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Inﬂation and Changing
Expenditure Shares
Alexander L. Wolman and Fan Ding

nﬂation is an index of price changes for many goods. As such, the behavior of inﬂation is determined by the behavior of (1) price changes for
individual goods, as well as (2) the weights that the index puts on the price
changes of different goods. Most macroeconomic analyses of the time-series
behavior of inﬂation—whether empirical or theoretical—implicitly emphasize the former determinant of inﬂation.1 Theoretical analyses tend to focus
on one-sector models in which there are no weights to shift, and empirical
analyses tend to focus on the univariate properties of some broad inﬂation
rate.
If rates of price change did not differ much across goods, then shifts in
the weights would not matter much for inﬂation. In fact, there has been substantial variation in price change behavior across goods, and the weights on
two of the three broad categories in consumption price indexes have shifted
dramatically over the last 50 years (Figure 1). Those facts motivate us to investigate the importance of changing weights for three fundamental time-series
properties of inﬂation: level, volatility, and persistence. The extent to which
shifting weights are important for these properties may have implications for
macroeconomic modeling. Suppose that inﬂation was highly persistent but
that all of the persistence was accounted for by long-term shifts in the weights
in the inﬂation measure. We might then conclude that in one-sector macroeconomic models, high inﬂation persistence is not a desirable feature.
We propose and implement two approaches to measuring the contribution
of changing expenditure shares to inﬂation behavior. Both involve constructing an alternative inﬂation measure that holds ﬁxed the weights on price
We wish to thank Bob Hetzel, Andreas Hornstein, Tom Humphrey, and Eric Nielsen for
helpful comments and Sam Malek for his assistance. The views here are the author’s and
should not be attributed to the Federal Reserve Bank of Richmond or the Federal Reserve
System.
1 Wolman (1999) is an example of an article that ﬁts this description.

Federal Reserve Bank of Richmond Economic Quarterly Volume 91/1 Winter 2005

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Sectoral Expenditure Shares
0.7

Services

0.6

0.5

0.4
Nondurables
0.3

0.2
Durables
0.1

0.0
1/47

1/51

1/55

1/59

1/63

1/67

1/71

1/75

1/79

1/83

1/87

1/91

1/95

1/99

1/03

changes for different goods. We describe the behavior of the level, volatility,
and persistence of the alternative inﬂation measures. The role of changing
expenditure shares is then revealed by the divergence between the behavior of
actual inﬂation and the ﬁxed-weight measures. Neither approach leads to a
dramatic revision in our understanding of post-war U.S. inﬂation; that is, the
broad features of inﬂation over the past 50 years cannot be accounted for by
changing expenditure shares. However, in more subtle ways, changing expenditure shares have been important for the behavior of inﬂation. For example,
we attribute 15 basis points of quarterly inﬂation, on average, to changing
expenditure shares over the period from 1947 to 2004. Expenditures have
shifted to services, and the relative price of services has risen persistently over
the last 50 years. This shift toward services has tended to make the overall
inﬂation rate higher, other things equal. The caveat “other things equal” is
important. Expenditure share shifts have been one factor inﬂuencing the behavior of inﬂation, but monetary policy has had the ability to counteract the
effect of shifting expenditure shares on inﬂation. Thus, one could reinterpret
the statement above as “in order to achieve the inﬂation behavior we have observed, monetary policy has had to counteract a 15-basis-point upward effect
on inﬂation coming from the long-run shift in expenditures toward services.”

A. L. Wolman and F. Ding: Inﬂation and Changing Expenditure Shares

It is important to make clear at the outset that we are not arguing that
one should measure inﬂation by holding ﬁxed the weights on different goods.
It is well known that good price indexes from the standpoint of economic
theory ought to have time-varying weights that reﬂect time-varying expenditure patterns. Our concern is instead one of fact-ﬁnding: Given the existence
of changes in expenditure shares, to what extent can those changes account
for the behavior of inﬂation? To answer this question, we construct alternative
ﬁxed-weight price indexes.
For the most part, recent literature on inﬂation in the United States has
abstracted from the heterogeneity that underlies overall inﬂation. Notable exceptions are Clark (2003) and Bauer, Haltom, and Peterman (2004). Bauer,
Haltom, and Peterman focus on the behavior of core inﬂation over the last 20
years. They decompose core inﬂation into contributions of different goods
and services. These contributions are the product of expenditure shares and
individual price changes. Bauer, Haltom, and Peterman ﬁnd that just two components, rent and used vehicles, account for much of the decline in consumer
price index (CPI) inﬂation over this period. Clark’s emphasis is on inﬂation
persistence, which we will discuss further. He contrasts the behavior of inﬂation persistence over time to the behavior of the persistence of disaggregated
price changes. He ﬁnds that the persistence of disaggregated price changes
tends to be lower than the persistence of inﬂation. Our article differs in its
explicit emphasis on changing expenditure shares over time. Clark’s ﬁndings, though, suggest that expenditure share behavior may be an important
determinant of inﬂation persistence.

INFLATION IN THE UNITED STATES

The variables we are concerned with are all produced by the Bureau of Economic Analysis of the United States Department of Commerce. They are the
price index for personal consumption expenditure; the subindexes for durable
goods, nondurable goods, and services; and the expenditure shares for durable
goods, nondurable goods, and services. Before turning to the behavior of these
variables, it is useful to provide some background on price indexes, and, in
particular, on the price index for personal consumption expenditure. (Henceforth, we will refer to this index as the PCE price index, and to its rate of
change as PCE inﬂation.)
PCE inﬂation data are constructed from underlying price and quantity data
for a large number of categories of goods and services. In turn, the price data
for those underlying categories are constructed from more direct observation
of prices on an even larger number of speciﬁc items (i.e., goods and services).
The latter construction is performed mainly by the Department of Labor’s
Bureau of Labor Statistics. For the most part, the same item prices that form
the basis for PCE inﬂation also form the basis for the more widely known CPI

Federal Reserve Bank of Richmond Economic Quarterly

inﬂation, which is produced by the Bureau of Labor Statistics. We focus here
on PCE inﬂation for two reasons. First, the methodology used to produce the
PCE inﬂation numbers corresponds more closely to notions of price indexes
suggested by economic theory. Second, the PCE methodology makes it more
straightforward to decompose inﬂation in a way that isolates the effect of
changing expenditure shares.
The formula used to create the PCE inﬂation rate is known as a Fisher ideal
index. We will ﬁrst provide the formula and then interpret it.2 We deﬁne π t to
be the PCE inﬂation rate in quarter t, xi,t to be the period t dollar expenditures
on category i, and π i,t to be the rate of price change for category i from period
t − 1 to period t. The PCE inﬂation rate is
I

πt =

ωi,t−1 π i,t
i=1

θ i,t π i,t ,

(1)

i=1

where
ωi,t

≡

θ i,t

≡

xi,t
I
j =1 xj,t

, and

xi,t /π i,t
I
j =1 xj,t /π j,t

, .for i = 1, ..., I .

Both objects in square brackets in (1) are weighted averages of the rates of
price change for each good and service. The weights, ωi,t−1 , are simply the
expenditure shares for category i in period t − 1; thus, the ﬁrst weighted
average, I ωi,t−1 π i,t , measures the rate of price change for the basket
i=1
of goods purchased in period t − 1. The weights, θ i,t , are the hypothetical
expenditure shares that are derived by combining period t real quantities with
period t−1 prices. Thus, the second weighted average, I θ i,t π i,t , measures
i=1
the rate of price change in period t for the basket of goods purchased in period
t. Finally, PCE inﬂation (π t ) is the geometric average of these two inﬂation
rates.
It is clear from (1) that changes in expenditure shares on different goods
and services are incorporated in the behavior of the PCE. In contrast, the CPI
is a ﬁxed-weight index; changes in expenditure shares are incorporated in the
CPI only every two years. The precise way in which changing expenditure
shares are incorporated in PCE inﬂation is somewhat complicated, as seen in
(1). Fortunately, for our purposes, the true PCE inﬂation rate is well approximated by a simpler formula that aggregates prices for the three major spending
categories using what is known as a Divisia index. The Divisia approximation
2 See Webb (2004) and Clark (1999) for more detailed discussions of how the PCE price
index is constructed.

A. L. Wolman and F. Ding: Inﬂation and Changing Expenditure Shares

Figure 2 PCE Inﬂation
14
12
10

Percent

8
6
4
2
0
-2
-4
4/47 4/51

4/55

4/59 4/63

4/67 4/71

4/75 4/79

4/83

4/87 4/91

4/95 4/99

4/03

to the PCE which we will use is
πD =
t

ωi,t−1 π i,t ,

(2)

i=N,D,S

that is, the expenditure-share-weighted average of price changes for nondurable goods, durable goods, and services. This approximation is convenient
because it allows us to easily decompose the behavior of inﬂation into the part
accounted for by changing expenditure shares and the part accounted for by
changing rates of price change for the main spending categories.

The Level of Inﬂation
Figure 2 displays the quarterly PCE inﬂation rate from 1947 to 2004, expressed
in annualized percentage terms.3 This ﬁgure displays the major facts about
inﬂation in the United States. Inﬂation was highly volatile immediately after
World War II, then declined and became more stable during the 1950s. In the
3 In all ﬁgures, the month and year on the x-axis indicate the ﬁrst month of the quarter
represented by the tick mark.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Volatility and Persistence
A: Variance of Inflation and Variance of Shock
12
Variance of Inflation
Variance of Shock

10
8
6
4
2
0
1/57 1/61 1/65 1/69 1/73

1/77

1/81 1/85

1/89 1/93

1/97

1/01

B: Inflation Persistence (Sum of Coefficients in Autoregression)
1.5
95 percent
1.0
0.5
0.0
5 percent
-0.5
-1.0
1/59 1/63

1/67

1/71

1/75

1/79

1/83

1/87

1/91

1/95

1/99

1/03

mid-1960s, inﬂation began a steady rise that continued for the rest of the
decade. The 1970s were characterized by high and volatile inﬂation, and then
in the early 1980s inﬂation declined dramatically. Over the last 15 to 20 years,
inﬂation has been low and stable, apart from a moderate increase in the late
1980s. The average PCE inﬂation rate from 1947 to the present has been 3.42
percent. Though these basic facts are clear, much about the behavior of the
level of U.S. inﬂation remains in dispute. For example, economists agree that
the Federal Reserve can determine the average level of inﬂation over periods
of several years. Thus, there is consensus that the Federal Reserve could have
brought about a much lower average inﬂation rate in the 1970s. However,
there is no consensus about why the Fed behaved as it did. We direct interested
readers to Hetzel (1998), Orphanides (2003), and Cogley and Sargent (2003)
for an introduction to the vast literature analyzing that question.

A. L. Wolman and F. Ding: Inﬂation and Changing Expenditure Shares

Inﬂation Volatility
Panel A of Figure 3 displays two measures of inﬂation volatility. The ﬁrst, the
solid line, is the variance of inﬂation, measured over ten-year rolling windows
ending at the date on the horizontal axis. For example, the entry labeled “4/79”
is the sample variance of inﬂation from the third quarter of 1969 through the
second quarter of 1979.
Variance is the most natural way to measure volatility. However, variance
can be a misleading measure of volatility if a time series is serially correlated.
For example, consider the ﬁrst-order autoregressive process,
yt = ρyt−1 + ε t ,

(3)

where εt is an i.i.d. normal random variable with mean zero and variance v.
−1
v. Thus, even though v is the only
The variance of yt is var(y) = 1 − ρ 2
source of random volatility in y, the autoregressive coefﬁcient ρ contributes
to the variance of y.
The effect of serial correlation (that is, persistence) on variance leads us
to present a second measure of volatility along with variance. The dashed line
is the variance of the residual in an autoregressive representation of inﬂation,
where the autoregression is estimated by OLS, and the lag length is chosen by
the Akaike information criterion (AIC). This residual variance can be thought
of as a measure of the volatility that remains after taking out predictable variation in the series during the particular ten-year window. For both measures,
volatility fell dramatically until 1961, then remained low until the early 1970s.
It rose in the 1970s, fell in the 1980s, and has been historically low over the
last ﬁve years. The fact that the variance of inﬂation rose much more than the
shock variance from the late 1960s through the late 1980s suggests that there
were changes in the serial correlation properties of inﬂation over this period.
We consider these next.

Inﬂation Persistence
“Inﬂation persistence” refers to the degree to which a sudden change in the
inﬂation rate tends to persist over time. As we just saw, persistence leads to
higher variance, other things equal. In recent years much research has been
devoted to estimating the persistence of inﬂation in the United States. This
literature was spawned by Fuhrer and Moore (1995), who argued that inﬂation
in the United States was characterized by high persistence and that models
with forward-looking pricing behavior were unable to replicate the observed
level of persistence. Fundamentally, however, interest in inﬂation persistence
dates back to Lucas (1972) and Sargent (1971). These authors showed that
the accuracy of econometric procedures for estimating Phillips curve slopes
could be sensitive to the univariate persistence properties of inﬂation. Recent
research on inﬂation persistence has, like Fuhrer and Moore, been concerned

Federal Reserve Bank of Richmond Economic Quarterly

with quantifying the degree of inﬂation persistence and then assessing whether
and to what degree observed persistence is an inherent structural feature or an
artifact of the particular monetary policy in place. The extent to which inﬂation
persistence is structural has important implications for the consequences of
alternative monetary policies.4
There are several ways to measure inﬂation persistence. Pivetta and Reis
(2004) discuss the different measures in detail. In the case of the ﬁrst-order
autoregression discussed above, the different measures of persistence are all
equivalent, and persistence is summarized by the parameter, ρ. For more complicated processes, the different measures can give different rankings of persistence. We will follow Levin and Piger (2003) and Clark (2003) in measuring
inﬂation persistence by the sum of autoregressive coefﬁcients in a univariate
autoregressive representation of inﬂation.5 If the sum of autoregressive coefﬁcients is ρ, then 1/ (1 − ρ) represents the long-run effect of a permanent
unit shock to the autoregression. That is, if in each period from t = 0 to ∞,
the autoregression in (3) is hit by ε t = 1, and εt = 0 for t < 0, then at t = ∞,
we have yt = 1/ (1 − ρ) .
Panel B of Figure 3 displays ten-year rolling-window estimates of PCE
inﬂation persistence from the second quarter of 1959 to the ﬁrst quarter of
2004. For each quarter, we take the ten years of prior data and estimate an
autoregression for inﬂation, using the AIC to select lag length. The sum of
autoregressive coefﬁcients is then plotted in this panel, along with centered 90
percent conﬁdence intervals constructed by semiparametric bootstrapping.6
Persistence ﬂuctuates between 0.16 and 1.20 over the full sample. It was
low until the late 1960s, then jumped up in late 1968 and early 1969, and
remained high (roughly 0.8 or above) until 1999, apart from a brief period
in 1983 and some rapid ﬂuctuations between 1991 and 1995. In the last ﬁve
years, our persistence measure has declined steadily, reaching 0.23 in the ﬁrst
quarter of 2004. The conﬁdence intervals are quite wide. However, they
encompass zero a much greater percentage of the time than they encompass
unity, shedding some doubt on the conventional wisdom that inﬂation is inherently highly persistent.7 The increase in inﬂation persistence in the late 1970s
corresponds to the divergence (panel A of Figure 3) between the variance of
inﬂation and the variance of the shock to the inﬂation autoregression. It is
4 Different degrees of structural inﬂation persistence correspond to different degrees of price

rigidity or other nominal frictions. Different speciﬁcations of nominal frictions, in turn, correspond
to different real implications of changing policy rules.
5 In the ﬁrst-order example, the sum of coefﬁcients is simply ρ.
6 To generate the conﬁdence intervals for a given quarter, we simulated 5000 samples by
combining the estimated autoregressive coefﬁcients with resampled residuals. These conﬁdence
intervals should be interpreted with caution; Hansen’s (1999) grid bootstrap method deals more
effectively with the bias associated with persistence being close to unity.
7 This statement requires the caveat that the conﬁdence intervals will be misleading when
persistence is near unity.

A. L. Wolman and F. Ding: Inﬂation and Changing Expenditure Shares

not as easy to reconcile the joint behavior of these three objects later in the
sample when the variance of inﬂation drops sharply. That is, the sharp drop in
the variance of inﬂation without a sharp drop in the shock variance is not explained by a sharp drop in inﬂation persistence. Such a discrepancy can occur
because, for autoregressions with more than one lag, the relationship between
variance of the series and variance of the shock depends on the individual
autoregressive coefﬁcients, not just their sum.

SECTORAL INFLATION AND OVERALL INFLATION

Having laid out the basic features of inﬂation behavior in the United States,
we now turn to the components of inﬂation, expenditure shares, and price
changes for the three consumer spending categories of durable goods, nondurable goods, and services. In this section we document the behavior of
expenditure shares and price changes. The changes in expenditure shares
over time and the variation in rates of price change across sectors then motivate our attempts in the next section to quantify the contribution of changing
expenditure shares to the behavior of overall inﬂation.
Figure 1 plots expenditure shares for durable goods, nondurable goods,
and services from 1947 to the present. Whereas the expenditure share for
durable goods has ﬂuctuated narrowly, between 12 and 18 percent, the shares
of nondurables and services have respectively risen and fallen dramatically. In
January 1947 services accounted for only 31 percent, and nondurable goods
accounted for 56 percent of personal consumption expenditure. In January
2004, services accounted for 59 percent, and nondurable goods only 29 percent
of personal consumption expenditure.
Figure 4 plots rates of price change for the three ﬁrst-level components
of personal consumption expenditure, together with the overall PCE inﬂation rate. Each series differs somewhat from overall inﬂation. Services price
changes have generally been above PCE inﬂation, averaging 4.22 percent,
compared to 3.42 percent for overall inﬂation. Durables price changes have
generally been below PCE inﬂation, averaging 1.59 percent. The main distinguishing feature of nondurables price changes—which have averaged 3.09
percent—is that they have been more volatile than PCE inﬂation. This feature
is reﬂected in Figure 5, which plots rolling-window variances of the sectoral
rates of price change.8 Figure 6 shows that the differences in rates of price
8 Volatility of price changes of nondurables will not be a surprise to readers
the concept of core PCE inﬂation. Core PCE inﬂation excludes food and energy
are notoriously volatile and comprise a large share of nondurables expenditures.
monetary policy purposes, core PCE inﬂation is generally preferred to overall PCE

familiar with
prices, which
For short-run
inﬂation.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Sectoral Price Changes
A: Durables and Inflation
16

Durables

PCE inflation

Percent

8
0

-8
4/47

4/55

4/71

4/63

4/79

4/87

4/95

4/03

B: Nondurables and Inflation
16

Nondurables

PCE inflation

Percent

8
0

-8
4/47

4/55

4/63

4/71

4/79

4/87

4/95

4/03

C: Services and Inflation
16

Services

PCE inflation

Percent

8
0

-8
4/47

4/55

4/63

4/71

4/79

4/87

4/95

4/03

change across sectors have cumulated signiﬁcantly over time: the price index
for services rose by a factor of eleven since 1947, whereas the price index for
durables rose by less than a factor of three. In the last eight years, the price
index for durable goods has actually been falling.
Figure 7 plots persistence for rates of price change of durables, nondurables, and services. The persistence measure is, again, the sum of auto-

A. L. Wolman and F. Ding: Inﬂation and Changing Expenditure Shares

Figure 5 Variance of Sectoral Price Changes
25
Durables
Services

20
15
10
5
0
1/61

1/69

1/77

1/85

1/93

1/01

25
Nondurables
Services

20
15
10
5
0
1/61

1/69

1/77

1/85

1/93

1/01

regressive coefﬁcients. The persistence measure moves broadly together
across sectors, with services usually being the most persistent. Early in the
sample, nondurables price changes are more persistent than durables price
changes, but this ordering is reversed after about 1980. At the end of the sample, when persistence of PCE inﬂation is declining, the same is happening to
rates of price change for services and nondurables, but persistence rises dramatically for durables price changes in 1998 and stays high until the present.
Together with the large swing in expenditure shares, differential behavior of price changes across sectors suggests that expenditure share changes
may have been important contributors to the behavior of inﬂation. We will
estimate this contribution in the next section. However, even if we ﬁnd little
contribution, the existence of expenditure shifts together with differing rates
of price change across sectors is an important observation. Sectoral shifts
and heterogeneous price behavior across sectors may have implications for

Federal Reserve Bank of Richmond Economic Quarterly

Figure 6 Sectoral Price Levels
1,200
1,100
1,000
900

Services

800
700
600
Nondurables
500
400
Durables
300
200
100
0
1/47 1/51

1/55

1/59 1/63

1/67

1/71

1/75

1/79

1/83

1/87 1/91

1/95 1/99

1/03

monetary policy. For example, the nature of optimal monetary policy may be
sensitive to these factors.9

REINTERPRETING CHANGES IN THE BEHAVIOR
OF INFLATION

To assess the importance of changing expenditure shares for the behavior of
inﬂation, we construct two series that control for long-run shifts in expenditure
shares. The ﬁrst series we call “1947 inﬂation,” and we create it by replacing
the actual expenditure shares, ωi,t−1 , in (2) with expenditure shares that ﬂuctuate only transitorily around their 1947:4 levels. We generate 1947 inﬂation in
two steps. First we estimate quadratic time trends for the expenditure shares
under the restriction that the trends sum to one. Then we create a series of synthetic weights (expenditure shares) for each date in our sample by adding the
1947:4 value of the trend weight to the difference between the actual weight
9 Aoki (2001), Erceg and Levin (2002), and Huang and Liu (2003) study cyclical ﬂuctuations

and monetary policy in multi-sector models. Wolman (2004) considers the optimal steady state
inﬂation rate when there are relative price trends across sectors.

A. L. Wolman and F. Ding: Inﬂation and Changing Expenditure Shares

Figure 7 Persistence of Sectoral Price Changes
1.50
Durables
Services

1.25
1.00
0.75
0.50
0.25
0.00
1/63

1/71

1/79

1/87

1/95

1/03

1.50
Nondurables
Services

1.25
1.00
0.75
0.50
0.25
0.00
1/63

1/71

1/79

1/87

1/95

1/03

at each date and the trend weight estimated for that date. The initial values
for the trend weights are 0.12 for durables, 0.31 for services, and 0.56 for
nondurables. We allow for ﬂuctuations around the trends because these may
be independent of the long-run sectoral shifts we want to control for.
Our second approach to controlling for changing expenditure shares involves extracting the ﬁrst principal component of the three sectoral rates of
price change. The principal component is a weighted average of the three
sectoral rates of price change, with the weights being chosen in order to maximize the variance of the weighted average. The weights are 0.76 for services,
0.21 for durables, and 0.03 for nondurables. The principal component can
be viewed as the common component of the sectoral rates of price change.
Because actual expenditure shares are not used to compute the principal component, they do not directly inﬂuence this series. Kapetanios (2002) suggests
a similar measure as reﬂecting a notion of core inﬂation. The weighted median inﬂation measure emphasized by Bryan and Cecchetti (1994) is similar

Federal Reserve Bank of Richmond Economic Quarterly

Figure 8 1947 and PCE Inﬂation
14
PCE inflation
1947 inflation

12
10

Percent

8
6
4
2
0
-2
-4
1/48

1/52

1/56

1/60

1/64

1/68

1/72

1/76

1/80

1/84

1/88

1/92

1/96

1/00

1/04

in spirit to the ﬁrst principal component in that it attempts to cut down the
contribution of noisy components of inﬂation.10

The Level of Inﬂation
Figure 8 displays the time series for 1947 inﬂation, and Figure 9 displays the
ﬁrst principal component of sectoral inﬂation. In each case we plot annual
averages of the series and display them along with the corresponding series
for actual PCE inﬂation. Both series share the broad patterns that characterize
actual PCE inﬂation. If someone familiar with postwar U.S. inﬂation were
shown either panel, it might not be difﬁcult to convince them that it was a plot
of actual inﬂation. However, there are some differences between both series
and actual PCE inﬂation.
In the case of 1947 inﬂation, it is not surprising that these differences arise
in the latter part of the sample, when the actual weights are quite different
from the 1947 weights (services having risen and nondurables having fallen).
Because nondurables inﬂation is more volatile than services inﬂation, the
10 As a measure of core inﬂation, Bryan and Cecchetti (1994) use the weighted median of
36 components of the all-urban consumers CPI. This is the “central point, as implied by the CPI
expenditure weights, in the cross-sectional histogram of inﬂation each month” (p. 203).

A. L. Wolman and F. Ding: Inﬂation and Changing Expenditure Shares

Figure 9 Principal Component and PCE Inﬂation
14
12

PCE Inflation
Principal Component

Percent

8
6
4
2
0
-2
-4
1/48

1/52

1/56

1/60

1/64

1/68

1/72

1/76

1/80

1/84

1/88

1/92

1/96

1/00

1/04

1947 inﬂation series with its higher weight on nondurables is noticeably more
volatile than actual inﬂation in the last 20 years of the sample. In addition,
because the average rate of price change for nondurables has been lower than
that for services, 1947 inﬂation has a somewhat lower average level, 3.27
percent versus 3.42 percent. The lower level is obscured, however, by the
higher volatility.
The principal component of sectoral price changes has a higher average
than PCE inﬂation, at 3.64 percent. This is attributable to the high weight the
principal component places on services. The high weight on services and low
weight on volatile nondurables explains the fact that the principal component
is less volatile than either PCE inﬂation or 1947 inﬂation. A notable feature
of the principal component’s behavior is that, unlike actual inﬂation and 1947
inﬂation, it is quite stable between 1983 and 1991. The other two series exhibit
a sharp fall around 1986 and then a sharp rise followed by an additional steady
increase. Referring to the sectoral price changes in Figure 4, we can understand
this divergence as reﬂecting the fact that the volatility in the mid-to-late 1980s
is largely accounted for by volatility in nondurables price changes.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 10 Volatility and Persistence of 1947 Inﬂation
A: Variance (1947 Inflation) and Variance (PCE Inflation)
12.0

1947 Inflation

PCE Inflation

8.0

4.0

0.0
1/57 1/61

1/65

1/69

1/73

1/77

1/81

1/85

1/89

1/93

1/97

1/01

B: Variance (Shock to 1947 Inflation) and Variance (Shock to PCE Inflation)
8.0

1947 Inflation

PCE Inflation

6.0
4.0
2.0
0.0
1/57 1/61

1/65

1/69

1/73

1/77

1/81

1/85

1/89

1/93

1/97

1/01

C: Persistence (1947 Inflation) and Persistence (PCE Inflation)
1.2

PCE Inflation

1947 Inflation

0.8

0.4

0.0
1/59 1/63

1/67

1/71

1/75

1/79

1/83

1/87

1/91

1/95

1/99

1/03

Volatility and Persistence
Figures 10 and 11 display volatility and persistence of our alternative measures in the same way that Figure 3 displays volatility and persistence of actual
inﬂation. Neither 1947 inﬂation nor the principal component of sectoral price

A. L. Wolman and F. Ding: Inﬂation and Changing Expenditure Shares

Figure 11 Volatility and Persistence of Principal Component
A: Variance (Principal Component) and Variance (PCE Inflation)
12
PCE Inflation
Principal Component

10
8
6
4
2
0
1/61

1/69

1/77

1/85

1/93

1/01

B: Variance (Shock to Principal Component) and Variance (Shock to PCE Inflation)
PCE Inflation
Principal Component

8
6
4
2
0
1/61

1/69

1/77

1/85

1/93

1/01

C: Persistence (Principal Component) and Persistence (PCE Inflation)
PCE Inflation
Principal Component

1.2

0.8

0.4

0.0
1/63

1/71

1/79

1/87

1/95

1/03

changes displays markedly different volatility patterns than does actual inﬂation. There are some minor differences across the series, however. Figures 10
and 11 conﬁrm that the principal component has lower volatility than actual inﬂation or 1947 inﬂation. The inﬂation shock volatility displayed in the middle

Federal Reserve Bank of Richmond Economic Quarterly

panels behaves similarly for actual inﬂation and the principal component, declining smoothly from the mid-1970s until the early 1980s. In contrast, for
1947 inﬂation, there is a sharper decline in shock volatility, and it does not
occur until the mid-1980s.
Rolling-window estimates of inﬂation persistence for the two new series
are in the bottom panels of Figures 10 and 11. Over the ﬁrst two-thirds of the
sample, there is little difference between the persistence of 1947 inﬂation and
the persistence of PCE inﬂation. This similarity is to be expected, because
the underlying inﬂation series for the two ﬁgures do not differ much from
each other. Since 1990, however, the two sets of estimates have diverged
noticeably. For PCE inﬂation, persistence has been generally high over this
period (with an average of 0.63), declining below 0.50 only in the last four
years. In contrast, persistence of 1947 inﬂation has been generally low since
1990, averaging 0.45.
To some degree, the lower level of persistence in recent years for 1947
inﬂation is easy to explain. Nondurables has generally been the least persistent
component of inﬂation (see Figure 7)—at least during the second half of the
sample; therefore, because our 1947 inﬂation series places a relatively higher
weight on nondurables later in the sample, this direct effect will make 1947
inﬂation more persistent than PCE inﬂation. However, this direct effect cannot
explain all of the differences between the persistence of 1947 inﬂation and
PCE inﬂation. The persistence of 1947 inﬂation is not simply the expenditureshare-weighted average of the persistence of the components. Our persistence
measure has the ﬂavor of a covariance, and, as such, it depends in a complicated
manner on the covariance between sectoral rates of price change.
The bottom panel of Figure 11 plots the same rolling-window estimate of
persistence for the principal component. Unlike 1947 inﬂation, the principal
component places a very low weight on nondurables. Thus, it is not surprising that its persistence behaves quite differently than that of 1947 inﬂation.
Although persistence of the principal component has declined in recent years,
the decline has been smaller in magnitude than that of actual inﬂation; the
relatively high weight on durables means that the increase in persistence of
price changes of durables is reﬂected more in the principal component than in
1947 inﬂation. More generally, ﬂuctuations in the persistence of the principal
component have been smaller than ﬂuctuations in the persistence of actual
inﬂation or 1947 inﬂation.

CONCLUSION

We began by noting the dramatic changes in consumption expenditure shares
that have occurred in the United States over the last 50 years. The fact that
these shares serve as weights in consumption price inﬂation measures then led
us to investigate the quantitative importance of shifts in expenditure shares for

A. L. Wolman and F. Ding: Inﬂation and Changing Expenditure Shares

the behavior of U.S. inﬂation. Using two different methods, we found that
controlling for expenditure share changes led to a picture of U.S. inﬂation over
the last 50 years that was somewhat—but not dramatically—different from the
picture provided by actual PCE inﬂation. This analysis is exploratory only.
That changing expenditure shares do not account for much of the behavior of
inﬂation does not mean that those changes are inconsequential for monetary
policy. Large changes in expenditure shares, together with trend changes in
relative prices across sectors (as displayed in Figure 6) may interact with other
differences across sectors in a way that has important implications for monetary policy. For example, if the nature of price stickiness differs systematically
across sectors (as tentatively suggested by the work of Bils and Klenow [2004])
or if money demand varies systematically across expenditure types, then the
monetary policy prescriptions from one-sector models may differ markedly
from those in models with multiple categories of consumption.

REFERENCES
Aoki, Kosuke. 2001. “Optimal Monetary Policy Response to Relative Price
Changes.” Journal of Monetary Economics 48 (December): 55–80.
Bils, Mark, and Pete Klenow. 2004. “Some Evidence on the Importance of
Sticky Prices.” Journal of Political Economy 112 (October): 947–85.
Bauer, Andrew, Nicholas Haltom, and William Peterman. 2004. “Examining
Contributions to Core Consumer Inﬂation Measures.” Federal Reserve
Bank of Atlanta Working Paper 04-07.
Bryan, Michael, and Stephen Cecchetti. 1994. “Measuring Core Inﬂation.”
Monetary Policy, ed. N. Gregory Mankiw. Chicago: University of
Chicago Press: 195–215.
Clark, Todd E. 1999. “A Comparison of the CPI and the PCE Price Index.”
Federal Reserve Bank of Kansas City Economic Review 84 (Third
Quarter): 15–29.
. 2003. “Disaggregate Evidence on the Persistence of
Consumer Price Inﬂation.” Federal Reserve Bank of Kansas City
Research Working Paper 03-11.
Cogley, Timothy, and Thomas J. Sargent. 2003. “The Conquest of U.S.
Inﬂation: Learning, Model Uncertainty, and Robustness.” Manuscript.
Erceg, Christopher, and Andrew Levin. 2002. “Optimal Monetary Policy
with Durable and Nondurable Goods.” FRB International Finance

Federal Reserve Bank of Richmond Economic Quarterly
Discussion Paper 748 and ECB Working Paper 179.

Fuhrer, Jeffrey, and George Moore. 1995. “Inﬂation Persistence.” Quarterly
Journal of Economics 110 (February):127–59.
Hansen, Bruce E. 1999. “The Grid Bootstrap and the Autoregressive Model.”
The Review of Economics and Statistics 81 (November): 594–607.
Hetzel, Robert L. 1998. “Arthur Burns and Inﬂation.” Federal Reserve Bank
of Richmond Economic Quarterly 84 (Winter): 21–44.
Huang, Kevin, and Zheng Liu. 2003. “Inﬂation Targeting: What Inﬂation
Rate to Target?” Journal of Monetary Economics. Forthcoming.
Kapetanios, George. 2002. “Modelling Core Inﬂation for the UK Using a
New Dynamic Factor Estimation Method and a Large Disaggregated
Price Index Dataset.” Queen Mary, University of London, Department of
Economics Working Paper 471.
Levin, Andrew, and Jeremy Piger. 2002. “Is Inﬂation Persistence Intrinsic in
Industrial Economies?” Federal Reserve Bank of St. Louis Working
Paper 23E.
Lucas, Robert E. 1972. “Econometric Testing of the Natural Rate
Hypothesis.” The Econometrics of Price Determination, ed. O. Eckstein.
Washington, D.C.: Board of Governors of the Federal Reserve System:
50–9.
Orphanides, Athanasios. 2003. “The Quest for Prosperity Without Inﬂation.”
Journal of Monetary Economics 50 (April): 633–63.
Pivetta, Frederic, and Ricardo Reis. 2004. “The Persistence of Inﬂation in
the United States.” Manuscript.
Sargent, Thomas J. 1971. “A Note on the ‘Accelerationist’ Controversy.”
Journal of Money, Credit and Banking 3 (August): 721–25.
Webb, Roy. 2004. “Which Price Index Should a Central Bank Employ?”
Federal Reserve Bank of Richmond Economic Quarterly 90 (Spring):
63–76.
Wolman, Alexander L. 1999. “Sticky Prices, Marginal Cost, and the
Behavior of Inﬂation.” Federal Reserve Bank of Richmond Economic
Quarterly 85 (Fall): 29–48.
. 2004. “The Optimal Rate of Inﬂation with Trending
Relative Prices.” Manuscript.

On the Aggregate Labor
Supply
Yongsung Chang and Sun-Bin Kim

ssues of labor supply are at the heart of macroeconomic studies of large
cyclical ﬂuctuations. The population puts forth more work effort in booms
than in slumps. Economists’ explanations of this phenomenon range
from a pure market-clearing supply-and-demand view at one extreme to a
dismissal of almost any role of supply and of market clearing at the other
extreme. Disagreement is intense because labor markets’ failure to clear may
create a strong case favoring activist macroeconomic policy. According to the
equilibrium business cycle models led by Lucas and Rapping (1969), people
work more hours in some years than in others because the market rewards
them for this pattern. Even in a non-equilibrium model in which the role of
labor supply is dismissed in the short run, its slope is still important for the
welfare cost of departing from the supply schedule. Labor supply elasticity is
also crucial in evaluating the effect of taxes and government spending (e.g.,
Auerbach and Kotlikoff 1987; Judd 1987).
Figure 1 shows the cyclical components of total hours worked and wages
for the U.S. economy for 1964:I–2003:II (detrended using the Hodrick-Prescott
ﬁlter). Hours worked represent the total hours employed in the nonagricultural business sector. The wages are real hourly earnings of the production
and nonsupervisory workers. Fluctuations of hours of work are much greater
than those of wages.1 If the intertemporal substitution hypothesis were to
explain ﬂuctuations in hours, it would require a labor supply elasticity beyond
We would like to thank Andreas Hornstein, Thomas Humphrey, Yash Mehra, and Pierre
Sarte for their helpful comments. The views expressed herein are not necessarily those of the
Federal Reserve Bank of Richmond or the Federal Reserve System.
1 Moreover, wages are not strongly correlated with hours, casting further doubt on the intertemporal substitution mechanism. While the contemporaneous and dynamic correlations between
hours and wages are important for business cycle analysis, we focus on the slope of the labor
supply schedule only in this article. See Chang and Kim (2004b) on this issue.

Federal Reserve Bank of Richmond Economic Quarterly Volume 91/1 Winter 2005

Federal Reserve Bank of Richmond Economic Quarterly

the admissible estimates from the empirical micro studies, which are typically
less than 0.5.2
In this article, we demonstrate both qualitatively and quantitatively how
the slope of the aggregate labor supply schedule is determined by the reservation wage distribution, rather than by the willingness to substitute leisure
intertemporally.3 Based on our recent studies (Chang and Kim 2004a, 2004b),
we present a fully speciﬁed general equilibrium model economy where the
reservation wage distribution is nondegenerate. While the model is parsimonious, it provides a laboratory in which we can investigate the mapping
from individual to aggregate labor supply functions. The model economy is
populated by many workers who face uninsurable idiosyncratic productivity
shocks—as demonstrated in Aigagari’s (1994) incomplete capital market—
and make decisions on the labor market participation—as demonstrated by
Rogerson’s (1985) study of indivisible labor. The cross-sectional distributions of earnings and wealth are comparable to those in the U.S. data. We ﬁnd
that the aggregate labor supply elasticity of such an economy is around one,
even though the intertemporal substitution elasticity of leisure at the individual
level is assumed to be 0.4. This aggregate elasticity is greater than the typical
micro estimates but smaller than those often assumed in the aggregate models.
The article is organized as follows: Section 1 provides various models
of aggregate labor supply based on individuals’ work decisions. Section 2
presents illustrative examples that demonstrate how the aggregate labor supply
depends on the reservation wage distribution. Section 3 lays out the model
economy where the reservation wage distribution is dispersed. In Section 4,
we calibrate the model parameters using various microdata and investigate the
properties of aggregate labor supply of the model. Section 5 summarizes our
ﬁndings.

LABOR SUPPLY: INDIVIDUAL VERSUS AGGREGATE

In this section, we consider various models on individuals’ labor supply decisions and derive the corresponding aggregate labor supply schedules. For
2 In his survey paper, Pencavel (1986) reports that most estimates are between 0.00 and 0.45
for men. In their parallel survey of research on the labor supply of women, Killingsworth and
Heckman (1986) present a wide range of estimates, from -0.3 to 14.0; they do not venture a guess
as to which is correct but conclude that the elasticity is probably somewhat higher for women
than men. See Blundell and MaCurdy (1999) for a more recent review of the literature. An
alternative (equilibrium) approach is to introduce shifts in labor supply through shifts in preference (Bencivenga 1992), home technology (Benhabib, Rogerson, and Wright 1991; Greenwood and
Hercowitz 1991), or government spending (Christiano and Eichenbaum 1992).
3 Hansen’s (1985) indivisible labor economy, based on the theory of employment lotteries
by Rogerson (1988), generates a very high aggregate labor supply elasticity—in fact, inﬁnity—
regardless of individual labor supply elasticity. However, the existence of employment lotteries
is not strongly supported by the data, as the persons with greater hours or greater earnings per
hour consume more. Our analysis illustrates that such an economy is a special case where the
reservation wage distribution is degenerate.

Y. Chang and S. Kim: On the Aggregate Labor Supply

the moment, we abstract from the intertemporal decisions. Hence, models in
this section are static and of partial equilibrium. We will study a fully speciﬁed
dynamic general equilibrium model in Section 3.

Homogeneous Agents with Divisible Labor
Suppose there is measure one of identical agents with the following preferences
over consumption, c, and hours worked, h:
U = max lnc − B
c,h

h1+1/γ
1 + 1/γ

(1)

subject to
c = wh + ra,

(2)

where w is the hourly wage; r, the interest rate; and a, asset holdings. The
ﬁrst order condition for hours of work is
w
(3)
Bh1/γ = .
c
The marginal disutility from additional hours of work equals the marginal
utility of consumption from income earned. The labor supply function can be
written as
w γ
.
(4)
h=
Bc
The Frisch elasticity—elasticity of hours with respect to wage holding
wealth (consumption) constant—is γ . With homogeneous agents, the aggregate labor supply elasticity is also γ . According to the empirical micro studies,
the labor supply is inelastic since a typical value of γ is less than 0.5. As Figure 1 illustrates, inelastic labor supply is hard to reconcile with the fact that
hours ﬂuctuate greatly without much variation in wages.

Homogeneous Agents with Indivisible Labor
A large fraction of cyclical ﬂuctuations of total hours worked reﬂects the decisions to work or not (the so-called extensive margin), whereas the micro
elasticities reﬂect the variation of hours for employed workers (intensive margin). The indivisible labor model has been developed to highlight the extensive
¯
margin of labor supply.4 Suppose an agent supplies h hours if he works and
zero hours otherwise. With homogeneous agents, the labor supply decision is
4 In general, the labor supply decision operates on both the extensive and intensive margins.

However, workers are rarely allowed to choose completely ﬂexible work schedules or to supply a
small number of hours.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Cyclical Components of Total Hours and Wages
0.06

ln (Hour)
ln (Wage)

0.04

0.02

0.00

-0.02

-0.04

-0.06
1965

1970

1975

1980

1985

1990

1995

2000

Notes: Hours worked represent the nonagricultural private sector. Wage is real hourly
earnings for nonsupervisory and production workers.

randomized (see Hansen 1985 and Rogerson 1988). An agent chooses prob¯ 1+1/γ
ability of working, p, and the expected utility is p(lnc − B h
) + (1 −
1+1/γ
p)(lnc − 0). Then the agent’s maximization problem with the existence of a
complete insurance market is
U = max lnc − pB
c,p

¯
h1+1/γ
,
1 + 1/γ

subject to
¯
c = wph + ra.
The equilibrium value of p is equal to the fraction of agents that work, and
¯
the aggregate labor supply is given by H = p h. The aggregate labor supply
elasticity is inﬁnite, as the stand-in agent’s utility is linear in p. While the
aggregate labor supply is inﬁnitely elastic in this environment, the underlying assumptions—homogeneity and complete market—are vulnerable even
to casual empiricism.

Y. Chang and S. Kim: On the Aggregate Labor Supply

Heterogeneous Agents with Indivisible Labor
Suppose workers differ in both preference (B) and asset holdings (a) and that
the complete insurance of idiosyncratic risks is not available. With indivisible
labor, the agent, i, works if
¯
log(wh + rai ) − Bi

¯
h1+1/γ
≥ log(rai ).
1 + 1/γ

(5)

The reservation wage, w, is
w=

rai
exp(Bi ) − 1 ,
¯
h

(6)

¯ 1+1/γ

where
= h
is a constant, independent of individual characteristics.
1+1/γ
Workers with high Bi (those who value leisure more relative to commodity
consumption) exhibit a higher reservation wage. The richer (ai ) a worker
is, the higher his reservation wage. In general the reservation wage depends
on various dimensions of cross-sectional heterogeneity. In Section 3, we
investigate the fully speciﬁed dynamic general equilibrium model where the
shape of (w) is parsimoniously characterized by the microdata and depends
on the agent’s earnings ability as well as wealth.

ILLUSTRATIVE EXAMPLES

Before we present our formal analysis, we provide the examples that illustrate
the dependence of aggregate labor supply on the shape of reservation wage
distribution. Suppose that equal numbers of two types of workers exist in
the economy, with reservation wages of $10 and $20, respectively. Suppose
also that labor supply is indivisible in the sense that a worker supplies one
unit of labor if he works. Figure 2 shows that the aggregate labor supply—
the horizontal sum of individual labor supply—can have two elasticities. At
a wage rate of $10 and $20, the elasticity is inﬁnity. Otherwise, it is zero.
Whenever a mass in the reservation wage distribution exists, the aggregate
labor supply elasticity can take a large value. Suppose that many types of
¯
workers exist and that a worker works h hours if the market wage, w, exceeds
the reservation wage, w:
h(w) =

¯
h
0

if w ≥ w,
otherwise.

The aggregate labor supply function, H (w), is
w

H (w) =
0

¯
hφ(w)d w =

¯
(w)h.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Individual and Aggregate Labor Supply
30

+ 15

= 15

Wage

0.5
Type 1

0.5
Type 2

The aggregate labor supply elasticity, (w) =
(w) =

0
50
100
Aggregate Employment Rate (%)

H (w)w
,
H (w)

(w)w
.
(w)

The aggregate elasticity depends on the concentration of workers—the
marginal density, (w), relative to the cumulative density, (w). In the
two-type workforce example, the aggregate elasticity is inﬁnity where there
is a mass of workers, ( (10) = (20) = ∞), and zero elsewhere. In the
lottery economy of Hansen (1985) and Rogerson (1988), the reservation wage
distribution is degenerate (as the agents are identical) at the equilibrium wage
rate ( (w) = ∞), and the aggregate elasticity becomes inﬁnity.
The aggregate elasticity depends on the relative concentration of workers
even when workers are allowed to work longer hours at higher wages. Suppose
the labor supply of a worker is
h(w; w) =

¯ ˆ
h + h(w; w)
0

if w ≥ w,
otherwise.

Y. Chang and S. Kim: On the Aggregate Labor Supply

ˆ
¯
Here h(w; w) is hours worked beyond the minimum hours, h, and satisﬁes
ˆ
ˆ (w; w) > 0.5 The aggregate
h(w; w) ≥ 0 with equality when w = w and h
labor supply function is
w

H (w) =

¯
h(w; w)φ(w)d w = h (w) +

ˆ
h(w; w)φ(w)d w,

where the total hours worked consists of the sum of the extensive margins,
w ˆ
¯
h (w), and that of intensive margins, 0 h(w; w)φ(w)d w. Given that
w

H (w) = h(w; w)φ(w) +

h (w; w)φ(w)d w,
0

the aggregate elasticity is
(w) =

¯
[hφ(w) +

w
0

h (w; w)φ(w)d w]w

.
h(w; w)φ(w)d w
For illustrative purposes, suppose the individual labor supply elasticity, γ , is
h (w; w)w
. Substituting h (w; w)
constant across workers and wages: γ =
h(w; w)
with γ , the aggregate elasticity can be again expressed as the sum of the
relative concentration of reservation wages and the individual elasticity:
¯
h (w)w
(w) =
+ γ.
w ˆ
¯
h (w) + 0 h(w; w)φ(w)d w
These examples illustrate two important aspects of aggregate labor supply:
the aggregate elasticity can be different from that of microelasticity and the
aggregate labor supply elasticity is not time-invariant because the reservation
wage distribution evolves over time as the wealth distribution and the level of
employment change over time. However, these examples are silent about the
magnitude of the aggregate labor supply elasticity for which the exact shape
of the empirical reservation wage distribution must be uncovered. In the next
section, we present a model economy—a simpliﬁed version of Chang and Kim
(2004a)—where the reservation wage distribution, (w), is determined by
the asset accumulation of households that face different types of uninsurable
income risks.6 While the model is parsimonious, it allows for a complete
characterization of the reservation wage distribution.
w
0

3. A FULLY SPECIFIED GENERAL EQUILIBRIUM MODEL
There is a continuum (measure one) of workers who have identical preferences but different productivity. Individual productivity varies exogenously
5 The minimum-hours restriction can be easily justiﬁed, for example, by ﬁxed costs, such as
commuting time.
6 In Chang and Kim (2004a), the economy consists of many households made up of a husband and wife. Here we present a model that is populated by many single-agent households.

Federal Reserve Bank of Richmond Economic Quarterly

according to a stochastic process with a transition probability distribution
function, π x (x |x) = P r(xt+1 ≤ x |xt = x). A worker maximizes his utility
over consumption, ct , and hours worked, ht :
∞

U = max E0
∞
{ct ,ht }t=0

β t u(ct , ht ) ,
t=0

with
1+1/γ

u(ct , ht ) = lnct − B

ht
,
1 + 1/γ

subject to
at+1 = wt xt ht + (1 + rt )at − ct .

(7)

Workers trade claims for physical capital, at , which yields the rate of
return, rt , and depreciates at the rate, δ. The capital market is incomplete.
Physical capital is the only asset available to workers who face a borrowing
constraint, at ≥ a for all t. We abstract from the intensive margin and assume
¯
¯
that the labor supply is indivisible. If employed, a worker supplies h units of
¯
labor and earns wt xt h, where wt is wage rate per effective unit of labor.
The representative ﬁrm produces output according to a Cobb-Douglas
technology in capital, Kt , and efﬁciency units of labor, Lt :7
Yt = F (Lt , Kt , λt ) = λt Lα Kt1−α ,
t
where λt is the aggregate productivity shock with a transition probability
distribution function, π λ (λ |λ) = P r(λt+1 ≤ λ |λt = λ).8
The value function for an employed worker, denoted by V E , is
¯
h1+1/γ
V E (a, x; λ, µ) = max lnc − B
a ∈A
1 + 1/γ
+ βE max V E (a , x ; λ , µ ),
V N (a , x ; λ , µ ) x, λ

subject to
¯
c = wx h + (1 + r)a − a ,
7 This production function implicitly assumes that workers are perfect substitutes for each
other. While this assumption abstracts from reality, it greatly simpliﬁes the labor market equilibrium.
8 In this model economy, the technology shock is the only aggregate shock. This restriction
does not necessarily reﬂect our view on the source of the business cycles. As we would like to
show that the preference residual contains a signiﬁcant speciﬁcation error rather than true shifts in
preferences, we intentionally exclude shocks that may shift the labor supply schedule itself (e.g.,
shifts in government spending or changes in the income tax rate) from the present article.

Y. Chang and S. Kim: On the Aggregate Labor Supply

a ≥ a, and
¯
µ = T(λ, µ),
where T denotes a transition operator that deﬁnes the law of motion for the
distribution of workers, µ(a, x).9 The value function for a nonemployed
worker, denoted by V N (a, x; λ, µ), is deﬁned similarly with h = 0. Then,
the labor supply decision is characterized by
V (a, x; λ, µ) = max V E (a, x; λ, µ), V N (a, x; λ, µ) .
¯
h∈{0,h}

Equilibrium consists of a set of value functions, {V E (a, x; λ, µ), V N
(a, x; λ, µ), V (a, x; λ, µ)}; a set of decision rules for consumption,
asset holdings, and labor supply, {c(a, x; λ, µ), a (a, x; λ, µ), h(a, x; λ, µ)};
aggregate inputs, {K(λ, µ), L(λ, µ)}; factor prices, {w(λ, µ), r(λ, µ)}; and a
law of motion for the distribution µ = T(λ, µ) such that:
1. Individuals optimize:
Given w(λ, µ) and r(λ, µ), the individual decision rules—c(a, x; λ, µ),
a (a, x; λ, µ), and h(a, x; λ, µ)—solve V E (a, x; λ, µ), V N (a, x; λ, µ),
and V (a, x; λ, µ).
2. The representative ﬁrm maximizes proﬁts:
w(λ, µ) = F1 L(λ, µ), K(λ, µ), λ , and
r(λ, µ) = F2 L(λ, µ), K(λ, µ), λ − δ
for all (λ, µ).
3. The goods market clears:
a (a, x; λ, µ) + c(a, x; λ, µ) dµ = F L(λ, µ), K(λ, µ), λ +
(1 − δ)K
for all (λ, µ).
4. Factor markets clear:
L(λ, µ) =

xh(a, x; λ, µ)dµ, and

K(λ, µ) =

adµ

9 Let A and X denote sets of all possible realizations of a and x, respectively. The measure
µ(a, x) is deﬁned over a σ -algebra of A × X .

Federal Reserve Bank of Richmond Economic Quarterly

Table 1 Parameters of the Benchmark Model Economy
Parameter
α = 0.64
β = 0.9785504
γ = 0.4
B = 151.28
h = 1/3
a = −2.0
¯
ρ x = 0.939
σ x = 0.287
ρ λ = 0.95
σ λ = 0.007

Description
Labor share in production function
Discount factor
Individual labor supply elasticity with divisible labor
Utility parameter
Labor supply if working
Borrowing constraint
Persistence of idiosyncratic productivity shock
Standard deviation of innovation to idiosyncratic productivity
Persistence of aggregate productivity shock
Standard deviation of innovation to aggregate productivity

for all (λ, µ).
5. Individual and aggregate behaviors are consistent:
µ (A0 , X 0 ) =

A0 ,X0

A,X

1a =a (a,x;λ,µ) dπ x (x |x)dµ da dx

for all A0 ⊂ A and X 0 ⊂ X .

QUANTITATIVE ANALYSIS

Calibration
We brieﬂy explain the choice of the model parameters. The unit of time is a
business quarter. We assume that x follows an AR(1) process: lnx = ρ x lnx +
ε x , where ε x ∼ N (0, σ 2 ). As we view x as reﬂecting a broad measure of
x
earnings ability in the market, we estimate the stochastic process of x based on
the wages from the Panel Study of Income Dynamics (PSID) for 1979–1992.
The values of ρ x = 0.939 and σ x = 0.287 reﬂect the persistence and standard
deviation of innovations to individual wages.10 The other parameters of the
article are in accordance with the business cycle analysis and empirical labor
supply literature. A working individual spends one-third of her discretionary
¯
time: h = 1/3. The individual compensated labor supply elasticity of hours,
γ , is 0.4. The labor share of output, α, is 0.64, and the depreciation rate,
δ, is 2.5 percent. We search for the weight parameter on leisure, B, such
10 These are maximum-likelihood estimates of Heckman (1979), correcting for a sample selection bias. Our estimate for income shocks does not purge the life-cycle effect. In our companion
paper, Chang and Kim (2004a), we use both cases. When the life-cycle effect (accounted for by
observed characteristics such as age, education, and sex) is purged, the aggregate labor supply
elasticity becomes slightly bigger because the reservation wage distribution becomes less dispersed.

Y. Chang and S. Kim: On the Aggregate Labor Supply

Table 2 Characteristics of Wealth Distribution
Quintile
3rd
4th

1st

2nd

PSID
Share of wealth
Group average/population average
Share of earnings

-0.52
-0.02
-7.51

0.50
0.03
11.31

5.06
0.25
18.72

Model
Share of wealth
Group average/population average
Share of earnings

-2.05
-0.10
9.70

2.46
0.12
15.06

10.22
0.51
19.01

5th

Total

18.74
0.93
24.21

76.22
3.81
38.23

100
1
100

23.88
1.19
23.59

65.49
3.27
32.63

100
1
100

Notes: The PSID statistics reﬂect the family wealth and earnings levels published in their
1984 survey.

that the steady state employment rate is 60 percent, the current population
survey average for 1967:II–2000:IV. The discount factor, β, is chosen so that
the quarterly rate of return to capital is 1 percent. The aggregate productivity
shock, λt , follows anAR(1) process: lnλ = ρ λ lnλ+ε λ , where ελ ∼ N (0, σ 2 ).
λ
We set ρ λ equal to 0.95 and σ λ equal to 0.007, following Kydland and Prescott
(1982). Table 1 summarizes the parameter values of the benchmark economy.

Cross-Sectional Earnings and Wealth Distribution
As we investigate the aggregation issue, it is desirable for the model economy
to possess a reasonable amount of heterogeneity. We compare cross-sectional
earnings and wealth—two important observable dimensions of heterogeneity
in the labor market—found in the model and in the data.
Table 2 summarizes both the PSID and the model’s detailed information
on wealth and earnings. Family wealth in the PSID (1984 survey) reﬂects the
net worth of houses, other real estate, vehicles, farms and businesses owned,
stocks, bonds, cash accounts, and other assets. For each quintile group of
wealth distribution, we calculate the wealth share, ratio of group average to
economy-wide average, and the earnings share.
In both the data and the model, the poorest 20 percent of families in
terms of wealth distribution were found to own virtually nothing. In fact,
households in the ﬁrst quintile of wealth distribution were found to be in debt
in both the model and the data. The PSID found that households in the fourth
and ﬁfth quintile own 18.74 and 76.22 percent of total wealth, respectively,
while, according to the model, they own 23.88 and 65.49 percent, respectively.
The average wealth of those in the fourth and ﬁfth quintile is, respectively,
0.93 and 3.81 times larger than that of a typical household, according to the

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Reservation Wage Schedule
4

Reservation Wages

3.5

A: All Asset Levels

x 10

3.0
2.5
2.0
1.5
1.0
0.5
0.0
0

B: Assets less than $200,000

8,000

Reservation Wages

6,000
4,000
Mean Wealth

2,000

Median Wealth

0
0

20
4
x 10

Notes: The graphs denote the reservation wage schedule of the benchmark model. Wages
(quarterly earnings) and assets are in 1983 dollars.

PSID. These ratios are 1.19 and 3.27 according to our model. The fourth and
ﬁfth quintile groups of the wealth distribution earn, respectively, 24.21 and
38.23 percent of total earnings, according to the PSID. The corresponding
groups earn 23.59 and 32.63 percent, respectively, in the model.
Overall, the wealth distribution is found to be more skewed in the data.
In particular, our model fails to match the highly concentrated wealth found
in the right tail of the distribution. In the PSID, the top 5 percent of the
population controls about half of total wealth (not shown in Table 2), whereas,
in our model, they possess only 20 percent of total wealth. Since our primary
objective is not to explain the top 1 to 5 percent of the population, we argue
that the model economy presented in this article possesses a reasonable degree
of heterogeneity, thus making it possible to study the effects of aggregation in
the labor market.

Reservation Wage Distribution
The reservation wage distribution is crucial for the mapping from individual
to aggregate labor supply. In Figure 3, we plot the reservation wage schedule

Y. Chang and S. Kim: On the Aggregate Labor Supply

Figure 4 Reservation Wages and Participation Rates
14,000

12,000

Reservation Wages

10,000

8,000

6,000

4,000

2,000

0
0

100

Participation Rates (%)

Notes: The graph denotes the inverse cumulative distribution functions of reservation
wages. Wages are quarterly earnings in 1983 dollars.

of the benchmark model for all asset levels (panel A) and for assets less than
$200,000 (panel B). At a given asset level, workers with wages (productivity)
above the line choose to work. The reservation wage increases as the asset
level increases. To illustrate, we adjust the units so that the mean asset of the
model matches the average asset in the 1984 PSID survey, $60,524; thus, the
values are in 1983 dollars.11 Consider a worker whose assets are $29,880, the
median of the wealth distribution from the model. According to the model,
he is indifferent between working and not working at quarterly earnings of
$3,287. Another worker whose assets are equivalent to the average asset
holding of the economy, $60,524 (which belongs to the 66th percentile of the
wealth distribution in our model and to the 72nd percentile in the PSID), is
indifferent about working at $4,273 per quarter.
In Figure 4 we plot the inverse cumulative distribution of reservation
wages of the model. In practice, the reservation wage distribution is neither
observed nor constant over time. Based on the reservation wage schedule and
11 The mean asset in our model is 14.48 units. The reservation wages in the vertical axis
¯
reﬂect quarterly earnings (the reservation wage rate multiplied by h).

Federal Reserve Bank of Richmond Economic Quarterly

Figure 5 Total Hours Worked from the Models
0.03
Heterogenous Agent Model
Representative Agent Model
0.02

0.01

0.00

-0.01

-0.02

-0.03
0

invariant distribution, µ(x, a), we can infer the responsiveness of labor market participation. In Table 3 we compute the elasticities of participation with
respect to the reservation wage around the steady state. These values may be
viewed as the aggregate labor supply elasticity with zero wealth effect as they
assume the entire wealth distribution held is constant. For the model economy,
the elasticities are 1.12, 1.05, and 0.97, respectively, at the employment rates
of 58, 60, and 62 percent. Overall, these values are bigger than typical micro
estimates, but they remain in a moderate range. In particular, a very high
elasticity—in fact, inﬁnity—generated by a lottery economy with a homogeneous workforce (in which the reservation wage distribution is degenerate)
does not survive serious heterogeneity.
Finally, we would like to emphasize that, when labor supply is indivisible,
the slope of the aggregate labor supply schedule is mostly determined by the
distribution of reservation wages rather than by the willingness to substitute
leisure intertemporally. In fact, the aggregate labor supply is independent of γ
in our economy. With a binary choice of hours, utility of market participants
¯ 1+1/γ
and non-participants differs by a constant term, B h
[Recall (6)]. Given
1+1/γ
γ , we adjust B (the weight parameter on disutility from working) to match
the 60 percent employment rate in the steady state, leaving the above constant

Y. Chang and S. Kim: On the Aggregate Labor Supply

Table 3 Labor Supply Elasticity Implied by the Reservation Wage
Distribution
Employment Rate
E = 60%

E = 58%
1.12

E = 62%

1.05

0.97

Notes: The numbers reﬂect the elasticity of the labor market participation rate with respect to reservation wage (evaluated at employment rates of 58, 60, and 62 percent) based
on the reservation wage distribution in the steady state.

term unchanged. As a result, the steady state reservation-wage distribution
remains the same regardless of γ .

Comparison with the Representative Agent Model
We compare the volatility of hours from our model economy to that of
the representative agent economy. Both model economies will be subject to
identical stochastic aggregate productivity shocks that resemble that of the
post-war total factor productivity (Solow residual).
The value function of the representative agent, V R (K, λ), is
V R (K, λ) = max lnC − B
C,H

H 1+1/γ
+ βE V R (K , λ ) λ
1 + 1/γ

subject to
K = F (K, H, z) + (1 − δ)K − C.
Except for β, the same parameter values are used, β = 0.99.12 Fluctuation of
the heterogeneous agent model is solved by the method developed by Krusell
and Smith (1998). Figure 5 shows the sample paths of total hours worked
(percentage deviations from the steady states), respectively, from the heterogeneous agent economy and the representative agent economy, γ = 0.4. In
the face of aggregate productivity shocks whose stochastic process resembles
that of the post-war total factor productivity, hours of work from the heterogeneous agent economy exhibit a much greater volatility than those of the
representative agent model.
12 B is a free parameter in a sense that it does not affect the dynamics around the steady

state.

36
5.

Federal Reserve Bank of Richmond Economic Quarterly
SUMMARY

We demonstrate that, at the aggregate level, the labor supply elasticity can signiﬁcantly depart from the microelasticity. In an economy where households
make decisions on labor market participation, the slope of the aggregate labor
supply curve is determined by the distribution of reservation wages rather than
by the willingness to substitute leisure intertemporally. We present a model
economy where households face uninsurable idiosyncratic income shocks.
While the model is parsimonious, the cross-sectional distributions of earnings
and wealth are comparable to those in the U.S. data. We ﬁnd that the aggregate labor supply elasticity of such an economy is around 1.0—despite the
low intertemporal substitution elasticity of leisure, assumed to be 0.4. The
equilibrium approach of business cycle analysis has been criticized on the
grounds that it requires an elasticity higher than the intertemporal substitution
elasticity estimated from the microdata. Our analysis shows that, while the
aggregate labor elasticity can depart from a microelasticity, it remains in a
moderate range as the reservation wage distribution is dispersed.

REFERENCES
Aiyagari, Rao S. 1994. “Uninsured Idiosyncratic Risk and Aggregate
Savings.” Quarterly Journal of Economics CIX: 659–83.
Auerbach, A. J., and L. J. Kotlikoff. 1987. Dynamic Fiscal Policy.
Cambridge, U.K.: Cambridge University Press.
Bencivenga, Valerie. 1992. “An Econometric Study of Hours and Output
Variation with Preference Shocks.” International Economic Review (33):
448–71.
Benhabib, Jess, Richard Rogerson, and Randall Wright. 1991. “Homework
in Macroeconomics: Household Production and Aggregate
Fluctuations.” Journal of Political Economy 99: 1166–87.
Blundell, Richard, and Thomas MaCurdy. 1999. “Labor Supply: A Review
of Alternative Approaches.” In Handbook of Labor Economics, Vol. 3A.
Ed. O. Ashenfelter and D. Card. Amsterdam: North Holland: 1599–695.
Chang, Yongsung, and Sun-Bin Kim. 2004a. “From Individual to Aggregate
Labor Supply: A Quantitative Analysis Based on a Heterogeneous Agent
Macroeconomy.” Manuscript, Federal Reserve Bank of Richmond.
. 2004b. “Heterogeneity and Aggregation in the Labor
Market: Implications for Aggregate Preference Shocks.” Manuscript,

Y. Chang and S. Kim: On the Aggregate Labor Supply

Federal Reserve Bank of Richmond.
Christiano, Lawrence J., and Martin Eichenbaum. 1992. “Current
Real-Business Cycle Theories and Aggregate Labor-Market
Fluctuations.” American Economic Review 82: 430–50.
Greenwood, Jeremy, and Zvi Hercowitz. 1991. “The Allocation of Capital
and Time over the Business Cycle.” Journal of Political Economy 99:
1188–215.
Hansen, Gary D. 1985. “Indivisible Labor and the Business Cycle.” Journal
of Monetary Economics 16: 309–27.
Heckman, James. 1979. “Sample Selection Bias as a Speciﬁcation Error.”
Econometrica 47 (1): 153–62.
Judd, Kenneth L. 1987. “The Welfare Cost of Factor Taxation in a Perfect
Foresight Model.” Journal of Political Economy 95(4): 675–709.
Killingsworth, Mark R., and James Heckman. 1986. “Female Labor Supply.”
Handbook of Labor Economics, Vol. 1. Ed. O. Ashenfelter and R.
Layards. Amsterdam: North Holland: 103–204.
Krusell, Per, and Anthony Smith. 1998. “Income and Wealth Heterogeneity
in the Macroeconomy.” Journal of Political Economy 106: 867–96.
Kydland, Finn E., and Edward Prescott. 1982. “Time to Build and Aggregate
Fluctuations.” Econometrica 50: 1345–70.
Lucas, Robert E. Jr., and Leonard Rapping. 1969. “Real Wages,
Employment, and Inﬂation.” Journal of Political Economy 77: 721–54.
Pencavel, John. 1986. “Labor Supply of Men.” Handbook of Labor
Economics, Vol. 1. Ed. O. Ashenfelter and R. Layards. Amsterdam:
North Holland: 3–102.
Rogerson, Richard. 1988. “Indivisible Labor, Lotteries and Equilibrium.”
Journal of Monetary Economics 21: 3–16.

Depression-Era Bank
Failures: The Great
Contagion or the Great
Shakeout?
John R. Walter

eposit insurance was created, at least in part, to prevent unfounded
bank failures caused by contagion. The legislation that created the
Federal Deposit Insurance Corporation (FDIC) was driven by the
widespread bank failures of the Great Depression. In the years immediately
before the 1934, when the FDIC began insuring bank deposits, over onethird of all extant banks failed. Many observers argue that these failures
occurred because the banking industry is inherently fragile since it is subject to
contagion-induced runs. Fragility arises because banks gather a large portion
of their funding through the issuance of liabilities that are redeemable on
demand at par, while investing in illiquid assets. Speciﬁcally, loans, which
on average account for 56 percent of bank assets, tend to be made based on
information that is costly to convey to outsiders. As a result, if a signiﬁcant
segment of bank customers run, that is, quickly require the repayment of their
deposits, the bank is unlikely to be able to sell its assets except at a steep
discount. Bank failure can result.
But do Depression-era bank failures imply the need for governmentprovided deposit insurance, or is there another explanation of the failures
other than contagion and inherent fragility? Some observers question the
view that banks are inherently fragile. They argue instead that the banking
industry developed various market-based means of addressing runs such that
the danger of failure was reduced. They also argue that the banks that failed
The author beneﬁted greatly from comments from Tom Humphrey, Ned Prescott, John Weinberg, and Alex Wolman. Able research assistance was provided by Fan Ding. The views
expressed herein are not necessarily those of the Federal Reserve Bank of Richmond or the
Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 91/1 Winter 2005

Federal Reserve Bank of Richmond Economic Quarterly

in response to runs were weak and likely to fail regardless of runs (Calomiris
and Mason 1997; Benston and Kaufman 1995).
If not fragility, what might explain the widespread failures before 1934?
One possible explanation is that the banking industry was experiencing a
shakeout, not unusual in industries that have previously enjoyed signiﬁcant
growth. The number of banks had grown briskly from the mid-1880s until
1921. Beginning in 1921, bank failures increased signiﬁcantly, such that the
number of banks began a precipitous decline that continued until 1934. There
are reasons to think that the industry had become overbuilt and that macroeconomic shocks, in conjunction with overbuilding, produced a retrenchment
in the industry that lasted for the next 12 years. Indeed, many authors point to
the relationship between bank failures and weakening economic conditions1 .
This article suggests that overbuilding could have made the banking industry
all the more sensitive to macroeconomic shocks.
A number of other industries provide examples of growth followed by
shakeouts, the most recent of which is the telecom industry. If a large portion
of Depression-era banking failures were the result of a shakeout rather than
contagion, an important argument for deposit insurance is undercut.
Though the termination of bank failures and the creation of the FDIC
in 1934 occurred simultaneously, implying that contagion must have been at
work, other explanations are just as credible. First, deposit insurance augmented the proﬁts of risky banks, protecting them from failure. Second, the
creation of deposit insurance undercut a market process that caused supervisors to close troubled banks quickly.

GROWTH IN THE NUMBER OF BANKS

The number of U.S. banks grew rapidly from 1887 until 1921 (Figure 1).
Much of the increase coincided with improving economic conditions. Yet,
commentators also claim that a good portion of the increase resulted from a
statutory change that lowered the minimum capital required to form a new bank
as well as careless application of entry standards by regulators. Many of the
new banks were viewed by commentators as being ill-prepared for the business
of banking. In other words, too many banks were formed without adequate
ﬁnancial or managerial resources. The banking market was overbanked.
As shown in Figure 1, the number of banks began growing rapidly in the
late 1880s. The initial run-up in the number of banks followed an economic
recovery occurring in 1885 and 1886. The increase in the number of banks
was rapid enough, and the size of new banks small enough, to drive down the
U.S. average bank size fairly signiﬁcantly. The average size bank shrank from
1 Temin (1976, 83–95) discusses banking failures that resulted from macroeconomic weakness
during the Depression.

J. R. Walter: Depression-Era Bank Failures

Figure 1 Number of Banks
35,000

30,000

25,000

20,000

15,000

10,000

5,000

0
1834 1844 1854 1864 1874 1884 1894 1904 1914 1924 1934 1944 1954 1964

$1.04 million in 1886 to a low of $660,000 in 1896 and did not return to its
1886 level until 1916. The growth in number of banks was much faster than
the pace of economic growth, so that the increase in the number of banks is
still quite apparent even when the number of banks is deﬂated by the level of
real GDP (Figure 2).
Most commentators focus on the increase in the number of banks, especially of very small banks, after the beginning of the 20th century. Figure
1 shows that the growth in the number of banks was indeed rapid from 1900
until 1921. An important explanation for the growth in the number of banks
during these two decades was the reduction in the minimum capital required to
form a bank (Mengle 1990; Wheelock 1993). Speciﬁcally, the Currency Act
of 1900 lowered from $50,000 to $25,000 the minimum capital needed from
investors to start a national bank. In turn, over the next ten years, two-thirds
of newly formed banks were quite small, averaging capital of only slightly
more than the minimum $25,000 (Mengle 1990, 6).
Beyond this reduction in minimum capital, regulatory laxity was also
thought to have contributed to the rapid increase in the number of banks. For
example, Federal Reserve analysts concluded that during the ﬁrst two decades
of the 20th century “insufﬁcient attention was paid to the qualiﬁcations of those

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Number of Banks Divided by Real GDP (2000 Dollars)
60.00

50.00

40.00

30.00

20.00

10.00

0.00
1850

1890

1930

1970

to whom charters were granted” (Federal Reserve Board 1933, 63–65). These
observers saw the banking industry as overbuilt by 1920 (Federal Reserve
Board 1933, 67).
Most of these new small banks were formed in small towns and rural
communities—especially in the corn and cotton belts of the country. Rising
prices of farm commodities along with rising farm real estate values may
have played a signiﬁcant role in the attractiveness of rural banking to new
investors (Federal Reserve Board 1933, 65). More generally, economic growth
was strong between 1887 and 1920, with the annual rate of growth of GDP
averaging over 6 percent for the period. GDP growth was especially strong
during 1916, and in the two years of the U.S. participation in World War I,
1917 and 1918.
The formation of state deposit insurance systems in a number of states
may also have contributed to a perception of safety and allowed the rapid
growth of new small banks. Following the banking panic of 1907, eight
states adopted such programs for state-chartered banks (Wheelock 1993, 860).
Using regression analysis, Wheelock (1993, 865) ﬁnds that the presence of
deposit insurance systems encouraged bank formation.

J. R. Walter: Depression-Era Bank Failures

Figure 3 Number of Banks per Thousand Persons
0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00
1834 1844 1854 1864 1874 1884 1894 1904 1914 1924 1934 1944 1954 1964

An important trend associated with rapid entry was gradually declining
banking proﬁtability. Contemporary writers blamed declining returns on increased competition from new banks. For example, a 1933 Federal Reserve
study claimed that “the overbanked condition, which reached its peak shortly
after 1920, caused units struggling for existence to increase services to their
clients, thus adding to expenses. It served to introduce into many banks high
risk and marginal business” (Federal Reserve Board 1933, 67). Net proﬁts
relative to assets for the industry fell fairly consistently from 1900 through
1920, from about 2.55 percent to about 1.70 percent (Federal Reserve Board
1933, 67).2 Bank regulators also noted declining loan standards as rapid entry
occurred (Federal Reserve Board 1933, 4).
By several measures the banking industry appears to have become overbuilt. As noted earlier, the numbers grew faster than did overall economic
growth. Additionally, as shown in Figure 3, the number of banks increased
much more rapidly than did U.S. population. The expansion in the number
of competitors may also have been driving down bank proﬁtability and loan
2 Earnings ﬁgures are for national banks only. Until the formation of the Federal Deposit
Insurance Corporation, ﬁgures on state bank earnings were not collected in any uniform manner.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Number of Bank Failures
4,500
4,000
3,500
3,000
2,500
2,000
1,500
1,000
500
0
1834 1844 1854 1864 1874 1884 1894 1904 1914 1924 1934 1944 1954 1964

standards beginning as early as 1900. This declining proﬁtability implies that
even without the agricultural shocks of the 1920s, and the macroeconomic
shocks of the Depression, the banking industry would have experienced some
retrenchment.

1921–1933 BANKING FAILURES

Banking failures, which began growing in number in the early 1920s, coincide
with regional agricultural problems, and later with broader economic problems of the Great Depression. Analysts argue that contagion and branching
restrictions account for a signiﬁcant portion of the failures.
The number of U.S. banks peaked in 1921 at about 31,000 banks. The
year also produced the beginning of a period of rapid annual rates of bank
failure. In 1921 there were 505 failures. As shown in Figure 4, during most of
the next eight years failures remained between 500 and 1,000 per year. From
1930 through 1933 failure rates were in the thousands.
The shift in banking failures in 1921 was precipitated by widespread crop
failures of that year. Farm problems were evident in falling farm real estate
values in corn- and cotton-producing regions. Real estate values fell each year

J. R. Walter: Depression-Era Bank Failures

from 1921 through 1930 (White 1984, 126). The bank failures of the 1920s
were heaviest in states with the most rapid growth prior to the 1920s (Wicker
1996, 7). Difﬁculties suffered by farmers in the Midwest seem to have driven
much of the failure.
Between 1921 and 1930, half of all small banks in agricultural regions
failed. Larger banks, however, suffered much less. For example, on average
between 1926 and 1930, 74 percent of the smallest banks, those with assets
less than $150,000, had weak proﬁts. Here, weak proﬁts are deﬁned as return
on equity of less than 6 percent. In contrast, only 21 percent of those banks in
the largest size category, with assets greater than $50 million, produced proﬁt
rates averaging below 6 percent between 1926 and 1930.
A regulatory shift may also account for the disappearance of some small
banks. In the early 1920s the Comptroller of the Currency, the agency that
regulates national banks, dropped its branching prohibitions (Mengle 1990,
6). In turn, the number of bank branches grew from 1,400 to 3,500 between
1921 and 1930 (Calomiris and White 2000, 170). These new branches would
have brought fresh competition to banking markets, and since branch banks
probably had advantages in diversity and scale over small unit banks, unit
banks would have been imperiled. Therefore, this liberalization of branching
restrictions acted as a shock to small bank proﬁtability, occurring in the 1920s.
Some contemporary commentators claim that improving transportation
technology accounts for the decline of small banks, which were once protected
from competition by the costs their customers faced to travel to other towns
and cities to conduct banking business. These small banks were suddenly
faced with new competition once customers’ travel costs fell. The growing
availability of the car opened the opportunity to purchase services, including
banking services, in central cities (Wheelock 1993).
While the number of banking failures (and therefore the decline in the
number of banks) grew rapidly in the 1920s, it grew even more rapidly after
the onset of the Depression. Between 1930 and 1932, the number of failures
per year averaged 1,700. In 1933, slightly more than 4,000 banks failed.
Contagion is often cited to explain the rapid pace of failures between
1930 and 1933. Contagion could work as follows. A prominent bank fails,
and because there is no federal deposit insurance protection, depositors of
the failed bank suffer losses.3 Customers of other banks learn of the failure,
believe that their bank might suffer the same fate, and run their banks—i.e.,
demand cash repayment of their deposits. Since bank assets are typically
tied up in loans and securities, to meet these demands for cash, banks must
liquidate these assets. If many banks attempt to sell their securities, prices will
fall, and banks will suffer losses on the sales. Further, because outsiders have
3 Between 1907 and 1917, eight states created deposit insurance systems (White 1983, 207–
18). By 1928, all of these state systems had failed.

Federal Reserve Bank of Richmond Economic Quarterly

difﬁculty determining the worth of bank loans, they will sell at a steep discount,
i.e., at ﬁresale prices. Therefore runs of otherwise healthy banks could cause
such banks to suffer losses large enough that they would be unable to meet all
depositor demands, creating failures of the banks experiencing the runs. The
process would become a cycle, spreading widely.
Friedman and Schwartz (1963) identify three banking crises during the
Depression involving widespread runs. During these crises, they, along with
others, argue that waves of widespread runs created by a “contagion of fear”
produced bank illiquidity and the failure of otherwise healthy banks. They
hold that much of the bank failure was the result of such contagion and that
healthy banks failed as a result.
Branching restrictions are also viewed as an important explanation of
bank failures (Mengle 1990, 7–8). While in the 1920s branching restrictions
were liberalized for national banks, most states placed severe restrictions on
branching, or banned it altogether. As of 1929, 22 states prohibited branching
and another ten states restricted it somewhat (Mengle 1990, 6). Branching
restrictions prevented banks from diversifying their lending, forcing them to
concentrate their lending in one geographic area. The lack of diversity made
banks more susceptible to failure caused by localized economic weaknesses.
Therefore, oddly enough, both branching restrictions and the branching liberalization, discussed earlier, could have contributed to bank failures.

CONTAGION IS AN INCOMPLETE EXPLANATION
OF FAILURES

Contagion is an incomplete explanation of banking failures for two reasons.
First, contagion was not a factor in the failures that occurred in the 1920s.
The bank failures of the 1920s were not caused by and did not create banking
panics, that is, banking runs or heavy withdrawals of currency. There was
no increase in currency in circulation during the period (Wicker 1996, 1). If
factors other than contagion were important in the 1920s, it seems likely that
these same factors would also be at work in the 1930s as well. Therefore, contagion is unlikely to account for at least some of the failures in the Depression
years of the 1930s.
Second, in their inﬂuential work on U.S. banking and monetary history,
Friedman and Schwartz (1963) maintain that the bank failures of the 1930s
were contagion-induced. Later reviews, however, cast doubt on the contagion
explanation. Using regression analysis to identify factors that accounted for
individual bank failures during the 1930 crisis, which occurred in November
and December of that year, White (1984) ﬁnds that these failures were no different from those occurring in the 1920s. In other words, he ﬁnds no evidence
that these failures were driven by contagion-sparked illiquidity. Instead, these

J. R. Walter: Depression-Era Bank Failures

failures were the result of bad loans. Friedman and Schwartz (1963) give
special emphasis to the failure of the Bank of the United States in December
1930 as a cause of contagion-induced bank failures. Wicker (1996, 36–38)
questions this view, concluding that the bank’s failure did not lead to major
deposit withdrawals and could not have accounted for the failures of other
banks.
Further, of the bank failures that took place between 1930 and 1932,
more than 60 percent occurred outside of panic months (Wicker 1996, 1).
While some of these failures might have been the residual effect of runs, it
seems likely that most of the failed banks had ﬁnancial problems unrelated to
runs. If an otherwise healthy bank survived a panic, it would have survived the
aftermath. Last, Calomiris and Mason (1997) examined the ﬁnancial condition
of Chicago banks during the 1932 banking panic in that city. They found that
“while depositors did confuse panic survivors with panic failures, the failure
of solvent banks did not result from that confusion.” Calomiris and Mason
note that the Chicago situation may have been special since Chicago banks met
the panic by joining forces to protect banks the group viewed as solvent. Such
combined efforts would have been more difﬁcult for the many far-ﬂung banks
outside of major cities. Nevertheless, through correspondent relationships,
support of banks could have transpired even in a sprawling banking system.
Still, one might wonder: if contagion was not the cause of bank failures,
then why did bank failures largely come to a halt with the creation of federal
deposit insurance in 1934 (as seen in Figure 4)? If, as I argue, a portion of
the bank failures of the 1920s and 1930s were the result of a typical shakeout,
there is no reason to expect the shakeout to have ended with the creation of the
FDIC. One would only expect failures to be ended by the FDIC’s creation if
they were caused by contagion, a problem overcome by the creation of federal
deposit insurance.
Part of the reason for the cessation of failures, and one that is not dependent on the existence of contagion, is the shifting economic backdrop.
Those inherently low-proﬁt banks that were created during the rapid growth
of the banking industry would have been the ﬁrst to be driven to insolvency
by the extreme macroeconomic problems of the early 1930s. In other words,
economic difﬁculties concentrated the shakeout in the early 1930s. As a result, low-proﬁt banks created during the growth of the industry—banks which
might have continued to fail over a number of years after 1933—were quickly
expunged by the severe economic times. The severity of the macroeconomic
problems is shown by the declines in economic output, which fell by 8.61
percent in 1930, and by 6.42 percent, 13.00 percent, and 1.27 percent in 1931,
1932, and 1933, respectively. But then in 1934 economic output began growing rapidly, increasing by 10.81 percent, and averaged 7.08 percent from 1934
through 1939 so that banks were strong enough to weather the early 1930s the
following years.

Federal Reserve Bank of Richmond Economic Quarterly

An additional reason exists—not dependent on contagion—as to why failures ended at the same time the FDIC was formed: Prior to the FDIC’s creation,
depositors had strong incentive to monitor their banks’ health and, in the case
of signs of weakness, withdraw deposits. When depositors withdrew funds,
government supervisors were forced to review the state of the bank and either
close it or allow it to reopen if shown healthy. Once deposits gained FDIC
protection, this disciplining mechanism was removed. Without the mechanism, the opportunity for supervisors to forbear arose. Certainly, in the years
immediately after the widespread bank failures of the 1920s and early 1930s,
it seems that supervisors would tend to err on the side of stability and be
reticent to close banks unless the evidence of a bank’s problems was quite
strong. Consequently, that failures largely ceased at the same time the FDIC
was created is not necessarily evidence that contagion was the cause of most
bank failures.
Further, FDIC insurance provided a signiﬁcant proﬁt-boosting subsidy to
the riskiest banks. With the government backing their deposits, in 1934 all
banks could suddenly gather deposits at the risk-free interest rate. Those banks
that might have failed in the near future—the riskiest banks—beneﬁted most.
Unless depositors were completely oblivious to their bank’s health, in the absence of deposit insurance, such banks would have had to pay depositors high
interest rates. Had the FDIC charged risk-adjusted deposit insurance premia,
the riskiest banks would have enjoyed no beneﬁt. But premia were calculated
as a simple percentage of deposits. Therefore, troubled banks enjoyed a sudden boost in their proﬁts due to the introduction of FDIC insurance. Failures
would naturally be minimized, not because contagion was halted, but instead
because FDIC insurance provided a subsidy to those banks most likely to fail.

SHAKEOUTS IN OTHER INDUSTRIES

Rapid increase in the number of producers followed by an equally rapid decline
is a pattern not only evident in banking, but also in a number of industries.
Examples include automobiles, tires, televisions, penicillin, and most recently,
telecommunications. While the banking industry failures are blamed on heavy
reliance on liabilities that are redeemable upon demand, other factors must
have been at work to produce rapid failures in these other industries since
they are not reliant upon demand liabilities. Perhaps many of the failures in
banking were simply the result of a typical shakeout, driven by factors other
than contagion, as in these other industries.
The growth pattern in banking—a signiﬁcant increase in the number of
banks, followed by a rapid decline—is similar to the growth and shakeout that
a number of industries experienced, industries for which there are no claims
of inherent fragility or contagion-driven runs. Klepper (2002, 37) notes that
“After their commercial introduction, the number of producers of automobiles,

J. R. Walter: Depression-Era Bank Failures

Figure 5 Automobiles
275
Firms
220

165

110
Entry
55
Exit
0
1894

1912

1930

1948

1966

Source: Klepper 2002

tires, televisions, and penicillin initially grew and then experienced a sharp
decline or shakeout.” For example, Figure 5 shows the pattern of growth and
decline for automobiles.
More recently, the same pattern was displayed in the telecommunications
sector.4 In the mid-1990s, three factors together implied great opportunities
for growth in the industry. First, rapidly growing use of the Internet generated
an expanded demand for data transmission services over phone, cable, and
long-haul ﬁber networks. Observers claimed that Internet use was doubling
every year, or even several times a year.
Second, an important regulatory change was brought to the telecommunications industry by the Telecommunications Act of 1996. The goal of the
Act was to introduce new competition to local telephone service, which was
largely monopolized by the regional Bells. It opened local telephone service
to competition, for example, by requiring incumbent local service providers
4 See Couper, Hejkal, and Wolman (2003) for a thorough review of the telecommunications
industry’s growth in the 1990s and shakeout that began in 2000.

Federal Reserve Bank of Richmond Economic Quarterly

to sell entrants access to the networks that reach homes and businesses. It
was thought that entrants would provide local phone service and that selling
access would avoid duplication of existing telephone lines to individual homes
and businesses. The entrants, known as competitive local exchange carriers
(CLECs), rapidly increased in number and earnings. From 30 CLECs in 1996,
their number had grown to 711 in 2000. At the same time, revenues of the
CLECs rose from $5 billion to $43 billion (Couper et al., 15).
Third, advances in ﬁber optic technology were occurring rapidly in the
mid-1990s, lowering the cost of providing data and voice services to households
and businesses. Existing ﬁrms, as well as founders of new ﬁrms, expected
these factors to open huge new markets and responded by rapidly increasing
investment in telecommunications equipment and communications lines.
However, as it turned out, by 2000 the promise of the 1996 Act had not
been borne out, long-haul ﬁber communications lines were signiﬁcantly overbuilt, and the overall economy began to slow. The Act did not lead to nearly as
much growth for competitors in local service. The Act’s pricing ambiguities
meant that rules that would allow entrants to buy access into homes and businesses were slow to be developed by regulatory agencies and were held up
by lawsuits. Overcapacity in ﬁber lines was the result of rapid improvement
in the technology for transmitting data over these lines, meaning that fewer
were needed than expected. Further, the growth in demand for data communications, while rapid, was not as rapid as expected (Couper et al., 13 and
19). Beginning in mid-2000, the telecom industry began a rapid retrenchment
that involved huge numbers of failures of new ﬁrms that had only recently
appeared to have bright futures. For example, the number of CLECs declined
by about 80 percent from 1999 to 2001 (Grossi, 4).

EXPLANATION OF THE BANKING SHAKEOUT

Several important industries displayed a pattern of rapid growth followed by
widespread failure, similar to that in the banking industry. Yet failures in
these industries cannot be blamed on contagion resulting from a reliance on
demandable liabilities, implying that something else may also have been at
work during the similar boom and bust in banking. Still, these industries
differed from banking: Automobiles, tires, televisions, and penicillin were all
new industries, and the telecommunications industry was experiencing rapid
technological change. Therefore a good bit of instability can be expected as
the efﬁcient industrial structure evolved. In contrast, the banking industry of
the late 19th and early 20th centuries was not new.
While not new, the banking industry was undergoing rapid change. The
industry was a primary source of capital to a nation undergoing rapid technological and industrial change. The expansion of railroads drove down transportation costs. The spread of electronic communication, the telegraph and

J. R. Walter: Depression-Era Bank Failures

telephone, rapidly lowered communications costs. As noted earlier, the popularity of the automobile meant that communities were less isolated from one
another, and commerce was better able to ﬂow across local communities. Also,
the growth of the corporation as a business structure and the issue of debt by
corporations radically changed the ﬁnancial structure of the business world.
Further, branching and capital regulations in banking were being signiﬁcantly
modiﬁed.
In an environment of wide-ranging industrial, technological, and regulatory change, it should not be surprising that the banking industry would
struggle in ways similar to a new industry. Bank organizers perceived proﬁt
opportunities in the changing setting and rapidly formed banks to take advantage of such opportunities. In doing so, they drove down bank size and
proﬁtability, as noted earlier. Ultimately they caused the industry to become
overbuilt, and failures ensued.
Were bank organizers acting irrationally? Not according to theories economists have advanced to explain the fairly common phenomenon of industry
shakeout. Such theories argue that ﬁrms can often be expected to expand new
investment too far. One such theoretical explanation argues that shakeouts are
a result of investments in research and development (R&D) (Klepper 2002,
38).5 Under this explanation, ﬁrms invest in R&D to lower their costs, but the
cost advantage grows with size, such that large ﬁrms beneﬁt more from R&D.
Further, some ﬁrms are better at R&D than others.
Firms enter and make R&D investments to acquire the high margins that
are expected to accrue from such actions. Instead, rapid entry drives down
proﬁt margins. Eventually entry stops, and smaller ﬁrms, which have higher
per-unit R&D costs, fail. Firms that make less productive use of R&D expenditures also fail, since their costs will be relatively high. In this environment,
entry seems to progress too far, since many of the ﬁrms that were initially
proﬁtable fail when proﬁt margins are driven down. Unanticipated increases
in costs or decreases in earnings can also cause failure.
More broadly, overinvestment works as follows. A technological or business process innovation occurs, and ﬁrms make investments to take advantage
of the new technology. Firms are uncertain concerning how much their output might increase as they implement the new technology but must invest
before knowing. Alternatively, ﬁrms are uncertain of the extent of demand
for their new product, but must invest before knowing. Ultimately ﬁrms often
overshoot, proﬁts decline, and the least efﬁcient ﬁrms fail.
Was such overshooting likely in banking in the late 19th and early 20th
centuries? Evolving telecommunications and transportation technology as
well as shifting ﬁnancial arrangements were inﬂuencing both the technology
5 Alternative explanations of boom and shakeouts are offered by Jovanovic and MacDonald
(1994) and Barbarino and Jovanovic (2004).

Federal Reserve Bank of Richmond Economic Quarterly

of banking and of the ﬁrms to which banks make loans. In this environment,
existing banks and potential investors in new banks faced a great deal of
uncertainty about the proper scale of the industry, and entry was rapid, relative
to GDP growth and population growth. Average proﬁts were driven down in
the banking industry, and after 1921, while larger banks remained strong, small
bank proﬁts fell signiﬁcantly. Clearly the demand shocks of the 1920s and
the Depression played a major role in the shakeout in banks, but overbuilding
appears to have been of signiﬁcant importance.

SUMMARY

As the U.S. economy grew and evolved in the late 19th and early 20th centuries,
the banking industry grew even more rapidly, especially in raw numbers of
banks, as well as in assets relative to GDP and numbers relative to population.
Contemporary analysts maintained that the growth produced an overbuilt industry. Ultimately, failures shrank the number of banks. Failures ﬁrst became
signiﬁcant in the early 1920s, continued throughout the 1920s, and became
even more numerous during the Depression. They largely ended in 1934, at
the time of the formation of the FDIC.
A long-held explanation for bank failures during the Depression is
contagion, whereby the initial failure of one bank leads to widespread runs
on other banks and their failure. According to this explanation, many of the
Depression-era failures were inappropriate, meaning that the failed banks were
solvent and would have survived without contagion-induced runs. The solution to contagion was deposit insurance provided by the federal government,
which put a stop to failures.
Still, given that the cycle of failures began in the early 1920s, long before
contagion was evident, one must question contagion as the overriding cause.
Instead the banking industry appears to have been experiencing a shakeout,
exacerbated by weakened economic conditions during the Depression. While
at ﬁrst blush, the fact that failures stopped virtually simultaneously with the
formation of the FDIC implies that contagion must have been at work, other
explanations for this simultaneity are just as credible. For example, risky
bank proﬁts were certainly boosted by the provision of deposit insurance at
premiums that did not reﬂect bank risk, protecting these banks from failure.
Further, the process that drove supervisors to quickly close troubled banks
was undercut once deposit insurance was established.

J. R. Walter: Depression-Era Bank Failures

REFERENCES
Barbarino, Alessandro, and Jovanovic, Boyan. 2004. “Shakeouts and Market
Crashes.” National Bureau of Economic Research Working Paper
10556. Also available online at http://www.nber.org/papers/w10556.pdf
(accessed 4 February 2005).
Benston, George J., and George G. Kaufman. 1995. “Is the Banking and
Payments System Fragile?” Journal of Financial Services Research
9: 209–40.
Calomiris, Charles W., and Joseph R. Mason. 1997. “Contagion and Bank
Failures During the Great Depression: The June 1932 Chicago Banking
Panic.” American Economic Review 87 (December): 863–83.
, and Eugene N. White. 2000. “The Origins of Federal
Deposit Insurance.” U.S. Bank Deregulation in Historical Perspective.
Cambridge: Cambridge University Press, 164–211.
Couper, Elise A., John P. Hejkal, and Alexander L. Wolman. 2003. “Boom
and Bust in Telecommunications.” Federal Reserve Bank of Richmond
Economic Quarterly 89 (Fall): 1–24.
Federal Reserve Board. 1933. Banking Proﬁts, 1890–1931. Federal Reserve
Committee on Branch, Group, and Chain Banking.
Friedman, Milton, and Anna Jacobson Schwartz. 1963. A Monetary History
of the United States, 1867–1960. Princeton: Princeton University Press
(for the National Bureau of Economic Research).
Grossi, Michael. 2004. “A New Ear in Radio Broadcasting: The Coming of
Broadband.” Flashpoint, Commentary from Adventis. Adventis
Corporation.
Jovanovic, Boyan, and Glenn MacDonald. 1994. “The Life Cycle of a
Competitive Industry.” Journal of Political Economy 102 (April):
322–47.
Klepper, Steven. 2002. “Firm Survival and the Evolution of Oligopoly.”
Rand Journal of Economics 33 (Spring): 37–61.
Mengle, David L. 1990. “The Case for Interstate Branch Banking.” Federal
Reserve Bank of Richmond Economic Review 76
(November/December): 3–17.
Temin, Peter. 1976. Did Monetary Forces Cause the Great Depression? New
York: W. W. Norton and Company, Inc.

Federal Reserve Bank of Richmond Economic Quarterly

Wheelock, David C. 1993. “Government Policy and Banking Market
Structure in the 1920s.” The Journal of Economic History 4 (December):
857–79.
White, Eugene N. 1983. The Regulation and Reform of the American Banking
System, 1900–1929. Princeton, New Jersey: Princeton University Press.
. 1984. “A Reinterpretation of the Banking Crisis of 1930.”
Journal of Economic History 44 (March): 119–38.
Wicker, Elmus. 1996. The Banking Panics of the Great Depression. New
York: Cambridge University Press.

Banking Markets in a
Decade of Mergers: A
Preliminary Examination of
Five North Carolina
Markets
John A. Weinberg

he decade of the 1990s was a period of dramatic consolidation in
the banking industry. From 1990 to 2000, the number of banking
institutions in the United States fell from 12,212 to 8,252. During
this period, the percent of all banking assets held by the largest 1 percent of
all banks rose from 54 percent to 70 percent. This consolidation was partly
facilitated by the 1994 legislation allowing full interstate branching. Further
legislation in 1999 made consolidation across the broader ﬁnancial services
industry easier by loosening restrictions on the combination of commercial
and investment banking activities in one company.
On its face, the consolidation of the 1990s appears to be part of a longer
wave that began in the mid-1980s. The total number of banks in the United
States was notably stable at around 14,000 for a number of years prior to 1986,
then began a steady decline. The striking difference in trends is captured in
Figure 1.1 Unsurprisingly, this sustained decline in the number of banks is
associated with an historically high level of merger activity, as seen in Figure
2. These ﬁgures present a picture of structural change in the banking industry
stretching over a period of close to two decades. There is a distinct difference,
Thanks to Patricia Wescott and Shelia Jackson for assistance compiling the data used in this
paper. Thanks also to John Walter, Kartik Athreya, and Margarida Duarte for the readings
of and comments on an earlier draft, and to Tom Humphrey for his editorial guidance. The
views expressed herein are the author’s and do not represent the views of the Federal Reserve
Bank of Richmond or the Federal Reserve System.
1 The same ﬁgure appears in Ennis (2004), as does a more detailed description of the aggregate trends in failures, mergers, and entry of new banks.

Federal Reserve Bank of Richmond Economic Quarterly Volume 91/1 Winter 2005

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Number of Banks in the United States, 1972–2002
16,000

14,000
Total Institutions at Year End

12,000

10,000

8,000

6,000

4,000

2,000

0
1974

1978

1982

1986

1990

1994

1998

2002

however, between the earlier and later parts of this period. In the 1980s and
through the recession of the early 1990s, the banking industry was in a period
of crisis, with many undercapitalized or insolvent institutions. Consequently,
there was a peak in the number of bank failures in 1988, and much of the
merger activity represented the acquisition of weak banks by stronger ones.
In contrast to the earlier part of the period, the banking system as a whole has
been well capitalized since the mid-1990s, and bank failures have been few
in number. Further evidence for differences between the two periods can be
seen in the behavior of the concentration of banking assets. As noted above,
the percent of assets held by the top 1 percent of banks rose signiﬁcantly in
the 1990s. Before 1990, however, this measure of aggregate concentration
changed very little.
Given the difference in the overall condition of the banking industry, the
forces driving merger decisions may have been different around the two peaks
in merger activity in Figure 2. In the earlier part of the period, both acquirers’
strategic considerations and the needs associated with the resolution of weak
institutions were important in determining what mergers occurred. In the later
part of the period, acquirers’ interests were probably predominant. One such
consideration is the desire of an acquiring institution to establish or solidify

J. A. Weinberg: Banking Markets and Mergers

Figure 2 Bank Mergers, 1972–2002
900

800

700

600
Total Mergers
500

400

300

200

100

0
1974

1978

1982

1986

1990

1994

1998

2002

its position in particular product market segments. That is, a bank with a
large share of some of the markets in which it participates might seek to
enlarge its share through acquisitions, so as to exercise more control over
market prices and enjoy the enhanced proﬁts that come with such market
power. Alternatively, mergers might be simply a means of transferring banking
resources from less to more efﬁcient users in response to changes in ﬁrmspeciﬁc or marketwide conditions. This article explores the effect of the
merger wave of the 1990s on product markets by examining the evolution
of market structure in metropolitan retail banking markets over this period.
Speciﬁcally, this article explores the changes in market structures in ﬁve North
Carolina metropolitan areas and asks whether these changes shed light on
alternative views of the forces driving mergers.

LOCAL BANKING MARKETS

Banks participate in many distinct markets. They provide credit to households
and businesses, and credit markets can be further segmented along such lines
as the type of household loan (e.g., credit card balances or home-purchase
mortgage) or the size of business borrower. Banks also provide deposit

Federal Reserve Bank of Richmond Economic Quarterly

services and the payment services that come with the provision of checkable deposits. Finally, banks provide an increasing array of other ﬁnancial
services, either directly or through holding company afﬁliates.
Antitrust policy toward bank mergers has long been based on the presumption that bank customers look mainly to nearby institutions for at least some
of the ﬁnancial services they purchase. In particular, attention has centered
on services provided to households and small businesses as being most likely
to be local in nature. While technological innovations and the development
of specialized institutions for some products has certainly made many markets less geographically limited, recent studies suggest that local institutions
remain important as providers of certain core banking products to these customers. Such products include consumer and business checkable deposits and
unsecured line of credit lending to small businesses. Kwast et al. (1997), in an
analysis of the Federal Reserve’s Survey of Consumer Finances and National
Survey of Small Business Finances, found that these types of customers tend
to have a primary banking relationship with a local institution. Examining interest rates on retail deposit accounts, a number of studies, including Heitﬁeld
and Prager (2004), ﬁnd evidence of market segmentation in the form of rate
differentials at the level of metropolitan areas. Further, they ﬁnd such differences as recently as 1999, suggesting that markets for such deposit services
continue to be local.
The Federal Reserve’s role in bank merger policy, and that of the other
federal bank regulatory agencies, derives most signiﬁcantly from the Bank
Merger Act, passed in 1960 and amended in 1966. Under this authority,
the Fed examines proposed mergers for possible effects on the competitive
structure and behavior of banking markets. Consistent with the evidence on
the local nature of markets for some retail banking services, this analysis
takes place primarily at the level of local markets. In particular, when there
is geographic overlap between the merging institutions’ retail operations, the
Fed assesses the effects of the merger on the degree of concentration in local
markets. For the purposes of this analysis, the Reserve Banks deﬁne banking
markets in their districts. Many of the deﬁned markets coincide with the
metropolitan areas that are used for other statistical purposes.2 In rural areas,
market deﬁnitions attempt to link areas according to where people engage in
a range of economic activities. Such factors as commuting patterns and the
location of major shopping and health care facilities are important for deﬁning
markets beyond the well-established metropolitan areas.
The approach to merger policy adopted by the banking regulatory agencies
was originally based on the view that banking could be deﬁned as a bundle
of services including deposit services and credit to both households and busi2 The Federal Reserve Bank of Richmond’s metropolitan area markets are based on the RandMcNally designations of “regional metropolitan areas,” or RMAs.

J. A. Weinberg: Banking Markets and Mergers

nesses. The notion of a ﬁxed bundle of services suggested that the relative
sizes of two banks would be fairly consistent across services. Hence, a measure of local market concentration in one service, such as deposits, could be
used as a broader measure of concentration in the entire bundle of services.
Changes in ﬁnancial services markets, especially in services to large businesses and in some consumer credit products, have weakened the connections
among the various services in the traditional bundle. Still, the continuing local
nature of markets for retail deposits and small business lending suggests that
the approach of assessing concentration in local deposits continues to have
some validity in measuring concentration and the possible competitive effects
of mergers.3
In North Carolina there are 19 banking markets that correspond to
metropolitan areas, and 48 rural markets. These markets do not cover the
entire state, since a rural area can remain undeﬁned until there is a merger
case involving banks in the area. The metropolitan markets range in size from
Goldsboro, with a population just over 113,000, to Charlotte, with a population
of over 1.3 million.4 The ﬁve markets examined in this article (and their 2000
metropolitan area populations) are Raleigh (797,071), Greensboro (643,430),
Durham (426,793), Wilmington (274,478), and Rocky Mount (143, 026).

CONCENTRATION AND PRICES

Merger policy is based on the presumption that there is a link between market
concentration and the behavior of market prices. The more concentrated a
market becomes, it is feared, the more likely are market prices to deviate from
the competitive ideal and perhaps approach the pricing of a monopolized market. This concern is founded both on the theory of price-setting in imperfectly
competitive markets and on a long history of empirical studies of the relationship between market concentration and prices charged or proﬁts earned
by sellers. In banking, a number of studies have found a negative correlation
between concentration in local markets and the interest rates paid on retail
deposit accounts.
Concentration is typically measured by the Herﬁndahl-Hirschman Index
(HHI), which is the sum of the squares of sellers’ market shares. That is, in a
market with N sellers, with seller i’s share of market sales (or deposits, as market shares are typically measured in banking) denoted by si , this concentration
3 Gilbert and Zaretsky (2003) provide a history and an assessment of the underlying assumptions in the approach to merger policy in banking.
4 Metropolitan area population numbers are from the 2000 census.

Federal Reserve Bank of Richmond Economic Quarterly

measure is
N

(100si )2 .

HHI =
i=1

The greatest possible HHI, for a fully monopolized market, is 10,000,
while a market consisting of 100 equal-sized sellers would have an HHI of
one. Compared to other potential measures of concentration, for instance, the
total share of the top four ﬁrms in the market, the HHI has the advantage of
being sensitive to both the number of ﬁrms and the inequality of market shares
among the active ﬁrms.
The observation that deposit rates paid to retail customers are negatively
correlated with local market concentration is consistent with the hypothesis
that mergers are motivated by the desire of acquirers to gain market share
and pricing power. Analogously, a large literature ﬁnds that, across many
industries, seller concentration is positively correlated with prices and seller
proﬁts.5 These same observations, however, are also consistent with a very
different theory of the determination of market structure. A critique of the
market-power-based hypothesis, originating with Demsetz (1973), argues that
the observed correlations between concentration and proﬁts or prices could
emerge even if no ﬁrms ever exercised any market power. Consider two distinct
markets with similar demand conditions. In each market, sellers and potential
entrants have access to a production technology with decreasing returns to
scale (for large enough output levels) and ﬁrm-speciﬁc productivity factors
that result in cost differences across ﬁrms. These factors, which may arise
from unique talents of personnel or from locational factors, give some sellers
cost advantages that cannot be replicated by competitors, at least in the short
run. Now, if in one market, these ﬁrm-speciﬁc factors tend to be fairly similar
across ﬁrms (and potential entrants), then in a competitive equilibrium, ﬁrms
in this market will have relatively equal market shares. Further, with low costs
of entry, all ﬁrms’ proﬁts and prices will be prevented from rising far above
normal competitive levels. Contrast this situation with a market in which ﬁrmspeciﬁc productivity factors vary widely. Now sellers with a cost advantage
will enjoy larger shares of market sales. Competitive forces will only drive
down the proﬁts of marginal sellers (those with relatively high costs). Lowcost ﬁrms will earn higher proﬁts. In short, greater inequality in costs across
ﬁrms will lead to both greater concentration of total market sales and higher
average proﬁts.
What implications does the critique of the market-power hypothesis have
regarding the relationship between prices and concentration? The connection
here is not as clear as in the case of concentration and proﬁts, and the answer
5 Gilbert and Zaretsky (2003) provide an excellent review of the literature on banking markets.

J. A. Weinberg: Banking Markets and Mergers

is likely to depend on additional characteristics of the markets in question.
Plausible models of market behavior might imply either a positive or a negative
correlation between concentration and prices. One such speciﬁcation that
implies a positive correlation replaces or supplements the assumption of ﬁrmspeciﬁc variation in costs with an assumption of ﬁrm-speciﬁc variation in
product characteristics. A seller who is industrious and fortunate enough to
produce a product more desirable than its competitors’ will enjoy a larger
market share and greater proﬁts, and will be able to sell at a higher price. As
before, a market with a more unequal distribution of product qualities will be
more concentrated and have higher average proﬁts, as well as higher average
prices.
In banking, one characteristic that appears to matter for attracting retail
deposit customers is location. A bank with a more convenient location may
be able to attract deposits while offering a lower interest rate than its competitors. Further, banks with multiple locations may have a competitive advantage,
suggesting that size and product quality are somewhat complementary characteristics within a banking market. This dimension of locational advantage,
combined with ﬁrm-speciﬁc differences in the costs of managing multiplelocation networks could then result in a distribution of banks according to
size, proﬁts, and prices (interest rates). The expected correlations of rates,
proﬁts, and concentration would then correspond with those found in crossmarket regressions.
So are the observed correlations in banking between local concentration
and prices (deposit rates) driven by market power or by competition among
heterogeneous sellers? A deﬁnitive answer to this question would be difﬁcult
to ﬁnd, and it is likely that both these forces are at work in actual banking markets. But even if purely competitive forces play an important role in driving
these cross-market differences, a merger policy based on limiting concentration could still be warranted. Even if large market shares result from the
product or cost advantages that some ﬁrms have over others, a ﬁrm with large
market share is more likely to be capable of exercising market power over
prices and earning economic proﬁts at the cost of reduced consumer welfare
and overall market efﬁciency. A merger policy that recognizes the possibility
of cost efﬁciencies arising from some large mergers can also recognize that the
resulting costs in terms of increased market power could outweigh the gains.

MERGERS AND MARKET STRUCTURE

Do mergers lead to increasingly concentrated markets? The trivial answer
to this question is yes, in the short run. The immediate effect of a merger
between two sellers operating in overlapping markets is that, in the areas of
overlap, the total amount of business in the market is divided among a smaller
set of competitors than before the merger. Beyond this simple response, the

Federal Reserve Bank of Richmond Economic Quarterly

study of how mergers affect market structure and opportunities for the exercise
of market power involves two theoretical questions regarding the behavior of
imperfectly competitive markets. First, can two ﬁrms in a market increase
their pricing power and proﬁts by combining? Second, what are the longrun effects of a merger on market structure, once competitors’ responses and
the dynamic behavior of the merging ﬁrms have been taken into account?
The second of these questions inherently refers to dynamic models of market
behavior, while the ﬁrst can be (and has been) addressed in the context of
either a static or a dynamic model.
Several papers study the question of whether two ﬁrms in an imperfectly
competitive market can increase their joint proﬁts by merging. The answer
depends on the nature of the strategic interaction among ﬁrms. One possibility,
pointed out by Salant et al. (1983), is that a reduction in the number of sellers
through a merger could cause other rivals to seek to beneﬁt by increasing
their own output. These output increases offset the merger’s effect on the
market price, eliminating any gains for the merging parties. Under alternative
models of strategic behavior, other authors have identiﬁed conditions under
which the merger partners do indeed beneﬁt. Denekere and Davidson (1985),
for instance, show that under price competition (with differentiated products),
the merger causes other rivals to raise their own prices, leading to gains for
everyone, including the merging ﬁrms.
Perry and Porter (1985) consider a model of asymmetric competition
among sellers with increasing marginal costs that depend on ﬁrms’ productive
capacity. They assume that capacity is tied to physical assets and that there
is a ﬁxed amount of such assets available to the sellers in the market.6 These
assumptions have the effect of limiting the competitors’ increase in output in
response to rising prices. As a result, two ﬁrms can ﬁnd it proﬁtable to merge,
reduce their combined outputs, and enjoy the resulting higher prices. Asymmetry in the initial distribution of the productive capacity among the sellers
can reinforce this result, making it particularly attractive for two relatively
large sellers to merge.
Perry and Porter’s analysis can be viewed as a bridge between a static and
a dynamic model of market competition. In fact, with freely variable capacity
and constant returns to scale, their model is identical to that of Salant et al. If
increasing capacity is subject to adjustment costs, and ﬁrms make dynamic,
strategic investment decisions, the steady state of the model’s equilibrium, for
a given number of ﬁrms, would coincide with the equilibrium of the standard
Cournot model. Comparing proﬁts across steady states with different numbers
of ﬁrms, then, would give the impression that mergers are not proﬁtable, as
in Salant et al. But adjustment costs give rise to a transition period, during
6 Alternatively, they assume that the adjustment costs associated with acquiring and installing
new productive capacity are high.

J. A. Weinberg: Banking Markets and Mergers

which the merged ﬁrms can beneﬁt, as in Perry and Porter. Gowrisankaran
(1999) studies mergers in dynamic oligopoly models.
All of these investigations of merger incentives in imperfectly competitive
markets share the assumption that changes in market structure do not change
the manner in which prices are determined. In all of the foregoing cases, the
prices resulting from a given market structure are the equilibrium outcomes
of static noncooperative behavior, whether price-setting or quantity-setting.
It’s possible that dynamic interaction among sellers in a concentrated market
could enable sellers to sustain higher prices than those associated with static
noncooperative equilibrium. If the feasibility of such tacit collusion depends
on market concentration, then the incentives for mergers to gain market power
could be considerably strengthened. This type of motivation would tend to
favor mergers among sellers that are already fairly large relative to the market.
In many actual banking markets, especially relatively large markets like
those examined in the next section, some participants are small enough so
that one can reasonably assume that they do not exercise market power. Such
markets might best be represented as having some ﬁrms with market power
and a “competitive fringe” of price-taking ﬁrms. Gowrisankaran and Holmes
(2000) investigate mergers in a dynamic dominant ﬁrm model. For a given
initial distribution of productive capacity between the dominant ﬁrm and the
fringe, they examine the equilibrium path of investment in new capacity and
purchase of capacity from the fringe by the dominant ﬁrm (mergers). They
ﬁnd that the tendency of the market to become more concentrated over time
depends on the initial concentration. Speciﬁcally, the greater the dominant
ﬁrm’s initial market share, the more likely the dominant ﬁrm will grow by
acquiring capacity from the fringe.
In the studies of merger incentives discussed in this section, the driving
force is the desire to proﬁt by the exercise of market power. This body of work
suggests that such a motivation for mergers is plausible in a variety of market
settings, even though entry and growth by smaller ﬁrms will eventually erode
the monopoly proﬁts acquired. Stigler’s (1950) characterization of the merger
waves of the early 20th century was consistent with this view. He shows in
particular how mergers in many industries created ﬁrms with dominant market
shares, only to have those dominant positions dwindle over time.
The forgoing discussion focused on studies of merger incentives where
the primary motivation was the acquisition or maintenance of market power.
But what if market structure is driven by the relative efﬁciencies of competing ﬁrms, rather than by the desire to gain market power? What does this
alternative approach imply about the causes and consequences of mergers?
In a dynamic version of such a model, like that in Hopenhayn (1992), ﬁrms
and their market shares grow or decline as their ﬁrm-speciﬁc characteristics

Federal Reserve Bank of Richmond Economic Quarterly

Table 1 Population and Population Growth 1990–2000
Market
Raleigh
Greensboro
Durham
Wilmington
Rocky Mount

1990 Population
541,100
540,030
344,625
200,124
133,235

2000 Population
797,071
643,430
426,793
274,478
143,026

Percent Growth
47.3
19.1
23.8
37.2
7.3

evolve.7 A ﬁrm that has a productivity advantage at one point in time may see
that advantage diminish over time. Such a model predicts market shares that
rise or fall but does not distinguish between growth through new investment
and growth through acquisition. One can imagine a model in which both internal growth (new investment) and external growth (acquisition) are subject
to adjustment costs. The relative costs of the two forms of growth, together
with the evolution of ﬁrm-speciﬁc productivity factors, would then determine
the joint pattern of investment and mergers.

FIVE NORTH CAROLINA MARKETS

This section examines the behavior of market shares in ﬁve North Carolina
metropolitan markets from 1991 to 2002. The ﬁve markets studied are Durham,
Greensboro, Raleigh, Rocky Mount, and Wilmington. These metropolitan
areas range in 2000 population from Rocky Mount with 143,026 to Raleigh
with 797,021. These two cities, respectively, also had the slowest and fastest
population growth of the group between 1990 and 2002. Population and population growth ﬁgures for these metropolitan areas are given in Table 1.
This group of markets does not include all the largest banking markets
in the state. Most notably, Charlotte and Winston-Salem are not included.
Both of these cities housed the headquarters of banks that were among the
10 largest in the United States during this period. Charlotte was the home
of Nationsbank, which merged with Bank of America in 1999 to become the
second largest bank holding company in the United States, with the combined
Bank of America headquartered in Charlotte. Charlotte is also the headquarter
city of Wachovia, the fourth largest bank holding company. Winston-Salem
was previously the home of Wachovia until it was acquired by First Union
(keeping the Wachovia name for the combined institution) in 2001. The
status of these cities as headquarters for very large institutions complicates
7 Erickson and Pakes (1995) provide a dynamic model that includes both imperfect compe-

tition and stochastically varying ﬁrm-speciﬁc productivities. While that model does not address
mergers, it could form the basis of a general treatment of merger incentives.

J. A. Weinberg: Banking Markets and Mergers

Table 2 Banking Market Characteristics in 1990
Market
Raleigh
Greensboro
Durham
Wilmington
Rocky Mount

Deposits/
Population
$9,990
$11,780
$8,800
$9,310
$16,690

HHI
786
747
1286
1008
1365

Leading Bank’s
Share (%)
15.66
15.05
24.15
19.98
25.84

5 Largest Banks’
Share (%)
45.02
48.13
63.50
54.13
64.89

the interpretation of the deposit data on which market concentration information is based. These data are drawn from the FDIC’s Summary of Deposits
and are based on banks’ reported allocations of their total deposits to their
various ofﬁces. Large banks that serve large corporate customers may have
deposits booked in their headquarter locations that come from more widely
dispersed customers. This tendency may have become particularly important
after interstate banking powers were expanded by 1994 legislation. The objective of studying market concentration in geographically deﬁned markets is
to examine the extent to which relatively few banks dominate a market for
local business. For the headquarter cities of large banks, a substantial portion
of reported deposits may represent nonlocal business.
Table 2 summarizes some characteristics of these banking markets in 1990.
With the exception of Rocky Mount, the markets are similar in terms of deposits relative to population, around $10,000 of deposits per capita. In terms
of market concentration, all ﬁve markets were either unconcentrated (HHI
less than 1,000) or moderately concentrated (HHI between 1,000 and 1,800),
as deﬁned by the Department of Justice’s merger guidelines. The leading
bank’s market share ranged from around 15 percent in Greensboro to nearly
26 percent in Rocky Mount. These 1990 market structures fall into three
groups. Greensboro and Raleigh appear similar, with HHI less than 800 and
the leading ﬁrm’s share in each market around 15 percent. The “four ﬁrm
concentration ratios”—the combined market share of the four largest ﬁrms in
the market—are also similar for Greensboro and Raleigh. These are the two
largest metropolitan areas by population, consistent with the general tendency
for concentration to be decreasing in city size. The two most concentrated of
this group of markets in 1990 were Durham and Rocky Mount. Rocky Mount,
the most concentrated, is also the smallest of these metropolitan areas. Wilmington’s market concentration characteristics lie between the other pairs of
markets.
The differences among the market structures are consistent with evidence
that metropolitan areas constitute distinct retail deposit markets. Given that
several banks are signiﬁcant participants in many or all of these cities, one
might expect that large, statewide banks would have similar positions in

Federal Reserve Bank of Richmond Economic Quarterly

different cities if the market were integrated on a statewide basis. Instead,
in 1990 four different banks had the largest market shares in the ﬁve cities.
While there are some respects in which the market structures of these cities
become more similar over the time period, individual banks’ positions remain
quite different across the markets.
Between 1991 and 2002, there were 45 mergers involving banks that
participated in at least one of these markets.8 Over 80 percent of these were
truly horizontal mergers, meaning that the merging banks were competitors
in at least one market prior to the acquisition. The remaining transactions
are better characterized as market extension mergers, in that they involved the
purchase of a bank in a market in which the acquirer had no previous presence.
In 13 cases, the merging banks had overlapping activities in more than one of
the markets. Transactions vary in size from Southern National Bank of North
Carolina’s 1993 purchase of East Coast Savings Bank, which had a single
ofﬁce in Raleigh with deposits of $6.5 million, to the 2002 merger of First
Union and Wachovia, which had overlapping activities in all of ﬁve markets,
with combined deposits ranging from around $370 million in Rocky Mount
to nearly $3 billion in Raleigh.
How did this decade of mergers affect the market structures in these
metropolitan areas? Figures 3–6 present information on the evolution of market characteristics from 1990 to 2002. Figure 3 begins with the number of
banks operating in this market. In all markets, this period saw a substantial
decline in the number of banks. There has also been entry of new banks in
all of the markets, with net gains in the number of banks coming toward the
end of the period. While all of the markets had fewer banks in 2002 than in
1990, markets did not necessarily receive fewer banking services. As shown
in Figure 4, changes in the number of ofﬁces (branches) were generally not
as dramatic as changes in the number of banks. Rocky Mount experienced
a fairly substantial decline in ofﬁces (about 25 percent), and Raleigh saw a
large increase (about 14 percent). In the other markets the number of ofﬁces
changed very little (less than 3 percent). It is true that deposits per capita fell
slightly in all but one (Rocky Mount) of the markets. While this decline could
be due to an overall reduction in supply of deposit services, it is just as likely
the result of increasing competition from nonlocal banks or nonbank ﬁnancial
service providers for some segments of customers.
Figures 5 and 6 turn more directly to measures of market concentration.
Figure 5 shows the evolution of the HHI for each market. Overall, the markets
appear to be more similar at the end of the period than at the beginning,
with the two least concentrated markets at the beginning of the period having
experienced the largest increases in concentration. But a large part of the
8 This count includes commercial bank and thrift acquisitions.

J. A. Weinberg: Banking Markets and Mergers

Figure 3 Number of Banks, 1990–2002
40

10
Greensboro-High Point
Durham-Chapel Hill
Raleigh
Rocky Mount
Wilmington

0
1990

1992

1994

1996

1998

2000

2002

increase in concentration in Raleigh and Greensboro is associated with the First
Union-Wachovia merger. These two banks each had market shares in excess
of 10 percent in both of these markets at the time of the merger. Differences
in concentration across these markets appear to be fairly persistent before the
last observation in the data. Markets that start out more concentrated remain
more concentrated.
Figure 6 underscores the importance of the First Union-Wachovia merger
for the Raleigh and Greensboro markets. This ﬁgure shows the market share
of the leading bank in each market.9 In Raleigh and Greensboro, this number
changes very little until the last year in the data. A single transaction also
plays a large role in the Wilmington market. The relevant merger in this case
is BB&T’s purchase of United Carolina Bank in 1997. Durham displays a
steady increase throughout the period, as does Rocky Mount in the ﬁrst part of
the period, after which the top ﬁrm’s share declines. In general, the behavior
of the top seller’s market share seems more idiosyncratic than the broader
measure of concentration.
9 Note that the identity of the leading bank in a market can change over time.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Ofﬁces, 1990–2002
350

300

Greensboro-High Point
Durham-Chapel Hill
Raleigh
Rocky Mount
Wilmington

250

200

150

100

0
1990

1992

1994

1996

1998

2000

2002

How do the observed patterns in these ﬁve markets relate to theoretical
views on the motivations for and effects of mergers? First, note that the persistence of differences in concentration across markets suggests that, whatever
the forces driving consolidation, local factors are important in determining
local market structures. There does not appear to be a unique structure toward
which these markets are converging. Also, it is important to bear in mind that
banking markets in the United States operate under an existing merger policy
that limits the degree of concentration that one might expect to observe. Mergers that would create too much concentration might not be allowed, or might be
allowed subject to the sale of some of the combined company’s branches to a
third party. So if there was a tendency, for instance, for all banking markets to
eventually become monopolies, that tendency would not show up in the data.
Still, these markets are, for the most part, below the level of concentration at
which merger policy tends to intervene, and there is not strong evidence that
less concentrated markets are consolidating faster than those that are already
more concentrated.
While differences between markets seem to persist, it is the case that
all of the markets have become more concentrated. Broadly speaking, this
rising concentration is consistent with the models of merger incentives in

J. A. Weinberg: Banking Markets and Mergers

Figure 5 HHI, 1990–2002
2,500

2,000

1,500

1,000

Greensboro-High Point
Durham-Chapel Hill
Raleigh
Rocky Mount
Wilmington

500

0
1990

1992

1994

1996

1998

2000

2002

imperfectly competitive markets. Some of these models, Perry and Porter
(1985) and Holmes and Gowrisankaran (2000) in particular, suggest that the
incentive for a market’s large participants to grow by acquisition is increasing
in the initial level of concentration. This feature does not appear to be present
in the cases examined here. Those same models, however, suggest that the
increasing incentives may display a threshold effect, changing discretely once
concentration becomes big enough. It is possible then, that all of the markets
examined are on the same side of the relevant threshold.
The behavior of the leading ﬁrms’ market shares (Figure 6) contains an
interesting mix of patterns. Two of the markets (Rocky Mount and Wilmington) evolve in a way that seems consistent with Stigler’s (1950) evidence on
early merger waves. A leading ﬁrm in a market increases its share through
acquisition, and then sees its share decline over time. This pattern suggests
an environment in which, due to entry and adjustment costs, gaining market power through acquisition is possible, but only temporarily. In two other
markets (Raleigh and Greensboro), the large increase in the leading ﬁrm’s
share comes at the end of the period, so it’s not possible to say whether these
markets will follow the same pattern. The last market shows a sustained

Federal Reserve Bank of Richmond Economic Quarterly

Figure 6 Share of Largest Bank, 1990–2002
40.00

35.00

30.00

25.00

20.00

15.00

10.00
Greensboro-High Point
Durham-Chapel Hill
Raleigh
Rocky Mount
Wilmington

5.00

0.00
1990

1992

1994

1996

1998

2000

2002

increase in the leading ﬁrm’s share, which seems consistent with Holmes and
Gowrisankaran’s model of a dominant ﬁrm growing through acquisition.
While the behavior of these markets’ structures is consistent with models
in which mergers are motivated by the prospect of gains in market power,
they are also consistent with the view that mergers are one of the means by
which an industry evolves toward an efﬁcient allocation of productive capacity
among ﬁrms with heterogeneous characteristics. Given the sustained increases
in concentration in these markets, one might conclude that the entire period
from 1990 to 2002 represents part of a transition from one steady state market
structure to another. This view seems consistent with the behavior of the
aggregate number of banks, as shown in Figure 1.

CONCLUSION

The title of this article includes the phrase “preliminary examination,” and
the article has attempted to view the evolution of market structures in light of
alternative theoretical perspectives on the motives for mergers. The ﬁndings
suggest that observed behavior of markets is consistent either with a theory
based on the acquisition of market power or one based on the efﬁcient allo-

J. A. Weinberg: Banking Markets and Mergers

cation of productive capacity in local banking markets. A less preliminary
analysis of this topic might proceed in one of two ways. First, one could proceed with a more detailed analysis of a small number of markets. Such a study
would consider details of the local economies that might affect the demand for
banking services. Important factors may include information about business
activities and changes in local labor market conditions. Differences in such
demand characteristics are likely to be important for explaining differences in
concentration across markets or over time. Accounting for such factors could
give one insight into the extent to which changes in market structure represent
efﬁcient responses to changes in demand conditions.
A second path to follow would be to develop equilibrium models of industry structure and to take those models to the rich data on banking markets. This
is the program set forth by Berry and Pakes (1993) and to which Gowrisankaran
(1999) constitutes an important contribution. These authors propose models
that incorporate both market power (imperfect competition) and the possibility
for efﬁciency reasons to drive differences in ﬁrm size and market share. Such
models create the potential for the data to speak more directly to the relative
importance of the various forces driving consolidation in markets.

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