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Economic
Review
Federal Reserve Bank
of San Francisco
1995
Number 1
Chan G. Huh and
Bharat Trehan
Modeling the Time-Series Behavior
of the Aggregate Wage Rate
Kenneth Kasa
Comovements among National Stock Markets
Elizabeth S. Ladennan
Changes in the Structure of Urban Banking
Markets in the West
Table o f Contents
Modeling the Time-Series Behavior of the Aggregate Wage Rate ..................... .
3
Chan G. Huh and Bharat Trehan
Comovements among National Stock Markets ............................ ...................... .
14
Kenneth Kasa
Changes in the Structure of Urban Banking Markets in the W est.............................. 21
Elizabeth S. Laderman
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Modeling the Time-Series Behavior
of the Aggregate Wage Rate
This paper studies the behavior of wages relative to prices
and productivity in a framework that places relatively few
restrictions on the interactions among these va..-iables. The
Chan G. Huh
and Bharat Trehan
Economist and Research Officer, respectively, Federal Reserve Bank of San Francisco. We would like to thank
participants at a Federal Reserve System conference in
Chicago, Tom Sargent, and editorial committee members
for helpful comments on an earlier draft of this paper.
Research assistance by Robert Ingenito is gratefully
acknowledged.
This paper looks at the time-series behavior of the real
wage relative to that ofproductivity. Given an exogenous,
nonstationary process for productivity, we use a simple
model ofdynamic labor demand to show that the real wage
and the marginal product of labor will be cointegrated if
the representative firm chooses the profit-maximizing level
of employment. Data for the postwar period satisfy this
condition. On the basis of this result we estimate a vector
error correction model containing prices, wages, andproductivity and examine the dynamic relationships among
these variables. This specification provides a natural
setting for looking at a number of issues of interest,
including the role of the unemployment rate in the wage
rate equation, issues of wage-price causality, and the
effect of exogenous wage rate changes on productivity.
use of the level of productivity as an anchor for the level of
the real wage is a significant element of our analysis; it
allows us to examine the behavior of wages without resorting to the common practice of arbitrarily detrending this
variable and focusing on the residual. We use this specification to examine a number of key issues in the literature,
including such questions as the relationship between wages
and prices, the relationship between the unemployment
rate and prices, and the way in which productivity shocks
affect the wage rate.
We begin with a condition that can be found in any
simple model of competitive firm behavior-specifically,
the firm sets the real wage equal to the marginal product of
labor. In a time-series context this suggests that real wages
and the marginal product of labor should move together
over time. Starting with the assumption that the exogenous
productivity process is nonstationary, we use a simple
model of dynamic labor demand to showthat the real wage
and the marginal product of labor will be cointegrated.
Empirical tests over the post-war period reveal that the data
are consistent with this condition.
We go on to show that there exists a single cointegrating
relationship among the nominal wage, the price level, and
labor productivity. Cointegration allows us to cast the
relationship among these vm:iables as a vector error correction model (VECM) and provides a natural framework for
looking at a number of hypotheses about the wage rate.
One issue has to do with the role of the unemployment
rate in wage equations. We show that the role of the
unemployment rate in such equations is sensitive both to
the dynamic specification (in particular to whether the
error correction term is included) and to the inclusion of a
contemporaneous measure of productivity.
Another issue has to do with the causal relationship
between wages and prices. We find that prices Granger
cause wages but that wages do not Granger cause prices.
This is evidence against models that specify prices as a
markup on wages. There does exist a non-negligible contemporaneous correlation among the innovations to these
variables, and wage innovations could have an impact on
prices if firms were to complete their adjustment to a wage
shock within the quarter in which the shock occurred.
4
FRBSF ECONOMIC REVIEW 1995,
NUMBER
1
Complete adjustment at such a rapid rate would appear to
be at odds, however, with the large body of work on the
sluggish behavior of prices.
The remainder of the paper is organized as follows.
Section I focuses on the long-run relationship between
wages and productivity. We begin by laying out a simple
model that allows us to derive testable restrictions upon the
evolution of the real wage and labor productivity. Turning
to the data, we first establish the univariate properties of the
series and then examine the joint behavior of the real wage
and productivity, with a view to determining whether the
representative firm can be said to be on its long-run
demand curve. Section II presents the estimated VECM;
three sub-sections use this model to analyze the issues
raised above as well as to examine the dynamic interrelationships among wages, prices, and productivity more
generally. Section III concludes.
I.
THE RELATIONSHIP BETWEEN
WAGES AND PRODUCTIVITY
A Simple Model
In this section we use a simple model to determine the
kinds ofrestrictions that can be placed upon the behavior of
the wage rate. We begin by assuming that the labor market
is perfectly competitive. The model we employ is a version
of the kind of dynamic labor demand model found, for
instance, in Sargent (1978) or Nickell (1986).
The representative firm produces a single output (whose
price is taken as a numeraire) and maximizes the objective
function given by
00
V = Et i~O WV t + j ,
where E t denotes the date t expectation and 13 is the
discount factor for the firm. The one period profit function
v t is
(1)
Vt
=
g(Lt, at) - W,L, - h (IlL t).
g(.) denotes the production function in which labor (L) is
the only input. We assume thatiJglaLt=gL>O andgLL<O.
Labor is augmented by the technology shock term at,
which can be thought of as measuring increases in knowledge that make the same unit of labor more productive over
time. 1 We assume that at is nonstationary with positive
drift, an assumption that is consistent with the empirical
results below; W t denotes the real wage rate defined as
1. An alternative interpretation of this variable is that it represents the
productive contribution of capital stock in the economy.
W/P t' where Wt is the nominal wage and P t is the price of
the firm's output; Il denotes the first difference, so that the
function h(·) measures the cost of changing employment,
which is borne by the firm. We assume the function h(·) to
be such that there are symmetrical costs to both hiring and
firing.
The competitive solution can most easily be characterized as a situation in which the firm is on its dynamic
labor demand curve Ld, which is implicitly defined by
condition (2). The firm chooses L to maximize V, taking
stochastic processes {at, w,} as given, so that
(2)
we == gL - [hL(IlL t )
-
I3hL(E tIlLt+l)] ,
where the subscript c denotes the real wage rate (in terms of
the product price) determined in a competitive labor market, hL = ah/aL, and the term in parentheses denotes the
adjustment costs of changing the labor input in period t as
well as in t+ 1.
For our purposes, it suffices to note that, in equilibrium,
(2) has to hold in each period. Equation (2) simply states
that over time the marginal product of labor and the wage
rate will move together, apart from deviations caused by
the costs of changing employment. The nature of the
adjustment costs will determine the relative behavior of
the wage rate and productivity over time. By the symmetry
assumption, both an increase and decrease in employment
incur labor adjustment costs, which in turn depend only on
the net amount of change (IlL t). Thus, the term in parentheses in (2) above is likely to be small and temporary for
both constant or trending levels of employment, because it
is the difference between the marginal cost of adjustment
in two adjacent periods.
Despite the apparent intuitive appeal of condition (2),
there are alternative theories of the wage-employment
determination mechanism that cannot be characterized in
this way. The efficient wage bargaining theory that focuses
on unionized labor markets is a case in point. Both the
static version of the efficient wage bargaining model (e.g. ,
Abowd 1987, MaCurdy and Pencavel 1986), and its dynamic extension (Espinosa and Rhee 1989), emphasize and
focus on the strategic nature of the interaction between
firms and workers in determining wages and employment.
In these models, factors such as the relative strength of
unions and firms and the union's preferences over wages
versus employment are crucial determinants of the actual
bargaining equilibrium outcome.
There is a critical implication of this view that is relevant
to our exercise. Typically, the solution set of wage-employment pairs for either the static or the dynamic efficient
bargaining problem does not include points that lie on the
representative firm's demand-for-Iabor curve. Thus, (2)
HUH AND TREHAN/TIME SERIES BEHAVIOR OF THE AGGREGATE WAGE RATE
does not apply to this situation. 2 The fact that unions have
played a significant role in the U. S. over our sample period
provides a priori grounds for considering the efficient
bargaining model seriously. In other words, there appears
to be sufficient reason to believe that the behavioral prediction of (2) might not hold for our sample period.
TABLE
1
UNIT ROOT TESTS AGAINST
ALTERNATIVE OF
While our discussion above has been in terms of the
marginal product of labor, we have data only on average
product. How closely does the latter approximate the
former? The answer depends upon the underlying production function. If the production function is Cobb-Douglas,
for instance, the log of the marginal product is just a
constant plus the log of the average product. More generally, the results below will go through if there is a linear
relationship between the log of the average and marginal
products of labor. We can relate the two measures by
introducing the elasticity of output with respect to labor,
which is defined as the ratio between the marginal product
and the average product. Thus, the log of the marginal
product of labor equals the log of the average product plus
the log of the elasticity, which is a constant for a wide range
of production. function specifications (e. g., linear and
CES).
The measure of average product we use is the output per
hour of all persons in the business sector, which is compiled by the Department of Labor. The log of this series is
denoted by LYHR. For wages we use compensation per
hour in the business sector, and denote the log of this
variable by LNWAG. This measure seems most relevant to
our purposes, since it includes total payments made by
firms to all workers. Our focus upon labor productivity as
an anchor for the real wage implies that we need a measure of the product wage, that is, a real wage measured in
units of the firm's output. Consequently, we use the implicit price deflator for business sector output (whose log
we denote by LDEF) to deflate the nominal wage. We use
LRWAG to denote the log of the real wage. All series are
available on the Citibase data tape.
The first order of business is to establish some facts about
the long-run behavior of the individual series. Accordingly,
Table 1 presents tests of the unit root hypothesis for each of
2. Among models of unionized labor markets, the monopoly union
model provides an exception. According to the model, the monopoly
union unilaterally chooses the wage rate, leaving the employment
decision entirely up to the firm; the firm, in tum, takes the wage rate as
given and determines employment using its demand-for-labor curve.
However, contrary to this model, in practice bargaining usually takes
No TREND BREAK
A. loG LEVELS
Variable
A First Look at the Data
5
LYHR
LNWAG
LDEF
LRWAG
Dickey-Fuller Test
-1.74
-1.27
-1.43
-1.12
Phillips
-1.19
-1.84
-1.88
-1.07
B. DIFFERENCES
Variable
dLYHR
dLNWAG
dLDEF
dLRWAG
Dickey-Fuller Test
Phillips
-4.94**
-3.19*
-3.26*
-4.43**
-12.76**
-11.56**
-9.33**
-12.74**
NOTES:
Regressions in panel A contain a constant and a time trend. For both
test statistics reported here, the 10 percent significance level is
- 3.15. Regressions in panel B contain a constant only; * denotes
significance at 5 percent; ** denotes significance at 1 percent.
Dickey-Fuller test equations contain four lags of first difference of the
dependent variable.
To compute the Phillips test statistics, we use Schwert's (1987) /12
formula, which implies the use of thirteen autocovariances.
these series against the alternative that it can be described as
stationary around a linear trend over the 1948.Q2-1990. Q3
sample period. The results for the Dickey-Fuller test reveal
that in no case are we able to reject the unit root hypothesis at
even the 10 percent significance level. 3 Table 1also contains
results from Phillips' (1987) test. This test al1lows the error
term to follow a more general process than the DickeyFuller test. It turns out that the second test leads to the same
results as the first.
While we have allowed for a linear trend in these tests,
visual inspection of the data suggests that the trend growth
place over both wages as well as employment. Further, Espinosa and
Rhee (1989) show that the outcome described by the monopoly union
model is unlikely to occur in a general dynamic bargaining game setup.
There is a set ofPareto superior solutions that dominate such an outcome
in a repeated game context.
3. In the case of the Dickey-Fuller test, the test statistic is calculated as
the ratio ofthe coefficient of the lagged level to its standard error (from a
regression where the first difference is regressed on a constant, a time
trend, lagged first differences, and a lagged level); critical values are
available in Fuller (1976).
6
FRBSF ECONOMIC REvIEW 1995, NUMBER 1
rate of LYHR and LRWAG may have changed over the
sample. Indeed, the productivity slowdown over this period has been widely noted. Consequently, we test whether
the unit root specification (with no change in drift) can be
rejected against an alternative that allows for a single
change in a deterministic trend. This specification has
been suggested as a reasonable alternative (in a somewhat
different context) by both Rappoport and Reichlin (1989)
and Perron (1989). Here we implement a procedure suggested by Christiano (1988). Specifically, we employ his
"min-ta " procedure. 4
The results from this procedure are shown in Table 2.
For LYHR, for example, the procedure finds the most likely
break date to be 1964.Q1, where the computed t statistic
has a value of - 3.45. However, this value is considerably
smaller than the expected value obtained under the null,
and the computed t statistic has a marginal significance
level of .79. Similar results are obtained for the other
variables. Thus, in no case are we even close to rejecting
the unit root null against the alternative of a break in a
deterministic trend.
Are Firms on Their Demand Curves?
The results in Tables 1and 2 imply that the individual series
contain unit roots. What can we say about the joint
behavior of these series? Equation (2) implies that gL
(labor's marginal product) and We (the real wage in a
competitive labor market) will be cointegrated. This result
4. The intuition behind the procedure is as follows. In attempting to
determine whether a break has occurred, the date of any potential break
is usually determined after looking at the same data. However, using a
(formal or informal) search procedure to determine the break date
implies that the distribution of the resulting test statistic will no longer
be the same as it would be if the break date had been determined
independently of the data at hand. Christiano suggests a number of
alternative techniques to choose the most likely date for a break in the
trend and then constructs empirical distributions which take this "pretesting" into account.
The null hypothesis is that the process in question contains a unit root,
while the alternative is
AYt = ao + aPT + bo*trnd + blDT*trnd + QYt-1
+ d(L) AYt-1 + Vt
O<t<T
where
= 1,
T';; t.;;
T,
and trnd denotes a linear time trend. Thus, this specification allows for
both a jump in the level ofthe variable and a change in the slope at date T.
The value of T is then allowed to vary over the entire sample (that is, we
allow each date in the sample to be the break date), and we compute the
value of tot at each date. We then define the date at which ta attains its
minimum value as the most likely break date. An empirical distribution
for this statistic is obtained by using the bootstrap to construct 1000 new
series.
TABLE
2
UNIT ROOT TESTS AGAINST ALTERNATIVES
THAT ALLOW FOR BREAK IN TREND
SIGNIFICANCE
VARIABLES
LYHR
LNWAG
LDEF
LRWAG
MOST LIKELY
LEVEL/EXPECTED
BREAK DATE
VALUE
1964.Ql
1957.Q2
1959.Q4
1969.Q2
-3.45
-2.01
-2.81
-3.45
.79/ -4.02
1.0/ -4.00
1.0/ -4.02
.80/-4.00
NOTES:
All regressions allow both the constant and time trend to change over
the sample.
Calculation of the Most Likely Break Date excludes three years of
data at either end of the sample. The dates reported are those that
lead to the smallest t statistic on the lagged level of the dependent
variable.
is intuitive; it says that ifthe firm stays on its demand curve,
the marginal product of labor and the wage rate should
move together over time, apart from temporary deviations
caused by adjustment costs.
It should be noted that temporary deviations between
labor productivity and the wage rate can occur for a
number of reasons besides the costs of adjusting employment. For example, Bils (1990) shows that in sectors with
long-term contracts, real wages increase significantlyrelative to wages elsewhere in the economy-in the first
year of the contract, but then decline over the life of the
contract. Our empirical approximation of the marginal
product of labor by the average product is another reason
for not expecting an exact relationship between LYHR and
LRWAG, even if the firm is on its demand-for-labor curve
in the long run.
Turning to the data, a regression of the real wage on
labor productivity over the 1947.Q1-1990.Q3 period leads
to
LRWAG t = -0.01 + 0.995 LYHR,.
The Augmented Dickey-Fuller (ADF) test (see Engle and
Granger 1987) leads to a test statistic of - 5.02, which
compares to a 1 percent significance level of - 3.73. 5 Use
of Johansen's maximum likelihood procedure leads to the
same result. Under the null hypothesis that there is no
cointegrating vector, the computed value of the trace test is
5. The critical values are from Engle and Yoo (1988). The equation used
to estimate the test statistic contains one lag of the dependent variable.
The lag length was arrived at by starting with six lags and eliminating
HUH AND TREHAN /TIME SERIES BEHAVIOR OF THE AGGREGATE WAGE RATE
39.2, which is significant at the 1 percent level. The
statistic for the maximal eigenvalue test (with a computed
value of 31.0) also is significant at 1 percent. 6 (See Johansen and Juse1ius 1990 for a discussion of the tests and
tabulated critical values.)
These results reveal that labor productivity and the
observed real wage have shared the same stochastic trend
component during our sample period and consequently are
consistent with models that imply that the representative
firm is on its demand-for-Iabor curve.
The test for cointegration between real wages and productivity is actually a test for cointegration among nominal
wages, prices, and productivity, where the coefficient on
(the log of) the price level is set equal but opposite in sign to
the coefficient on wages. An alternative way to proceed is
to estimate the cointegrating vector among these three
variables without imposing any restrictions. Removing this
restriction introduces prices explicitly into the model and
allows us to look at a larger system in the analysis that
follows. One advantage of looking at this system is that we
can now allow for the possibility of exogenous shocks to
the price level. For example, we can now allow a union's
actions to affect LNWAG, while LDEF is influenced by the
actions of the monetary authority or by OPEC. More
generally, the point is that we can now allow for a greater
number of disturbances to the model.
Repeating the cointegration test above leads to
LNWAGt = -4.56
+
1.02 LDEFt
+
0.97 LYHRr
We obtain a test statistic of - 5.02, which is again
significant at 1 percent. 7 Increasing the number of variables in the model raises the possibility of more than one
cointegrating relationship among these variables. We use
Johansen's maximum likelihood approach to determine the
number of cointegrating vectors. Under the null hypothesis
that no cointegrating relationship exists among these variables, the value of Johansen's trace test is 48.5, which is
significant at 1 percent. 8 By contrast, we cannot reject the
null hypothesis that there is at most one cointegrating
vector at the 10 percent level. (The computed value of the
trace-test statistic is 15.3.) The maximal eigenvalue test
the insignificant terms. (In no case do we fail to reject the null of no
cointegration. )
6. The estimated model contains six lags of the first-differenced
variables; the error terms from these equations are well-behaved.
7. The residual equation contains one lag.
8. The model included six lags as before. However, the residuals
indicate that the normality assumption is violated because of too much
kurtosis. Induding up to four more lags does not solve this problem.
Gonzalo (1989) points out that the Johansen procedure is robust to
violations of the normality assumption.
7
yields the same results. These results indicate that there are
two distinct stochastic trends driving these three variables,
and that there is one cointegrating vector. With the variables ordered as LNWAGt , LDEFt , and LYHRt , the estimated cointegrating vector is (1 - .995 - .951).
Recent research has shown that the estimates obtained
from the Johansen procedure are superior to those obtained from the OLS regression; consequently, this is the
cointegrating vector that \ve "viII employ belov/. 9
II.
THE ESTIMATED VECM
AND ITS ApPLICATIONS
The finding that the real wage rate and productivity are
cointegrated implies that we can specify the model as a vector error correction model (VECM).lO The equations of the
estimated VECM are shown in Table 3. Notice that the error
correction term (EC t -1) enters significantly in the LNWAG
equation and has a negative sign. This implies, for example, that the nominal wage falls whenever it gets too high
relative to the price level and the productivity of labor. By
contrast, ECt _ 1 does not enter significantly into either the
LDEF or the LYHR equation; it actually has the wrong sign
in the LYHR equation. This implies that, in general, it is
LNWAG that adjusts to correct the "error" among these
variables. We will return to this issue below. Note also that
the adjusted R2 of the ~LYHR equation is close to zero,
implying that the model does not do a very good job of
explaining changes in productivity.
In the rest of this section we use this model to study
several issues regarding the behavior of wages as well as
the interaction of wages, prices, and productivity. The first
extension is to introduce the unemployment rate into the
model and to examine the relationship between unemployment and wages. This allows us to look at the "Phillips
curve" in a framework that does not impose a potentially
artificial separation between the short and long run on the
data. Note that the inclusion of the unemployment rate in
the equation for wages also can be motivated by appealing
to efficiency wage theories of wage determination.
Next, we look at the relationship between wages and
prices. Recent papers by Gordon (1988) and Mehra (1991)
have looked at the causal relationships between these
variables. Our model offers an alternative way of examining these issues. Finally, we will use the model to examine
the dynamic relationships among wages, prices, and
productivity.
9. See Gonzalo (1989), for example.
10. See Granger's Representation Theorem (Engle and Granger 1987).
8
FRBSF ECONOMIC REvIEW 1995, NUMBER 1
TABLE 3
Introducing the Unemployment Rate
THE ESTIMATED VECM
Perhaps the most straightforward way of introducing the
unemployment rate in our wage equation is by appealing to
Phillips (1958), who modeled the change in wages as a
function of the unemployment rate. A recent example of an
analysis carried out along these lines is Vroman and
Abowd (1988), who regress the growth in hourly earnings
on alternative measures of the civilian unemployment rate,
the lagged consumer price index, and some other variables.
The literature on efficiency wages provides another motivation. In Shapiro and Stiglitz (1984), for example, firms
are unable to monitor workers' efforts fully. To offset this
and provide the right incentive to workers, a firm has to pay
a wage rate that meets a "no shirking constraint." The
prevailing unemployment rate is a key determinant of such
a wage rate and is inversely related to it, because the
prevailing unemployment rate affects the probability of a
worker finding a new job if he is found shirking and fired. 11
It is not difficult to motivate the inclusion of the unemployment rate in the price equation, either. For example,
specifying prices as a cyclically sensitive markup on wages
would imply a relationship between prices and the unemployment rate as well.
Our strategy is simply to include the unemployment rate
into the VECM presented earlier. 12 While the resulting
specification will not include many of the wrinkles of
recent Phillips curve analyses, it improves upon conventional specifications in two ways. First, it allows changes in
productivity to affect wages and prices directly. Second, it
allows us to examine the cyclical relationship between
wages and the unemployment rate in a framework that also
models the long-run behavior of these variables, rather than
assuming it away either by linear detrending or by first
differencing the data.
Consider first what happens when six lags of the level of
the unemployment rate are included in our model. The null
that the (lagged) unemployment rate does not belong in the
price equation can be rejected only at a marginal significance level of 60 percent, while the null that it does not
EXPLANAIDRY VARIABLES
IlLNWAG t
Constant
-0.54
( -3.0)
IlLNWAGt~l
IlLNWAG t _ 2
IlLNWAGt~3
IlLNWAGt~4
IlLNWAG t _ 5
IlLNWAGt~6
IlLDEFt~l
IlLDEFt~2
IlLDEFt _ 3
IlLDEFt~4
IlLDEFt~5
IlLDEFt _ 6
IlLYHRt~l
IlLYHRt~2
IlLYHRt~3
IlLYHRt~4
IlLYHRt~5
IlLYHRt _ 6
ECt -l
R2/ adj. R2
S.E.E. (x102)
Q(36)/SIG. LEVEL
IlLDEFt
0.19
(1.1)
IlLYHRt
-0.22
(1.0)
0.13
(1.3)
0.11
(1.2)
-0.12
( -1.2)
0.04
(0.4)
0.14
(1.5)
0.07
(0.8)
-0.11
( -1.3)
0.21
(2.5)
0.08
(0.9)
0.01
(0.1)
0.02
(0.2)
( -0.2)
0.15
(1.3)
0.04
(0.3)
-0.12
( -1.0)
0.10
(0.9)
0.01
(0.1)
0.08
(0.8)
0.37
(3.4)
0.22
(2.0)
-0.05
( -0.5)
-0.31
( -2.8)
0.05
(0.4)
0.06
(0.6)
0.46
(4.5)
0.19
(1.8)
-0.02
( -0.2)
-0.06
( -0.6)
-0.08
( -0.8)
0.10
(1.0)
-0.24
( -1.8)
0.05
(0.4)
-0.04
( -0.3)
-0.22
( -1.6)
-0.07
( -5.0)
-0.06
( -0.5)
-0.14
(-1. 7)
0.03
(0.3)
-0.11
( -1.3)
-0.19
( -2.4)
-0.13
( -1.7)
0.09
(1.1)
0.15
(1.9)
0.01
(0.1)
-0.06
( -0.8)
0.03
(0.5)
-0.17
( -2.2)
0.01
(0.1)
-0.10
( -1.0)
0.05
(0.5)
0.02
(0.2)
-0.31
(-3.1)
0.02
(0.2)
-0.06
( -0.6)
-0.12
( -3.0)
0.04
(1.1)
-0.05
( -1.0)
-0.D2
.41/.33
.49/ .42
.16/ .06
0.70
0.65
0.87
32.7/.63
9.1/.79
6.8/.87
NOTES:
t statistics are in parentheses.
The error correction term is ECt = LNWAGt - .995 LDEFt - .951
LYHRt ·
11. Also see Blanchard and Fisher (1989) pp. 455-463 for a more
general discussion of efficiency wage theories.
12. We began by considering the time-series properties ofthe unemployment rate. We carried out the two tests in Table 1 in order to test for
stationarity. While it is possible to reject the null that the unemployment
rate contains a unit root (at the 6 percent level of significance) when the
augmented Dickey-Fuller test is used, we fail to reject when the Phillips
test is used. Given this conflict, we chose to go with our prior, which is
that the unemployment rate is stationary. Accordingly, we decided to
include the level, and not the first difference, of the unemployment rate
in the VECM. Another alternative would be to model the unemployment
rate as being stationary around a shifted mean. See Evans (1989).
HUH AND TREHAN /TIME SERIES BEHAVIOR OF THE AGGREGATE WAGE RATE
belong in the wage equation can be rejected only at a
marginal significance level of 79 percent. The error correction term remains significant in the wage equation (with its
estimated coefficient getting noticeably larger in absolute
terms) and insignificant in the price equation even after the
unemployment rate is introduced. As an alternative, we
tried including the log levels of the unemployment rate in
the VECM. Once again, the null that the unemployment
rate does not belong in the equation cannot be rejected in
either case at the 50 percent level of significance. Thus, we
find no evidence to suggest that the lagged unemployment
rate should be included in either of these equations.
The experiments described so far do not match up
precisely with the Phillips curve literature, since we have
omitted the contemporaneous unemployment rate. Note
that introducing the contemporaneous unemployment rate
into this systemis not innocuous, since it begs the question
of whether the unemployment rate is exogenous. However,
we decided to include the contemporaneous term in order
to allow a direct comparison with the Phillips curve
literature. An F test on the contemporaneous and six
lagged values of the unemployment rate fails to reject the
null that these terms are zero at the 35 percent level of
significance. However, the contemporaneous unemployment rate term has a t statistic of - 2. I in the wage equation
(and -1.8 ill the price equation).
In addition to the problem of exogeneity discussed
above, another problem in trying to gauge the significance
of this result is that the unemployment rate is the only
contemporaneous variable included in the wage equation.
Thus, its importance may result from the fact that it is the
only way that contemporaneous developments are allowed
to affect wages. There is an easy way around this problem
in our model: Specifically, we introduce the contemporaneous change in productivity into the wage equation and
see what effect this has on the significance of the unemployment rate. 13 It turns out that doing so reduces the t
statistic on the contemporaneous unemployment rate to
- 1. 5, and we cannot reject the null that both contemporaneous and lagged unemployment terms are zero at the 70
percent level of significance. By contrast, the contemporaneous productivity term has a t statistic that is close to 3.
It also is worth mentioning that the error correction term
remains significant in the wage rate equation through all
the exercises described above. Finally, if we drop the error
correction term from the specification just described, the t
statistic on the contemporaneous unemployment rate goes
to - 2 while the null that the current and lagged unemployment rate terms are zero can be rejected at 11 percent.
13. We consider the issue of whether LYHR is predetermined with
respect to LNWAG below.
9
Our results demonstrate that inferences regarding the
inclusion of the unemployment rate in an equation for
wages are sensitive to how the dynamics of the wage rate
are specified, as well as to whether the contemporaneous
effects of changes in productivity are taken into account.
While our search has not been exhaustive, we have shown
that the unemployment rate is not very important in explaining the wage rate in a framework where the long-run
behavior of wages is modeled explicitly. However, we do
not wish to claim that unemployment can never matter for
wages within our framework. Instead, we prefer to thillk of
this exercise as an illustration of the usefulness of studying
a "cyclical" relationship (between wages and the unemployment rate in this case) in the context of a model that
ties down long-run behavior (here, of the wage rate).
Wage-Price Causality
Our model also provides a straightforward way to study
another set of issues, namely, the relationship between
wages and prices. Causal relationships between these
variables can be motivated in a number of ways. For
example, Keynesian models commonly specify prices as a
markup over wages. In these models a permanent change
in the level of wages will have a permanent effect on the
level of prices. Similarly, it is not hard to find models of
the real wage rate in which nominal wages react to price
innovations.
Two papers that recently looked at the empirical relationship between wages and prices are Gordon (1988) and
Mehra (1991). Gordon looks at the relationship between
prices and unit labor costs, with the latter variable defined
as the difference between nominal wages and an exogenous
(piecewise linear) trend in productivity. He concludes that
wages and prices are determined independently of each
other, though the evidence that wages do not have much
effect on prices is stronger than the other way around. More
recently, Mehra (1991) has carried out a similar analysis. In
his model, prices are specified as markups over productivity-adjusted labor costs and are subject to various shocks.
Wages are specified as a function of cyclical demand and
expected prices. He then goes on to discuss how such
equations imply that wages and prices must be related in
the long run. Mehra carefully analyzes the time-series
behavior of individual series and finds that the two are
integrated of order 2, and that it is the first difference
of wages that is cointegrated with the first difference of
prices. He finds that the rate of inflation is Granger causally
prior to the rate of change of wages, not vice versa.
The VECM specification we employ here allows us to
look at the long-run relationship between wages and prices
as well. In addition, our specification allows a potential
10
FRBSF ECONOMIC
REvIEW
1995,
NUMBER
1
role for feedback from wage or price shocks to productivity
(an issue we will return to below). Before going further, it is
worth pointing out that the error correction term we employ
has an interesting antecedent in a term used in Gordon
(1988). Specifically, Gordon includes the difference between the lagged level of trend unit labor costs and the
price level in equations for both the rate of change of prices
and of trend unit labor costs, and he interprets this term as
labor's income share. It turns out that
t.~is
term does not
enter significantly into either the inflation or unit labor cost
equations.
We begin by asking about the nature of the long-run
adjustments between these variables. First, does either of
these variables adjust to maintain the long-run relationship
estimated above? Table 3 shows that the estimated error
correction term does not enter significantly into the price
level equation. We obtain the same result when we use the
test discussed in Johansen and Juselius (1990); the X2
statistic calculated under the null that the error correction
term does not belong in the price equation has a marginal
significance level of .3. By contrast, restricting the error
correction term to be zero in the wage equation leads to a
X2 (1) statistic of 19, which is significant at any reasonable
level. Thus, it is the level of wages-and not the price
level-that adjusts to maintain the cointegrating relationship in our model. This influence of prices on wages
through the error correction term means that the common
practice of estimating a single equation where the price
level is regressed on the contemporaneous wage rate (and
other variables) is inappropriate. (See Banerjee, et al.,
1993 for a discussion ofthe issues involved.) The appropriate way to proceed in studying this issue would be to
estimate this equation as part of a system that also includes
an equation for the wage rate.
It is, of course, still possible that changes in the growth
rate of wages temporarily affect the growth rate of prices.
However, the data do not provide much support for this
hypothesis either (the computed F statistic has a marginal
significance level of 18 percent). By contrast, we cannot
reject the hypothesis that changes in inflation affect the
growth rate of wages (we obtain an F statistic with a
marginal significance level of 1 percent). Thus, we find that
prices Granger cause wages but that wages do not Granger
cause prices. Our evidence against the wage markup model
echoes the results of both Gordon and Mehra, although the
results are not exactly the same. 14
14. These differences probably reflect both differences in specification
(including the precise variables used) as well as differences in modeling
strl;Ltegy. Of the latter, it is worth noting that our specification does not
include dummies or other exogenous variables.
The Dynamics of the Wages-Productivity
Relationship
We now look at how wages, prices, and productivity
respond to various disturbances to the system. Our VECM
can be used to analyze a number of interesting issues, some
of which are related to the issues raised above. For instance, we can use the model to estimate the responses to a
permanent change in productivity. Do firms react to productivity shocks by raising the nominal wage, or is the
resulting long-run increase in real wages achieved by
falling prices? Similarly, do shocks to productivity have a
significant effect on the real wage or are nominal wage
innovations more important for the real wage?
To study these and related questions we use the unrestricted VECM presented inTable 3 above. As a robustness
check, we also looked at two simplified versions of our
model. First, we used a statistical criterion to select lag
lengths; however, the resulting shorter lag lengths did not
lead to noticeable changes in the dynamic responses obtained from the model. Second, we also estimated a model
that imposed the long-run restrictions that we tested for
above; specificaHy, the model excluded the error correction
term from the price and productivity equations. We will
point out any difference in the dynamics below.
There is still the matter of identification. While there are
a number of alternative ways of imposing identifying
restrictions on vector autoregressions, none is completely
unproblematic; see Hansen and Sargent (1989) for a recent
critique. Here, we present results using the earliest such
method of identification, suggested by Sims (1980), with
the hope that we can get at some of the issues we are interested in by using relatively simple restrictions. 15 Given our
concern with productivity and the wage rate, we examined
two orderings that alternatively place productivity and
nominal wages at the top of the system. Our discussion
below focuses on the case where productivity is placed
first; however, we also discuss how the results differ in the
case where wages are placed first. 16
Figure 1 shows impulse responses from the system
where productivity is placed first, prices are placed second,
and wages are placed last. The top left panel shows the
response of LRWAG and LYHR to productivity shocks,
15. Given two variables X and Y, for example, one could leave the
residuals from the equation for X unchanged and transform the residuals
from the Y equation so that they are orthoganal to those from the X
equation. Thus, the covariance between the estimated error terms is attributed to the innovation in X, and X is said to be ordered first.
16. The correlation between LDEF and LYHR residuals is - .33, that
between LDEF and LNWAG residuals is .43, and that between LYHR
and LNWAG residuals is .30.
HUH AND TREHAN / TIME SERIES
BEHAVIOR OF THE AGGREGATE WAGE RATE
FIGURE 1
DYNAMIC RESPONSES
(ORDERING: LYHR, LDEF, LNWAO)
LYHR INNOVATIONS
240
I
40 [
LNWAG
~~~---=======~
180
LYHR
....... .............
'
-80
120
.".
'" '"
LDEF
....
""."""""."
... .. .
""
"
-140
60
.....
-200
10
30
20
50
40
60
1.u.L
...........
10
20
30
40
Quarters
50
60
Quarters
LDEF INNOVATIONS
270
o~----------------,
-60
210
LRWAG
.... "" .. """" .
-120
150
-180
90
-240 I.u.a.
...........
10
30
20
40
50
60
30
.. ,
.' .. '
LDEF
..
..
10
....... ...................
30
20
40
50
60
LNWAG INNOVATIONS
120.....----------------,
180.....-----------------,
120
60
....
LDEF
LRWAG
..,
60~ ....
Ol-.~·'
.•••••
TVHR
'.
:-O--~L-N=W...A - : G - - - - - -
•..........
~~'.:.:.'
. .~
•• ~
. . ':.:..:,'
'.=.:."
Ld
-60
. ...................
.... .
-120 I.u.a.
1
.
o IT·:...---------------;
...........
10
20
30
40
50
60
10
20
30
40
50
60
11
12
FRBSF EcONOMIC REVIEW 1995, NUMBER 1
while the top right panel shows the individual responses of
LNWAG and LDEF. (The LRWAG response is obtained as
the difference between the LNWAG and the LDEF responses.) The left panel shows that the effects of productivity innovations grow over time; the real wage changes little
over the first four to six quarters but does catch up with the
change in productivity after a while. The right panel
reveals that nominal wages do not go up very much following a positive shock to productivity; instead, the required
increase in the real wage is achieved by a fall in the price
level. Such a response might occur, for instance, if firms
tend to introduce improved products or technology at the
old prices. In the alternative ordering, where wages are
placed first, productivity second, and prices third, positive
productivity shocks also lead to permanently higher real
wages because of a reduction in the price level; however,
anomalously, the nominal wage falls somewhat.
The middle right panel shows that price level shocks are
persistent as well, and that they tend to grow over time. It
also shows that while the nominal wage does go up in
response to the price shock, it never catches up. The
outcome, shown in the middle left panel, is a permanently
lower real wage (LRWAG). Thus, price level surprises are
associated with lower productivity and real wages. A
similar result is obtained with the alternative ordering.
Such a response might result, for instance, if a negative
supply shock manifests itself first as an increase in prices.
The panels at the bottom show the effects of a positive
nominal wage shock. While the nominal wage is persistently higher as a result, the price level increases by more
than the increase in wages, so that the ultimate outcome is a
reduction in both the real wage and productivity. We obtain
a similar result in the system with the alternative ordering,
although the nominal wage shock has a larger effect on
LNWAG and LDEF than in the first ordering.
As might be expected, the effects of the nominal wage
shock are sensitive to whether the error correction term is
included in the price and productivity equations, regardless of the ordering. If this term is not included, both the
real and nominal wage return to zero over a six to seven
year horizon following a nominal wage shock (in the
LYHR, LDEF, LNWAG ordering). The initial response of
the price level in that model also is much smaller than that
shown in the bottom panels.
The variance decompositions associated with Figure 1
are shown in Table 4. LYHR appears to be largely exogenous. Note also that in the long run, LNWAG is driven
largely by LDEF innovations. LDEF is driven largely by its
own innovations, with LYHR innovations playing a small
role. The bottom panel shows that while nominal wage
innovations have a substantial impact on real wages in the
short run, they become less important as the time horizon
TABLE 4
VARIANCE DECOMPOSITIONS
ORDERING: LYHR LDEF LNWAG
QUAlITERS
AHEAD
LYHR
LDEF
LNWAG
LRWAG
LYHR
LDEF
4
8
12
60
100
99
92
87
66
26
1
4
8
12
60
10
5
9
12
16
90
94
88
84
77
1
4
8
12
60
9
2
1
0
0
81
86
94
1
4
8
12
60
34
36
54
71
66
10
7
12
10
25
1
0
1
7
11
31
72
LNWAG
0
0
1
2
8
0
1
3
4
7
60
23
19
14
t:-
v
56
57
34
19
8
NOTE: This table reports the percentage of forecast error variance that
is attributed to each of the three shocks.
lengthens, while productivity innovations become more
and more important.
The alternative ordering does lead to a greater role for
LNWAG innovations in both the LNWAG and LDEF
forecasts. For instance, at a horizon of 60 quarters, wage
innovations are somewhat more important than price innovations for predicting wages and are roughly as important
for predicting prices. However, LNWAG innovations explain almost none of the forecast error variance of LYHR or
LRWAG in the long run. And neither LDEF nor LNWAG
innovations account for much of the variation in LYHR.
Overall, despite differences between the two orderings,
they share a number of features. Thus, in both orderings
productivity shocks affect the real wage rate through price
level adjustments; price level innovations lower the real
wage, and nominal wage shocks have little effect on the
real wage in the long run.
Before concluding this section it also is worth reviewing
some of the evidence presented here in light of the results
HUH AND TREHAN / TIME SERIES BEHAVIOR OF THE AGGREGATE WAGE RATE
13
discussed in prior sections. Our results indicate that shocks
to the price level have a significant effect on wages. By
contrast, the proportion of the price level forecast error
attributable to the nominal wage shock is relatively small,
even when the nominal wage is placed first.
There is, of course, significant contemporaneous correlation between the innovations to these two variables; if
this correlation were assumed to be the result of shocks to
the wage rate, then wage shocks couid be said to have a
non-~egligible effect on pricesP However, this inference
can be reconciled with the Granger causality tests presented above only if firms complete the required price
adjustment (to wage shocks) within the quarter in which
the wage shocks occur. Such rapid adjustment seems
rather unlikely to us.
Finally, there is no evidence to suggest that shocks to the
nominal wage rate have any permanent effect on either real
wages or productivity.
REFERENCES
ill.
Espinosa, Maria Paz, and Changyong Rhee. 1989. "Efficient Wage
Bargaining as a Repeated Game." Quarterly Journal ofEconomics
(August) pp. 565-588.
SUMMARY AND CONCLUSIONS
We have argued that the time-series behavior of aggregate
wages should be studied in relation to the time-series
behavior of productivity. If productivity is nonstationary,
relatively tight restrictions on the joint behavior of these
variables can be derived from models in which the representative firm is on its demand curve in the long run. We
find that data for the postwar U.S. economy are consistent
with the hypothesis that the representative firm is on its
demand-for-Iabor curve in the long run.
This finding-which in terms of the empirics is that
productivity, wages and prices are cointegrated-allows
us to cast the data in the form of a vector error correction
model. Using this specification we find that (Granger)
causality runs from prices and productivity to wages but
not the other way around. Further, our analysis reveals that
the measured impact of cyclical variables, such as the
unemployment rate, is sensitive both to how the long run is
modeled and to the inclusion of a measure of productivity
in the wage equation. Our analysis also reveals that nominal wage innovations have little, if any, influence on the
long-run behavior of real wages (or, by implication, of
productivity). Instead, the long-term behavior of the real
wage rate is determined largely by innovations to productivity, and these innovations act almost entirely through
changes in the price level.
Abowd, 1.M. 1987. "Collective Bargaining and the Division of the
Value of the Enterprise." NBER Working Paper No. 2137.
Banerjee, Anindya, Juan Dolado, John W. Galbraith, and David E
Hendly. 1993. Cointegration, Error-Correction, and the Econometric Analysis ofNon-stationary Data. New York: Oxford University Press.
Bils, Mark. 1990. "Wage and Employment Patterns in Long-Term
Contracts when Labor Is Quasi-Fixed." NBER Macroeconomics
Annual, pp. 187-226.
Blanchard, Olivier, and Stanley Fischer. 1989. Lectures on Macroeconomics. Cambridge: MIT Press.
Christiano, Lawrence 1. 1988. "Searching for a Break in Real GNP."
NBER Working Paper No. 2695.
Engle, Robert E, and C. W. 1. Granger. 1987. "Cointegration and Error
Correction: Representation, Estimation and Testing." Econometrica (March) pp. 251-276.
Engle, Robert E, and Byung Sam Yoo. 1988. "Forecasting and Testing
in Co-integrated Systems." Journal of Econometrics, pp. 143159.
Evans, George W. 1989. "Output and Unemployment Dynamics in the
United States:1950-1985." Journal ofAppliedEconometrics 3, pp.
213-237.
Fuller, Wayne A. 1976. Introduction to Statistical Time Series. New
York: John Wiley & Sons.
Gonzalo, Jesus. 1989. "Comparison of Five Alternative Methods of
Estimating Long-Run Equilibrium Relationships." Unpublished
manuscript. University of California San Diego (November).
Gordon, Robert 1. 1988. "The Role of Wages in the Infll(ltion Process."
American Economic Review Papers and Proceedings, pp. 276283.
Hansen, Lars P., and Thomas 1. Sargent. 1989. "Two Difficulties in
Estimating Vector Autoregressions." In Rational Expectations
Econometrics. Boulder: Westview Press.
Johansen, Sl'lren, and Katarina Juselius. 1990. "Maximum Likelihood
Estimation and Inference on Cointegration-with Applications to
the Demand for Money." Oxford Bulletin of Economics and
Statistics, pp. 169-210.
MaCurdy, Thomas E., and John H. Pencavel. 1986. "Testing between
Competing Models of Wage and Employment Determination in
Unionized Markets." Journal ofPolitical Economy, pp. S3-S39.
Mehra, Yash. 1991. "Wage Growth and the Inflation Process." American Economic Review, pp. 931-937.
Nickell, Stephen. 1986. "Dynamic Models of Labor Demand." In
Handbook ofLabor Economics, eds. Orley Ashenfelter and Richard Layard. Amsterdam: Elsevier Science Publishers B. V.
Perron, Pierre. 1989. "The Great Crash, the Oil Price Shock and the
Unit Root Hypothesis." Econometrica, pp. 1361-1401.
17. The one exception to this statement is the case where we restrict the
error correction term to be zero in the price and productivity equations.
In this case, wage shocks have almost no long-run effect on prices.
Phillips, A.W. 1958. "The Relationship between Unemployment and
the Rate of Change of Money Wage Rates in the United Kingdom,
1861-1957." Econometrica, pp. 283-299.
Phillips, Peter C. B. 1987. "Time Series Regressions with a Unit Root."
Econometrica, pp. 277-301.
Comovements among National Stock Markets
Kenneth Kasa
Economist, Federal Reserve Bank of San Francisco. I
would like to thank Tim Cogley, Mark Levonian, and Carl
Walsh for helpful suggestions. Barbara Rizzi provided
excellent research assistance.
International capital markets play an important role in the
world economy. It is through these markets that risk and
investment resources are allocated across countries. Gauging the extent to which international bond and equity
markets perform these functions efficiently has therefore
been a topic of great interest to economists. Traditionally,
this question has been posed as whether or not national
capital markets are "integrated" or "segmented." That is,
do assets issued in different countries yield the same riskadjusted returns, or do they consistently yield different
returns because of informational and governmentally imposed barriers? Clearly, if international capital markets are
to provide appropriate signals to savers and investors,
national bond and equity markets must be integrated.
Attempts to answer this question are plagued by two
difficulties not encountered in studies of domestic capital
This paper uses the methodology of Hansen and Jagannathan (1991) to derive a lower bound on the correlation
between any pair of asset returns under the hypothesis of
complete markets. The bound is a simple function of the
two assets Sharpe ratios and the coefficient ofvariation of
a unique stochastic discount factor. The paper uses this
bound to conduct robust1 nonparametric tests of the hypothesis that international equity markets are integrated.
Using monthly stock return datafrom the U.S., Japan,
and Great Britain for the period 1980 through 1993, I find
that conclusions about market integration depend sensitively on the assumed variation of the (unobserved)
common world discount rate. Given the observed correlations in returns, markets are more likely to be integrated
the more volatile is the discount rate.
market efficiency. First, assets issued in different countries
tend to be denominated in different currencies, and exchange rate volatility adds an additional element of uncertainty to international investments. As a result, when
testing the integration hypothesis one must either include a
model of the pricing of exchange rate risk, or consider
returns that have been "covered" against exchange rate
risk. Second, because of taste differences and transportation costs, consumption patterns differ across countries
much more than they do across regions within a single
country. Since investors want to hedge their real consumption risks, this means that the riskiness of a given asset
depends on the owner's country of residence. These problems make it even more difficult than usual to define a riskadjusted return, and consequently, make the results in this
literature difficult to interpret.
Studies of international bond markets generally conclude that markets are becoming increasingly integrated.
This is particularly true when exchange risk and consumption differences are not an issue, e.g., when testing Covered Interest Parity. 1 Tests of Uncovered Interest Parity,
however, have led to more ambiguous results. Although the
hypothesis is typically rejected, no one has yet formulated
1. See Frankel (1993) for a survey of the evidence on short-term covered
interest parity. Popper (1993) provides evidence on long-term covered interest parity.
KAsA/COMOVEMENTS AMONG NATIONAL STOCK MARKETS
an economic model of exchange rate risk that can explain
these rejections. This has led some observers to question
the efficiency of the foreign exchange market. 2 Even more
stringent tests of international bond market integration,
which require assumptions about both foreign exchange
risk and international consumption differences, are conducted by Cumby and Mishkin (1986). They document
close, but imperfect, linkages among the (ex ante) real
interest rates of the U. S. and Europe. Glick and Hutchison
(1990) apply the same methodology to real interest rate
linkages between the U. S. and a set of Pacific Basin
countries and find that financial liberalization has increased the linkages among these markets.
In this paper, I examine the integration of international
stock markets. Early work on this topic followed the same
basic logic as bond market studies. That is, the extent of
integration was judged by the correlation of returns, the
idea being that greater equity market integration should
lead to greater correlation among national stock markets. 3
Although this idea seems plausible, and in fact remains the
conventional wisdom within the business community, we
know. from the work of Lucas (1982) that the important
implication of integrated capital markets is the equalization among countries of marginal rates of substitution in
consumption, both intertemporally and across states of
nature. Stock returns in an integrated market mayor may
not be highly correlated, depending upon the nature of
international specialization and the correlation of national
productivity shocks. For example, stock markets may be
segmented, yet stock returns could nonetheless be highly
correlated if countries produce similar goods or if productivity shocks are highly correlated across countries. Conversely, stock markets might be integrated even if national
stock returns are weakly correlated if countries are specialized in the production of different goods and if productivity shocks are weakly correlated across countries. This
suggests that the coherence among national consumption
growth rates probably provides a better metric for the
degree of international capital market integration than does
the correlation of stock returns.
Obstfeld (1993) pursues this strategy and concludes that
the weak relationships observed among national consumption growth rates are inconsistent with the hypothesis of
internationally integrated capital markets, although he
does find that markets have become more integrated over
time. However, as Obstfeld himself acknowledges, this
2. Froot and Thaler (1990) survey the evidence on Uncovered Interest
Parity.
3. See lorion (1989) for a survey of early work on international stock
market integration.
15
approach suffers from a couple of severe drawbacks. First,
in order to link consumption data to the marginal rate of
substitution, one must specify a utility function. That is,
this strategy is "parametric," and as a result one can never
be sure whether a given rejection represents a bona fide
rejection of the hypothesis of integrated markets or merely
represents a rejection of the posited utility function. Second, it is widely recognized that consumption data contain
measurement error. This creates econometric difficulties in
implementing this approach.
This paper adopts a strategy that avoids these problems.
Not only is it nonparametric, and therefore robust to
functional form misspecification and measurement error
biases, but it also resurrects the intuitive notion that
integration of equity markets should place restrictioJ:ls on
the observed correlation among national stock markets. In
particular, I adapt the methodology of Hansen and Jagannathan (1991) to derive a lower bound on the correlation between national stock market returns under the hypothesis
of integrated markets. If the observed correlation between
a pair of stock market returns is below its lower bound,
then we can conclude that these markets do not share the
same discount rate, or in other words, are not integrated.
The basic idea behind this approach is as follows.
Hansen and Jagannathan derive a lower bound on the
volatility of an unobserved stochastic discount factor. This
discount factor translates future state-contingent payoffs
into current asset prices. Economic theories of asset pricing are distinguished according to how they link this
discount factor to observable variables. For example, in the
approach taken by Obstfeld the discount rate is assumed to
be equal to the intertemporal marginal rate of substitution
in consumption, while in the static CAPM it is assumed to
be proportional to the return on the "market portfolio."
Now, the hypothesis of integrated markets means that this
discount factor is the same across countries, which implies
that the Hansen-Jagannathan bound must be the same
across countries. In particular, the lower bound on the
standard deviation of the common world discount rate
becomes a function of the observed variances and covariances of national stock market returns. In essence, all I do
in this paper is invert this volatility bound to derive a lower
bound on the correlation coefficient of returns as a function
ofthe standard deviation of the unobserved discount factor.
If the observed correlation is below this bound, then we
must reject the joint hypothesis of integrated markets and
the given value for the volatility of the stochastic discount
factor.
Before proceeding, one should understand the caveats to
this approach. First, as always we are testing a joint
hypothesis. This manifests itself here as the need to specify
16
FRBSF ECONOMIC REVIEW 1995, NUMBER 1
the standard deviation of the unobserved discount rate
process. As we will see, we can always accept the hypothesis of integrated markets if we are willing to entertain a
sufficiently volatile discount rate. The advantage of this
approach,·therefore, is the flexibility it provides in linking
the integration hypothesis to a broad spectrum of asset
pricing models. We merely have to determine whether the
volatility of the model-implied discount rate falls in a
region that is consistent with the observed correlation of
stock returns. If not, then either the discount rate model is
false, or markets are segmented.
The second caveat to keep in mind is that we are actually
testing a stronger hypothesis than stock market integration.
In particular, we are testing whether markets are complete,
i. e., whether individuals have access to a full menu of dateand state-contingent securities, so that everyone, regardless of country of residence, has the same marginal rate of
substitution in consumption, across all points in time and
across all states of nature. Clearly, this is a very strong
assumption. Stock and bond markets might be perfectly
integrated, yet individuals could nonetheless end up with
different marginal rates of substitution if these markets do
not provide adequate insurance for all the risks that individuals face. Thus, as Obstfeld (1994) stresses in his recent
survey, it would be desirable to develop a framework that
allows us to test the stock market integration hypothesis
without at the same time making such strong assumptions
about the integration of goods markets and the nature of
uncertainty. 4
The remainder of the paper is organized as follows.
Section I briefly outlines the derivation of the HansenJagannathan bound on the volatility of stochastic discount
factors. Section II then inverts this bound to get a lower
bound on the correlation between asset returns. The correlation bound turns out to be a simple function of the two
assets' Sharpe ratios and the coefficient of variation of the
unobserved discount factor. Section III turns to empirical
evidence. In particular, I consider whether the pairwise
correlations among the stock markets of the U.S., Japan,
and Great Britain satisfy their lower bounds. For standard
models of the discount factor, observed correlations lie
well below their lower bounds. This is because these
models imply lower bounds that exceed unity. Of course, as
noted above, rather than concluding that stock markets are
segmented, an equally valid interpretation of this result is
to reject the posited models of the discount factor. In fact,
4. In a related context, Tesar (1993, 1994) has stressed the need to
incorporate nontraded goods into models of international capital market
equilibrium.
this has been the typical finding in this literature. 5 Not
surprisingly, if we instead consider discount factors with
volatilities approaching the Hansen-Jagannathan bounds
reported in Bekaert and Hodrick (1992), we find that
observed correlations satisfy their lower bounds. Finally,
Section IV contains the conclusion and offers some suggestions for future research.
I.
DERIVING BOUNDS
ON STOCHASTIC DISCOUNT FACTORS
This section outlines how Hansen and Jagannathan (1991)
use a set of observed asset returns to derive a lower bound
on the volatility of an unobserved stochastic discount
factor. The discussion will be brief, and the interested
reader is urged to consult Hansen and Jagannathan's paper
for full details.
The starting point for the analysis is the following
equation, which relates the price, 7T(P), of a given future
state-contingent payoff, p, to an unobserved stochastic
discount factor, m:
7T(P) = E(mp).
(1)
There are several ways to interpret this expression. The
most general is to view m as the continuous linear pricing
functional that is guaranteed to exist (by the Riesz Representation Theorem) as long as asset prices satisfy the "Law
of One Price." If we also assume there are no arbitrage
opportunities, then m must be nonnegative at all dates and
in all states. Moreover, of particular relevance for this
paper is the fact that if markets are complete, then m is
unique (i.e., the same for all assets and all investors).
While viewing m as an implication of the Riesz Representation Theorem provides a powerful unifying principle
for asset pricing theories, a more intuitive interpretation of
eq. (1) is to use the definition of the covariance operator to
write it as follows:
(2)
7T(P)
= E(m)E(p) + cov (m,p) ,
Equation (2) illustrates the sense in which m plays the role
of a discount rate. The first term on the right hand side of
eq. (2) uses E(m) to discount the mean payoff, while the
second term adjusts for the payoff's riskiness.
Next, it often proves convenient to normalize asset
prices to unity and rewrite eq. (1) in terms of asset returns:
(3)
1 = E(mr) ,
5. Employing standard utility function specifications, Obstfeld (1993)
soundly rejects the consumption-based model of the discount factor.
Frankel (1994) discusses the poor performance of static CAPM models
of the discount factor.
KASA / COMOVEMENTS AMONG NATIONAL STOCK MARKETS
where r denotes the (gross) rate of return on an asset.
Clearly, eq. (3) by itself imposes no restrictions on the data,
since for a single asset we could always take m = 1/r.
However, because the same m must satisfy eq. (3) for all
returns, we have a set of overidentifying restrictions that
can be tested if an explicit model for m is specified. This is
the strategy pursued by Obstfeld (1993). However, to
impose as little structure on the data as possible, Hansen
and Jagannathan (1991) proceed nonparaInetrically and
infer.bounds on the moments of m from the observed
moments of a set of portfolio returns.
To do this, note that since eq. (3) must hold for all assets
(and, indeed, for all portfolios of assets), we can use the
linearity of the expectations operator to subtract the analogous expression for the risk-free rate and get:
(4)
o=
E(mre),
where re denotes an asset's excess rate of return. Finally,
define the n x 1 column vector of excess returns, Re, and
write the vector analogue of eq. (4):
(5)
<T~ ~
WI13,
where <T~ denotes the variance of m. Finally, from the
algebra of least squares we know that
(7)
13 = I-l [E(mRe)
- E(m)E(Re)].
Using eq. (5), this can be simplified to:
(8)
Finally, plugging eq. (8) into eq. (6), and then rearranging,
we get:
(9)
variation of the unobserved stochastic discount factor must
be at least as large as the quadratic form on the right-hand
side of (9). In the next section, I write out this quadratic
form for the case of two stock returns, and then rearrange it
to get a bound on their correlation coefficient as a function
of <Tm/E(m).
II.
INVERTING THE HANSEN-JAGANNATHAN
BOUND TO GET A CORRELATION BOUND
The following proposition is the major result of this section. It relates the lower bound on the correlation between
two assets to the two assets' Sharpe ratios and the volatility
of a stochastic discount factor.
PROPOSITION: Ifmarkets are complete, then the correlation
between any pair ofexcess returns must satisfy the following lower bound:
(10)
p
~ x m2 -4(S.-S.)2
'
J
l
where Sj and Sj are the observed Sharpe ratios of assets i
where m is a scalar, and 0 is an n X 1 column vector of
zeros. Equation (5) provides a succinct representation of
capital market equilibrium.
Now, although m is not directly observable, imagine
regressing m onto a constant and the vector of excess
Re, where 0. is the regression
returns, i.e., m = 0. + W
intercept and 13 is the vector of slope coefficients. Of
course, this regression will not provide a perfect fit. That
is, there will be a regression error term, which by construction is uncorrelated with the fitted value from the regression. As a result, the variance of m must be at least as large
as the variance of its predicted value. This variance is just
equal to WI13, where I is the variance-covariance matrix
of excess returns. In other words, it must be the case that
(6)
17
( <Tm
E(m)
.
..
.
an d j,. anu-l X m · is
th"e coe).(fi'
£Clent OJ+ variation
OJ+ a unique
(unobserved) stochastic discount factor. 6
The proof consists of two steps. First, with complete markets eq. (9) must hold (with the same unique m)
for all collections of assets. By writing out the q~adratic
form on the right-hand side of (9) for the case of just two
assets, and then simplifying, we get:
PROOF:
(11)
(
<T
_m_
E(m)
)2 ==
x2
m
~
2s.s.
__
' J_
l+p
+
(1 +p)(l-p)
Since this is nonlinear in p, it is convenient to take an
approximation in order to be able to isolate p. Thus, the
second step involves taking a first-order Taylor series
expansion of 1/(1- p) around the point p = .5. Given the
strict convexity of 1/(1 - p), this delivers the inequality
4p<1/(1- p). Using this in (11) and rearranging gives the
bound in the proposition.
Three points need to be made about this correlation
bound. First, note that we could apply the quadratic
formula in (11) and get a more precise bound. The only
reason I take a linear approximation is to obtain a simple
and easy to use expression for the bound. Calculations have
shown that unless the true correlation bound is well outside
the interval (0, 1) the approximation works quite well.
)2 ~ E(Re)'I-lE(Re).
Equation (9) is a version of Hansen and Jagannathan's
volatility bound. It says that the (squared) coefficient of
6. The Sharpe ratio of an asset is its mean excess return divided by its
standard deviation.
18
FRBSF ECONOMIC REVIEW 1995,
NUMBER
1
Second, as noted earlier the bound contains no information that is not already contained in the volatility bound of
Hansen and Jagannathan. In fact, plugging in the volatility
bound implied by the two assets under consideration simply yields the actual observed correlation coefficient as the
correlation bound! (Up to a second-order approximation
error that is involved in deriving the bound.) Thus, the
correlation bound is just an alternative expression for
the Hansen-Jagannathan bound, although one that is perhaps more convenient to apply and interpret when assessing the market integration hypothesis.
The third point to note is that the bound declines as the
volatility of the discount factor increases. In other words,
the more volatile is the discount rate implied by a given
economic model, the more likely it is that the model will be
consistent with the market integration hypothesis. At first
it might seem puzzling that greater volatility in the discount rate lowers the required correlation between two
stock markets. After all, the discount rate is a common
factor in the stochastic evolution of the two markets, and
increasing the variance of a common factor should increase
the degree of comovement between the two markets. This
intuition is indeed correct, but it ignores the distinction
between covariance and correlation. Increasing the volatility of the discount rate also increases the standard
deviation of stock returns, and it turns out that this offsets
the greater covariance of returns, so that in the end the
correlation bound decreases with CJ'm'
m. EMPIRICAL EVIDENCE
The previous section showed that the hypothesis of international stock market integration imposes restrictions on the
correlations among national stock markets. Specifically, if
markets are integrated, then the observed correlation between each pair of returns must exceed its lower bound
given by eq. (10). If it doesn't, then we must either reject
the posited value for the volatility of the discount rate, or
conclude that these two markets do not share the same
discount rate, and therefore are not integrated.
Clearly, the crucial input in the analysis is the presumed
volatility of the unobserved discount rate. From inspection
of eq. (10), we can always accept the integration hypothesis
if we posit a large enough value for CJ',jE(m). Thus, this
section considers various specifications for this parameter
and their associated implications for the hypothesis of
international stock market integration.
Before doing this, however, we must take a look at some
data, since we also need to have values for the stock market
correlations and the Sharpe ratios in each market. In this
paper I consider the global economy's three major stock
markets: those ofthe U.S., Japan, and Great Britain. The
data are monthly, end-of-period observations on Morgan
Stanley's CapitalInternational indices for the period 1980:1
through 1993:11. These indices are value-weighted and are
based on a large sample of firms in each market. Crosslisted securities have been netted out. Returns are inclusive
of (gross) dividend reinvestment and are expressed in U.S.
dollar terms. Each return series is converted to "excess
returns" by subtracting the one-month U.S. CD rate.
Tne three pairwise correlations between excess returns
are:
(US, JP) = .246 (US, UK) = .531 (JP, UK) = .430
While the mean excess returns are (in units of percent
per month):
US = .563
JP = .847
UK= .747
And the standard deviations are:
US = 4.46
JP = 7.42
UK = 6.30
Therefore, the Sharpe ratios tum out to be:
US = .126
JP = .114
UK = .119
Thus, from the perspective of the static CAPM, it appears
that over this period the U. S. market offered investors the
best (dollar-denominated) risk/return trade-off. 7
Using these data, Figure 1 plots out the correlation bound
for each country pair as a function of CJ',jE(m). The dotted
line in each figure represents the actual observed value for
the correlation coefficient. Evidently, of the three bivariate
relations, the UK-Japan pair exhibits the strongest evidence
in favor of market integration. That is, the bound is
satisfied with the smallest value for CJ'm/E(m). On the other
hand, the US-Japan pair exhibits the strongest evidence
against the integration hypothesis, since it takes the largest
value of CJ'm/E(m) to satisfy its correlation bound. Still, the
differences are not large. Any value of CJ'm/E(m) below .135
indicates market segmentation, while a value greater than
.155 would suggest market integration.
What does economic theory tell us about the value of
CJ'm/E(m)? As emphasized by Hansen and Jagannathan,
traditional economic models ofthe discount rate have a hard
time producing discount rates with this much volatility. For
example, the two most commonly employed discount rate
models are the static CAPM, which links the discount
rate to the return on a (value-weighted) world market port-
7. As noted in the introduction, this inference can be misleading since
residents of different countries consume different goods. As a result, it
would probably be more accurate to consider own-currency excess
returns, under the supposition that investors completely hedge the
exchange rate risk associated with foreign equity investments.
KASA / COMOVEMENTS AMONG NATIONAL
folio, and the consumption-based CAPM, which links the
discount rate to a representative agent's intertemporal
marginal rate of substitution in consumption. Constructing
a value-weighted portfolio from the U.S., Japanese, and
British markets produces a value for CTm/E (m) of just.045.
Moreover, unless you introduce habit persistence or statenonseparabilites, the consumption-CAPM produces even
smaller values for CT,jE(m). Values for CT,jE(m) of this
order of magnitude then produce lo~ver correlation bounds
well in excess of unity. By itself, this suggests that international stock markets are segmented. However, remember
that an alternative interpretation of these results is to reject
the posited models of the discount rate.
How are we to decide between these two inferences?
While the joint nature of the integration hypothesis can
never be eluded entirely, the approach in this paper facilitates the choice between the two interpretations. Clearly, it
makes no sense to test the hypothesis of international stock
market integration using a model for the (common) discount rate that produces a value for CTm/E(m) that is below
the maximum Sharpe ratio of the considered countries.
After all, two markets cannot be "integrated" if each
individually violates the Hansen-Jagannathan bound. 8 In
the context of this paper, this means that it only makes
sense to consider discount rate models with implied volatilities (i.e., coefficients of variation) in excess of .126,
which is the maximal Sharpe ratio among the markets of
the U.S., Japan, and Great Britain. Testing the integration
of these three markets using a model that implies a less
volatile discount rate is bound to lead to ambiguous
results, as it is not even consistent with domestic stock
market efficiency.
Figure 1 illustrates that it is possible to conclude that
individual national stock markets are efficient, but not
integrated. For example, any value of CT,jE(m) that lies
between .13 and .15 is a viable model of the U.S. and
Japanese equity markets considered in isolation, but is
inconsistent with the hypothesis that these two markets are
integrated. As noted earlier, however, it is quite difficult to
formulate economic models with implied discount rate
volatility anywhere near .13. This suggests that parametric
testing of the international stock market integration hypothesis must await further advances in dynamic asset
pricing theory.
Given this state of affairs, the nonparametric approach
of this paper provides a valuable tool for the assessment of
international stock market integration. Specifically, by
SroCK MARKETS
FIGURE 1
CORRELATION BOUNDS
JAPAN AND
0'8
K
0.7
_ _.
0.6
U.S.
Lower Bound
0.5
0.4
0.3
0.2
0.1
o +---,---,-----,--,---..,..---,
0.13
U. S.
0.135
0.14
0.145
0.15
0.155
0.16
AND GREAT BRITAIN
0.8~
0.7
Accept ---1"~
Reject...
0.6
~
~ __
0.5
0.4
0.3
0.2
0.1
0
0.13
0.135
0.14
0.145
0.15
0.155
0.16
0.155
0.16
JAPAN AND GREAT BRITAIN
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.13
8. By the Cauchy-Schwarz inequality, adding countries to the calculation of the Hansen-Jagannathan bound must increase(or at least not
decrease) the lower bound on the volatility of the discount factor.
0.135
0.14
0.145
0.15
NOTE: The horizontal axis measures the coefficient of variation of
the discount factor.
19
20
FRBSF EcONOMIC REVIEW 1995, NUMBER 1
checking to see by how much the minimum integrationconsistent discount rate volatility exceeds the maximal
Sharpe ratio, we get a rough idea of how likely it is that
two markets are integrated. This is the basis for the previous conclusion that the integration hypothesis is most
strongly supported in the case of Japan and Great Britain,
and least supported in the case of the U.S. and Japan.
1 V. CONCLUSIONS AND EXTENSIONS
This paper has developed a simple, "back-of-the-envelope"
procedure for determining whether the observed correlation between two national stock markets is consistent with
the hypothesis of international stock market integration.
All you have to do is get data on the countries' Sharpe
ratios, and then specify a parameter that captures the
volatility of the common world discount rate. The advantage of the approach is that it provides a flexible and
intuitive method for mapping out the relationship between
economic theory (as expressed in a discount rate model)
and normative conclusions about capital market efficiency.
Perhaps not surprisingly, conclusions about market integration depend sensitively on this parameter. The more
volatile is the posited discount factor, the more likely it is
that observed comovements among national stock markets
are consistent with the hypothesis of internationally integrated markets. As noted above, none of the standard
economic models of asset pricing produce discount factors
that are sufficiently volatile to be consistent with the
hypothesis of integrated markets. However, I argued that at
this stage it is more appropriate to reject the models than it
is to reject the integration hypothesis. In addition, I argued
that the nonparametric approach of this paper provides
guidance on how to construct models that are minimally
capable of addressing the integration hypothesis, in the
sense that they are at least viable models of domestic
capital market efficiency.
As a final caveat, one should keep in mind that all of the
analysis here has been based on point estimates that are
subject to sampling variability. Future work along these
lines should attempt to incorporate standard statistical
inference considerations. This would enable us to assess
the statistical significance of observed differences between
market correlations and their lower bounds. The recent
work of Hansen, Heaton, and Luttmer (1993) should
provide the necessary tools for such an extension.
REFERENCES
Bekaert, Geert, and Robert 1. Hodrick. 1992. "Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets." Journal ofFinance 47, pp. 467-508.
Cumby, Robert E., and Frederic S. Mishkin. 1986. "The International
Linkage of Real Interest Rates: The European-US. Connection."
Journal ofInternational Money and Finance 5, pp. 5-23.
Frankel, Jeffrey A. 1993. "Quantifying International Capital Mobility
in the 1980s. in On Exchange Rates (Chapter 2). MiT Press.
_ _ _ _ . 1994. "Introduction." In The Internationalization of
Equity Markets, ed. 1. Frankel. NBER.
Froot, Kenneth A., and Richard H. Thaler. 1990. "Anomalies: Foreign
Exchange." Journal of Economic Perspectives 4, pp. 179-192.
Glick, Reuven, and Michael Hutchison. 1990. "Financial Liberalization in the Pacific Basin: Implications for Real Interest Rate
Linkages." Journal of the Japanese and International Economies
4, pp. 36-48.
Hansen, Lars P., John Heaton, and Erzo Luttmer. 1993. "Econometric
Evaluation of Asset Pricing Models." NBER Technical Working
Paper No. 145.
Hansen, Lars P., and Ravi Jagannathan. 1991. "Implications of Security
Market Data for Models of Dynamic Economies." Journal of
Political Economy 99, pp. 225-262.
Jorion, Philippe. 1989. "The Linkages between National Stock Markets." In The Handbook ofInternational Financial Management,
ed. R. Aliber. Dow Jones-Irwin.
Lucas, Robert E., Jr. 1982. "Interest Rates and Currency Prices in a
Two-Country World." Journal of Monetary Economics 10, pp.
335-359.
Obstfeld, Maurice. 1993. "Are Industrial-Country Consumption Risks
Globally Diversified?" NBER Working Paper No. 4308.
_ _ _ _ . 1994. "International Capital Mobility in the 1990s."
In Understanding Interdependence: The Macroeconomics of the
Open Economy, ed. Peter Kenen. Princeton Univ. Press.
Popper, Helen. 1993. "Long-Term Covered Interest Parity: Evidence
from Currency Swaps." Journal of International Money and
Finance 12, pp. 439-448.
Tesar, Linda L. 1993. "International Risk-Sharing and Nontraded
Goods." Journal ofInternational Economics 35, pp. 69-89.
_ _ _ _ . 1994. "Evaluating the Gains from International RiskSharing." Unpublished manuscript.
Changes in the Structure of Urban Banking
Markets in the West
Elizabeth S. Laderman
Economist, Federal Reserve Bank of San Francisco. The
author wishes to thank Jennifer Catron and Deanna Brock
for research assistance.
This paper begins with a discussion of the influence of
the number of firms and the variance of market shares
on the Herfindahl-Hirschman Index (HH/) measure of
market concentration. The paper then reports the changes
in the number of depository institutions (DIs) and in the
HHI in the Twelfth District and its 65 individual urban
banking markets between 1982 and 1992, attributing these
changes to underlying causes. I find that, although an
increase in concentration need not accompany a decrease
in firms, more than two-thirds of the 53 markets with DI
decreases showed concentration increases. This suggests
that regulatory review of DI mergers has been and will
continue to be important in assuring the competitiveness of
banking markets.
Over the past decade, consolidation has led to many
changes in the banking landscape. In the West, mergers
such as those between Wells Fargo Bank and Crocker
National Bank and between Bank of America and Security
Pacific National Bank, as well as many less dramatic
combinations, have eliminated banks from Alaska to Arizona. At the same time, numerous banks and even more
thrifts have failed. Although brand new banks and thrifts
continue to be formed, between 1982 and 1992, the Twelfth
District saw the number of depository institution competitors decline by 15 percent, from 932 to 792,1
In this paper, I will discuss the changes wrought by a
decade of bank and thrift mergers, failures, and entry on
the structure of urban banking markets in the West. 2
Market structure is important because it is thought to
influence competition, which, ultimately, can affect the
welfare of the entire economy. The paper will focus on two
aspects of market structure: the number of competitors and
the concentration of market shares.
The paper will proceed as follows. In the first section, I
briefly discuss the structure-conduct-performance paradigm of industrial organization theory. I also introduce the
concept of market concentration and the statistic often used
to measure it, the Herfindahl-Hirschman Index (HHI). The
second section discusses how changes in the distribution of
market shares and the number of depository institutions
affect concentration. In the third section, I discuss the
changes in concentration and in the number of depository
institutions in the Twelfth District overall. In the fourth
section, I report the changes in concentration and in the
number of depository institutions in 65 local urban markets
between 1982 and 1992 and attribute these changes to
underlying causes. I also draw some general conclusions
1. Here and throughout the paper, I refer to the states ofAlaska, Arizona,
California, Hawaii, Idaho, Nevada, Oregon, Utah, and Washington
collectively as the Twelfth District. The Federal Reserve Bank of San
Francisco, which serves the Twelfth Federal Reserve District also
serves American Samoa, Guam, and the Commonwealth of the Northern Mariana Islands.
2. Relatively little research of this type has been conducted. However,
David Holdsworth (1993) does provide some information on changes in
the structure of banking markets in New York and New Jersey between
1980 and 1991.
22
FRBSF ECONOMIC REvIEW 1995, NUMBER 1
regarding causes for changes in concentration and competitiveness in these markets. The fifth section concludes the
paper.
1.
THE STRUCTURE-CONDUCT-PERFORMANCE
PARADIGM AND THE HHI
The structure-conduct-performance paIadigm states that
market structure influences firm conduct and, in tum,
economic performance, and that the direction of such
effects often is predictable. Elements of market structure
include the number and size distribution of sellers and
buyers, the degree of product differentiation, and the
existence and extent of barriers to entry into the market.
Characteristics of firm conduct include pricing behavior,
advertising strategy, and technological innovation. Performance includes the efficiency of production and resource allocation. 3
It is one of the most fundamental structure-conductperformance theories of industrial organization that the
smaller the number of firms dominating a market, the more
likely those firms will be able to collude to maintain prices
above the competitive level and thereby operate at an
inefficient point on the production function. This link
makes the study of market concentration valuable. Ideally,
one would study market performance directly, because this
is what we really care about, but this usually is infeasible.
For example, determining the efficiency of production
requires knowing the production technology, which often
is very difficult, especially for multidimensional services
such as banking. Alternatively, the structure-conductperformance paradigm suggests that the conduct of firms is
closely connected to performance. Here again, however,
we often cannot directly observe firms' behavior. However,
market concentration usually is fairly easy to measure.
Determining changes in market concentration, then, can
help to suggest the changes that may have taken place in
competitiveness and productive efficiency.
However, the relationship between concentration and
efficiency is not necessarily as unambiguous as just described. Many economists have pointed out that more
concentrated markets may in fact be more efficient. This
could be because efficient firms are more profitable, which
causes them to grow and acquire market share. Therefore,
efficient markets are ones in which there are a few large,
profitable, and efficient firms, and inefficient markets are
3. EM. Scherer discusses the structure-conduct-perfonnance paradigm
and uses it as the organizing theme for his classic textbook of industrial
organization theory, Industrial Market Structure and Economic Performance (1980).
ones in which no such efficient firms have emerged to take
the lead in market share. In addition, economies of scale or
scope in production may mean that being large causes a
firm to be efficient. Again, this may mean that a market
with a few large firms is more efficient than a market with
many smaller firms.
Despite the validity of these arguments, numerous empirical studies support the view that, in many industries
and under many circumstances, the greater the concentration of output in a small number of firms, the greater the
likelihood of welfare losses due to weak competition and
thereby low efficiency of production.
The Herfindahl-Hirschman Index
In fact, the link between concentration and the likelihood
of welfare losses is sufficiently accepted that an assessment
of the change in concentration is central to regulators'
analyses of the effects of proposed mergers between firms
in many industries, including banking. Banks and bank
holding companies must apply to one or more ofthe federal
banking agencies for approval of mergers and acquisitions.
If regulators find that the proposed transaction would raise
market concentration too much, the merger or acquisition
application may be denied, or divestitures of branches or
other assets to third parties may be required.
To measure concentration in banking markets, the federal bank regulatory agencies and the Department of Justice (DOJ) use a statistic called the Herflndahl-Hirschman
Index (HHI). The HHI is computed as the sum of the
squares of the percentage of deposits held by each of
the competitors in a market. For example, if a market has
only one firm, then the HHI is 1002 , or 10,000. If the
market is evenly divided between two firms, the HHI is 502
+ 502 , or 5,000.
The following example illustrates the use of the HHI for
the evaluation of a hypothetical merger. Say that there are
four banks in a market: A, B, C, and D. Say that, before the
merger, A produces 35 percent of the output in the market,
B 30 percent, C 20 percent, and D 15 percent. The premergerHHI, then, is35 2 + 302 +202 + 15 2 ,or2,750. Now,
assume that banks B and D merge. The HHI after the merger
would be 35 2 + (30+ 15)2+ 202 , or 3,475. The merger inreases the HHI by 725.
For evaluating individual mergers, the DOl's bank merger policy indicates that a bank merger that increases the
HHI in a local market by 200 points or more and results in
an HHI of at least 1,800 would raise competitive concerns.
While the policy is not hard and fast, its use has led to the
denial of merger applications and, more often, to the divestiture of banking offices to third parties to reduce the
effects on market concentration. As a result, the policy has
LADERMAN / STRUCTURE OF URBAN BANKING MARKETS IN THE WEST
helped contain the adverse effects of individual mergers on
competition.
In addition to being used for individual merger analysis,
the HHI can be used to track changes in concentration over
a period of time. Changes in concentration may be due to
mergers, acquisitions, failures, withdrawals from the market, or simple shifts in market shares due to the dynamics of
competition among an established set of banks and thrifts.
The purpose of this paper is to describe how concentration
and competitiveness in urban banking markets in the West
changed between 1982 and 1992 and to discuss underlying
causes for these changes and implications for policy. Because of its use in the competitive analysis of bank mergers, the HHI is an intuitively appealing measure of
concentration and will be used in this paper. 4
ll.
DETERMINANTS AND DYNAMICS
OF THE-HIll
In this section, I will discuss the relationship between the
HHI and its two underlying determinants: the number of
firms in a market and the distribution of market shares
among those firms. The key to this relationship is the
recognition that the HHI can be decomposed into the sum
of two terms, one that depends on the number of firms and
one that depends on the variance of their market shares. 5
The HHI is given by
N
HHI = ;~1
(1)
xl,
where Xi is the percentage market share held by firm i and N
is the total number of firms in the market. The variance of
market shares, V, is
1
V = N
(2)
N
! (x.
;=1
- x)Z ,
1
where x is the mean market share. Noting that
I
V = -
(3)
N
x=
1
- XZ
1
'
N
N
! x
;=1 i
--
100
N
'
we have, from (1),
(5)
HHI
Equation (5) states that the HHI is the sum of two terms,
the first a function of the number of firms and the variance
of market shares and the second a function only of the
number of firms. Two conclusions emerge directly from
equation (5). First, the HHI increases with the variance of
market shares. Therefore, given the number of firms, if the
variance is at its minimum, the HHI also must be at its
minimum. The minimum value of the variance is zero, and
this yields a minimum HHI of lO,OOO/N. Second, if the
HHI exceeds 1O,000/N, it must be because the variance is
greater than zero. By definition, the variance of a group of
numbers is zero if and only if all of the numbers are equal.
Therefore, the first term on the right-hand side of equation
(5) can be interpreted as the contribution to the HHI ofthe
dispersion of market shares away from equality, the "inequality effect," while the second term is what the HHI
would be were the market shares of all N firms equal, the
"number of firms" effect.
Because the HHI depends on the variance of market
shares, shifts in the distribution of market shares affect the
HHI. The effect of a change in market shares, holding N
constant, can most easily be seen for the case in which only
two market shares change. Let the original HHI be given by
(1). Then, let the new HHI be given by
N
(6)
HHI' =
yZ
+
zZ
+
! x.Z •
;=3
1
Here, in the new distribution of market shares, Xl and Xz
have been replaced by y and z, but none of the other market
shares have changed. Subtracting (1) from (6), one finds
that the HHI rises if and only if
(7)
yZ
+
ZZ
> x1Z +
xl .
However, we know that the sum of market shares must
always be 100, so we can use the requirement that Xl + Xz
equal y + z, and therefore that their squares be equal, to
simplify the above condition to
(8)
N
! x.z
;=1
and that
(4)
23
= NV + Nx Z = NV + 10,000
N
4. For more on the HHI, see Rhoades (1993).
5. I thank Mark Levonian for pointing out this relationship.
We now see that, if two of the market shares change, the
new HHI will exceed the old HHI if and only if the product
of the new shares is less than the product of the old shares.
The product of two numbers, the sum of which is a
constant, increases as the two numbers converge and
decreases as they diverge. Therefore, the new HHI will exceed the old HHI if the two shares have diverged and will
be less than the old HHI if the two shares have converged.
This also is the condition under which the variance of
market shares increases when two market shares change.
This is expected: From (5), it is apparent that, if the number
of firms is held constant, concentration increases if and
only if the variance of market shares increases.
24
FRBSF ECONOMIC REvIEW 1995,
NUMBER
1
The insight offered by equation (8) also provides a
convenient way to prove that within-market mergers must
increase concentration if none of the market shares of the
uninvolved firms change. Let N be the number of firms in
the market before the merger, and let the firms that will
merge, firm I and firm 2, have market shares of Xl and x2 .
After the merger, one can still think of the market as having
N firms. The new, merged firm, has market share y=xI +
x 2 ' and it can be thought to have repiaced, say, firm L Firm
2's new share, z, is now zero. As long as the market shares
of all of the N - 2 uninvolved firms have not shifted,
concentration must have increased because the shares of
the involved firms have diverged. 6 Likewise, the entry of a
new firm into a market must decrease concentration as long
as the market share of only one firm already in the market is
affected.
The condition under which the HHI will increase when
more than two market shares change is a simple generalization of the condition expressed in (8): In order for any
number of changes in market shares to increase the HHI,
the sum of all of the cross-products of the new market
shares has to be less than the sum of all of the crossproducts of the shares that they replaced. (This is exactly
the condition under which the variance of market shares
increases when market shares change.) For example, if, in
two lists .of equal numbers of market shares, three market
shares differ across lists, the HHI for the new list will be
greater than the HHI for the old list if and only if
(9)
X IX2
+
X I X3
+
Xr3
> wy +
wz
+ yz,
where w, y, and z are the new market shares, and Xl' x2 , and
x 3 are the shares that they replaced.
A final point regarding the relationship between the HHI
and the distribution of market shares is that, using (5),
(to)
aHHI
av
= N.
Holding N constant, a given increase in the variance
increases the HHI more, the greater the number of firms.
Regarding the relationship between the number of competitors and the HHI, equation (5) offers several insights. It
says that the minimum HHI, obtained when the variance is
zero and all market shares are equal, is lower with more
firms in the market (higher N). In addition, equation (5)
provides intuition for the meaning of the DOl's definition
6. There is a tendency for some acquiring banks to lose some of the
combined market share of the merged firms following an acquisition.
Sometimes, competitors have been able to attract customers from
merged institutions because they closed branches or otherwise changed
bank practices. This type of effect helps to reduce the concentrating
effects of within-market mergers.
of a "highly concentrated" banking market. 7 Express any
value of the HID as 10,000 times the inverse of some
number. Then, that number is the number of equal-sized
firms that would give the same value of the HHI. The DOJ
definition of a highly concentrated banking market as one
with an HHI of at least 1,800 means that a market with
six equal-sized banks is not too concentrated, but one
with five equal-sized banks is. This is because
10,000
10,000
(11) - 6 - = 1,666.67 < 1,800< - 5 - = 2,000.
If market shares are not equal, the relationship between
the number of firms and the HHI is somewhat more
complicated. If V is held constant, we can determine the
effect on the HHI of an increase in the number of firms by
taking the partial derivative of the HHI with respect to N.
From (5), we have
aHHI
(12)
aN
10,000
= V -
~
Holding V constant, an increase in N lowers the HHI if V is
less than 10,0001N2 and raises the HHI if V is greater than
1O,OOOIN2. Also, note that
(13)
a2H
aN2
=
2
N3 > 0,
so that, the larger is N, the less the decline in the HHI when
firms are added. In addition, note that the first term on the
right-hand side of (12), the partial derivative of the inequality effect with respect to N, is positive as long as V is
positive. This means that, as long as V is positive, an
increase (decrease) in the number of firms will increase
(decrease) the effect of the inequality of shares on concentration, even if inequality as measured by the variance
does not change.
However, it is likely that, in many situations, equations
(12) and (13) do not apply. This is because, in practice, a
change in the number of firms must change some market
shares and therefore likely will change the variance of
market shares. If the variance changes, the derivative of the
HHI with respect to N is given by:
(14)
dHHI
dV
dN = V + N dN -
10,000
~
Unfortunately, the variance of market shares can change
any number of ways as the number of firms changes, so
neither the sign nor the size of dVl dN is known.
7. The DOJ classifies markets with an HID below 1,000 as "unconcentrated," those with an HHI between 1,000 and 1,800 as "moderately concentrated," and those with an HHI above 1,800 as "highly
concentrated."
25
LADERMAN / STRUCTURE OF URBAN BANKING MARKETS IN THE WEST
However, it is straightforward to derive an expression for
the discrete change in the HHI in terms of given discrete
changes in N and V. Using equation (5), the change in the
HHI due to moving from initial levels No and Vo to levels N 1
and VI is:
(15) aBBI
= BBI1 = N1V1 +
BBIo
10,000
-NoVo -
aBBI = N1a V
+
(VO -
EFFECTS ON HHI OF CHANGES IN INEQUALITY
EFFECT, VARIANCE, AND NUMBER OF FIRMS
PANEL
N Increases
~.
o
10,000
NoN )aN.
NV Increases
NV Decreases
Here, one can see that, as long as the initial variance of
market shares is greater than 1O,000INoNI' an increase in
the number of firms along with an increase in the variance
of market shares guarantees that concentration will increase. On the other hand, if initial variance exceeds
1O,000/NoNl and V decreases, an increase in the number
of firms will not necessarily increase concentration. The
condition that initial variance exceed 1O,OOOINoNl is the
discrete analogue to the condition in equation (12) that
initial variance exceed 10,000/!V2 in order for an increase
in N to increase concentration if the variance of market
shares does not change. If initial variance is less than
10,0001NoNI' then an increase in N along with a decrease
in V definitely will lower concentration. However, if V
increases under these circumstances, concentration may
increase.
Equation (5) also yields an alternative decomposition of
discrete changes in concentration. Simply,
aBHI = (N1V1 - NoVo)
10,000
10,000
+ ( N - ~).
I
0
The first term in (17) is the change in the inequality effect,
and the second term is the change in the numbers of firms
effect, that is the change in concentration in going from No
equal-sized firms to N 1 equal-sized firms. Equivalently, it
is the change in concentration in going from No firms to N 1
firms, while holding the inequality effect constant. Clearly,
the second term is positive if and only if N 1is less than No.
Of course, the changes in the variance of market shares,
the number of firms, and the inequality effect all interact
with one another, and one can combine the two decompositions in (16) and (17). Table 1 shows what happens to
concentration given various combinations of increases and
decreases in the number of firms, the inequality effect,
and the variance of market shares. Panel A gives the
breakdown for the case in which the initial variance of
No Change
in N
N Decreases
V Increases
+
+
+
V Decreases
+ or-
n.a.
n.a.
V Increases
n.a.
n.a.
+ or-
V Decreases
I
(17)
A: Vo > (lO,OOO/NoNl)
10,000
Subtracting and adding N1Vo and gathering terms, this
yields:
(16)
TABLE 1
PANEL
B: Vo < (lO,OOO/NoNl)
N Increases
NV Increases
V Increases
+ or-
V Decreases
NV Decreases
V Increases
V Decreases
n.a.
No Change
in N
N Decreases
+
+
n.a.
n.a.
n.a.
+
+ or-
NOTE: NV = inequality effect
V = variance
N = number of firms
market shares is greater than 1O,0001NoNl and Panel B
gives the breakdown for the case in which it is less than
1O,000INoNl. Some of the cases in the table have ambiguous implications for concentration. The decomposition
given in this table will be used to show the underlying
causes for increases and decreases in concentration in local
banking markets in the Twelfth District.
To summarize the important conclusions of this section:
1. Concentration depends on a "number of firms effect"
and an "inequality effect," so changes in concentration
depend on changes in these factors
2. The inequality effect itself depends on the number of
firms and the variance of market shares
3. When both the number of firms and the variance of
market shares change, the change in concentration depends on changes in these factors and on the size of the
initial variance of market shares relative to a function of
the initial and terminal numbers of firms.
26
FRBSF ECONOMIC REVIEW 1995,
NUMBER
1
ill.
CHANGES IN THE NUMBER
OF DEPOSITORY INSTITUTIONS AND
IN THE HHI IN THE TWELFTH DISTRICT
The number of bank and thrift competitors in the Twelfth
District declined by approximately 15 percent between
1982 and 1992, as the number of bank competitors went
from 631 to 612, and the number of thrift competitors
went from 301 to 180. 8 f'.~ote that these are the numbers of
separate bank and thrift competitors, not the numbers
of banks and thrifts. Many banks and some thrifts are
subsidiaries of holding companies, and some of these
holding companies have more than one bank or thrift
subsidiary. Because they have common corporate control, I
do not count separate subsidiaries of the same holding
company as separate competitors. 9 I will refer to bank and
thrift competitors as depository institutions (DIs). The
number of DIs is the sum of all bank and thrift holding
companies plus the number ofbanks and thrifts that are not
holding company subsidiaries.
The number of DIs in the District has been influenced by
several forces. First, there have been mergers between DIs.
A merger between an in-District DI (a DI with at least one
branch in the District, but not necessarily headquartered in
the District) and another in-District DI, or an acquisition of
an in-District DI by an in-District DI, reduces the number
of DIs in the District by one. When the assets and liabilities of one DI are split up and sold to multiple DIs, this also
reduces the number of DIs by one. Some mergers or acquisitions may have involved an out-of-District DI merging
with or acquiring an in-District DI. These would have only
changed DIs' names and would not have affected the
number of DIs in the District.
Second , some DIs have failed, and their assets and
liabilities have been taken over by other DIs. In essence,
these were acquisitions, although it is likely that many of
them differed from ordinary acquisitions in that the buyer
received government assistance for the purchase. However,
some DIs failed and were completely liquidated, with
insured depositors paid off by the bank or thrift deposit
insurance fund. Each such failure reduced the number of
DIs by one.
Finally, some new DIs came into being, and each
occurrence raised the number of DIs by one. New DIs arise
when an applicant receives a new bank or thrift charter.
Note, however, that when a holding company already in the
8. Only bank and thrift organizations that held deposits in these years
were counted.
9. This is consistent with the practice followed by the federal depository
institution regulatory agencies in the analysis ofthe competitive effects
of bank and thrift mergers and acquisitions.
market establishes a new subsidiary bank or thrift in
the market by obtaining a new charter, this does not
change the number of DIs in the market. On the other hand,
ifeither an out-of-market holding company or a completely
new entity obtains a new charter and sets up a new bank or
thrift in the market, this raises the number of DIs in the
market by one. lO
The actual numbers of mergers, failures, and new entries of DIs in the Threifth District between 1982 and 1992
are somewhat difficult to pinpoint. For example, it is much
easier to determine the number of bank and thrift mergers
than the number of DI mergers and acquisitions, and the
two are not necessarily the same. Two banks that are
subsidiaries of the same bank holding company may
merge, but this does not change the number of DIs. In
addition, a bank holding company may merge with another
bank holding company, and each of several target banks
may be merged into separate subsidiaries of the surviving
bank holding company. Such a transaction would eliminate
only one DI, even if it generated several bank mergers. On
the other hand, a· bank holding company can acquire a
bank without merging it into another bank, and a list
ofbank mergers would not include such acquisitions. If the
acquired bank was not part of a holding company, or if its
former holding company had only one bank, this reduces
the number of DIs by one. If the acquired bank was part of a
holding company that still has at least one bank subsidiary
after the acquisition, the acquisition does not affect the
number of DIs.
Other complications involve the number of DI failures
and new entries. It is fairly straightforward to determine
the number of liquidated banks and thrifts. However, some
of the liquidated banks or thrifts may be subsidiaries of
holding companies with other still solvent subsidiaries, in
which case the disappearance of the bank or thrift does not
constitute the disappearance of a DI. Finally, one can easily
determine the number of new bank and thrift charters
granted between 1982 and 1992, but it is much more
difficult to know whether or not those charters were
granted to existing DIs.
10. Branching by established out-of-market DIs also can increase the
number of DIs. Also, acquisition of only some of the branches of a DI in
a market by an out-of-market DI will increase the number of DIs by one.
Most states in the District pennit nationally chartered out-of-state thrifts
to branch into their state by setting up new branches or acquiring
existing branches, but only two states in the District pennit interstate
branching by banks. Utah pennits out-of-state banks to operate offices
in Utah as branches, and Nevada pennits out-of-state banks to set up
new branches in Nevada counties with a population less than 100,000.
However, it is likely that any interstate thrift or bank branching would
have had a very minor effect on the change in the number of DIs in the
District as a whole.
LADERMAN / STRUCTURE OF URBAN BANKING MARKETS IN THE WEST
Given the above complications, the following numbers
of bank and thrift liquidations, new charters, and mergers
will only approximate the number of banking competitor
and thrift competitor liquidations, mergers, and new formations. There were 13 bank liquidations and 13 thrift
liquidations in the District between 1982 and 1992. There
were 113 new thrift charters granted and 324 new bank
charters. Finally, there were 333 mergers in which the
acquirer was a Twelfth District bank and the target was a
Twel~h District bank or thrift and 208 mergers in which the
acquirer was a Twelfth District thrift and the target was a
Twelfth District bank or thrift. Subtracting the total number of bank liquidations and mergers from the 631 bank
competitors existing in 1982 and adding the number of new
bank charters yields 609 bank competitors, which is close
to but slightly less than the actual number in 1992, 612.
Subtracting the total number of thrift liquidations and
mergers from the 301 thrift competitors existing in 1982
and adding the number of new thrift charters yields 193
thrift competitors, which is close to but somewhat greater
than the actual number in 1992, 180.
However, these estimates of the changes in the numbers
of bank and thrift competitors, obtained by using the above
numbers for failures, mergers, and new entries, is close
enough to the actual change that two conclusions seem warranted. First, the complete disappearance of DIs through
failure likely was relatively uncommon between 1982 and
1992. Many failing banks and thrifts may have been
eliminated by way of merger or acquisition, but few were
entirely liquidated. Second, the decrease in the number of
DIs between 1982 and 1992 was caused by a massive
number of mergers and acquisitions (about 541) that was
not quite balanced by the very large number of new entries
(about 437). The 15 percent net decrease in the number of
DIs between 1982 and 1992 may be considered to be
relatively modest, but the large gross numbers suggest that
the underlying forces causing that decrease likely were not.
In addition, the disappearance of thrift competitors
accounted for a much larger proportion of the net decrease
in DIs than did the disappearance of bank competitors.
Over the ten-year period, on net 121 thrift competitors
disappeared, accounting for 86.4 percent of the 140 DIs
eliminated on net.
As discussed in the last section, within-market mergers
and acquisitions must raise market concentration if the notinvolved firms' market shares do not change. On the other
hand, unless shifts in the market shares of more than one
preexisting bank accompany new entry, new entry will
lower concentration, thereby increasing the likelihood of
vigorous competition. It appears that there were more DI
mergers and acquisitions than new entry of DIs between
1982 and 1992 in the Twelfth District. Therefore, taking
27
into account only the changes in the number of DIs and not
any shifts in market shares among existing competitors, it
is likely that banking market concentration in the Twelfth
District as a whole increased between 1982 and 1992.
To investigate this possibility, I calculated HHls for
1982 and 1992 for the banking and thrift industry for the
entire Twelfth District. I calculated the HHI the same way
that the Federal Reserve does in its analysis of the competitive effects of D1 mergers. Specifically, each DI's market
share is the percent of total market deposits (in this case,
total deposits in the Twelfth District) that it holds. In
addition, thrifts are considered to be only partial competitors of banks. This is because thrifts usually are prohibited
from engaging in all of the activities in which banks
participate. For example, thrifts' commercial lending often
is restricted. Therefore, it is customary to give only a 50
percent weight to thrift deposits when calculating the size
of the market and market shares. 11 For example, say that a
market is comprised of two banks and a thrift. The first
bank has $500 million in deposits, the second bank has
$300 million, and the thrift has $300 million. Weighting
the thrift deposits at 50 percent and the bank deposits at 100
percent, total deposits in the market are $950 million. The
first bank's percent market share is 52.6 percent, the
second bank's share is 31.6 percent, and the thrift's share is
15.8 percent. Summing the squares of these market shares
yields an HHI of 4,015.
Using deposits to measure market share and applying a
50 percent weight to thrift deposits, the HHI for the Twelfth
District did indeed rise between 1982 and 1992, from 586
to 820. Apparently, the inequality effect either increased or
did not decrease enough to outweigh the effect of the net
decrease in DIs on concentration in the Twelfth District.
This suggests that the competitiveness and productive
efficiency of banking in the Twelfth District fell between
1982 and 1992.
11. When a bank merges with or acquires a thrift, the pre-merger
calculation of the HHI weights all thrift deposits at 50 percent, but the
post-merger calculation of the HHI weights the merged or acquired
thrift's deposits at 100 percent and the other thrifts' deposits at 50
percent. This procedure reflects the post-merger control ofthe acquired
thrift's deposits by a banle When a bank merges with or acquires another
bank, both the pre- and post-merger calculations of the HHI weight all
thrift deposits at 50 percent. Consistent with this, all HHIs and total
deposit figures that are reported in this paper were derived by applying a
100 percent weight to all bank-controlled deposits and a 50 percent
weight to all thrift-controlled deposits. Specifically, if a bank holding
company has a thrift subsidiary, that thrift's deposits are weighted at 100
percent, not 50 percent. This, however, is relatively unusual.
28
FRBSF ECONOMIC REVIEW 1995,
NUMBER
1
IV
CHANGES IN THE NUMBER
OF DEPOSITORY INSTITUTIONS
AND IN CONCENTRATION IN
LoCAL URBAN MARKETS
My ultimate focus is on changes in the level of competition
between banking organizations, and therefore changes in
concentration in meaningfully defined banking markets
are more important than changes at the District level.
Because many banking services are supplied locally, and
many bank customers find it very costly to look for
alternatives outside their local area, the antitrust analysis
of bank mergers typically defines banking markets to
be local.
Therefore, I investigated changes in the structure of 65
local urban banking markets between 1982 and 1992 in the
Twelfth Federal Reserve District states of Alaska, Arizona,
California, Hawaii, Idaho, Nevada, Oregon, Utah, and
Washington. 12 These urban banking markets are geographically defined to correspond to Rand McNally's "RaNally
Metro Areas," or RMAs. The geographic boundaries of
RMAs are delineated by Rand McNally to include the
areas around important cities that are developed and economically integrated with the urban center. RMAsjnclude
satellite communities and suburbs as well as one or more
centralcities.l3 Every RMA in the Twelfth District is
represented in my urban banking market sample.
Most of the Twelfth District population lives in RMAs,
and most of the DI deposits reside in branches in RMAs. In
1980,86.8 percent of the Twelfth District population lived
in RMAs, and, in 1990, 86 percent lived in RMAs. In
1982, approximately 88.9 percent of the total deposits
in the Twelfth District were held in branches located in
RMAs, and in 1992 this percentage was about 88.3.
Tables 2a and 2b present rank order listings of the
RMAs by the change in HHI between 1982 and 1992; 2a is
ordered by HHI increases and 2b is ordered by HHI
decreases. As described above, the HHls are calculated
using 100 percent of bank deposits and 50 percent of thrift
deposits to calculate market sizes and market shares. To be
consistent, total deposits are reported as 100 percent of
bank deposits plus 50 percent of thrift deposits.
12. Bank regulators also review bank mergers affecting local rural
markets for their.competitive effects.
13. Geographic boundaries of RMAs are given in Rand McNally's
Commercial Atlas and Marketing Guide. Rand McNally states that there
are two basic criteria which determine inclusion within an RMA. In
general, an area must have at least 70 people per square mile, and at least
20 percent of the labor force must commute to the central urban area of
the RMA. RMAs have been defined for all areas with a population of at
least 50,000 and selected areas of less than 50,000.
Tables 2a and 2b show that net increases in DIs were
relatively rare; only 8 out of 65 urban markets (12.3
percent) showed a net increase in the number of DIs
between 1982 and 1992. Data presented in Section III
suggested that net decreases in the number of DIs in the
Twelfth District were the result of very numerous mergers
unmatched by a significant number of new DI charters. It is
possible that mergers accounted for the elimination of
fe\ver DIs in local markets than in the T\velftu~ District as a
whole. This is because, unless the local markets of the DIs
overlap, a merger or acquisition will not reduce the number
of DIs, it will only change the target DI's name. In
addition, the number of DIs in local markets can increase
either through new charters or branching from outside of
the market. However, the preponderance of markets with
net decreases in DIs despite these factors suggests that
many mergers may have been between DIs that operated in
the same local urban market and that de novo branching
into new local markets by established DIs may have been
relatively uncommon.
As shown in Section II, a decrease in the number of
firms need not necessarily increase concentration if the
inequality effect decreases. However, the majority of urban
banking markets in the Twelfth District also did experience
an increase in concentration and a presumed decrease in
competitiveness between 1982 and 1992. Concentration
increased in 43 markets (66.2 percent) and decreased in 22
(33.8 percent). Overall, average concentration in these 65
urban markets increased between 1982 and 1992, from an
HHI of 1,643 to 1,747. Section III showed that average
concentration also increased at the District level, but both
1982 and 1992 HHIs were much lower than in local urban
markets. This is because DIs tend to operate in geographically restricted areas, so market shares are diluted in
moving from the local to the District level, and concentration falls.
The increase in average concentration also can be seen
in Figure 1. Figure 1 shows that the number of markets in
the second and third highest concentration categories increased, while the number of markets in the two lowest
concentration categories decreased. The number of markets in the very highest concentration category stayed the
same. However, note that the pattern of the distribution has
remained roughly the same, with the largest number of
markets having HHIs ranging from 1,200 to 1,499 in 1982
and 1992.
Relatively few banking markets went from being "unconcentrated" or "moderately concentrated" in 1982 to
"highly concentrated" in 1992. Anchorage, Honolulu,
Hilo, Provo, Bellingham, Portland, Porterville, Eureka,
an.d Tucson are the nine urban banking markets in which
concentration went from below 1,800 in 1982 to at least
LADERMAN / STRUCTURE OF URBAN BANKING MARKETS IN THE WEST
29
TABLE2A
HHI, DIs, AND DEPOSITS IN TWELFTH DISTRICT RMAs WITH HHI INCREASES, RANKED BY CHANGE IN HHI
RMA
Anchorage, AK
Honolulu, HI
Hi],., , .........
HT
..................
Provo, liT
Santa Barbara, CA
Bellingham, WA
Portland, OR
Porterville, CA
Nogales, AZ
Oxnard, CA
Pocatello, ID
Logan, UT
Riverside, CA
Fairbanks, AK
Fresno, CA
Eugene, OR
Bakersfield, CA
Saiem, OR
Oceanside, CA
Merced, CA
Boise, ID
Eureka, CA
San Diego, CA
Chico, CA
Bremerton, WA
Calexico, CA
Corvallis, OR
Modesto, CA
Salt Lake City, UT
Medford, OR
Los Angeles, CA
Palm Springs, CA
Ogden, UT
Longview, WA
Lancaster, CA
Monterey, CA
Nampa, ID
Phoenix, AZ
Visalia, CA
Davis, CA
Hemet, CA
Tucson, AZ
Olympia, WA
a
1992 level minus 1982 level
HHI CHANGEa
1992 HHI
1,463
942
2,786
2,633
2,579
2,043
1,544
1,958
1,959
1,905
4,360
1,334
2,701
2,587
1,698
2,382
1,796
1,643
1,567
1,527
1,296
1,714
2,727
1,986
1,084
1,753
1,291
3,697
1,476
1,178
1,518
1,645
935
1,294
1,551
1,427
1,621
1,459
1,950
1,970
1,349
1,760
892
1,802
1,085
860
828
736
707
538
493
461
432
385
377
359
337
307
306
287
284
272
267
265
262
256
244
241
222
215
207
192
184
175
170
168
143
120
120
94
86
74
55
39
24
23
1992 DIs
6
14
9
12
18
12
25
7
3
25
6
6
45
5
22
15
16
12
19
10
10
9
67
9
15
5
10
19
26
13
247
25
12
10
11
15
7
37
15
8
19
13
16
DI CHANGEa
-6
-2
-3
-8
-7
-4
-25
-4
-1
-6
-2
-4
6
-3
-7
-9
-6
-7
-6
-7
-3
-3
-4
-4
-4
0
-6
-9
-9
-6
-1
-10
-7
-6
-1
-4
-2
12
-2
-1
-4
0
2
1992 DEPOSITS
(in thousands)
1,846,818
13,471,008
610,082
1,087,577
2,603,852
975,536
12,627,241
409,257
396,583
3,078,416
343,774
367,505
6,065,474
404,289
4,285,529
1,560,167
2,216,097
1,520,888
1,238,270
616,317
2,002,730
856,112
20,296,121
755,132
789,754
264,730
682,661
2,003,905
5,705,748
946,818
142,715,994
1,899,900
1,035,804
407,076
876,243
1,428,103
509,264
20,789,450
872,042
418,639
1,267,005
4,759,219
797,127
30
FRBSF ECONOMIC REvIEW 1995,
NUMBER
1
TABLE 2B
HHI, DIs, AND DEPOSITS IN TWELFfH DISTRICT RMAs WITH HHI DECREASES,
RANKED BY ABSOLUTE VALUE OF CHANGE IN HHI
RMA
Stockton, CA
Watsonviiie, CA
Santa Cruz, CA
San Francisco--Oakland, CA
Yuba City, CA
Las Vegas, NV
Salinas, CA
Yuma, AZ
Redding, CA
Idaho Falls, ID
Fairfield, CA
Santa Rosa, CA
Santa Maria, CA
Napa, CA
Lewiston, ID
Sacramento, CA
Reno, NV
Lompoc, CA
Yakima, WA
Seattle, WA
Pasco-Kennewick-Richland, WA
Spokane, WA
a
HHICHANGEa
1992 HHI
1992 Dis
DICHANGEa
-2,168
-681
-663
-638
-462
-379
-330
-329
-279
-256
-216
-213
-203
-125
-115
-106
-104
-69
-59
-43
-14
-13
1,217
1,622
1,288
1,424
1,408
1,822
1,252
1,866
1,624
1,805
1,495
878
1,492
1,296
1,377
1,241
2,392
1,977
1,388
1,589
1,894
1,722
22
-3
0
-6
-6
-1
1
-3
1
-3
0
-2
2
-1
-1
-1
-7
2
1
-3
-11
-5
-3
11
15
128
13
15
14
8
13
9
14
29
14
15
11
45
13
8
10
61
11
13
1992 DEPOSITS
(in thousands)
2,637,372
589,672
1,555,037
87,220,301
773,151
6,763,318
1,319,883
575,167
1,151,968
602,044
850,920
2,525,034
904,191
951,443
428,995
10,152,322
2,195,682
295,032
942,979
25,171,338
747,770
2,561,116
1992 level minus 1982 level.
1,800 in 1992. In Alaska, the largest bank's acquisitions of
several ofthe mid-sized banks in the state were allowed due
to consideration of the acquired banks' poor financial conditions, leading to the inclusion of Anchorage in the above
list. There are at least two possible reasons for the increases
in the other markets. Frrst, the dynamics of competition
may have caused shifts in market shares that would have
increased concentration even in the absence of mergers.
Second, the breach of the 1,800 level may be the result of
the cumulative effect of multiple mergers, each of which
passed the regulatory screen when considered on its own. 14
Similar reasons may have played a role in the Nogales,
Pocatello, Logan, Fairbanks, Boise, and Calexico markets. All of these markets were already highly concentrated
14. For example, the market may start with an HHI of 1,650 and two
separate mergers may be approved at different times, each of which
increases the HHI by 100 points.
in 1982 and saw cumulative changes of at least 200 points
over the following ten years.
Note that 7 of the 9 banking markets that went from
being unconcentrated or moderately concentrated in 1982
to highly concentrated in 1992 rank in the top 8 banking
markets in Table 2a in terms of increase in concentration.
Accordingly, on average, the change in the HHI, at 680, for
these 9 "crossover" markets, was considerably higher than
the average change in the HHI of 203 for the other 36
markets that were unconcentrated or moderately concentrated in 1982. 15 However, it is also true that the crossover
markets were, on average, more concentrated to begin with
than the 36 noncrossover. markets. The average HHI in
1982 in the crossover markets was 1,504 and in the other
36 unconcentrated or moderately concentrated markets it
was 1,298.
15. These 36 markets include 10 in which concentration decreased
between 1982 and 1992.
LADERMAN / STRUCTURE OF URBAN BANKING MARKETS IN THE WEST
FIGURE 1
HHI IN
TWELFTH DISTRICT
RMAs
NUMBER OF MARKETS
25
•
20
1
1982
~ 1992
15
10
5
o
<
1,200
1,2001,499
1,5001,799
1,8002,099
2
2,100
HHI
For the sample as a whole, however, there appears to be
a negative correlation between initial concentration and
change in concentration. In the 43 markets in which
concentration increased, the average HHI in 1982 was
1,517, whereas, in the 22 markets in which concentration
decreased, the average HHI in 1982 was 1,888. In addition,
with an average HHI increase of 331 and an average HHI
decrease of 339, the absolute values of the average changes
for the increasing and decreasing concentration groups
were about equal to each other and about equal to the
difference between the groups' initial average concentration levels. As a result, on average, the group with concentration increases ended up with about the same level of
concentration as the initially high concentration group had
in 1982, and the group with concentration decreases ended
up with about the same level of concentration as the
initially low concentration group had in 1982.
Given the apparent tendency for concentration to increase in relatively unconcentrated markets and decrease in
relatively concentrated markets, I tested whether there was
in fact any statistical correlation. Using the urban banking
market sample, I regressed the change in the HHI on a
constant and the initial level of the HHI, using ordinary
least squares. The coefficient on the 1982 HHI was indeed
negative and highly statistically significant. This very
simple fitted model indicated that, over a lO-year period,
concentration increased about 596 points minus 29.9 percent of the initial HHI. This means that, according to the
31
model, markets in which the HHI is below about 1,985
tend to increase in concentration and markets in which the
HHI is above that point tend to decrease in concentration.
However, the model is misleading in that it specifies that
the higher the initial concentration, the higher the terminal
concentration. 16 In other words, according to the model,
although concentration will fall in the more concentrated
markets and rise in the less concentrated markets, the
ordering of markets by HHI will not change. Tne flip in
average concentration between the initially low concentration group and the initially high concentration group
suggests that this is not necessarily the case. Concentration
in a given market may fluctuate within a band, tending to
increase up to the ceiling of the band ifit hits the floor of the
band and tending to decrease down to the floor of the band
if it hits the ceiling, thereby changing the concentration
ordering of markets over time. The increase in the overall
average indicates that any such band may have shifted up
between 1982 and 1992. The model's specification of a
decrease in concentration in the more concentrated markets along with an increase in concentration in the less
concentrated markets and no change in the concentration
ordering also erroneously suggests a decrease in the dispersion of concentration. In fact, the standard deviation of the
HHI across urban banking markets barely changed between 1982 and 1992, increasing from 598 to 604.
The negative correlation between initial concentration
and the change in concentration partially may be a consequence of the application of the DOl's bank merger policy
to individual mergers. Under a strict application of the
policy, the farther below 1,600 is a pre-merger HHI,
the larger an increase in the HHI will be permitted. This
also is true for pre-merger HHIs between 1,600 and 1,800,
but, here, 200 is the maximum change in the HHI allowed.
(Under a strict application of the bank merger policy, for
pre-merger HHIs of at least 1,800, there is no negative
correlation between the level of the HHI and the permissible change in the HHI.) It may also be the case that the
supracompetitive profits presumably found in very concentrated markets attract entry into those markets that helps to
reduce concentration and restore competition.
Underlying Causes for Increases and Decreases
in Concentration
Table 3 fills in the cells of Table 1 with the identities of
urban markets in each category.17 Table 3 thereby shows
16. The 1992 HHI is approximately 0.7 times the 1982 HHI plus 596,
according to the model.
17. There are 37 markets represented in Panel A of Table 3. These are
the markets with initial variance ofmarket shares above the critical value
32
FRBSF ECONOMIC REVIEW 1995, NUMBER 1
TABLE 3
HHI CHANGES
AND THEIR CAUSES IN TWELFfH DISTRICT URBAN MARKETS
N Increased
V Increased
+
+
Riverside
Tucson
NV Increased
V Decreased
+
+
Portland
Fresno
Bakersfield
Boise
Modesto
Los Angeles
Honolulu
Oxnard
Eugene
Oceanside
San Diego
Salt Lake City
Palm Springs
n.a.
n.a.
Reno
Phoenix
n.a.
n.a.
V Increased
NDecreased
No Change in N
+
Medford
Ogden
Monterey
Visalia
NV Decreased
Sacramento
Seattle
Pasco/Kennewick/Richland
Spokane
V Decreased
Watsonville
Las Vegas
Santa Rosa
PANEL
B: Vo < (1O,OOOINoN1)
No Change in N
N Increased
V Increased
NDecreased
+
+
Lompoc
Olympia
Calexico
NV Increased
+
n.a.
n.a.
+
n.a.
Portland
Logan
Merced
Chico
Longview
NV Decreased
Pocatello
Salem
Eureka
Corvallis
Hemet
+
V Decreased
Yuma
NOTE: NV = inequality effect
V = variance
N = number of firms
Hilo
Santa Barbara
Bremerton
Anchorage
Provo
Bellingham
Lancaster
n.a.
V Decreased
V Increased
Santa Cruz
Yuba City
Salinas
Fairfield
Napa
Stockton
San Francisco/
Oakland
Redding
Santa Maria
Idaho Falls
Nogales
Fairbanks
Nampa
Davis
Lewiston
Yakima
LADERMAN / STRUCTURE OF URBAN BANKING MARKETS IN THE WEST
underlying causes for increases and decreases in concentration in each market. For example, concentration
increased in the Boise banking market because the number
of DIs decreased and variance increased enough that the
inequality effect also increased. On the other hand, concentration increased in the Riverside banking market because, even though the number of DIs increased, the
variance of market shares increased, and initial variance
was above the critical value of 10,000 divided by the
product of the 1982 and 1992 number of DIs. Equivalently,
concentration increased in the Riverside market because,
even though the number of DIs increased, the variance of
market shares also increased enough that the increase in the
inequality effect outweighed the negative effect that an
increase in DIs by itself would have had on concentration.
The experiences of the largest markets, those with over
$10 billion in deposits in 1992, varied somewhat. These
markets are Honolulu, Portland, San Diego, Los Angeles, Phoenix, Sacramento, Seattle, and San FranciscoOakland. In the Honolulu, Portland, San Diego, and
Los Angeles markets, concentration increased because the
number of DIs decreased and the variance of market shares
increased enough that the inequality effect also increased.
In the Phoenix market, even though the number of DIs
increased and· the variance of market shares decreased,
concentration increased because the inequality effect increased sufficiently. Note that the increase in the inequality
effect in the Phoenix market was due solely to an increase
in the number of DIs. The experience in the Sacramento
and Seattle markets was the opposite of that in the Phoenix
market. In these markets, even though the number of DIs
decreased and the variance of market shares increased,
concentration decreased because the inequality effect decreased sufficiently. The decreases in the inequality effects
in the Sacramento and Seattle markets were due solely to
decreases in the number of DIs. In the San FranciscoOakland market, even though the number of DIs decreased, concentration decreased because variance also
decreased, so that the decrease in the inequality effect
outweighed the concentrating effect that a decrease in the
number of DIs has by itself. Note that, because initial
variance was above the critical value in the San FranciscoOakland market, a decrease in the number of DIs had to
decrease concentration if variance either did not change or
decreased. 18
derived in Section II. There are 28 markets in Panel B of Table 3, with
initial variance below the critical value.
18. Note, however, that, given the initial number of firms, the larger the
decrease in the number of firms, the higher initial variance must be to
exceed the critical value.
33
The counts of markets in each cell also suggest general
conclusions regarding underlying causes for changes in
competitiveness and efficiency, as measured by concentration, in Twelfth District urban markets.
In 38 of the 53 markets in which the number of DIs
decreased, concentration increased. In twenty of these
markets, the change in the inequality effect reinforced the
effect of the decline in the number of competitors. In
the others, the change in the inequality effect partially
mitigated the effect of the decrease in the number of DIs,
but not enough to outweigh the concentrating effect that a
decrease in the number of firms has if the inequality effect
is held constant.
There were 15 markets that became less concentrated
despite a decline in the number of DIs. Concentration
decreased in these markets because the decrease in the
inequality effect outweighed the concentrating effect of a
decrease in the number of firms, holding the inequality
effect constant.
In markets overall, increases in the variance of market
share were more common than decreases (43 increases
versus 22 decreases). However, due to the preponderance
of markets in which the number of DIs decreased, decreases in the inequality effect were more common than
increases (38 decreases versus 27 increases).
Average sizes of increases and decreases in concentration depended on whether the direction of change in the
number of DIs, the variance of shares, and the inequality
effect worked in the same direction or not. In the 33
markets in which, given only the direction of change of
these factors, concentration had to increase, the average
increase in the HHI was 382. In the 14 markets in which
concentration had to fall, the average decrease in the HHI
was 496. 19 For the 18 markets in which the effects worked
in opposite directions, the average absolute change in the
HHI was 118.
For markets in which the inequality effect and change in
the number of DIs worked in the same direction, one can
calculate the proportion of the change in concentration that
was due to each factor. For the 3 such markets in which
concentration decreased, on average 73.3 percent of the
19. The Stockton, California market, which showed an HHI decrease of
2,168, may be considered to be an outlier. The large decrease in
concentration in the Stockton market primarily was due to an outflow of
deposits from the largest DI, a thrift. This thrift had been paying above
market interest rates to attract deposits and held 56 percent of the
deposits in the market in 1982. When it encountered financial trouble
and stopped paying high rates, it lost deposits to other DIs in the market,
greatly reducing the overall variance of market shares. If the Stockton
market is excluded, the average decline in the HHI in markets in which
concentration had to decrease was 367.
34
FRBSF ECONOMIC
REVIEW
1995,
NUMBER
1
change in concentration was due to the decrease of the inequality effect. For the 20 such markets in which concentration increased, on average 56 percent of the change
in concentration was due to the increase of the inequality
effect. 20 These percentages suggest that when the change
in the inequality effect and in the number of DIs (holding
the inequality effect constant) work together, the former is
somewhat more important than the latter.
V.
CONCLUSION
Both the Twelfth District as a whole and local urban
banking markets in the District saw a widespread reduction in the number of DIs between 1982 and 1992. Nearly
82 percent of the 65 urban banking markets in the District
saw a net decrease in the number of DIs. Although this
trend need not necessarily have been accompanied by
an increase in concentration, in most markets it was.
As a result, concentration in the Twelfth District overall increased between 1982 and 1992. Concentration also
increased in approximately two-thirds of the 65 urban
banking markets in the Twelfth District. On the other
hand, there is some evidence that if a market becomes concentrated enough, concentration will start to
fall, thereby helping to strengthen competition and productive efficiency.
The preponderance of urban banking markets in which
the number of DIs decreased likely was a consequence of
numerous within-market mergers that were unmatched by
significant numbers of new charters. District level data also
suggest that a large proportion ofthe net decrease in DIs was
accounted for by a net decrease in the number ofthrifts. This
likely also played a role in local urban markets. Given a
slowdown in the disappearance of thrifts, the decreasing
trend in the number of DIs should abate somewhat.
Shifts in market shares can reduce the effect of the
inequality of shares on measured concentration. If this inequality effect decreases sufficiently, it can overcome the
concentrating effect that a decrease in the number of firms
has if the inequality effect is held constant. However, less
than a third of the markets in which the number of DIs
decreased showed decreases in concentration. This suggests that regulatory review of bank and thrift mergers and
acquisitions has been and will continue to be important in
assuring the competitiveness of banking markets.
20. Markets counted exclude those in which the number of DIs did not
change.
REFERENCES
Commercial Atlas and Marketing Guide. 1992. 123rd edition. Skokie,
Illinois: Rand McNally.
Holdsworth, David G. 1993. "Is Consolidation Compatible with Competition? The New York and New Jersey Experience." Federal
Reserve Bank of New York Research Paper #9306.
Rhoades, Stephen A. 1993. "The Herfindahl-Hirschman Index." Federal Reserve Bulletin (March) pp.l88-189.
Scherer, EM. 1980. Industrial Market Structure and Economic Performance. 2nd edition. Boston: Houghton Mifflin.
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