

Springs

Tallahassee

Ocean City

Bank of Heath

Bank

Bank of Ocean City
Bank

Bank

Junction

Bank of Plain City

National

Lansford

Deshler

Junction

Bank

East Prospect

Summit

Bank

Bank in Sylacauga

National

Bank of Chicago

Bank of N. Evanston
Bank of Fairmount

Co.

Sunset

Rutledge

Abingdon

Albany

Algonquin

Chicago

Evanston

Fairmount

Palatine

Latta Bank & Trust Co.

Latta

Reynolds

Dorn Banking

McCormick

First National

Bank of Ridgeway

Ridgeway

Tiskilwa

State Bank

Tiskilwa

Bank of York

York

Vermont

State Bank

Vermont

Middleburg

Auburn

Middleburg

Co.

National

First & Citizens

Bank

State Bank
Bank of Schiller

State Bank

Reynolds
Park

Schiller

IL
Park

IL
IL

Monterey

Rockville

Tazewell

Iowa State Bank

Calmar

Bank of Waverly

Waverly

Ossian State Bank

Ossian

Farmers

Windsor

Palmer

Hamlin

Home State Bank

Royal

Northfork

Solon State Bank

Solon

Rainelle

State Bank of Hesperia

Hesperia

Cleveland

Tazewell

Lincoln

National

Bank

Bank
National

Bank of Hamlin

First Clark National

Bank of Northfork

First State Bank & Trust Co.
Western

Greenbrier

National

Bank

National

State

Bank

Rainelle

Cleveland

Bank of War

War

Citizens

Bank

Delavan

Citizens

Fayette

Kilbourn

State Bank

Milwaukee

State Bank

Bank

First National

Bank of Fayette

State Bank

Fayette

Palmyra

Peoples

Bank of Greensboro

Greensboro

Sharon State

Peoples

Bank

Red Level

Bank of South Wayne

ECONOMIC

REVIEW,

NOVEMBER/DECEMBER

Bank

1989

Palmyra

Sharon

South Wayne

City

Bank
Stoughton

State Bank

First National
Farmers

Bank of Altheimer

& Merchants

Leachville

Bank

State Bank

Smackover
Egyptian

State Bank

state

Stoughton

Citizens

Smithville

Altheimer

Ashton State Bank

Ashton

Des Arc

State Bank of Du Bois

Du Bois

Leachville

First National

Bank of Friend

Friend

First National

Bank of Hooper

Hooper

Randolph

NE
NE

Smackover

State Bank

Carriers

Mills

Bank & Trust Co.

First State Bank

Bank of Christopher

Christopher

State Bank of Riverdale

Riverdale

State Bank of Farina

Farina

State Bank of Table

Table

First National

Staunton

Bank of Talmage

Fort Knox

First National

Fredonia

American

Poole

Bank of Locust Grove

Locust Grove

Sacramento

Park State Bank

Nicoma

Shepherdsville

First National

Pryor

luka

Vian State Bank

Vian

Bank of Okolona

Okolona

Farmers

State Bank

First National

Pontotoc

Western

Commerce

Water Valley

Citizens

Bank

Dexter

First National

Bank of Wellsville

Wellsville

Farmers

First Bank of Coon Rapids

Coon Rapids

Farmers

Lester Prairie
Maplewood

Bank of Staunton

Fort Knox National
Fredonia

Valley

Poole Deposit
Sacramento
Peoples

Bank

Bank
Bank

Deposit

Bank

luka Guaranty

Mechanics
Citizens

Bank
Bank of Pontotoc

Savings

Bank

State Bank

Town & Country
Farmers

Bank-Maplewood

State Bank

First WE Savings
Northern

Bank of St. Louis Park

State Bank

Bank of West Point

Exchange

Bank

Bank of Pryor

Bank

Bank of Albany

State Bank

TX
TX

Rothsay

Dilley State Bank

Dilley

St. Louis Park

First National

Falfurrias

Thief

First State Bank

Frankston

Hebronville

Hidalgo

Hillsboro

TX
TX

River Falls

Bank in Falfurrias

Forman

Citizens

National

Stock Growers Bank

Napoleon

Industry

State Bank

First Western

Wall

Muenster

Durand

First National

WI
co

Omnibank
Haxtun

Southeast

Community

Bank

State Bank of Wiley
Fort Riley National
Miners
Gypsum

Bank

State Bank
Valley Bank

First National

Bank of Howard

Bank of Hebronville

Industry
Muenster

TX
TX

First State Bank

Premont

Peoples

State Bank

Rocksprings

Citizens

Bank

Rusk

Denver

First State Bank

Rusk

Denver

Eisenhower

Haxtun

First State Bank

Wiley

First National

Fort Riley

Bank of Montreal

Frontenac

Gypsum

Boulder

County

Commerce

City

State Bank
Bank of Odonnell

San Antonio

Three Rivers

Coachella

San Francisco

First Bank of San Luis Obispo

San Luis Obispo

Torrance

Howard

First National

Pioneer Trust Co.

EIY
Salem

Kaysville

Morgan

National

State Bank

Moundridge

Farmers

State Bank

Winona

Barnes Banking

Leeton

First National

Bank

Bank in Coachella
California

National

Citizens

Bank of Leeton

Bank of Hillsboro

Odonnell

Ladysmith

Bank & Trust Co.

Devine

County Bank

Century

Albany

Columbus

Valley State Bank

Sargent

State Bank

Tucumcari

Medina

First National

Metropolitan

First State Bank

Border Bank

Carlsbad

of Gunbarrel

Pine Bluffs

State Bank

Park

Conrad

Firstbank

Warren

Security

Lindsay

Big Sandy

State Bank

Bank of Durand

West Point

First State Bank

State Bank

Bank

NE
NE

Bertram

Farmers

National

Rock

Talmage

Peoples

Security

Rock

Bank

Bank of Ely
Co.
Bank of Morgan

FEDERAL RESERVE BANK OF RICHMOND

Table

IIA

NORTHEAST
Higha

1982
INTEREST INCOME/ASSETSd
INTEREST EXPENSE/ASSETS
NONINTEREST
INCOME/ASSETS
NONINTEREST
EXPENSES/ASSETS
LOAN LOSS PROVlASSETS
SEC. GAINS/ASSETS
RETURN ON ASSETS
LOANS/ASSETS
SECURITIES/ASSETS
EQUITY/ASSET
TOTAL ASSETS (000)

11.22
5.25
0.36
2.64
0.14
-0.09
1.94
48.01
36.45
12.96
$31,892

SOUTHEAST

Allb
11.14
6.18
0.70
3.59
0.28
-0.01
1.00
50.58
27.92
9.11
$41,903

T St&
C.29)
c-2.92)**’
t-2.37)**
(-4.69)**”
y-;-a;;;***
(14.85)***
(- 1.04)
(3.42)**’
(5.34)‘*’
(-2.79)“’

CENTRAL

High

All

T Stat

High

All

12.20
5.92
1.52
3.63
0.18
-0.05
2.26
36.76
43.85
12.97

11.68
6.82
0.78
3.53
0.45
-0.02
0.93
47.48
31.00
9.48

(3.91)‘*’
( -(;:4;; * * *

11.87
6.18
0.55
2.55
0.10
-0.07
2.06
37.22
45.91
12.50

11.39
7.13
0.50
2.95
0.35
0.00
0.85
48.17
32.17
8.79

$27,044

$33,149

L 18)
t-7.93)***
(-1.30)
(8.59)***
t-6.27)***
(6.99)“’
(5.00)‘*’
c-3.011***

$26,250

$33,173

T Stat
(2.!7)***
C-4.05)“”
l.36)
C-2.16)**
-8.55)***
(- - 1.36)
(15.45)**’
-6.12)***
(6.99)“’
(6.27)*”
-2.77)“’

1983
INTEREST INCOME/ASSETS”
INTEREST EXPENSE/ASSETS
NONINTEREST
INCOME/ASSETS
NONINTEREST
EXPENSES/ASSETS
LOAN LOSS PROVlASSETS
SEC. GAINS/ASSETS
RETURN ON ASSETS
LOANS/ASSETS
SECURITIES/ASSETS
EQUITY/ASSET
TOTAL ASSETS (000)

10.71
4.63
0.39
2.63
0.09
0.00
2.06
46.63
38.02
13.26
$35,496

%80
0.51
3.25
0.23
0.01
1.04
49.78
31.08
8.85
$45,107

(2.02)**
c-3.45)**’
(-2.44j**
t-3.88)**’
t-4.66)***
(- .36)
(lO.BO)*‘*
I- 1.26)
(2.66)***
(5.95)“’
(- 1.91)

11.38
5.05
1.57
3.70
0.24
0.02
2.22
36.01
;S:t:
$29,973

10.62
5.85
0.77
3.43
0.52
0.00
0.88
47.03
33.57
9.02
$35,578

(7.16)***
(-5.03j”*
C.99)
C.38)
C-5.83)***
L99)
uo.53j***
t-6.24)***
(6.26)***
(7.23)**’

11.05
5.26
0.57
2.46
0.11
0.00
2.15
36.60
46.60
12.98
$29,298

(-2.50)”

10.45
6.19
0.51
2.91
0.40
0.01
0.84
48.02
34.66
8.69
$35,035

(3.56)***

(,-4.701***

t.48)
(-2.85)“’
f-10.54)***
t-.16)
(20.55)* * *
t-6.16)***
(6.04)***
(6.73)***
f-2.04)**

1984
INTEREST INCOME/ASSETS
INTEREST EXPENSE/ASSETS
NONINTEREST
INCOME/ASSETS
NONINTEREST
EXPENSES/ASSETS
LOAN LOSS PROV/ASSETS
SEC. GAINS/ASSETS
RETURN ON ASSETS
LOANS/ASSETS
SECURITIES/ASSETS
EQUITY/ASSET
TOTAL ASSETS (000)

5N..Aol
0.42
2.59
0.13
0.03
2.06
48.34
36.49
13.60
$39,067

NA
5.87
0.87
3.54
0.22
-0.02
1.04
52.53
28.70
8.96
$47,037

(-3.59)**’
(- 1.73)
(-3.14)“’
(-3.41)“’
L97)
(10.76)*‘*
(-1.53)
(2.96)***
(6.83)*”
(- 1.54)

:.A37
1.56
3.54
0.24
-0.02
2.15
38.40
44.16
13.80
$33,599

sN.?B
1.09
3.70
0.48
- 0.01
0.89
48.87
32.10
9.60
$37,349

-5.31)“’
t.62)
t-.26)
-5.441***
C-.38)
(11.79)***
-5.411***
(6.02)‘*’
(6.16)*+*

sNp59
0.62
2.48
0.14
0.01
2.06
39.51
43.10
12.88
$32,231

- 1.47)

NA
6.55
0.55
2.92
0.43
-0.01
0.80
50.05
32.42
8.68
$36,457

f-5.07)***
t.411
C-2.71)***
f-7.14)‘**
f.72)
(18.31)***
f-5.50)‘*’
(5.32)***
c7.11j***
(- 1.21)

1985
INTEREST INCOME/ASSETS”
INTEREST EXPENSE/ASSETS
NONINTEREST
INCOME/ASSETS
NONINTEREST
EXPENSES/ASSETS
LOAN LOSS PROV/ASSETS
SEC. GAINS/ASSETS
RETURN ON ASSETS
LOANS/ASSETS
SECURITIES/ASSETS
EQUITY/ASSET
TOTAL ASSETS (000)

10.84
4.66
0.40
2.46
0.12
0.05
2.19
47.15
38.23
13.98
$43,197

10.21
5.33
1.11
3.74
0.28
0.07
1.14
52.33
29.32
9.18
$49,477

(3.65)“’
c-3.00)***
(- 1.87)
t-3.24)“*
(-3.931’*’
(- .34)
(9.43)***
(- 1.77)
(3.19)***
(7.04)***
(- 1.22)

11.21
4.94
1.71
3.74
0.26
0.01
2.22
40.17
43.64
14.12
$36,820

10.61
5.64
1.18
3.86
0.54
0.06
1.02
49.88
31.36
9.89
$38,624

(5.59)***
(-5.18)**+
t.571
C-.15)
c-6.61)‘**
t-4.39)**’
(9.17)***
c-4.95)***
c5.941***
(4.98)’

l l

C-.56)

10.72
5.07
0.63
2.41
0.15
0.07
2.14
40.34
41.91
13.34
$35,181

10.25
5.92
0.55
2.94
0.62
0.07
0.79
48.87
32.57
8.69
$38,171

(2.88)***
C-4.86)‘*’
(.51)
f-3.49)***
(-13.25~***
Lll)
(21.41)***
f-4.32)“’
(3.67j”+
(7&u***
(- ,831

1986
INTEREST INCOME/ASSETS
INTEREST EXPENSE/ASSETS
NONINTEREST
INCOME/ASSETS
NONINTEREST
EXPENSES/ASSETS
LOAN LOSS PROVlASSETS
SEC. GAINS/ASSETS
RETURN ON ASSETS
LOANS/ASSETS
SECURITIES/ASSETS
EQUITY/ASSET
TOTAL ASSETS

(000)

10.03
4.10
0.38
2.35
0.10
0.12
2.10
45.77
35.84
13.77
$49,113

9.34
4.65
1.22
3.77
0.24
0.10
1.08
53.09
26.74
9.27
$50,730

(3.46)* * *
c-2.79)+**
(-1.37)
t-2.28)*’
t-5.26)***
t.27)
(9.48)***
t-2.48)‘*
(3.15)***
(6.34)***
(6.32)

10.32
4.30
1.54
3.52
0.29
0.04
2.08
41.48
38.76
13.77
$41,093

9.69
4.91
1.32
3.97
0.50
0.11
0.99
50.00
30.04
9.92
$40,797

(4.43)***
c-5.09)***
(. 28)
(- .68)
c-5.40)***
(-6.02)**+
(9.63)*‘*
c-4.351***
(4.25)***
(6.25)*”
LO91

10.03
4.50
0.60
2.37
0.21
0.12
2.05
40.45
39.78
13.61
$37,820

9.42
5.23
0.54
2.93
0.54
0.12
0.77
48.06
32.38
8.68
$39,696

c4.311***
f-4.54)***
I.37)
C-3.42)***
‘-W2;*”
(24.30)***
C-3.84)***
(3.43)*

l *

(7.92)‘**

t-.52)

1987
INTEREST INCOME/ASSETS’
INTEREST EXPENSE/ASSETS
NONINTEREST
INCOME/ASSETS
NONINTEREST
EXPENSES/ASSETS
LOAN LOSS PROV/ASSETS
SEC. GAINS/ASSETSRETURN ON ASSETS
LOANS/ASSETS
SECURITIES/ASSETS
EQUITY/ASSET
TOTAL ASSETS (000)

9.43
3.81
0.39
2.43
0.09
0.07
2.02
50.41
35.33
14.37
$52,300

8.94
4.35
1.46
4.06
0.21
0.04
1.07
58.04
25.42
9.67
$53,223

(2.99)***
(-3.31)***
(- 1.32)
(-2.02)*+
C-4.20)***
t.62)
(10.84)***
C-2.72)**
(3.32)***
(6.89)**’
t-.171

9.60
3.93
4.46
5.67
0.26
0.04
2.49
44.28
37.38
15.46
$43,519

9.07
4.47
1.33
3.86
0.46
0.02
0.96
52.18
29.89
10.00
$41,679

a Mean for all high performance banks, in percent terms unless otherwise stated.
b Mean for all small banks, in percent terms unless otherwise stated.
c *** indicates high performance and all banks are statistically significantly different at the 1 percent level.
‘* indicates high performance and all banks are statistically significantly different at the 5 percent level.
d INTEREST INCOME/ASSETS

is stated on a taxable-equivalent basis.
ECONOMIC REVIEW, NOVEMBER/DECEMBER 1989

(3.95)***
t-5.28)***
C.85)
t.65)
t-4.36)**’
(1.07)
(2.97)***
C-3.87)***
(3.72)‘**
(3.60)***
C.57)

9.16
4.06
0.60
2.41
0.18
0.05
1.89
42.25
39.52
14.00
$40,679

8.77
4.71
0.54
2.93
0.37
0.03
0.81
49.83
32.86
8.88
$40,631

(3.03)***
-4.26)***
C.41)
-2.96)***
-5.60)“*
C.66)
(19.77)**’
C-3.24)***
(3.08)**’
(7.86)“’
LO11

MIDWEST
High
12.36
5.74
0.48
2.62
0.19
-0.08
2.39
40.60
43.32
14.81
$18,851

11.61
5.02
0.53

2.69

0.22
-0.02
2.42
39.91
45.14
16.20
$20,759

!A33
0:79
2.69
0.24
-0.02
2.35
40.00
44.30
16.77
$22,585
10.72
4.66
0.75
2.63
0.30
0.09
2.27
37.54
44.27
16.94
$24.331
9.80
4.06
0.71
2.66
0.37
0.14
1.99
35.76
44.81
16.89
$26,345

9.03

3.65
0.70
2.63
0.28
0.00
1.95
36.61
44.34
17.61
$27,038

SOUTHWEST

All

T Stat

High

All

12.00
7.32
0.51
2.92
0.38
-0.02
1.10
50.57
32.48
9.06

(1.61)
C-3.69)“’
C-.21)
(- 1.22)
t-3.85)*‘*
(- 1.61)
(8.93)’
t-4.80)**
(4.92)***
t5.091***

12.20
6.00
0.75
2.74
0.20
-0.03
2.22
38.45
42.94
12.68

11.64
6.54
0.78
3.41
0.49
-0.01
1.13
49.57
26.82
9.67

$25,193

10.92
6.42
0.52
2.91
0.54
0.01
0.91
50.84
34.36
9.03
$26,394

!..A81
0.60
2.91
0.91
0.00
0.62
51.64
32.75
8.99
$27,188
10.46
6.13
0.60
2.97
1.31
0.11
0.41
48.69
33.36
8.91
$27,804
9.33
5.31
0.60
3.01
1.23
0.19
0.25
45.11
35.35
8.57
$28,981

8.61
4.66
0.62
2.97
0.64
0.02
0.56
45.25
37.67
8.81
$29,767

l *

C-2.59)**
(2.76)***
t-3.84)***
f.08)
(-‘.82j
t-3.50)‘**
(- 1.97)
(14.17)***
t-5.16)***
(4.90)**’
(5.15)***
(- 1.61)

(-3.93)“’
C.91)
(- ,921
C-10.38)***
(- 1.02)
(ll.ll)**’
C-5.33)*+*

(4.981***
(5.20)***
- 1.30)
(I.291

(.-4.4u***

f.67)
- 1.42)
(-- 18.82)“’
CF.811
(18.45)***
c-3.93)***
(4.38)“”
(5.24)***
C-.981

(2.16)**
c-4.45)‘**
C.45)
(- 1.50)
(-12.11)*”
C-.87)
(23.75)***
C-3.27)***
(3.65b”’
t5.541***
(- ,721
(2.23)**
t-4.17)***
C.40)
(- 1.36)
t-4.87)***
(- 1.80)
(20.12)***
t-2.77)***
c2.1u**
(5.691***
(- .73)

$25,633
11.50
5.14
0.80
2.63
0.32
-0.01
2.45
37.44
44.59
13.38
$29,313
NA
5.57
0.79
2.68
0.29
-0.01
2.13
38.10
44.47
14.28
$32,190
11.34
5.13
0.78
2.64
0.48
0.02
2.17
38.36
43.30
14.28
$35,030
10.56
4.51
0.79
2.62
0.52
0.08
2.12
37.27
42.87
14.78
$36,847

9.47

4.04
0.72
2.52
0.41
0.04
1.96
35.52
45.45
14.61
$39,661

WEST
T Stat

$34,003
10.52
5.72
0.82
3.39
0.72
0.02
0.85
50.66
28.00
8.94
$36,836
NA
6.45
0.87
3.42
0.87
0.00
0.64
53.30
25.40
8.63
$38,749
10.57
5.92
0.92
3.59
1.18
0.09
0.40
53.43
24.28
8.53
$39,644

(2.77)***
‘4;;;
c-4.451***
c-5.17)*”
(- ,921
i4.iij***
-4.a71***
(7.20)***
c4.941***
-3.38)***
(3.43)
(--3.06)***
C-.13)
C-3.82)+**
(64.26j***
(- 1.06)
(14.73)*”
t-5.431***
(7.02)***
(8.67)***

l l l

t-2.62)**

C-5.02)*‘*
(- .63)
t-3.62)‘*’
t-9.61)‘**
C-.19)
(i9.3Oj***
C-6.14)***
(7.88)‘**
(7.11)***
t-2.08)**
(4.17)“’
C-4.78)***
(- 1.19)
c-5.44)***
(-8.98)“’
(- 1.62)
(23.77)***
c-5.87)*‘*
(7.45)“’
(10.42)***
t-1.10)

9.50
t5.391***
5.22
C-7.18)***
0.90
(- 1.04)
3.68
C-6.53)***
1.56 (- 12.23)***
0.21
C-3.81)**’
-0.13
c25.2sj***
50.95
C-5.24)***
23.78
(7.211***
8.11
(9.88)**’
$39,930

C-.74)

8.81
(4.23)***
4.70
t-7.11)***
0.90
(-1.61)
3.63
t-7.30)+*’
1.29 t-12.05)***
0.04
(- .03)
-0.14
(26.94)“’
49.56
C-5.22)***
27.79
(6.21)**+
8.04
(lo.ol)***
$39,823

(- .04)

U.S.

High

All

T Stat

High

All

12.09
4.80
0.91
3.55
0.15
-0.12
2.36
45.25
31.25
15.44

11.15
5.78
0.90
4.84
0.60
0.01
0.36
55.69
18.83
12.21

<2.84)**
(--i.9ij
C.03)
t-2.41)**
(-6.72j**’
(- 1.67)
t10.741***
t-3.28)***
(3.12)***
(1.33)

12.03
5.79
0.83
2.97
0.16
-0.07
2.20

11.61
6.84
0.65
3.33
0.42
-0.01
0.95
49.83
29.56
9.47

$31,017
11.06
4.11
1.09
3.31
0.18
-0.04
2.50
45.43
32.73
16.22
$34,796

2.25
1.15
3.38
0.02
-0.03
2.68
46.52
31.89
18.64
337,433
11.49
3.91
1.03
3.34
0.31
0.09
2.80
44.84
34.52
18.24
$39,851

9.97

3.53
1.04
3.45
0.24
0.05
2.08
43.92
34.34
18.31
$42,840

9.35
3.25
1.20
3.51
0.30
0.03
2.05

$27,156
10.41
5.23
1.02
4.63
0.63
0.01
0.48
57.98
20.01
9.50
$31,218

!.tO
1.12
4.63
0.80
0.00
0.44
59.60
18.91
8.79
$33,669
10.47
5.40
1.20
4.75
1.08
0.08
0.08
58.56
18.64
8.39
$34,294

9.34

4.57
1.35
4.77
1.17
0.15
0.03
45.46
19.35
8.12
$36,337
8.87
4.09
1.21
4.72
0.91
0.03
0.11
55.49
22.78
8.35

43KE
19.24
$45,566

$36,664

FEDERAL RESERVE BANK OF RICHMOND

C.71)
(1.87)
t-2.81)**
L31)
C-4.12)***
C-6.57)***
C-1.10)
(5.42)*‘*
t-3.11)***
(3.99)^”
(2.01)
t.63)

t-3.42)***
C.17)
C-2.78)**’
(-4.991”’
(- 1.09)
(5.77)***
(--2.4oj**
c3.05j***
(1.80)
t.65)
11.77)
(-‘3.soj***
(- ,961
f-4.67)***
C-9.551***
C.32)
(5.39)***
f-2.45)**
t3.591***
(2.04)
C.981
(2.45)*‘
t--3.osj***
(-1.18)
t-3.09)***
(-11.61j**’
c-3.29)***
(14.62)“’
(-2.09)
t3.101***
(2.16)**
(1.09)
(1.82)
c-.2.89)**
(- .05)
C-2.52)**
t-6.30)***
t.291
(13.84)***
(- 1.70)
c3.33j***
(2.13)**
(1.48)

39.79

42.18
13.31
$26,193
11.26
4.98
0.88
2.94
0.20
0.00
2.28
39.03
43.60
13.99
$29,247

0.94

2.91
0.20
0.00
2.19
40.69
42.12
14.52
$32,224
11.02
4.84
0.96
2.91
0.26
0.05
2.24
40.69
41.95
14.75
$35,131
10.10
4.25
0.90
2.84
0.29
0.09
2.07
40.35
39.94
14.77
$38,388

9.35

3.86
1.67
3.41
0.25
0.04
2.10
42.02
39.92
15.53
$40,799

$31,131
10.61
5.98
0.66
3.26
0.53
0.01
0.84
50.20
31.55
8.97
$33,257

Et5
0.77
3.32
0.68
-0.01
0.71
52.01
29.61
8.91
$34,693
10.44
5.87
0.81
3.41
0.95
0.08
0.60
50.94
29.51
8.88

T Stat
(5.24)***
t-8.50)***
L94)
C-2.16)**
(-14.78)“’
C-3.36)***
(22.72)***
c-11.44)***
c13.37j***
(10.18)**’
c-4.44)***

(8.35)‘**
C-9.98)++*
(i.03j
(- 1.67)
t-12.60)***
(- 1.42)
(28.691***
t-12.22)***
u2.3ij***
(11.83)**’
C-3.21)***

c-11.15)***
L78)
(-2.34)”
t-19.64)“’
(.I51
(28.91)*”
(-11.93)***
(12.50)***
(10.06)** *
(- 1.78)
(7.02)‘**
(-11.19)“’
(.61j
t-2.36)**
c-27.991***
C-3.06)***
(29.361***
C-9.56)***

$35,715

9.44

(9.831***

5.12 C-12.38)***
0.84
C.31)
3.45
t-3.32)**’
1.00 (-26.49)“’
0.16
C-4.09)***
0.40
(40.60)“’
48.94
t-7.88)***
29.73
(9.271”’
8.66
u2.121***
$36,888
8.78
4.59
0.83
3.41
0.69
0.03
0.51
49.55
31.68
8.81
$37,482

c.901
(8.60)***
C-11.24)***
L86)
(0.001
t-17.70)***
t.85)
(11.56)***
C-6.27)***
t7.391***
uo.45j* * *
(1.81)

Full text of Economic Quarterly (Federal Reserve Bank of Richmond) : November-December 1989, Vol. 75

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