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Federal Reserve Bank
of San Francisco
1992
Number 3
Brian Motley
Controlling Inflation
with an Interest Rate Instrument
Frederick T. Furlong
Capital Regulation and Bank Lending
Ramon Moreno
Macroeconomic Shocks and
Business Cycles in Australia
Jonathan A. Neuberger
Bank Holding Company Stock Risk
and the Composition of Bank Asset Portfolios
John P. Judd and
I TaMe
Controlling Inflation with am Interest Mate Instrument 0.«. „„«»0. . . ». . . »„. »«, . 3
John P. Judd and Brian Motley
Capital Regulation and Bank Lending „0 „0„ 0„Q*., <,<>„0 „„„„„ 0 . „„. „*0 „ 23
Frederick T. Furlong
Macroeconomic Shocks ami Business Cycles in Australia 0. „0000. 0<>*0
, 34
Ramon Moreno
Bank Holding Company Stock Risk
ami the Composition of lank Asset Portfolios <,0<»00„oG* »0Q„<><,„0000 . 0„„o„ S3
Jonathan A. Neuberger
Federal Reserve Bank o f San Francisco
1
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2
E conom ic R eview / 1992, N um ber 3
Controlling Inflation
with an Interest Rate Instrument
John P Judd and Brian Motley*
The authors are Vice President and Associate Director of
Research, and Senior Economist, respectively at The Federal Reserve Bank of San Francisco. They would like to
thank Evan Koenig, Bennett McCallum, Ronald Schmidt,
Bharat Trehan, Adrian Throop, Carl Walsh and participants in the Conference on Operating Procedures at the
Federal Reserve Bank of St. Louis, June 18-19, 1992 for
helpful comments on an earlier draft, Andrew Biehl for his
efficiency and diligence in computing the many regressions and simulations in this paper, and Erika Dyquisto for
preparing the document.
In this paper we examine the effectiveness in controlling
long-run inflation offeedback rules for monetary policy
that link changes in a short-term interest rate to an
intermediate target for either nominal GDP or M2. We
conclude that a rule aimed at controlling the growth rate of
nominal GDP with an interest rate instrument could be an
improvement over a purely discretionary policy. Our results suggest that the rule could provide better long-run
control ofinflation without increasing the volatility ofreal
GDP or interest rates. Moreover, such a rule could assist
policymakers even if it were used only as an important
source of information to guide a discretionary approach.
*An earlier version of this paper (Judd and Motley 1992) will be
published under the same title in a forthcoming issue of Finance and
Economics Discussion Series, Board of Governors of the Federal
Reserve System.
Federal Reserve Bank of San Francisco
In Congressional testimony, Chairman Greenspan and
other Federal Reserve officials have made it clear that price
stability is the long-run goal of U.S. monetary policy! At
the same time, reducing fluctuations in real economic
activity and employment remains an important short-term
goal of the System. However, the desire to mitigate shortterm downturns inevitably raises the issue of whether this
goal should take precedence over price stability at any
particular point in time. At present, the Federal Open
Market Committee (FaMe) resolves this issue on a case
by case basis, using its discretion to set policy after
analysis of a wide array of real and financial indicators
covering the domestic and international economies.
Economic theory suggests that monetary policy tends to
have an inflationary bias under such a discretionary system. This bias can be eliminated by the monetary authority
pre-committing itself to a policy rule that would ensure
price stability in the long run (Barro 1986). Even if the
monetary authority is not willing to adhere rigidly to a rule,
a discretionary approach could benefit from the information provided by a properly designed rule. For example, the
instrument settings defined by the rule at any time could be
regarded as the baseline policy alternative that would serve
as the starting point for policy discussions. At its discretion, the FOMC could select a policy that was easier,
tighter or about the same as that called for by the policy
rule. Under such an approach, the rule could provide
information that would help to guide short-run policy
decisions toward those consistent with the long-run goal of
price stability.
In this paper, we assess the effectiveness of so-called
nominal feedback rules of the type suggested by Bennett
McCallum (l988a, 1988b). These rules specify how a
policy instrument (a variable that is under the direct control
of the central bank) responds to deviations of an intermediate target variable from pre-established values. Earlier
work (Judd and Motley 1991)suggests that a rule in which
the monetary base is used as the instrument and nominal
lSee Greenspan (1989) and Parry (1990).
3
GDP is used as the intermediate target could have produced price level stability with a high degree of certainty
over the past 30 years.
Over many years, the Fed has shown a strong preference
for conducting policy using an interest rate instrument, as
opposed to a reserves or monetary base instrument. In the
present paper, we examine rules that use an interest rate
instrument in conjunction with nominal GDP as the intermediate target. In addition, since the mid-1980s, the Fed
has used a broad monetary aggregate, M2, as its main
intermediate target or indicator. Hence, we also assess the
usefulness of a rule that combines an interest rate instrument with M2 as the intermediate target variable.
Evaluating the effects of policy rules in advance of
actually using them is an inherently perilous task. First,
the effects of a rule will depend on the structure of the
economy,including several features-such as the degree of
price flexibility and the way in which expectations are
formed-that remain subjects of debate and disagreement
among macroeconomists (Mankiw 1990). This lack of
consensus about issues that crucially affect the working
of the economy means that, in order to be credible, any
proposed rule must be demonstrated to work well within
more than one theoretical paradigm. Second, implementation of a rule could alter key behavioral parameters affecting price setting and expectations formation. This means
that history may not be a good guide in evaluating rules that
were not implemented in the past, and that the robustness
of empirical results to alternative parameter values also
must be examined.
In order to assess their effectiveness under alternative
macroeconomic paradigms, we conduct simulations of
two different macroeconomic models (a Keynesian model
and an atheoretic vector autoregression or error correction
system) that have significant followings among macroeconomists. 2 To assess the risks of adopting different rules,
we examine the dynamic stability of these models under
alternative versions of the rules. In addition, we use
stochastic simulations to determine the range of outcomes
for prices, real GDP and a short-term interest rate that we
could expect if these rules were implemented and the
economy experienced shocks similar in magnitude to those
in the past. Finally, to test for robustness, we re-examine all
of the results under plausible alternative values for key
estimated parameters in the models.
-Our earlier paper (Judd and Motley 1991), in which the policy instrument was the monetary base, also examined the effects of a rule within
the context of a very simple real business cycle (RBC) model. However,
with an interest rate instrument, the price level cannot be determined in
the context of that RBC model (see McCallum 1988b, pp. 61-66). Thus
we did not use the RBC model in this paper.
4
Using these simulations we evaluate the effectiveness of
the rules at controlling the price level. We also examine the
effect of the rules on the volatility of real GDP and a shortterm interest rate. Although we find that interest rate rules
could have held long-run inflation below levels that were
observed historically, they do not perform as well as baseoriented rules. However, there are reasons to believe that
the base would be a less effective instrument in the future
than it would have been in the past. Moreover, one simple
form of the interest rate rule does appear to offer an
improvement over a purely discretionary approach. finally, we suggest a way to use a feedback rule with an
interest rate instrument as an important source of information that could contribute to the effectiveness of a discretionary policy.
The remainder of the paper is organized as follows.
Section I presents a brief overview of the theoretical
advantages and disadvantages of alternative targets and
instruments. Section II discusses the nominal feedback
rules to be tested. In Section III, we present the empirical
results. The conclusions we draw from this work are
presented in Section IV.
I. CONCEPTUAL ISSUES
In this section, we discuss briefly the basic conceptual
issues determining the effectiveness of alternative intermediate targets and instruments of monetary policy. To
illustrate certain basic ideas, we introduce a generic form
of the feedback rule that links the instrument variable with
the intermediate target variable. This generic feedback
rule may be written in the form:
ti.I,
= l/;
+
A.[ZI~I - ZI_a·
The variable I represents the policy instrument, which is a
variable under the direct control of the monetary authority.
Z represents the intermediate target variable of policy. The
rule specifies that the change in the policy instrument
should be equal to the change desired in steady-state
equilibrium, 1jJ, plus an adjustmentterm, A[ZT-l - ZI_I]'
This latter term describes the monetary authority's response to deviations between the actual level of the intermediate target variable (Z) and its desired level (Z*). The
strength of the monetary authority's response to such
deviations is defined by A. Thus, the rule permits policy to
incorporate varying degrees of aggressiveness in pursuing
the intermediate target.
The policy instrument, I, responds only to lagged, and
hence observed, values ofthe intermediate targetZ. Hence,
the rule can be implemented without reference to any particular model. This is an advantage in view of the current
disagreement about the "correct" model of the economy.
Economic Review/ 1992, Number 3
Nominal feedback rules may gain wider appeal because it
may be possible to agree about the effectiveness of a
particular rule, while disagreeing about certain aspects of
how the economy actually works.
Alternative Intermediate Targets
The appeal of nominal GDP as an intermediate target
lies in the apparent simplicity of its relationship with the
price level, which is the ultimate long-term goal variable of
monetary policy (Hall 1983). As shown by the following
identity, the price level (P) is equal to the difference
between nominal GDP (x) and real GDP (y), where all
variables are in logarithms:
p = x - y.
This identity means that there will be a predictable longterm relationship between nominal GDP and the price level
as long as the level of steady state real GDP is predictable.
According to some economists, the levelof real GDP has
a long-run trend, called potential GDP, which is determined by slowly evolving long-run supply conditions in the
economy, including trends in the labor force and productivity (Evans 1989). To the extent that this view is correct, it
is straightforward to calculate the path of nominal GDP
required to achieve long-run price stability.
However,other research suggests that real GDP does not
follow a predictable long-run trend, and is stationary only
in differences (King, Plosser, Stock and Watson 1991). If
this were the case and nominal GDP were to grow at a
constant rate under a rule, the price level would evolve as
a random walk, and thus could drift over time. Unfortunately, statistical tests are not capable of distinguishing
reliably between random walks and trend stationary processes with autoregressive roots close to unity (Rudebusch
1993). This uncertainty over the long-run behavior of real
GDP means that there is corresponding uncertainty over
how the price level would behave under a nominal GDP
target. 3
Another potential problem is that the lags from policy
3In part because of this concern, a number of authors have argued that
the Federal Reserve should target prices directly (Barro 1986, and
Meltzer 1984). No matter what time series properties real GDP displays,
direct price level targeting obviously could avoid long-term price-level
drift. The major disadvantage of price level targeting is that in sticky
price models, the feedback between changes in the instrument and the
price level is very long (and, in fact, longer than for nominal GDP).
Thus, attempts by monetary policy to achieve a predetermined path for
prices are liable to involve instrument instability (i.e., explosive paths
for the policy instrument) and undesirably sharp movements in real
GDP. Our earlier empirical results (Judd and Motley 1991)confirm this
conjecture.
Federal Reserve Bank of San Francisco
actions to nominal GDP are relatively long, and thus
targeting nominal GDP might induce instrument instability. Shorter lags tend to exist between policy actions and
monetary aggregates. Hence, using an aggregate as an
intermediate target could reduce the likelihood of producing instrument instability compared to a nominal GDP
target.
Since the velocity of M1 began to shift unpredictably in
the early 1980s, M2 has been the main intermediate target
used by the Fed and so is a prime candidate for use in a
feedback rule. M2 also has been identified as a potential
intermediate target because its velocity (in levels) has been
stationary over the past three decades (Miller 1991, Hallman, Porter and Small 1991). Its short-run relationship
with spending, however, has not been very reliable. These
problems have intensified in recent years, with accumulating evidence of instability in M2 velocity in 1990-1992
(Judd and Trehan 1992, Furlong and Judd 1991). Nonetheless, it may be possible to exploit its long-run relationship
with prices to achieve price stability.
For present purposes, the important implication of the
preceding discussion is that the choice of an intermediate
target variable cannot be determined from theory alone.
This choice depends on empirical factors such as the time
series properties of real GDP, the degree of flexibility of
prices, and the predictability of the velocity of money.
Clearly an empirical investigation is needed.
Alternative Instruments
Instruments of monetary policy fall into two basic
categories: aggregates that are components of the Federal
Reserve's balance sheet, such as the monetary base or the
stock of bank reserves, and short-term interest rates, such
as the federal funds rate. Either category qualifies as a
potential instrument since either can be controlled precisely in the short run by the central bank and each is
causally linked to output and prices.
The monetary base has the advantage that, in principle,
it is the. variable that determines the aggregate level of
prices, and thus would appear to be a natural instrument to
use in a rule designed to achieve price stability. However, it
has a number of potential disadvantages. First, using the
base as an instrument could cause interest rates to become
excessively volatile, and thereby impair the efficiency of
financial markets. Second, the base is made up mainly
of currency in the hands of the public (currently, about
85 percent), and concern for efficiency in the payments
system argues for supplying all the currency the public
demands. This means that controlling the base requires
operating on a small component of it (bank reserves).
Hence, relatively small changes in the base might require
5
large proportional changes in reserves, which could disrupt the reserves market. Third, along with M1, the demand for the base has become relatively unstable in the
1980s compared with prior decades. The deregulation of
deposit interest rates and increased foreign demand for
U.S. currency apparently have induced permanent level
shifts in the demand for the base, and possibly a change in
its steady-state growth rate.
In Judd and Motley (1992, Appendix C) we examine the
stability of the demand for base money and the issue of
whether the need to supply currency on demand would
seriously inhibit the use of the base as a policy instrument.
We conclude that although these problems are legitimate
reasons for concern whether a base rule would work well,
they probably are not fatal. Nonetheless, it is worthwhile to
explore the possibility of using a short-term interest rate as
the instrument in the context of the feedback rule since the
FOMC has shown a preference over the years for using the
federal funds rate as its instrument. 4 This is our main
purpose in this paper.
It is well-known that an interest rate would not be a
satisfactory intermediate target for policy. The economy
would be dynamically unstable in the long run (i.e., the
price level would be indeterminate) if nominal interest
rates were held steady at a particular level and not permitted to vary flexibly in response to shocks. However, this
argument does not rule out its use as an instrument.
If interest rate movements are linked to changes in a nominal variable (such as nominal GOP, a monetary aggregate,
or the price level itself) through a rule, the price level
may be determinate (McCallum 1981). Thus the question
of whether an interest rate instrument would function
effectively within a feedback rule cannot be answered by
theory alone. Empirical work is required.
II.
NOMINAL FEEDBACK RULES
We examine two rules in which the interest rate is used
as the instrument and one that uses the monetary base. We
use the following symbols throughout: b = log of the
monetary base, R = the three-month Treasury bill rate,
m2 = log of the broad monetary aggregate, M2, x = log of
nominal GOP, yf = log offull-employment real GOP, and
"*" denotes a value desired by the central bank.
Equation 1 employs nominal GOP as the intermediate
target and the interest rate as the instrument.
(1) M
t
= -A.I[X;"_I - Xt-I]
= -a[x;"_1 - xt-d -
where a
=
(A.I - A. 2) , ,8
=
-
X t- 2]
,8[Ax;"_1 - Axt -
I]
A. 2.
Equation 2 is similar but uses M2 as the target.
(2)
AR,
=
_
* - V2l-1
- - m2l-1]
-ex [X,_I
15
L (xH
where V2,
-
Ie O
m2H )/16 .
In order to provide a standard of comparison, we also
examine a rule in which a base instrument is used to reach a
nominal income target. 5
(3)
Sb,
Ap,*] - A WJ,
=
[AY(
+
ex[X'~1 - xl-i] + 13 [AX'~I - AX,_I] ,
+
The left hand sides of these equations represent the
change in the policy instrument, either the annualized
growth rate of the monetary base or the percentage point
change in the short-term interest rate. Since in steady state
the rate of interest is constant, the left hand sides of (1) and
(2) are zero in equilibrium. Hence, the interest rate rules
contain only a feedback component, which specifies how
the interest rate is adjusted when the target variable (nominal GOP or M2) diverges from the path (in levels or growth
rates) desired in the previous quarter. In (2), the target level
of M2 (in logarithms) is defined as the target level of
nominal income less the average level of M2 velocity over
the past 16 quarters. The terms a and,8 define the proportions of a target "miss" (in levels and growth rates,
respectively) to which the central bank chooses to respond
in each quarter. In equilibrium, there are no misses and
hence the interest rate is constant.
The monetary base rule is more complicated. The first
SIn our earlier paper (Judd and Motley 1991), we also tested the
following two rules:
t:.b, = [t:.y(
+
this preference is based in part on the view that this
approach avoids imparting unnecessary volatility to financial markets
that would arise if policy were conducted using a reserves or monetary
base instrument.
+ A.2 [X ;"_ 2
+
t:.p,.] - t:.VB,
a[(yf-\ - y,_\)
+
(t:.p,:\ - t:.Pt-\)].
4 Apparently,
6
The price level target produced instability in the Keynesian model,
while the second rule, suggested by Taylor (1985), produced dynamic
instability in the vector autoregression.
Economic Review I 1992, Number 3
term on the right-hand side of (3) represents the growth
rate of nominal GDP that the central bank wishes to
accommodate in the long-run, which is equal to the sum of
the desired inflation rate (Llp*) and the steady-state growth
rate of real GDP (Llyf). The second term, LlVB, subtracts
the growth rate of base velocity over the previous four
years, and is designed to capture long-run trends in the
relation of base growth to nominal GDP growth. 6 The third
term specifies the feedback rule determining how growth
in the base is adjusted when there is a target miss in the
previous quarter. In steady state, this feedback term drops
out, so that the rule simply states that Llb, = Lly{ + Llp1LlVB,.
In all three rules, we use two lags on the levels of the
intermediate target variables. As shown in (1), this specification is equivalent to including one lag on the level and
one lag on the growth rate of the target variable (MeCallum, 1988b). Thus the instrument is subject to both
"proportional" (response to levels) and "derivative" (response to growth rates) feedback. The addition of derivative feedback can improve the performance of proportional
feedback rules in some circumstances (Phillips 1954). In
any event, we evaluate the performance of the rules under
all three possible categories of control: proportional only
(a>O, {3 = 0), derivative only (a = 0, {3>0), and both proportional and derivative (a>O, {3>0).
III.
EMPIRICAL RESULTS
For each of the rules tested, we performed a number of
dynamic simulations within the context of two types
of model: a simple structural model based on Keynesian
theory, and a theoretically agnostic vector autoregression
or error correction model.
The models are described in detail in Appendix A. The
Keynesian model embodies four equations, each representing a basic building block of this framework. First, there is
an aggregate demand equation, relating growth in real
GDP to growth in real M2 balances (or the monetary base).
Second, there is a Phillips-curve equation, relating inflation to the GDP "gap" (i.e., the difference between real
GDP and an estimate of its full employment level), and a
distributed lag of past inflation. This latter variable reflects
the basic Keynesian view that prices are "sticky," and
means that there are long lags from policy actions to price
changes. Third, full-employment real GDP (in levels) is
assumed to have a deterministic trend. Thus the supply of
6The 16-quarter average was designed to be long enough to avoid
dependence on cyclical conditions. As a consequence, the term can take
account of possible changes in velocity resulting from regulatory and
technological sources.
Federal Reserve Bank of San Francisco
real GDP in levels is unaffected by business cycle developments. Finally, the model includes an equation defining the
demand for (real) money (or the monetary base) as a
function of real GDP, and the nominal interest rate.
To simulate this model with a base instrument, this last
equation is replaced by the equation describing the policy
rule (3). In simulations with an interest rate instrument, (1)
and (2), the policy rule determines the interest rate, which
feeds into the M2 or base demand equation to determine
the monetary aggregate. Under both instruments, the simulation model includes the aggregate demand and supply
equations and the Phillips curve to determine y, yf and p.
In addition to the Keynesian model, we also use either a
vector autoregression (VAR) or a vector error correction
(VECM) framework. To simulate the effects of a rule with
a base instrument, we use a four-variable VAR system,
including real GDP, the GDP deflator, the monetary base,
and the three-month Treasury bill rate. In these simulations, the estimated equation for the base is replaced by the
policy rule (3). For the interest rate rules, we use a somewhat different system of equations. Since the second interest rate rule (2) involves M2 as the intermediate target,
we replace the base with M2 in the above list of variables.
We use this same system to simulate the effects of (1),
which uses nominal GDP as the intermediate target. In
simulating the interest rate rules, the estimated interest rate
equation is replaced by the appropriate policy rule.
In estimating these systems, we used standard statistical
techniques as described in Appendix A to test for stationarity, cointegration, and lag length. In the system that
includes M2, we found one cointegrating relationship,
which we interpret as an M2 demand function. This cointegrating vector was imposed in estimating the resulting
VECM. No cointegrating vector was found in the system
that includes the monetary base, and hence this system was
estimated as a VAR.
The simulation results fall into three categories. First,
we examine the dynamic stability of each macroeconomic
model when the rules are used to define monetary policy.
For a policy rule to be considered, it must produce a model
that has sensible steady state properties. In the long run, a
feedback rule will make the price level follow the desired
path, as long as it does not make the economy dynamically
unstable and induce explosive paths for the endogenous
variables. Given the uncertainty about the true structure of
the economy, a rule must produce dynamic stability in both
types of models examined, and with a range of alternative
values of a and {3, in order to be considered reliable.
We conduct numerous simulations to see if the rules meet
this test.
Second, we conduct repeated stochastic counterfactual
simulations of the alternative models and rules over the
7
1960-1989 sample period to see how the principal macroeconomic variables might have evolved if the rules had
been followed. In these simulations, we assume that the
shocks in each equation have the same variance as the estimation errors. This procedure allows us to construct probability distributions of alternative outcomes for each rule
and each model, and to calculate (95 percent) confidence
intervals for long-run inflation rates as well as for short-run
real GDP growth rates and for interest rate changes. This
enables us to compare different rules in terms of the full
range of alternative outcomes that each might produce.
To compare the simulated results under the rules with
the results of the policies actually pursued, we report the
means and 95 percent confidence bands of the actual data
over 1960-1989.
Third, we tested the robustness of these results by
repeating many of the above simulations under alternative
values of key parameters in our estimated models.
Dynamic Stability
The results of our analysis of the dynamic stability of the
models under the various rules are shown in Table 1. To
detect whether a particular combination of model, rule,
and pair of a and {3 was dynamically stable, we computed a
nonstochastic simulation covering 300 quarters. The size
of the simulation's last cycle for the price level (peak-to-
trough change) was divided by the size of its first cycle to
form a ratio that we call s. If s is greater than 1.0, the
simulation is unstable since the swings in the endogenous
variable become larger as time passes, while a value of s
less than 1.0 shows dynamic stability. 7 For each combination of model and rule, we performed a grid search over
various combinations of a (to measure proportional control) and {3 (to measure derivative control). The grid
extended from a = {3 = 0.0 to a = 0.8 and {3 = 1.1 (in
units of 0.1 for both a and {3). Excluding the combination
in which a = {3 = 0.0, which represents the no-rule case,
each grid search generated 107 values of s. Although the
exact specification of these searches is somewhat arbitrary,
they do appear to present an accurate picture of the stability
properties being investigated.
Table 1 provides a count of stable simulations for each
rule under each model. As shown, the nominal GDP/base
rule is dynamically stable in every simulation for both
models. Thus the conclusion that an economy guided by a
nominal GDP/base rule would have desirable steady state
properties is quite robust across models and choices of a
and {3. In fact, in the case of a base instrument, the simple
approach of proportional control (only) would seem to
"Nearly all of the simulations we observed exhibited cycles. However,
the method used for detecting dynamic instability also works for
simulations that do not exhibit cycles.
Table 1
Dynamically Stable Simulations by Type of Control
Rule
Proportional
Only
(10 trials)
Proportional and
Derivative
(89 trials)
Derivative
Only
(8 trials)
Nominal GDP/Interest Rate
Keynesian Model
VECM
6
1
68
13
7
7
81
21
M2/Interest Rate
Keynesian Model
VECM
8
0
82
11
8
8
98
19
10
10
89
89
8
8
107
107
Intermediate 'Iarget/Instrument
Nominal GDP/Monetary Base
Keynesian Model
VAR
Note: The number of trials is the total number of pairs of
Proportional Only:
Proportional and Derivative:
Derivative Only:
8
IX
and
Total
(107 trials)
13 for each combination of rule and model.
a> 0; f3 = 0
a> 0; f3 > 0
a = 0; f3 > 0
Economic Review / 1992, Number 3
make sense. In any event, the risk of inducing unstable
cycles by using this rule appears to be small.
The same cannot be said for the interest rate instrument,
using either nominal GDP or M2 as the intermediate
target. Under the vector error correction model, the rule
produces only 21 stable cases out of 107 trials when
nominal GDP is the intermediate target, and only 19 stable
cases when M2 is used. The results are considerably better
in the Keynesian model (81 and 98 stable trials, respectively, for nominal GDP and M2 targets). However, the
important characteristic of robustness across alternative
models is lacking when the full range of combinations of
proportional and derivative control is considered.
It is not entirely surprising that there is a tendency for
the models to produce more cases of dynamic instability when an interest rate instrument is used than when the
base is used. As noted above, economic theory predicts
that the price level would be determinate in the long run
and the economy dynamically stable if the monetary authority were to peg the base, but that the price level would
be indeterminate and the economy dynamically unstable if
the authority were to peg a nominal interest rate at a
constant level. Although the feedback rules attempt to
avoid this problem by tying interest rate changes to intermediate targets for nominal variables, the underlying tendency toward instability shows through in our results.
However, in the case of an interest rate rule that exerts
derivative control only-so that policy responds only to
the growth rates, and not the levels, of nominal GDP and
M2-there does not appear to be a problem with instability. As Table 1shows, the model is dynamically stable
in all 8 trials when the intermediate target is M2, and in
almost all trials (7 out of 8) when nominal GDP is the
target.
In this section we present the results of simulations that
attempt to assess how the macroeconomy might have
evolved over the past three decades if the various feedback
rules had been in use. In these "counterfactual experiments," the targeted values of the intermediate target
variables were set under the assumption that the Fed's goal
was to hold the price level constant over 1960-1989. We
chose values for a and f3 that produced stable simulations
across the two models. For each combination of rule and
model, we calculated 500 stochastic simulations." The
random shocks in each equation were drawn from probability distributions that had the same mean and variance as
the estimation error terms. Each set of 500 simulations is
called an experiment.
In presenting the results of these experiments, we focus
on two measures of economic performance that should reflect the concerns of policymakers-the price level and the
short-run growth rate of real GDP. Ideally, a policy rule
should deliver price stability without causing unacceptable
fluctuations in real GDP growth. To address possible
concerns about the short-run variability of the interest
rate under the rules, we also examine quarter to quarter
changes in the interest rate instrument.
We measure the price level performance of each rule in
terms of the average inflation rate that it produced over the
30-year simulation period. The volatility of real GDP is
measured in terms of the four-quarter growth rate of real
GDP. For each experiment, we calculated 95 percent confidence intervals for both of these variables. In the case of the
simulations using the interest rate instrument, we also
calculated 95 percent confidence intervals for the quarterly
changes in the interest rate.
Table 2 shows the performance of the various rules in
stabilizing the price level.? Using the monetary base as the
instrument, adoption of the norninal-GDP feedback rule
could have stabilized prices in the long run within narrow
limits. For example, under the base rule with both proportional and derivative control (a = 0.25 and f3 = 0.50),
average inflation (with 95 percent probability) would have
been between - 0.4 and + 0.3 percent in the Keynesian
model and between -0.8 and +0.7 percent in the VAR.
Under the policies actually followed during this period,
average inflation was 5.4 percent.
The rules in which the interest rate is used as the
instrument also are able to produce confidence bands that
generally are centered near an average inflation rate of
zero. However, these bands are wider than when the monetary base is used as the instrument. For example, under the
interest rate instrument (with either proportional control
alone or both derivative and proportional control), the
width of the confidence bands ranges from 1.1 to 4.2
percentage points compared with band widths of 0.7 to 1.5
percentage points when the base is the instrument. Thus
although both instruments produce confidence bands for
average inflation that are centered on zero, use of the base
as the policy instrument reduces price level uncertainty
more than use of the interest rate.
8There are nine alternative rules (i .e., three combinations of intermediate targets and instruments, and three combinations of a and 13) and
two models. Thus eighteen sets of 500 stochastic simulations were
computed.
9The average inflation results in Table 2 are not qualitatively changed if
alternative horizons, such as five, ten or twenty years, are used for the
stochastic simulations.
Counterfactual Simulations
Federal Reserve Bank of San Francisco
9
Table· 2
Simulated Average Annual Inflation Rate 1960-1989
95% Confidence Limit
Rule
Intermediate Thrget/Instrument
Proportional Only
Derivative Only
f3 = 0.00)
-0.6% to 0.5%
Explosive
(0:
= 0.25, f3 = 0.50)
- 1.3% to 0.9%
- 1.0% to 2.5%
(0: = 0.00, f3
f3 = 0.00)
-0.8% to 1.0%
Explosive
(0:
= 0.60, f3 = 0.25)
(0:
= 0.50, f3 = 0.00)
- 0.4% to 0.3%
-0.8% to 0.7%
(0:
Nominal GDP/Interest Rate
KeynesianModel
VECM
(0: = 0.75,
M2/Interest Rate
KeynesianModel
VECM
(0: = 0.75,
Nominal GDP/Monetary Base
KeynesianModel
VAR
(0:
Actual Data:
The confidence bands on average inflation are considerably wider under the interest rate rules if policy exerts only
derivative control (see the right-hand column of Table 2).
When policy attempts to control only the growthrate of the
intermediate target, misses in the level in effect are "forgiven" each quarter. Not surprisingly, the widths of the
resulting confidence bands on long-run inflation increase to
between 3.4 and 7.2 percentage points. However, it is
important to note that even at the top ends of these
confidence bands, average inflation is below the actual
inflation rate over 1960-1989.
Finally, the results suggest that there is little to distinguish the nominal GDP target from the M2 target under an
interest rate instrument. However, our use ofa sample
period that ends in 1989 abstracts from the widely discussed problems with instability in the demand for M2
that have occurred in 1990-1992 (Furlong and Judd 1991,
Judd and Trehan 1992). Since 1989, the velocity ofM2 has
been roughly constant, whereas historical relationships
suggest that it should have declined rather sharply in
response to declining nominal interest rates. This apparent
shift in M2 demand raises concerns that the future performance of M2 as an intermediate target may be worse than it
was in the past.
Table 3 shows the effects of the rules on the volatility of
real GDP. For each model, it reports 95 percent confidence
intervals for four-quarter growth rates of real GDP under
10
Proportional and
Derivative
-0.9% to 1.0%
-1.2% to 3.0%
= 0.25, f3 = 0.50)
-0.4% to 0.3%
-0.8% to 0.7%
= 0.50)
-2.3% to 4.9%
-0.3% to 3.1%
0.00, f3 = 0.50)
-1.5% to 3.2%
-0.2% to 3.5%
=
(0: = 0.00, f3
= 0.50)
-0.2% to 0.7%
-0.5% to 1.0%
5.4%
the alternative rules. 10 The table compares the simulation
results with the distribution of the actual historical data,
which is a measure of the volatility of real GDP during the
sample period under the discretionary policies actually
followed by the Federal Reserve.
In nearly every case, the confidence bands are wider
under the rules that use some proportional control (either
alone or in combination with derivative control) than they
were in the actual sample period, though in some cases the
differences are small. For example, in the Keynesian
model, use of the nominal GDP/base rule with both
proportional and derivative control is estimated (with 95
percent confidence) to yield four-quarter real GDP growth
rates of between - 4.0 and + 10.3 percent, which is wider
than the - 1.9 to + 7.9 percent band in the historical data.
In the VAR, the corresponding confidence interval is + 0.4
to + 9.3 percent, which has about the same width as the
historical measure.
Table 3 suggests that use of an interest rate instrument,
with at least some proportional control, would lead to
larger fluctuations in real GDP growth than a base instrument. The confidence bands are substantially wider under
rules that use an interest rate instrument than with a base
lOWe also looked at the volatility of the two-quarter and eight-quarter
growth rates of real GDP. The conclusions were qualitatively the same
as for the four-quarter growth measures.
Economic Review I 1992, Number 3
Table 3
Simulated Four-Quarter Real GOP Growth Rates
Rule
Intermediate Thrget/Instrument
95% Confidence Limit
Proportional Only
Proportional and
Derivative
Nominal GDP/Interest Rate
Keynesian Model
VECM
(a = 0.75, (3 = 0.00)
(a = 0.25, (3 = 0.50)
-16.7% to 20.6%
Explosive
-6.3% to 19.7%
-11.7% to 19.8%
M2/Interest Rate
Keynesian Model
VECM
(a = 0.75, (3 = 0.00)
(a = 0.60, (3 = 0.25)
Nominal GDP/Monetary Base
Keynesian Model
VAR
(a = 0.50, (3 = 0.00)
(a = 0.25, (3 =0.50)
-3.4% to 10.0%
-0.4% to 9.9%
-4.0% to 10.3%
0.4% to 9.3%
to 13.6%
Explosive
~7.2%
Actual Data:
instrument, especially in the VAR and VECM models.
There appears to be a slight tendency for the confidence
bands to be narrower under an M2 rule than a nominal
GDP rule, but the difference is small.
However, if only derivative control is exerted, the width
of the confidence bands on real GDP growth is noticeably
narrower than when there also is a significant element of
proportional control (see the right hand column of Table3).
In most cases, derivative control leaves the volatility of
GDP at about the same level as it was historically. This is
true whether an interest rate or a monetary base instrument
is used.
In Table 4, we present evidence on the quarter-to-quarter
volatility of the short-term interest rate that might result
from following the two rules that use the interest rate as the
instrument. When at least some proportional control is
used, the rules result in an increase in short-run interest
rate volatility compared with that experienced under the
discretionary policy pursued in our sample period. Thus
the width of the 95 percent confidence intervals varies from
5.2 to 16.9 percentage points under the rules, compared
with a width of 4.0 percentage points in the actual data.
However, use of derivative control only is estimated to
reduce interest rate volatility compared with history. As
shown in the right-hand column, the confidence bands
range in width from 1.3 to 2.4 percentage points compared
with the 4 point width in the actual data.
Federal Reserve Bank of San. Francisco
Derivative Only
(a
= 0.00, (3 = 0.50)
-1.3% to 8.2%
-0.6% to 10.2%
(a
= 0.00, (3 = 0.50)
-1.6% to 8.3%
0.8% to 10.0%
(a
= 0.00, (3 = 0.50)
-3.5% to 10.2%
0.6% to 9.0%
-4.7% to 10.6%
-16.4% to 15.3%
-1.9% to 7.9%
In summarizing the results in Tables 2, 3, and 4, it is
useful to compare the simulations under an interest rate instrument both with those under a base instrument and with
the historical record. Compared to the base-instrument
results, we conclude:
1. Use of the interest rate permits much more long-run drift
in the price level than use of the base.
2. An interest rate instrument also results in more volatility
of real GDP, except in the case of derivative control only,
when the interest rate instrument leads to less volatility.
Comparing the results under an interest rate instrument
with historical experience, we can make the following
generalizations:
1. If at least some proportional control is used, the interest
rate rule would hold inflation well below its historical
average, but would result in greater volatility in real
GDP and interest rates than experienced in the past.
2. If derivative control only is used, then the interest rate
rules would hold inflation somewhat below historical
experience, maintain real GDP volatility at about its
historical level, and result in less interest rate volatility
than actually occurred in the past.
11
Table 4
Simulated Quarter-to-Quarter Changes in the Short-Term Interest Rate
(percentage points)
95 % Confidence Limit
Rule
Intermediate Thrget/Instrument
f3 =0.00)
- 8.3% to 8.6%
Explosive
(a
= 0.75, f3 = 0.00)
(a = 0.60,
Nominal GDPllnterest Rate
Keynesian Model
VECM
(a = 0.75,
M2/Interest Rate
Keynesian Model
VECM
(a
-5.7% to 6.0%
Explosive
Actual Data:
Robustness
One problem with attempting to evaluate empirically the
likely effects of monetary policy' rules that were not actually followed during the period for which data are available
is that the estimated behavioral parameters of models
might have been different if the rule had actually been used
(Lucas 1973). In a crude attempt to deal with this issue, we
have recalculated many of the simulations discussed above
under alternative assumptions about key coefficients in our
estimated models. We ran these simulations under the
assumption that selected coefficients varied (one at a time)
from their estimated levels by plus and minus two standard
deviations. The results of these alternative simulations are
shown in Appendix B.
The coefficients that were varied in these tests included
the following:
1. In the Keynesian model, we altered the slope of the
Phillips curve, the elasticities of real GDP with respect
to both real M2 and the real base in the aggregate demand equations, and the interest elasticities of the
demand for both M2 and the base. In addition, we varied
the length of the lags on past inflation in the Phillips
curve, restricted the sum of these coefficients on past
inflation to unity, and introduced a unit root in potential
GDP.
2. In the VECM, we varied the interest rate, GDP and price
elasticities of M2 in the cointegrating vector that appears
in the M2 and price equations.
12
Derivative Only
Proportional and
Derivative
Proportional Only
= 0.25, f3 = 0.50)
-3.7% to 3.8%
-2.5% to 2.7%
f3 = 0.25)
- 3.0% to 3.0%
-3.5% to 3.7%
f3 = 0.50)
-1.1 % to 1.3%
-0.9% to 1.1%
(a = 0.00,
f3 = 0.50)
-0.8% to 0.9%
-0.6% to 0.7%
(a = 0.00,
- 2.0% to 2.0%
There are too many results in Appendix B to review in
detail. However, several general points stand out. First, the
results for average inflation are quite robust for all of
the rules within all of the models. When the monetary base
is the instrument, the results for real GDP growth also are
robust, although somewhat less so than for inflation.
As shown in Tables B.2 and B.4, the width of the
confidence bands for four-quarter real GDP growth is
relatively sensitive to coefficient variations when the interest rate is used as the instrument and the rule involves some
proportional control. In a few cases the bands become
somewhat narrower, but in many more they become considerably wider. On the other hand, interest rate volatility
is relatively less sensitive to the changes in the models'
coefficients. However, as shown in Tables B.3 and B.5,
when the interest rate rule involves derivative control only,
the simulation results are highly robust.
One issue of special concern is the restriction in the
Phillips curve that the coefficients on lagged inflation sum
to unity (point 2 in Tables B.1, B.2, and B.3). This restriction ensures that monetary policy is neutral with respect to
real GDP in the long run (i.e., it makes the Phillips curve
"vertical" in the long run), and is a central feature of the
theory underlying the Phillips curve. Although the restriction is rejected by the data in our sample (see the F test
under equation A. 2' in the Appendix), we imposed it in our
sensitivity analysis because of its theoretical importance.
In most cases, the imposition of this restriction leads to
dynamic instability.
Economic Review I 1992, Number 3
IV.
CONCLUSIONS
In this paper, we have examined the effectiveness of
nominal feedback rules that link short-run monetary policy
actions to an intermediate target with the ultimate goal of
controlling inflation in the long-run. Two subsidiary goals
are that the rules not induce unacceptably large variations
in real GDP or in interest rates. Given uncertainties about
the structure of the economy, these rules are designed to be
model-free in the sense that the monetary authority does
not need to rely on a specific model of the economy in order
to implement them. In addition, the rules are operational in
that they define specific movements in an instrument that
can be controlled precisely by the central bank.
We have focused mainly on rules that use a short-term
interest rate as the policy instrument, and either nominal
GDP or M2 as the intermediate target. As a standard of
comparison, we also have looked at a rule in which
the monetary base is the instrument and nominal GDP
is the intermediate target. This rule has been shown to have
desirable properties in earlier research. In addition, we
compare the results from the rules with actual experience
over the past three decades.
Our empirical results suggest that all of the feedback
rules examined, so long as they do not produce explosive
paths, would be highly likely to hold inflation below the average rate experienced in the U.S. over 1960-1989. When
comparing rules with alternative instruments, the interest
rate rule does not measure up to rules with the monetary
base as the instrument and nominal GDP as the intermediate target. The latter rule provides much tighter control of
the price level and induces somewhat less volatility in real
GDP than rules using an interest rate as the instrument.
Moreover, rules using the base as the instrument are
consistent with dynamic stability in the economy under a
wide range of assumptions, whereas the same cannot be
said for rules with interest rate instruments. In a number of
cases, the latter rules induced explosive paths in the
economies simulated.
Despite the strong results obtained for rules with a base
instrument, there are reasons to be concerned that their
performance in the future would not measure up to the
results obtained in our counterfactual simulations covering
the past three decades. One important consideration is that
the increase in foreign demand for U.S. currency in recent
years may have made the overall demand function less
stable than in the past.
So , what conclusions can be reached about the effectiveness of rules defined in terms of an interest rate instrument? First, within such rules, nominal GDP and M2 were
found over our 1960-1989 sample period to function about
equally well as intermediate targets. Given this result, and
Federal Reserve Bank of San Francisco
the evidence that the relationship between M2 and spending may have broken down during 1990-1992, rules defined in terms of nominal GDP would appear to be less
risky.
Second, based upon our simulations, interest rate rules
that involve some proportional control of nominal GDP (or
M2) do not appear to be viable alternatives for monetary
policy. We found a large number of cases in which these
rules produced explosive paths for the simulated economy.
Thus use of such a rule in the real world, where we do not
know with any precision the structure and size of parameters of the pertinent behavioral relationships, would run a
significant risk of inducing dynamic instability.
However, feedback rules with an interest rate instrument
that focus on the growth rate, rather than the level, of
nominal GDP (or M2) lead to dynamic stability in the
various models. Naturally, such rules automatically accommodate past misses of the level of the intermediate
target,and thus allow the possibility that the price level
may drift over time. Such drift would occur only when
there were a prolonged series of positive or negative
shocks. However, it should be noted that even after allowing for such drift, the worst case simulation that we
obtained still held the simulated average inflation rate over
1960-1989 below the historical average. Moreover, such an
approach is estimated with a very high probability to
involve about the same level of volatility in real GDP and a
reduction in interest rate volatility compared with historical experience.
This conclusion suggests that, although a rule that aimed
at controlling the growth rate of nominal GDP with an interest rate instrument is far from ideal, it might be an
improvement over a purely discretionary interest rate policy. It would seem to offer the likelihood of lower long-run
inflation without increasing the volatility of real GDP or
interest rates. A simple version of such a rule can be
written!'
~Rt
=
-0.50[~xi_l
-
~Xt-d·
Such a rule could make a contribution to policy, even if it
were used only to modify the Fed's traditional discretionary approach. When using an interest rate instrument
within the context of a purely discretionary policy, it is
natural for the policymaker to evaluate alternative policy
actions relative to a status quo policy ofleaving the interest
rate (currently the federal funds rate) unchanged. As a
11As notedabove, At refersto a changein the logof nominalGDP,while
M refers to a change in the interest rate expressedas a percent. Thus
when nominalGDP growth deviates from its target by I percent (4 percent annual rate), the rule calls for a changein the interestrate of.005,
or 50 basis points.
13
result, the debate tends to focus on a decision about
whether the funds rate should be raised or lowered from its
recent level. This approach may be misleading, since a
policy of leaving the funds rate unchanged does not necessarily imply that the future thrust of policy relative to key
macroeconomic variables will remain unchanged.
However, the instrument setting given by the feedback
rule at any point in time does provide a sensible way to
define no change in monetary policy, since it represents a
consistent policy regime, incorporating the long-run goal,
the intermediate-run target and the short-run instrument. A
debate that focused upon whether policy should ease,
tighten, or remain the same relative to what the feedback
rule calls for, would seem to be more informed than one
that focused upon whether the short-term interest rate
should be changed from recent levels. Occasional adjustments to the nominal GDP target could be used to offset
drift in the price level that may arise from exercising
derivative control (only) of nominal GDP.12
The approach outlined above could be considered as one
possible step to improve a purely discretionary interest rate
policy. In effect, the rule would be used to provide policymakers with information that could help them make shortrun discretionary decisions without losing sight of the
long-run goal of controlling inflation.
ApPENDIX A
MACROECONOMIC MODELS
We employed two alternative sets of assumptions about
the structure of the economy: a Keynesian model and a
vector autoregression (VAR) or vector error correction
model (VECM). As will become apparent, the models are
not attempts to describe the structure of the economy as
precisely as possible. Rather, the Keynesian model incorporates the fundamental features of this macroeconomic
paradigm. The VAR/VECM system is an atheoretic model
that captures the statistical relations among various macroeconomic time series. These models are meant to illustrate the basic nature of the responses of the economy to the
implementation of the monetary policy rules tested.
All of the equations below are estimated over 1960.Qlto
1989.Q4. The variables in the regressions below are defined as follows:
b
= log of monetary base
(adjusted for reserve requirement changes)
1 in 1980.Q2, and 0 elsewhere
cc
g
log of government purchases
m2 = log ofM2
mm = 1 in 1983.Ql and 0 elsewhere
log of GDP deflator
p
3-month treasury bill rate
R
= time trend
T
x
log of nominal GDP
log of real GDP trend (see equation A.3)
yf
y
= log of real GDP
Keynesian Model
The Keynesian, or "sticky price" model, consists of
four equations. First, the real aggregate demand equation
embodies the direct effects of monetary and fiscal policy on
macroeconomic activity. In one version, it specifies the
growth rate of real GDP as a function of current and lagged
growth rates of the real monetary base, real government
spending, and its own lagged values:
(A.l) ~YI = 0.0045
(4.45)
121f, for example, the level of prices were to drift significantly upward or
downward despite following the rule, an offsetting adjustment could be
made to the path of the nominal GDP target. Of course, the central bank
would have to guard against the temptation to make frequent adjustments to the target path, since this could undermine the value of the
feedback rule. One way to do this would be to define in advance the
amount of drift in the price level that would be tolerated before a level
adjustment would be made to the nominal GDP target.
14
+
0.17 ~Yt-I
(2.06)
+ 0.016~gl -
(2.52)
+ 0.47(~ bt-l
- ~PI-1)
(4.41)
0.016~gl_1
(-2.52)
R2
0.21
0.0083
SEE
Q = 21.34
D.F.
116
Economic Review / 1992, Number 3
An alternative version uses M2 as the monetary policy
variable:
(A.I')
Liy, = 0.0033
(3.18)
+
0.15LiYH
(1.84)
0,41(Lim2/_ 1
(5.09)
Lip/_I)
+
0.014Lig, - 0.014Lig,_ 1
(2.36)
(-2.36)
R2
= 0.25
SEE = 0.081
Q
D.P.
116
(A.2) Lip/ = 0.0014 + 0.022(y, - y() + 0.28LiPH
(1.89)
(2.78)
(3.02)
0.30Lip,_2
(3.20)
+
0.25Lip,_3
(2.20)
+
0.05Lip,_4
(0.58)
R2
0.70
SEE = 0.0037
Q
22.05
D.F.
113
Lip/
115
Equation (A.3) defines yf, the log of full-employment
real GDP, as the fitted values of a log linear time trend
of real GDP. This equation incorporates the idea, common
to Keynesian models, that real GDP is trend stationary.
(A.3)
SEE
Q
D.P.
The supply side of the Keynesian model is a simplified Phillips curve, which embodies the essential "sticky price"
characteristic of the paradigm. It specifies that the current
inflation rate depends on past inflation and the gap between
actual and full-employment real GDP (y - yf). Theory
suggests that the coefficients on lagged inflation should be
constrained to sum to 1, thus ensuring that, in steady state,
real GDP will be equal to its full-employment level, and
inflation will be constant. However, the data over the sample
period used reject this restriction at the 3.3 percent marginal significance level. Our basic model does not incorporate
this restriction, but we also show results in which it is
imposed (equation A.2').
(A.2')
D.P.
SEE
R2
27.26
+
Q
0.69
0.0038
23.20
(n
+
-
R2
= 7.56
(846.15)
+
0.32Lip/_l
(3.44)
119
To test for the robustness of the results under a unit root
in real GDP, we also estimate the following equation:
(A.3') Liy, = 0.0051 + 0.24LiYH
(4.00)
(2.56)
R2
SEE
Q
4
F(I,113)
0.014LiY,_2
(1.50)
= 0.065
0.0091
27.31
Equations (A.4) and (A.5) represent the financial sector
of the model, respectively defining the demands for the
monetary base and M2 as functions of the aggregate price
index, real GDP and a short-term nominal interest rate. As
in Miller (1991), we find that M2 is cointegrated with these
arguments, whereas the base is not. Thus the base demand
equation is specified in first differences, while the M2
demand equation has an error correction form.
=
R2
Q
D.F.
0.00029
(0.42)
+
O.064LiY/_1
(1.15)
+
0.17LiY,_2
(3.40)
0.42LiR/-l + 0.50(LibH -LiPH)
(-7.86)
(7.61)
= 0.54
0.0050
= 22.83
115
4
RESTRICTION: In L OJ Lip/_i' L 0i i=1
+
D.F. = 116
SEE
0.33Lip,_2 + 0.28Lip,_3 + 0.07Lip,_4
(3.51)
(2.98)
(0.86)
0.0079281;
(98.9)
0.0045
1662.32
-
(2.62)
+
= 0.97
(A.4) Lib/-Lip/
= 0.021(y, - y()
+
y(
1.
i=1
= 4.63.
Federal Reserve Bank of San Francisco
15
(A.5)
t.lm2t
= -0.079 (-2.49)
+
(3.27)
Table A.1
0.95Yt_l - 0.14Rt_ 1 + 0.70t.lm2t-l
(3.27)
+
0.89m2t-1 + 0.89Pt_l
(-3.27)
(-3.71)
Marginal Significance Levels of
Dependent Variables
(11.28)
0.17t.lpt - 0.074t.lYt - 0.26t.lRt
(1.93)
(-1.42)
(-4.56)
- 0.016cct + 0.029mmt
(-2.83)
(5.78)
l1y
I1p
I1R
I1b
R2
= 0.61
0.0049
Q = 28.16
D.F. = 110
SEE
R2
l1y
I1p
.509
.018
.00192
.666
.000
.0152
.0366
0.36
0.0080
26.55
101
SEE
Q
D.F.
0.71
0.0036
26.60
109
I1R
.000332
.168
.898
.039
.0077
43.18
102
I1b
.000
.000
.063
0.0035
27.85
110
The above equations were combined with the various
feedback rules to form three simulation models that were
used to generate results discussed in the text:
Nominal GDPllnterest Rate Simulation: Equation 1, with
equationsA.1, A.2, A.3, andA.4.
Table A.2
M21Interest Rate Simulation: Equation 2, with equations
A.I: A.2, A.3, and A.5.
Vector Error Correction Model
Nominal GDPIMonetary Base Simulation: Equation 3,
with equations A.I, A.2, and A.3.
Dependent Variables
l1y
I1p
11m2
y'-1
-0.033 a
( -1.66)
O.l3 a
(3.80)
In addition to the model just discussed, we also conducted simulations using an atheoretic framework. For the
case in which the monetary base is used as the instrument,
we used the following variables: real GDP, the price level,
the base and the nominal short-term interest rate. Following Johansen and Juselius (1990) we tested for cointegrating vectors in this system of variables. Finding none, we
estimated a VAR with all variables in first differences. We
selected lag lengths using the Final Prediction Error procedure (Judge, et al., 1985). The estimation results are
summarized in Table A.I.
The VARembodies no theoretical restrictions and therefore is agnostic about the structure of the economy. In
simulating this model with the nominal GDP/Base rule,
the estimated equation for the base was replaced by equation (3) defining the policy rule. This produced:
P'-1
-0.033 a
( -1.66)
O.l3 a
(3.80)
m2'_1
0.033 a
(1.66)
-O.l3 a
(-3.80)
R'_1
0.028
(0.26)
-0.11
(- 3.55)
Nominal GDPIMonetary Base Simulation: Equation 1,
together with the VAR equations for y, p, and R.
D.F.
Vector Autoregression-Error Correction Models
To evaluate the rules in equations 1 and 2, which use the
interest rate as the instrument, we incorporated the following variables: real GDP, the price level,M2, and the
16
I1R
(Marginal Significance Levels)"
l1y
.585851
.332590
.237394
.003320
I1p
.004468
.000000
.225075
.168222
11m2
.037828
.585279
.000000
I1R
.063848
.004459
.000037
R2
SEE
Q
0.31
0.0078
34.13
95
0.69
0.0036
17.44
103
0.66
0.0046
28.60
97
.898220
0.32
0.0077
43.18
102
aRestriction of coefficient equality imposed.
bLags chosen by Final Prediction Error procedure (Judge, et al.,
1985).
Economic Review I 1992, Number 3
treasury bill rate. In this case, the Johansen-Juselius tests
detected one cointegrating vector, which was statistically
significant in the M2 and price equations. Given the signs
and magnitudes of the coefficients in this vector, it appears
to be a money demand equation. Moreover, the JohansenJuse1ius test failed to reject the hypothesis that the coefficients on y, p and m2 were equal. The estimation results are
summarized in Table A.2.
ApPENDIX B
SENSITIVITY ANALYSIS:
In simulations to evaluate equations I and 2, the interest
rate equation above was replaced by the rule. This yielded:
Nominal GDP/Interest-Rate Simulation: Equation 1, together with VECM equations for y, p, and M2.
M2 /Interest-Rate Simulation: Equation 2, together with
VECM equations for y, p, and M2.
1960-1989
Table B.1
Rule: Nominal GOP/Monetary Base
Model: Keynesian
95% Confidence Limits"
Stability«
Dynamic
Average
Inflation
107
- 0.4% to 0.3%
- 3.4% to 10.0%
80
-1.1 % to 0.4%
-8.9% to 12.6%
3. (A.2):
One lag of i3,Pt-i
Eight lags of Apt-i
107
107
-0.4% to 0.3%
-0.3 to 0.3
-6.0% to 12.7%
-2.8 to 9.6
4. (A.2):
ai3,p/a(y-y!)
+2<T
-2<T
106
107
-0.4% to 0.1%
~0.1
to 1.3
- 4.3% to 11.0%
-3.1 to 9.8
94
81
- 0.4% to 0.6%
-0.5 to 0.6
-3.7% to 10.3%
-9.9 to 11.0
107
- 0.4% to 0.2%
- 3.6% to 10.0%
1. Basic Model
Four-Quarter
Real GDP Growth
Modifications
2. (A.2'):
n
n
In i::l
I: o/iPt-i, I: OJ
i=1
-
5. (A. 1):
ai3,y/a(Ab - Ap)
+2<T
-2<T
6. (A.3):
Use (A.3')
aThis column reports the number of combinations of a and f3 that produced dynamically stable simulations out of a total of 107 combinations
tried.
bSimulations use a = 0.50 and f3 = 0.00.
Federal Reserve Bank of San Francisco
17
Table B.2
Rule: Nominal GOP/Interest Rate
Model: Keynesian
95 % Confidence Llmits>
1. Basic Model
Dynamic
Stabilitya
Average
Inflation
82
- 1.3% to 0.9%
Four-Quarter
Real GDP Growth
One-Quarter
InterestRate
Change
-6.3% to 19.7%
-3.7% to 3.8%
Modifications
2. (A.2'):
n
n
In L O/:"P'_i' L s, ==
i=1
14
Explosive
Explosive
Explosive
i=1
3. (A.2):
One lag of !:lP'-i
Eight lags of !:lPt-i
77
77
- 1.4% to 2.0%
-0.6 to 1.0
-26.5% to 23.8%
-5.7 to 10.3
-6.5%to 7.1%
-2.5 to3.0
4. (A.2):
a!:lp/a(y-yf)
+20'
-20'
70
81
-1.4% to 3.0%
-0.5 to 1.6
-38.3% to 17.5%
-3.9 to 11.5
- 6.0% to 6.8%
-2.4 to 3.1
5. (A. I):
a!:ly/a(!:lb - !:lp)
+20'
-20'
38
95
-0.7% to 0.6%
-1.2 to2.7
-7.5% to 15.4%
-13.4 to 12.4
-2.7% to 3.2%
-5.6 to 6.3
6. (A.4):
a(!:lb - !:lp)/a!:lR
+20'
-20'
49
101
-1.5% to 1.4%
-1.0 to 0.7
-8.4% to 19.7%
-5.7 to 15.8
-4.7% to 5.2%
-3.1 to 3.2
72
-1.1 % to 0.8%
-9.1% to 16.1%
-3.8% to 4.0%
7 (A.3):
Use (A.3')
"This column reports the number of combinations of a and f3 that produced dynamically stable simulations out of a total of 107 combinations
tried.
bSimulations use a = 0.25 and f3 = 0.50.
18
Economic Review I 1992, Number 3
TableB.3
Rule: Nominal GDP/Interest Rate
Model: Keynesian; Derivative Control Only
95% Confidence Llmits>
One-Quarter
Interest Rate
Change
Dynamic
Stabilitya
Average
Inflation
7
-2.3% to 4.9%
-1.3% to 8.2%
-1.1 % to 1.3%
- 6.6% to 6.3%
-2.6% to 11.7%
-1.8% to 1.8%
1. Basic Model
Four-Quarter
RealGDP Growth
Modifications
2. (A.2'):
n
In
n
E o/'P,_j, i=1E OJ ==
;=1
3. (A.2):
One lag of I1pt-i
Eight lags of I1pt-i
7
7
- 1.9% to 4.9%
-1.9 t05.2
-2.2% to 8.9%
-2.7 to 9.3
-1.4% to 1.7%
-1.0 to 1.3
4. (A.2):
al1p/a(y-yi)
+2u
-2u
7
7
-2.9% to 4.2%
1.0 to 5.7
-1.7% to 8.2%
-1.5 to 7.2
-1.3% to 1.5%
-0.8 to 1.5
5
8
-0.7% to 4.8%
-4.3 to 5.3
-2.3% to 9.3%
-0.9 to 7.4
-1.0% to 1.5%
-1.3 to 1.3
6. (A.4):
a(11b - I1p)/al1R
+2u
-2u
8
6
-2.4% to 6.3%
-1.6 to 4.0
- 8.0% to 3.3%
-1.7 to 8.3
-1.1 % to 1.5%
-1.1 to 1.3
7 (A.3):
Use (A.3')
7
- 2.0% to 4.9%
-1.9%to 8.1%
-1.1% to 1.4%
5. (A. 1):
ol1y/a(11b - I1p)
+2u
-20-
-This column reports the number of valuesof{3 that produceddynamically stable simulations out of a total of 8 trials.
bSimulations use a = 0.00 and {3 = 0.50.
FederalReserve Bank of San Francisco
19
TableB.4
Rule: Nominal GDP/Interest Rate
Model: Vector Error Correction
95% Confidence Limits"
Dynamic
Stabilitya .
1. Basic Model
Average
Inflation
Four-Quarter
Real GDP Growth
One-Quarter
Interest Rate
Change
21
- 1.0% to 2.5%
-11.7% to 19.8%
-2.5% to 2.7%
10
13
-0.8% to 5.1%
-6.4 to 1.6
-49.7% to 3.8%
-42.2 to 199.2
-2.3% to 3.6%
-8.5 to 6.3
o
14
Explosive
-3.0% toO.l%
Explosive
-79.9% to 11.6%
Explosive
- 20.4% to 21.2%
7
17
- 5.0% to 3.3%
-1.3 to 1.9
- 3.4% to 40.8%
-23.9 to 33.0
-3.0% to 2.5%
-4.0 to 4.0
Modifications
2.
ssa
Equation:
Coefficients on M2, p, and y
+2a
-2a
3. I1p Equation:
Coefficients on M2, p, and y
+2a
~2a
4. lil12 Equation:
Coefficient on R
+2a
-2a
-This column reports the number of combinations of a and {3 that produced dynamically stable simulations out of a total of 107 combinations
tried.
bSimulations use a = 0.25 and {3= 0.50.
20
Economic Review 11992, Number 3
Table.B.5
Rule: Nominal GOP/Interest Rate
Model: Vector Error Correction; Derivative Control Only
95% Confidence Ltmtts>
Dynamic
Stabilitya
Average
Inflation
Four-Quarter
RealGDPGrowth
One-Quarter
Interest Rate
Change
7
-0.3% to 3.1%
-0.6% to 10.2%
-0.9% to 1.1%
8
8
- 8.8% to 12.5%
-5.1 to -2.2
-2.1% to 11.3%
-2.2 to 7.9
-0.4% to 1.6%
-1.2 to 0.8
o
8
Explosive
- 6.4% to - 3.4%
Explosive
-0.7% to 8.4%
Explosive
-1.3% to 0.8%
8
8
4.4% to
-1.0 to
- 2.0% to 7.0%
-0.6 to 9.4
-0.6% to 1.4%
-1.0 to 1.0
1. Basic Model
Modifications
2. !!.M2 Equation:
Coefficients on M2, p, and y
+2u
-2u
3. I:1p Equation:
Coefficients on M2, p, and y
+2u
-2u
4. !!.M2 Equation:
Coefficient on R
+2u
-2u
8.9%
2.2
aThis column reports the values of {3 that produced dynamically stable simulations out of a total of 8 trials.
bSimulations use a = 0.00 and {3 = 0.50.
Federal Reserve Bank of San Francisco
21
King, Robert G., Charles 1. Plosser, James H. Stock, and Mark W.
Watson. 1991. "Stochastic Trends and Economic Fluctuations."
American Economic Review (September) pp. 819-840.
REFERENCES
Barro, Robert 1. 1986. "Recent Developments in the Theory of Rules
Versus Discretion." The Economic Journal Supplement, pp.
23-37.
Lucas, Robert E. 1973. "Some International Evidence on OutputInflation Trade-offs." American Economic Review (June) pp.
326-334.
Evans, George W. 1989: "Output and Unemployment Dynamics in the
United States: 1950-1985." Journal of Applied Econometrics 4,
1989.
Mankiw, N. Gregory. 1990. "A Quick Refresher Course in Macroeconomics." Journal of Economic Literature (December) pp.
1645-1660.
Furlong, Frederick and John P. Judd. 1991. "M2 and the Business
Cycle." Federal Reserve Bank of San Francisco Weekly Letter
(September 27).
McCallum, Bennett T. 1981. "Price Level Determinacy with an Interest
Rate Instrument and Rational Expectations." Journal ofMonetary
Economics (November) pp. 319-329.
Greenspan, Alan. 1989. "A Statement Before the Subcommittee on
Domestic Monetary Policy of the Committee on Banking, Finance
and Urban Affairs, U.S. House of Representatives, October 25.
_ _ _ _ _ . 1988a. "Robustness Properties of a Rule for Monetary
Policy." Carnegie-Rochester Conference Series on Public Policy
29 pp. 173-204.
Hall, Robert E. 1983. "Macroeconomic Policy under Structural
Change." In Industrial Change and Public Policy, pp. 85-111.
Federal Reserve Bank of Kansas City.
_ _ _ _ _ . 1988b. "Targets, Indicators, and Instruments of Monetary Policy." In Monetary Policy in an Era of Change. American
Enterprise Institute, Washington, D.C., (November).
Hallman, Jeffrey 1., Richard D. Porter, and David Small. 1991. "Is the
Price LevelTied to the M2 Monetary Aggregate in the Long Run?"
American Economic Review (September) pp. 841-858.
Meltzer, Allan. 1984. "Credibility and Monetary Policy." In Price
Stability and Public Policy, Federal Reserve Bank of Kansas City,
Jackson Hole, Wyoming, (August 2-3) pp. 105-128.
Johansen, Soren, and Katarina Juselius. 1992. "Maximum Likelihood
Estimation and Inference on Cointegration-with Applications to
the Demand for Money." Oxford Bulletin of Economics and
Statistics 52.2, pp. 169-210.
Miller, Stephen M. 1991. "Monetary Dynamics: An Application of
Cointegration and Error-Correction Modeling." Journal ofMoney,
Credit, and Banking (May) pp. 139-168.
Judd, John P., and Brian Motley. 1991. "Nominal Feedback Rules for
Monetary Policy." Federal Reserve Bank of. San Francisco
Economic Review (Summer) pp. 3-17.
Parry, Robert T. 1990. "Price Level Stability." Federal Reserve Bank of
San Francisco Weekly Letter (March 2).
Phillips, A. W. 1954. "Stabilization Policy in a Closed Economy."
Economic Journal (June) pp. 290-323.
_ _ _ _ _ . 1992. "Controlling Inflation with an Interest Rate Instrument," Finance and Economics Discussion Series, Board of
Governors of the Federal Reserve System.
Rudebusch, Glenn D. 1993. "The Uncertain Unit Root in Real GDP."
American Economic Review (forthcoming).
Judd, John P., and Bharat Trehan. 1992. "Money, Credit and M2," Federal Reserve Bank of San Francisco Weekly Letter (September 4).
Taylor, John B. 1985. "What Would Nominal GDP Targeting Do to the
Business Cycle?" Carnegie-Rochester Series on Public Policy 22,
pp.61-84.
Judge, C.G., W.E. Griffiths, R.C. Hill, H. Lutkepohl, and T.C. Lee.
1985. The Theory and Practice of Econometrics. New York: John
Wiley.
.'
22
.~
Economic Review / 1992, Number 3
'J
Capital Regulation and Bank Lending
Frederick T. Furlong
Assistant Vice President, Federal.Reserve Bank of San
Francisco. I am greatly appreciative of the assistance of
Michael Weiss. I am also grateful to Sun Bae Kim, James
Booth, ElizabethLaderman,Jonathan Neuberger, andJack
Beebe for their comments.
Bank regulation in general and capital regulation in
particularare widely perceived as having become stiffer in
the 1990s. The stiffer regulatory environment in turn is
argued to have curtailed bank lending. This article determines the extent to which capital standards changed in the
1990s and examines the relationship between capital positions and the bank lending. The empirical results suggest
that capital standards did increase in the 1990s. The
analysis also shows that bank loan growth rates are
positively related to capital-to-assets ratios. Moreover,
sensitivity of bank lending to capital positions appears to
have increased in the 1990s. Regionally, capital regulation
likely had the most pronounced effect on bank lending in
New England.
The phasingin of international, risk-basedcapital standards and the growing concern over the risk-exposure of
the deposit insurance system are viewed as precipitating
stifferbank capital regulationin recent years. This stiffening of capital regulation is argued to have restricted bank
lending beginning in 1990, and, thereby, contributed to a
credit crunch.
Consistent with this view, Federal Reserve surveys on
bank lending practices find that many banks tightened
credit standards in 1990and 1991 in part due to the volume
of problemloans and capitalconstraints. In addition, some
recent studies finda positive relationship between levels of
bank capital and bank loan growth in 1990(Furlong 1991,
Bernanke and Lown 1991, and Peek and Rosegren 1991).1
The evidence, however, does not indicate the extent to
which the relationship between bank capital and bank
lending in recent years marks a change from the past.
Capital standards traditionally have been a component of
bank regulatorypolicy, and enforcement of such standards
could be expectedto have influenced lendingby individual
banks even prior to 1990. The purpose of this study is to
examine the extent to which bank capital regulation has
changedin the 1990s and the effect the changehas had on
the relationship between bank capital and lending. The
analysis in this paper differs from past studies by using
cross-section time series data for individual banks from
acrossthe United Statesrather thancross-section data for a
single time period.
The first sectionof this studydiscusses the link between
capital regulationand bank lending in terms of the regulatory objective of creating microeconomic incentives for
banks that are consistentwith limitingthe risk exposure of
the deposit insurance system. The second section compares effective capital standards among banks by size and
chartering authority and examines how bank capital standards have changed. The empirical analysis in the third
sectionlooks at how the relationship between the financial
conditions of banks and their lending has changed over
time and whetherthe effectson bank lendingvaryby bank
size and by geographic region.
IBaerand McElravey (1992) finda positiverelationship betweenbanks'
capital positions and growth rates in assets.
Federal Reserve Bank of San Francisco
23
1. THE LINK
In the U.S. banking system, the roles of the federal
deposit insurance system and the bank regulatory agencies
parallel those of liability holders in private contracts. The
deposit insurance system bears financial liability, and the
regulatory agencies have monitoring responsibilities analogous to those of private liability holders.
A major criticism of the current institutional arrangement is that, while the roles may be parallel, the deposit
insurance system and the regulatory agencies do not necessarily have the same incentive as private liability holders. 2
Nevertheless, regulatory measures are observed that at
least in form resemble those seen in private debt agreements that are intended to control risk-taking.
The most obvious example is capital regulation, which
is analogous to private debt covenants constraining leverage. Jensen and Meckling (1976) point out that equity
holders in general have an incentive to increase risk once
debt has been issued. One method for a firm to increase
risk is to increase its leverage. To control that incentive,
private debt contracts often include provisions limiting the
ability of a firm to dilute its capital position.
The importance of capital regulation in banking per se
is highlighted by Merton (1977) and the large number
of studies spawned by that study, which show that the deposit insurance guarantee is essentially a put option,
with the value varying negatively with a bank's capital-toasset position. The options model of deposit insurance
thus implies that, with subsidized deposit insurance, a
value-maximizing bank has an incentive to increase leverage indefinitely, thus making it necessary for leverage
to be constrained by the enforcement of bank capital
requirements.
The enforcement of capital requirements can link a
bank's capital position with its lending simply as part of the
process of a bank meeting regulatory standards. For example, if bank equity is not perfectly elastic, a bank with too
little capital could attempt to improve its capital position
by reducing its size, and one way to do that is to decrease
loans. Indeed, Keeley (1988) finds that in the 1980s, banks
deficient in capital did adjust their capital positions in part
by growing more slowly than other banks. More generally,
banks with stronger capital positions havemore capacity to
expand loans and still meet regulatory capital standards.
2To the extent that the incentive structure differs, regulatory policy and
bank behavior will not necessarily coincide with what would be predicted from models of unregulated, uninsured banks. Indeed, Kane
(1989) argues that much of the blame for the thrift crisis in the 1980s and
the demise of the Federal Savings and Loan Insurance Corporation falls
on the nonmarket incentives structure faced by regulators as well as on
the incentives inherent in the deposit insurance system for institutions to
take risk.
24
The recent adoption of risk-based capital standards for
banks could reinforce the link between a bank's financial
condition and its investment decisions. For example, when
determining the level of risk-adjusted assets, a zero weight
is given to assets with no default risk, such as Treasury
securities, while riskier assets, such as loans, are given
higher weights.> As a result, for a given level of capital,
a bank can increase its risk-based capital-to-asset ratio
simply by reducing the volume of loans held in its portfolio
and acquiring Treasury securities. Such an adjustment
would tend to reduce the growth rate of loans. 4
The options model of the deposit guarantee also suggests another regulatory rationale for linking leverage and
the growth of risky assets such as loans. Merton shows
that the value of the deposit insurance guarantee is positively related to the degree of asset or nonleverage risk of a
bank. This implies that regulatory policy that takes into
account the liability of the insurance system can be expected to extend effort to control nonleverage risk.
Moreover, Furlong and Keeley (1989) show that the positive effect of a rise in nonleverage risk on the value of the
insurance guarantee increases with a bank's leverage. That
is, with higher leverage and mispriced deposit insurance, a
bank would have more incentive to expand nonleverage
risk. This suggests that regulatory policy should be most
concerned with the expansion of nonleverage risk by
institutions with the least amount of capital.
Two ways a bank can increase nonleverage risk are to
grow and acquire loans (or other assets) that add to its
overall risk or to adjust the composition of its existing
portfolio toward riskier assets such as loans. From a
regulatory perspective, a link between loan growth and
leverage could be rationalized as one way of limiting a
bank's ability to exploit the insurance system through
either of these two options. Loan growth would be more
restricted at banks with less capital since they would have
the greatest incentive to increase nonleverage risk."
3Risk-based capital standards assign risk weights to all bank assets. The
weights are determined by considering the credit (default) risk of assets.
For example, the lowest risk category includes cash and U.S. Treasury
securities, and has a zero weight, which means holdings of these
securities do not add to a bank's risk-adjusted assets. The highest risk
category includes most loans to private entities (but not home mortgage
loans) and has a weight of 100 percent. The standards also account for
credit risk of off-balance sheet activities such as interest rate swaps and
stand-by letters of credit.
4Under the risk-based standards, banks also are subject to a leverage
ratio requirement, which is a ratio of capital to balance sheet assets
including Treasury Securities. Thus, a bank would not be able to
increase leverage indefinitely by shifting to assets with a zero weight.
5Bemanke and Gertler (1987) show that the financial condition of
uninsured, unregulated banks also could be expected to affect their
lending. In their model, banks invest in loans (risky assets) because they
Economic Review / 1992, Number 3
II.
CHANGING CAPITAL STANDARDS IN THE
1990s
Capital regulation has always played some role in bank
regulatory policy. Over the past several years, however, the
theoretical arguments connecting capital and bank risk and
the more concrete evidence of the problems in the thrift
and banking industries, which ultimately led to the demise
of the FSLIC and the "recapitalization" of the bank
insurance fund, heightened the awareness of the importance of equity in banking.
This awareness was reflected in the adoption of explicit
minimum regulatory capital ratios for all but the largest
banks in 1981 and the subsequent raising and extending
of the minimum ratio to all banks in 1985. In an evaluation of the effects of the changes in capital standards during
the first half of the 1980s, Keeley (1988) finds that they
were effective in raisingcapital-to-asset ratios for publicly
traded banks with low capital ratios.
Since 1985, additional important steps have been taken
to place capital regulation at the center of regulatory policy.
One in particular was the adoption of risk-based capital
standards by the bank regulatory agencies." The phase-in
of these standards started in 1990 and it will be completed
at the end of 1992. When fully phased in, the risk-based
standards will require banks to maintain a minimum 4
percent ratio of Tier 1 capital to risk-adjusted assets, and
an 8 percent ratio for Tier 1 plus Tier 2 capital. To be
considered well capitalized, however, a bank would have to
exceed the minimum ratios." Tier 1 capital consists primarily of common equity, while Tier 2 capital can include
have more information on loans than do liability holders and the
information cannot be transferred. Given the information asymmetry on
risky investments, the capital of a bank is necessary to assure liability
holders that the bank would be able to make good on the promised return
to depositors. Assuming a bank's capital equity is not perfectly elastic, a
negative shock to a bank's capital could impair its ability to meet its
obligation to liability holders unless the bank also shifts its investment
portfolio toward riskless assets and away from risky assets. This sa~s
that the adequacy of a bank's capital would affect the makeup of Its
portfolio.
6The prominence of capital regulations was heightened further by the
Federal Deposit Insurance Corporation Improvement Act (FDICIA) of
1991, which directs the regulatory agenciesto use the risk-based capital
standards to trigger specific regulatory responses in a protocol called
"prompt corrective action." Under the protocol, as a bank's capital
falls, the bank faces more restrictions and the regulatory agencies have
less flexibility in dealing with the bank.
"Using the current risk-based capital standards, the FDICIA established
five categories that are intended to reflect banks' capital adequacy. The
five categories are: (I) well-capitalized, which includes institutions that
significantly exceed the capital requirements; (2) adequately capitalized, which includes banks meeting all requirements; (3) undercapitalized, which includes banks not meeting at least one capital
requirement; (4) significantly undercapitalized, which includes banks
Federal Reserve Bank of San Francisco
subordinated debt and such instruments as cumulative
perpetual preferred stock.
Since the current capital standards use a risk-adjusted
measure of assets, the capital requirements under the
current standards are not directly comparable to ratios
associated with the standards applied in the 1980s. However, it is still possible to evaluate whether the new standards have led to more stringent regulatory regimes in
terms of leading banks to hold more capital relative to what
they held in the past. 8 To do so, this study examines the
impact of regulatory policy on banks' ratios of equitycapital to total assets. This study assumes that banks have
target equity-capital-to-asset ratios and that they adjust to
those targets gradually over time. The adjustment process
for bank i can be written as:
k j, t-kj, t-1 = a(kt t-kj, t-1),
where, k is the actual capital-to-asset ratio, k* is the target
ratio, and a is the rate of adjustment.
In the model, it is assumed that capital regulation is
binding and that k* reflects the level of capital the regulator
views as appropriate given the nonleverage risk of the
bank.? The target ratio, however, is not necessarily a
minimum ratio or a required regulatory ratio. For example,
if there are regulatory costs imposed on a bank that has a
ratio below the level deemed appropriate by the regulator,
the bank may choose to hold additional capital as a buffer
against shocks to equity. The target ratio for the bank also
would reflect such a buffer. Finally, the partial adjustment
process implies that adjusting capital is costly.
With data on the actual capital ratios, the expression
above was used to estimate average target ratios and rates
of adjustment for various groupings of banks. Average target ratios and adjustment parameters were estimated for all
banks, for large and small banks separately, and for national and state chartered banks. If capital regulation
became stiffer in 1990, the average target ratios or rates of
adjustment would be expected to have increased.
The data used for estimation are from year-end Call Reports for commercial banks over the period 1985 through
well below at least one capital requirement; and (5) critically undercapitalized, which includes banks falling below a predetermined critical capital level.
8A
general shift in bank portfolios could complicate comparisons over
time. In recent years; the most obvious shifts in banking have been to
Treasury securities and home mortgages. Under the risk-based standards, these assets have weights ofless than 100 percent and an increase
in their relative importance in bank portfolios could mask a shift to move
stringent capital regulation.
9In recent years, it is possible that some banks have been impelled to
improve capital positions by market pressures rather than by regulatory
requirements.
25
1991. The data are for banks with assets of $100 million or
more. Banks that acquired other banks in particular years
are excluded from the sample for those years.I?
The results from estimating the capital ratio adjustment
equation for the various groupings of banks are reported in
Table 1. The estimation procedure corrects for heteroskedasticity along the lines of White (1980). The figures in
the first column represent estimates of the average target
ratios and rates of adjustment for all banks in the sample. 11
The results show that for the period 1985-1989 the target
capital-to-asset ratio was about 7.2 percent. For the 19901991 period, the ratio increased to about 8.8 percent. The
increase in the ratio is statistically significant, and is
consistent with a shift to a more stringent regulatory
regime after 1989.
The estimate of the average adjustment factor also
increases for the 1990-1991 period. However, the decrease
is not statistically significant. Thus, while effective capital
lO'fhe sample also excludes banks like credit card banks that do not
engage in a broad array of banking activities. The sample also excludes
banks with negative capital-to-asset ratios or ratios greater than one
half.
llNonlinear adjustment equations also were estimated. The results
regarding changes in capital regulation are essentially the same as those
shown in table 1. The estimated target ratios, however, are about a
percentage point lower across the board.
standards appear to have increased, the rate of adjustment
in capital ratios for banks as a group is not indicative of
more vigorous enforcement of the new standards.
The table also reports statistics by bank size and charter.
Under bank asset size, the target ratios are higher for
smaller banks than for larger banks. This is consistent with
the view that smaller banks are required to hold more
capital to offset their tendency to be less diversified and,
thus, have higher nonleverage risk than larger banks. 12
On the other hand, the adjustment parameters are higher
for the large banks. This would be the case if regulators
enforced capital regulations more stringently for the larger
banks. It also could be the case if capital requirements
were binding more frequently for large banks than for
small banks.
In terms of changes in regulatory policy, the target ratios
increased for both large and small banks after 1989. The
increase is statistically significant for small banks, which
is consistent with an escalation in the stringency of capital
regulation for those banks. The adjustment parameter for
the sample of small banks declined slightly, though the
12Por example, results in Laderman, Schmidt, and Zimmerman (1991)
suggest that small banks tend to lend in local markets and to have less
diversified portfolios.
Table 1
Target Capital-to-Asset Ratios and Adjustment Parameters
By Asset Size
By Charter
Thrget
Ratio
$100 million
to $1 billion
$1 billion
All banks
or more
Difference
State
1990-1991
0.0880**
0.0923**
0.0740**
0.0183t
0.0961 **
.0822**
0.0139
1985-1989
0.0718**
0.0733**
0.0610**
0.0123**
0.0749**
.0664**
0.0085**
Difference
0.0162**
0.0191**
0.0130t
0.0212*
.0158**
1990-1991
0.0738**
0.0561**
0.1474t
-0.0913
0.0445
1985-1989
0.0762**
0.0740**
0.1268*
-0.0529
0.0964**
National
Difference
Adjustment
Parameter
Difference
*
-0.0024
-0.0179
0.0206
-0.0519
0.1154**
-0.0709
.0466**
0.0498
.0688:1:
significant at 5 percent level
** significant at I percent level
t significant at 10 percent level
:I:
26
significant at 6 percent level
Economic Review / 1992, Number 3
change is not significant. The target ratio and the adjustment parameter both increased for large banks after 1989,
but only the change in the target ratio is statistically
significant. The evidence, is then supportive of the hypothesis that capital regulation systematically became more
stringent for the large banks.
Looking at banks by type of charter, the increases in the
target ratios after 1989 are positive and significant for state-chartered and nationally chartered banks. Based on the
changes in the target ratios, the shift in capital regulation
was about the same for state-chartered banks as it was for
nationally chartered banks, with the difference not statistically significant. The changes in the adjustment parameters, however, are consistent with more of a tightening of
regulatory policy for the national banks. The adjustment
parameter for the sample of national banks increased, with
the change significant at the 6 percent level. For the statechartered banks, the estimated adjustment parameter declined, but the change was not significant. In evaluating the
overall stringency of regulatory policy it can be noted that
the level of the target ratio tends to be higher for statechartered banks. 13
III.
CAPITAL REGULATION AND BANK LENDING
Overall, the results in Table 1 indicate that capital
regulation has been more stringent in recent years, which is
consistent with regulatory policy that is increasingly concerned with the soundness of the deposit insurance system.
The earlier discussion also suggests that such regulatory
concerns could be expected to lead to a positive relation
between the capital position of a bank and its rate of loan
growth. The analysis in this section focuses on this relationship. In particular, it examines whether a bank's capital
position affects its lending and whether that relationship
has been affected by the shift in regulatory regime suggested by the results in the previous section.
The model used is a reduced form equation for the
growth in bank loans:
10g(Li, .ti; t-I) = f[g(k i, t-Ilkt t), Xi, t' ei, t].
contributed to slower bank loan growth, the positive effect
of the spread in the capital ratios on bank loan growth
would be expected to have increased.
The other supply and demand variables included in the
empirical analysis are the growth rate in personal income
for the state in which the bank operates, a bank's ratio of
current loans to total loans, and a bank's ratio of total loans
to assets. The income variable is intended to control for
general economic conditions faced by a bank and is expected to have a positive relation with loan growth. The
ratio of current loans also could be an indicator of the
economic environment in which a bank operates. 14 A
higher ratio could be indicative of a stronger economic
environment and could be associated with higher loan
growth. This variable also could capture regulatory effects
on a bank. Holding capital constant, banks with higher
ratios of current loans should be viewed as being stronger
financially. If so, the current loan ratio would be expected
to have a positive relationship with loan growth. The other
variable, the ratio of total loans to assets, is meant to
control for the capacity of a bank to boost loan growth by
shifting out of other assets in its portfolio. In this regard,
the ratio would be expected to have a negative relationship
with loan growth. Again, the effect of the loan-to-asset
ratio on loan growth may reflect regulatory influences. All
else equal, bank regulators could view banks with higher
loan-to-asset ratios as being less financially sound and,
therefore, may tend to limit the loan growth of such banks.
The basic equation used in estimation is:
In(Li, .tt.; t-I) =
C
+ BIln(INC i, /INC i, t-I)
+ B2ln(PIL)i, t-I
+ B 3ln(LlA);, t-I
+ B4ln(k;, t-Ilkt t) + e;, t'
where:
L is total loans
INC is the level of the income in the state in which a bank
operates
P is current loans
A is total assets
k is the actual equity capital-to-asset ratio, and
k* is the target equity capital-to-asset ratio.
This expression says that the growth rate of loans at a
given bank depends on the level of the actual capital ratio
relative to the target ratio, a set of variablesX, which represents other supply and demand factors, and an error term.
If capital regulation affects bank lending, loan growth
would be expected to be positively related to the spread
between the actual and the target capital ratios. If the
change in regulatory regime over the past few years has
14These are loans that are less than 30 days past due and accruing
interest.
13This result holds up even when controlling for bank size.
15The estimates of k* from a nonlinear adjustment equation also were
used in the loan growth equation. The statistical results are essentially
the same as those in Tables 2 through 4.
Federal Reserve Bank of San Francisco
The target ratios are derived from the capital adjustment
equation discussed earlier. IS The targets differ by size
27
leverage to its target leverage, has a positive and statistically significant effect on bank loan growth. This is
consistent with capital regulation having an effect on bank
lending. The results for loan quality and the loan-to-asset
ratio also may reflect regulatory influences on bank lending. Overall, these results support the view that regulatory
policy does limit the loan growth of banks in weaker
financial condition.
The last two columns in the table provide evidence on
the shift in the behavior of bank lending inrecent years and
its possible relationship to bank capital regulation. In the
second column, the shift in bank loan growth is measured
by the coefficient on the bivariate dummy variable D90-91,
which takes a value of 1in 1990 and 1991and a value of 0 in
the earlier years. The coefficient shows a negative and
statistically significant shift in the average growth rate of
of bank and by time period. Averagetargets were estimated
separately for small banks ($100 million to $1 billion
in assets) and large banks ($1 billion or more in assets)
for the 1985-1989 period and the 1990-1991 period.
Lagged values were used for P/L and LIA to avoid possible simultaneity problems. Once again, the interval used
is one year, and the estimation procedure corrects for
heteroskedasticity.
The loan growth equation was estimated over the period
1985 through 1991. The first column ofTable 2 shows that
the coefficients on state income growth and the quality ofa
bank's portfolio are positive and highly significant. The
loan-to-asset ratio has a negative effect but is not statisticallysignificant.
More central to the focus of this paper, the capital
position variable, measured by the ratio of a bank's actual
Table 2
All Banks
Total Loan Growth Regressions
(1985-1991 )
Explanatory Variables
(1)
(2)
(3)
4,063
(6.05)**
5.778
(8.53)**
5.741
(8.49)**
In (INC;, ,1INC;. '-I)
1.257
(27.04)**
1.105
(22.74)**
1.104
(22.71)**
In (PIL)i, , - I
106.948
(19.15)**
109.806
(19.47)**
109.760
(19.47)**
c
In (LiA )i,
,-I
-1.000
( -1.27)
4.952
(7.10)**
D9O-91
-1.044
( -1.33)
3.718
(4.84)**
2.221
(2.53)*
-2.535
(- 8.52)**
-1.932
( -4.96)*
4.373
(2.88)**
In (k i , '-llkt, ,). D90-91
N
-1.071
( -1.37)
0.126
0.13
0.131
16,261
16,261
16,261
Note: t statistics are in parentheses
* significant at 5 percent level
** significant at 1 percent level
28
Economic Review / 1992, Number 3
loans in the 1990-1991 period. This result is consistent
with the widely held view that bank lending was unusually
weak in 1990 and 1991.
To test for a change in the effects of capital regulation, in
the third column D90-91 is interacted with the log of the
ratio of actual leverage to target leverage. The results
indicate that the capital position of banks had a positive and
statistically significant effect on bank lending even in the
second half of the 1980s. This is consistent with other
evidence that regulatory policy was emphasizing capital
regulation during that period. The connection between
capital regulation and bank lending then is not a phenomenon that arose only in the 1990s.
That relationship, however, does appear to have intensified considerably in the past few years. The coefficient
for the interacted capital position.variable and the dummy
variable D90-9l is highly significant and points to a
relatively large increase in the sensitivity of bank loan
growth to capital positions. Overall, the coefficient on the
capital position variable is just about three times larger for
the period 1990-1991 than for the period 1985-1989.
Measured from the average target values, a 0.01 drop in a
bank's capital ratio would have lowered its loan growth for
a year by an estimated 0.3 of a percentage point during the
second half of the 1980s. In the 1990-1991, the same
decline in the capital ratio would have led to an estimated
0.8 of a percentage point drop in loan growth.
The finding that bank lending has become more sensitive to capital positions is consistent with a shift to a more
stringent regulatory regime in the 1990s.16 The difference
in the coefficient on D90-91 between columns (2) and (3)
also suggests that the shift in regulatory regime relating
to capital regulation may account for part, but not all,
of the unusually slow bank loan growth in the 1990 and
1991. The unexplained portion could be due to differences
in the behavior of bank lending during recessionary periods, special economic factors such as the condition of the
commercial real estate sector, or perhaps more general
regulatory influences on bank lending that were not tied
directly to capital positions.
Bank Size
To determine how lending may have been affected at
different size banks, Table 3 reports pooled cross-section
regression results in which separate coefficients are estimated for large and small banks. The coefficients on state
16The loan growth equationalso wasestimatedallowing for shiftsin the
relationship betweenloangrowthand each of theexplanatory variables.
This had virtually no effect on the change in the coefficient for the
capital regulation variable.
Federal Reserve Bank of San Francisco
income growth indicate that loan growth at small banks is
more sensitive to local market conditions. This is not
surprising, since bigger banks can be expected to engage in
more lending regionally, nationally, and even internationally. Lending by small banks and large banks is about
equally sensitive to the quality of loan portfolios.
The effect of the loan-to-asset variable also is different
for small and large banks. The effect for small banks is
what would be expected for banks with relatively constrained assetlliability management options,such as relying mainly on local, retail deposits. That would make
smaller banks with higher loan-to-asset ratios less able to
expand lending. The result for smaller banks also is
consistent with regulatory policy that tries to constrain
nonleverage risk.
For large banks, however, the coefficient for the loan-toasset ratio is positive, though only marginally significant.
One reason for the difference may be that large banks have
access to national and even international money and capital
markets, so their ability to expand loans is less constrained
by the makeup of their existing portfolios. Without this
constraint, it may be that the portion of assets invested in
loans is an indication of a bank's general investment
strategy; banks with high ratios lend more and so tend to
have faster loan growth. This is not, however, the relationship that earlier was argued would be expected if this
variable were capturing the effects of regulatory policy
concerned with controlling nonleverage risk.
The main focus of this analysis is on.theeffects of capital regulation. The results in Table 3 show that lending
by large banks in general is much more sensitive to capital ratios relative to target ratios. This is true even for
the 1985-1989 period. In that period, the coefficient for the
larger banks is positive and highly significant. In contrast,
the coefficient on the capital position variable is positive
but not statistically different from 0 for the small bank
sample. These results are consistent with the evidence in
Table 1 suggesting that capital regulation is more binding
for larger banks than it is for smaller banks.
In terms of the shift in regulatory policy, the coefficient
on the capital position variable interacted with the shift
dummy in the first column of Table 3 suggests that capital
regulation has become a factor for small banks in recent
years. The point estimate for the increase in sensitivity of
lending to capital positions is bigger for the large banks
than for the sample of small banks. However, the change
for large banks is not statistically significant.
The evidence, then, suggests that the capital regulation
has shifted for small banks but perhaps not for larger
banks, at least not beyond increases in target capital ratios
indicated in Table 1. At the same time, these results suggest
that standards under the new capital regulation regime, as
29
under the old, are relatively more binding for the larger
banks. Moreover, the larger unexplained decline in loan
growth in 1990-1991 for large banks could reflect a shift in
regulatory policy toward those banks relative to their
smaller counterparts.
Regional Effects
The financial condition of banks varies across geographic regions. The chart, for example, shows that in the
early 1990s bank capital positions weakened considerably
in New England compared to other regions of the country.
The earlier finding of a positive relation between bank
capital positions and lending suggests that bank lending
should have been more adversely affected in the areas
experiencing greater weakness in capital. 17 However, the
variation in the financial conditions of banks also raises
the possibility that the shift in regulatory regime was more
pronounced in some geographic regions.
Table 4 presents two sets of statistics relating to the shift
in the sensitivity of bank lending to capital positions across
regions. The first set consists of estimates from a pooled
cross-section time series in which the coefficients in the
loan growth equation are constrained to be the same for
17In testimony to the U.S. Congress, Richard Syron, President of the
Federal Reserve Bank of Boston, argues that the decline in bank capital
in the New England area was an important cause of the weakness in
lending, and contributed to the so-called credit crunch. See Syron
(1991).
Table 3
Large and Small Banks
Total Loan Growth Regressions
(1985-1991 )
30
Economic Review / 1992, Number 3
The Change in Capital-to-Asset Ratios
between 88/89 and 90/91 a
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
-0.002
-0.004
-0.006
I...--.L---I._....L.-----L.._L..--.L---I._..l.---l------l
aThe differrence between the average of the quarterly data 1988/89
and 1990/91
banks in all regions, with the exceptions of the dummy
variableD90-9land the capital position variable interacted
with the dummy. To simplify the presentation, only the
figures measuring the shifts in the intercept and the coefficient on the capital position variable are reported. The
geographic regions correspond to the Bureau of Economic
Analysis definitions. 18
The results suggest that the change in sensitivity of bank
lending to capital positions may have been more pronounced in some regions. Only three of the eight regions
show statistically significant increases, with the largest
change for the New England region. However, some shift
also may have occurred in the other regions. For example,
when the five regions not showing statistically significant
results in the second column of Table 4 are grouped
together, we can reject the hypothesis of no change in the
loan growth/capital position relationships after 1989.
In the pooled regression for all banks, it is possible that
systematic differences among regions prior to 1990 affected the measured shifts in the loan growth equation.
Accordingly, the second set of statistics in Table 4 is based
on separate cross-section time series regressions for each
region. Overall, the results show somewhat more evidence
of a shift in the effect of banks' capital positions than do the
results for the pooled regression for all banks. The three
regions showing significant positive shifts in the coeffi18A1aska and Hawaii are included in the West.
Federal Reserve Bank of San Francisco
cient for the capital position variable in the first set of
statistics also do so in the second set. One additional region
showing a shift in the loan growth/capital position relationship is the Southeast. Another difference is that the Great
Lakes region shows a marginally significant increase in the
response of bank lending to capital positions in the separate regression for that region.
The separate regressions still suggest regional differences in the shift in regulatory policy, again with the New
England region showing the largest increases in the sensitivity of bank lending to capital positions. These results,
coupled with the data on the decline in capital positions,
highlight why the credit crunch in 1990~1991 is most
closely associated with developments in New England.
That region shows the largest decline in bank capital ratios
and the biggest increase in the sensitivity of lending to
capital positions in the 1990-1991 period.
The results for the Southwest region provide an interesting comparison with those for the New England region.
The separate regression for the Southwest shows neither a
significant shift in the relationship between loan growth
and bank capital positions nor a negative intercept shift in
theloan growth equation after 1989. This may reflect the
improvement in capital positions of banks in the Southwest
as illustrated in the chart. More likely, these results reflect
the difference in timing of the problems hitting the banks
in the Southwest. In that region, the problems in the banking industry hit in the 1980s. As a result, bank loan growth
in the Southwest was already weak going into the 1990s.
The weakness in banking lending in the Southwest in the
1990-1991 period is reflected in the significant negative
shift in intercept in the first column of Table 4.
The evidence for the West also is interesting since it
suggests that bank lending became less sensitive to capital
positions in the 1990-1991 period. Indeed, with the change
in the sensitivity during the 1990-1991 period, the overall
effect of bank capital positions on lending was not statistically significant for the West. This does not necessarily
mean that the region was unaffected by regulatory policy,
however. The regression results for the West do indicate a
significant downward shift in loan growth in 1990-1991,
which leaves open the possibility that regulatory policy
affected lending in the region. It is still possible that
regulatory policy had a dampening effect on lending; it is
just not evident that such influences were systematically
related to the bank capital positions in the area.
IV.
CONCLUSION
This paper finds that loan growth for individual banks is
positively related to their capital-to-asset ratios. The analysis in this paper goes beyond that of previous studies by
31
using a much broader sample of banks and examining how
the relation between capital positions and lending has
changed in recent years. The analysis shows increases in
both bank capital standards and in the sensitivity of bank
lending to capital positions in the early 1990s compared
with the second half of the 1980s. The apparent shift in
regulatory regime affected small banks as well as large
banks. The overall sensitivity of lending to capital positions was more pronounced during both periods for the
large banks in the sample. This result is consistent with
the view that capital regulation tends to be binding more
often for larger banks than for smaller banks. The change
in the sensitivity of bank lending to capital positions varies
regionally, with the New England region being the most
affected.
With regard to the so-called credit crunch in the 1990s,
the findings in this paper support the view that the increase
in effective capital standards and the actual decline in
capital positions of some banks contributed to slow loan
growth in the 1990-1991 period. In addition, the increased
sensitivity of bank lending to capital positions accounts for
a portion of slower than normal bank loan growth in the
1990-1991 period. The impact of capital regulation on
lending likely was most pronounced in the New England
region, which experienced both the greatest decline in
bank capital ratios and the sharpest rise in sensitivity of
Table 4
Regional Effects
Total Loan Growth Regression
(1985-1991 )
Pooled Regression For All Banks
D90-91
New England
1.324
(1.09)
In (k i , t-llkf, t)
oD90-91
Separate Regressions by Region
D90-91
In (k i , t-llkf, t)
oD90-91
R2
N
14.966
(4.88)**
-5.300
( -1.44)
20.53
(3.31)**
0.311
790
Mideast
-0.665
( -0.61)
5.143
(1.20)
-6.079
( -4.62)**
4.310
(0.90)
0.118
2504
Great Lakes
-1.205
( -1.73)
3.044
(1.01)
-2.367
( -3.27)
5.328
(1.62)
0.082
4104
Plains
-1.697
(- 2.48)*
8.241
(3.22)**
-0.281
( -0.36)
9.783
(3.42)**
0.103
1604
Southeast
-3.586
(-8.46)**
1.724
(1.09)
-4.244
( -8.84)**
6.00
(3.59)**
0.186
3597
Southwest
-4.419
( -2.73)**
3.839
(1.09)
2.116
(1.14)
4.297
(1.12)
0.100
1924
Rocky Mtn.
-4.900
( -2.65)**
12.155
(2.58)**
1.279
(0.63)
13.68
(2.71)**
0.156
529
.063
1209
West
0.521
(0.38)
-4.717
( -0.95)
R2
0.135
N
16,261
-4.538
( -2.52)*
-12.742
( -1.82>*
NOTE: See note to Table 2.
32
Economic Review I 1992, Number 3
lending to bank capital positions. For banks nationally,
however, a good portion of the slower loan growth in 19901991 is not accounted for directly by movements in capital
positions or by changes in capital regulation. The unexplained portion may be due to the difference in the behavior
of the supply and the demand of bank loans during recessionary periods, special economic factors such as the
condition of the commercial real estate sector, or perhaps
more general regulatory influences on bank lending that
were not tied systematically to capital positions.
REFERENCES
Keeley, Michael C. 1988. "Bank Capital Regulation in the 1980s:
Effective or Ineffective?" Federal Reserve Bank of San Francisco
Economic Review 1, pp. 1-20.
Baer, Herbert, and John McElravey. 1992. "Capital Adequacy and the
Growth of U.S. Banks." Working Paper No. 92-11. Federal Reserve Bank of Chicago.
Bemanke, Ben, and Mark Gertler. 1987. "Banking and Macroeconomic
Equilibrium." In New Approaches to Monetary Economics, William A. Barnett and Kenneth 1. Singleton. Cambridge: Cambridge
University Press.
Bemanke, Ben, and Cara S. Lown. 1991. "The Credit Crunch."
Brookings Papers on Economic Activity 2, pp. 205~239.
Furlong, Frederick T. 1991. "Financial Constraints and Bank Credit."
Federal Reserve Bank of San Francisco Weekly Letter (May 26).
_ _~__ , and Michael C. Keeley. 1989. "Capital Regulation and
Bank Risk-Taking: A Note." Journal of Banking and Finance
(December) pp. 883-891.
Jensen, Michael, and William Meckling. 1976. "Theory of the Finn:
Managerial Behavior, Agency Costs and Ownership Structure."
Journal ofFinancial Economics (October) pp. 305-360.
Kane, Edward 1. 1989. The S&Llnsurance Mess: How Did It Happen?
Lanham, MD: Urban Institute Press.
Federal Reserve Bank of San Francisco
Ladennan, Elizabeth, Schmidt, Ronald H., and Zimmerman, Gary.
1991. "Location, Branching, and Bank Portfolio Diversification:
The Case of Agricultural Lending." Federal Reserve Bank of San
Francisco Economic Review 1, pp. 24-37.
Merton, Robert. 1977. "An Analytic Derivation of the Cost of Deposit
Insurance and Loan Guarantees." Journal of Banking and Finance, pp. 3"11.
Peek, Joe, and Eric Rosegren. 1991. "The Capital Crunch: Neither a
Borrower nor a Lender Be." Working Paper No. 91-4. Federal
Reserve Bank of Boston.
Syron, Richard R 1991. "Statement before the Subcommittee on
Domestic Monetary Policy of the Committee on Banking, Finance,
and Urban Affairs of the U.S. House of Representatives." Federal
Reserve Bulletin (July) pp. 539-543.
White, Halbert. 1980. "Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity." Econometrica, pp. 817-838.
33
Macroeconomic Shocks and Business Cycles
in Australia
Ramon Moreno
Economist, Federal Reserve Bank of San Francisco. I
am grateful to Chris Cavanagh, TIm Cogley, Michael
Gavin, Reuven Glick, Michael Hutchison, Kengo Inoue,
Eric Leeper, Robert Marquez, Glenn Stevens, Adrian
Throop, Bharat Trehan, and Carl Walsh for helpful discussions or comments. Any errors of interpretation or application are mine. I also thank Judy Wallen and Brian Grey for
capable research assistance.
A small vector autoregression model is estimated to
assess how demand and supply shocks influence Australian output and price behavior. The model is identified by
assuming that aggregate demand shocks have transitory
effects on output, while aggregate supply shocks have
permanent effects. The paper describes how Australian
macroeconomic variables respond to demand and supply
shocks in the short run and in the long run. It also finds
that demand shocks are dominant in determining fluctuations in Australian output at a one-quarter horizon,
but supply shocks assume the larger role at longer horizons. Supply shocks also account for most of the fluctuations in the Australian price level.
34
The recession. and sluggish growth that have characterized the U.S. economy beginning in the late 1980s have
renewed interest in the processes that govern business cycle
behavior. Recent studies by Blanchard and Quah (1989),
Shapiro and Watson (1988), Judd and Trehan (1989,1990),
and Gali (1992) have used structural vector autoregression
models to provide useful insights on U.S. business cycle
behavior,'
This paper extends their analyses to examine how demand and supply shocks affect business cycle behavior in
Australia. The application to Australia is of interest for at
least two reasons. First, previous studies give widely differing estimates on the importance of supply and demand
shocks in influencing cyclical behavior. A study of Australia may provide further evidence to help clarify this
question. Second, a comparison of the evidence from
Australia with the results from previous research may
highlight similarities or contrasts in business cycle behavior in small open economies and large, relatively closed
economies, like the United States.
The paper focuses on three closely related questions:
(i) How do macroeconomic variables respond to demand
and supply shocks? (ii) How much of the variance in output and inflation is explained by demand and supply
shocks? (iii) How do demand and supply shocks influence
cyclical behavior, particularly during recessions? These
three questions are addressed by estimating a small vector
autoregression model of the Australian economy. Unobservable demand and supply shocks are then identified
by assuming that aggregate demand shocks have transitory
I As discussed below, these studies identify a structural model by using
long-run identifying restrictions. Long-run identifying restrictions are
also used by Gerlach and Klock (1990) to study Scandinavian business
cycles and Moreno (1992a) to study Japanese business cycles. Other
studies using such restrictions address somewhat different questions.
Hutchison and Walsh (1992) examine the Japanese evidence on the
insulation properties of exchange rate regimes, while Hutchison (1992)
investigates whether the vulnerability of the Japanese and U.S.economies to oil shocks declined between the 1970s and the 1980s. Another
strand ofthe literature identifies demand and supply shocks by imposing
restrictions on the contemporaneous impact of these shocks (Blanchard
1989, Blanchard and Watson 1986, andWalsh 1987).
Economic Review / 1992, Number 3
business cycle theory. This paper finds that although supply
shocks have a strong influence on Australian business cycle
a significant role.
behavior, demand shocks
The paper is organized as follows. Section I provides
some background on the Australian economy. Section II
describes the model estimated (which closely resembles
that used by Shapiro and Watson (1988» and the identifying restrictions used. Section III discusses the univariate
properties of the data, and how these results are used in
VAR estimation. Section IV reports the results of VAR
estimation and applies them to answer the three questions
posed in this introduction. Section V summarizes the
findings of this paper and suggests possible extensions.
effects while aggregate supply shocks have permanent effects on output. One advantage of this approach is that
it does not assume that short-run fluctuations are entirely
due to temporary demand shocks (as in the traditional approach to macroeconomic modeling) or permanent supply
shocks (as in early real business cycle models). Instead,
the method estimates the relative importance of aggregate
demand and supply shocks at various forecast horizons. A
second advantage of this approach is that it avoids the
imposition of arbitrary identifying restrictions, thus addressing objections raised by Sims (1980). Finally, the
paper relies on economic theory to achieve identification,
addressing objections to atheoretical VAR methods cited
by Cooley and Leroy (1985) or Bernanke (1986).
The description of the dynamic responses of macroeconomic variables to demand and supply shocks obtained by
addressing the first question may provide insights that are
relevant to policy analysis. At the same time, answers to
the second and third questions can shed light on the relative
importance of demand and supply shocks in influencing
business cycle activity, a question that has acquired prominencein the 1980s with the growing popularity of real
I.
BACKGROUND
To provide a context for the analysis of Australian
business cycles that follows, Table 1 identifies peak-totrough dates, their duration, average output growth and
inflation rates and deviations of these rates from baseline
rates during recessionary periods. The baseline rates are
based on two subsamples, because statistical tests reported
Table 1
GDP Growth during Recession and Inflation Characteristics of Australia
Peak- 'Irough Dates
Quarters of
Downturn
GDP
Compound
Annual Growth
Inflation
Deviation from
Baseline"
(%)
Full-sample
1960.Q1-1989.Q4
Sub-sample Ib
1960.Ql-1973.Q4
1960.Q3-1961.Q3
1964.Q4-1966.Q2
1967.Ql-1967.Q4
1968.Q4-1972.Q3
Sub-sample 2b
1973.Q4-1989.Q4
1973.Q4-1975.Q4
1976.Q4-1977 .Q4
1979.QI-1980.Q1
198I.Q3-1983.Q2 .
Compound
Annual Rate
Deviation
from Baseline-
(%)
5.2
3.9
-81.2
6.9
5.2
8
5.0
-60.7
3.8
-9.5
5
7
4
16
-2.7
2.9
2.9
4.7
-153.8
-42.1
-42.0
-4.8
2.0
3.5
3.6
4.9
-47.3
-9.8
-7.0
26.1
7
3.0
-101.7
9.6
19.9
9
5
5
9
1.1
-0.4
0.2
-1.2
-63.8
-111.7
-93.3
-138.1
15.1
9.2
10.6
11.3
56.8
-4.7
9.8
17.6
-Compured as 100 x (cycle rate - subsample average rate) I subsample average rate.
bPeriodaverage.
Federal Reserve Bank of San Francisco
35
later indicate that therewasa break in the trend of both the
output and inflation series.?
Table1indicates that Australia grewat an annualrate of
about4 percentin the last threedecades. However, average
growth slowed sometime in the early 1970s from 5 percent
to around 3 percent. Over this period, Australia experienced eight recessions that on average lasted 7.5 quarters.
Output growthfell an average of 81 percentbelowbaseline
during recessions. By way of comparison, the U.S. has
experiencedfewerrecessions than Australia over a similar
period (five). U.S. recessions on average are shorter(under
four quarters) and steeper (output growth on average falls
170 percent below baseline during recessions) than Australia's. While these comparisons should be interpreted
with some caution, because they partly reflect differences
in how recessions are defined in each economy, they
suggestcontrastsin thecyclicalbehavior of Australian and
u.s. output."
According to Table 1 Australia's inflation averaged 6.9
percent overthe sampleperiod. Inflation rose overthe two
subsamplesfrom 3.8 percent to 9.6 percent beginning in
the mid-1970s. It is alsoapparentthat on average there was
no decline in inflation (in relation to baseline) during
recessions in the second period.
Three factors are likely to have influenced cyclical
output and inflation performance in Australia:
First, Australia meets most of its fossil fuel requirements through domestic production. In 1989, Australia
produced 22.5 million metric tons of crude petroleum,
about 86 percent of its domestic consumption. In 1989,
fuels accounted for 5 percent of total imports, which to
some degree were offset by exports.
Second, wage-setting is highly centralized due to the
dominant influence of the Australian Council of Trade
Unions. Nominal wages historically appear to have been
2The sample is broken at the date closest to the break date reported in
Table 3, subject to not splitting recessions across two samples. A similar
criterion determines the break dates in the tables describing the cyclical
behavior of inflation.
3Peak-to-trough dates for the U.S. are reported by the NBER, which
currently tracks the behavior of four series to date recessions: real
income, real sales, nonagricultural employment and industrial production. See Hall (1991). No comparable information is available for
Australia, so peak-to-trough dates are those reported in OECD (1987).
These peak-to-trough dates are based on the estimation of so-called
phase-average trend (using the peaks and troughs of sine waves as the
turning points of the cycle). It closely approximates a linearly deterministic trend if such a trend is unbroken, or a succession of segmented
linear trends. The recession dates selected include what the OECD calls
"minor cycles." In the absence of a more extensive dating procedure,
the cycles reported in Table 1 are necessarily imprecise and the VAR
analysis reported later provides additional information on whether they
are reasonable.
36
relatively rigid. Australian unions were highly successful
in putting upward pressure on wages until 1982. Some
researchers argue (Chapman 1990) that wage restraint
subsequently resultedfromthe Pricesand Incomes Accord
betweenthe government andthe unions signedin 1983,but
others argue that the econometric evidence on this is weak
(Blandy 1990).
Third, monetary policy appears to have played a largely
passive role in curbing inflation and focused more on
correcting external imbalances. The fiscal policy stance
has fluctuated sharply over the sample period, on several
occasions countercyclically. During the period of fixed
exchange rates in place until December 1983, money
growth and inflation are believed to have been influenced
by external factors (like oil price shocks), as the rise in
inflation in the 1970s mirrors similar increases in inflation
in OECDcountries.In contrast, afterAustraliaswitched to
floating in December 1983, inflation on average has exceededtheOECD average. Thereis a widelyheldviewthat
the government has soughtto curb inflation largely through
wage agreements under the Accord (Carmichael 1990,
Stevens 1991). Monetary policyplayed a secondary, or even
passive role in curbing inflation, but authorities appeared
to favor monetary stimulus and nominal exchange rate
depreciation to reduce current account deficits. Under
these circumstances, the relationship between monetary
policyandbusinesscyclefluctuations woulddependonthe
types of shocks accounting for current accountdeficits. If
current accountdeficitsweredue to adverse movements in
the terms of trade that would also tend to reduce domestic
economic activity, monetary policywouldoperatecountercyclically-that is, it woulddampenbusiness cyclefluctuations. However, if current account deficits were due to
strong domestic demandstimulus, monetary policy would
operate procyclically.
In contrast to the uncertain role of monetary policy in
influencing business cycle behavior, fiscal policy appears
to have operated countercyclically on a number of occasions. For example, the 1973.Q4-l975.Q4 recession was
associated with a sharp increase in government consumption spending and a related rise in public borrowing to
around 5 percent of GDP from 1to 2 percentin the 1960s.
The higher rate of borrowing was largelymaintained until
the early 1980s, when public sector borrowing rose to a
peak of 7 percent of GDP at the time of the 1981-1983
recession. Largerevenue increases and expenditure reductions subsequently reversed the upward trend in public
sectorborrowing, so that by 1988 the government wasa net
lender.
In Section IV, the preceding stylized facts are used to
suggestinterpretations of estimatedresponses to shocks in
Australia.
Economic Review I 1992, Number 3
II
(10)
THE MODEL
(1)
The specification in equation (10) reflects the assumption
that the price level is integrated (the first difference is
stationary) and all the shocks have a long-run effect on the
price level.
The model is now extended by including an exogenous
oil price shockthat has an effect on all of the othervariables
of the model,
(2)
(11)
where E Zt' E 3t are mutually uncorrelated shocks that influence long-run growth (E l t is definedlater), and en(L), e€(L)
are lag polynomials."
The long-run log level of output is determined by a
Cobb-Douglas production function:
To sum up, the model may be described as follows
Following Shapiro and Watson (1988), consider a standard growth model whereshocksto demand are allowed to
influence the behaviorof output in the short run. In such a
model, the log levels of the labor supply and technology
TT are governed by:
nt
yt = cxn/
(3)
+ (l-cx)kt
*+
T:.
Impose the theoretical restriction that the steady-state
capital-output ratio is constant:
k,* = Yt * + 'Y/,
(4)
where 7J is the constant log capital-outputratio. Substituting (4) into (3) yields
Y/ = nt* +
(5)
[~) Tr* '
where the constant term 7](l-a)
is suppressed.
a
Equations (1)to (5) describe areal business cycle model
with very simple dynamics. To close the model, introduce
an aggregate demand shock E4 t that is serially uncorrelated
and uncorrelated with growth shocks EZt ' E3f' and that
allows the labor input and output to deviate temporarily
from their long-run levels. Then we have
(6)
and
(7)
It is assumed that labor supply and output are nonstation-
ary. First-differencing to account for such nonstationarity,
and substituting (1), (2), and (5) into (6) and (7), yields
(8)
(9) LiY t
Lint = 8 n (L )E2t + (l-L)E h(L)[E2t
=
8 n(L )E2t
+
cx- 18 s(L )E3t
(12)
fit
Lint
= B(L)
E2t
LiY t
E3t
sp,
E4t
The shocks E l t to E4t respectively correspond to shocks to
the oil price, labor supply, technology, and a demand
shock.
In equation (12), shocksto the oil price are one sourceof
external supply shocks. However, in a smallopen economy
like Australia, other external disturbances may be important in influencing business cycle behavior. If external
effects are important, both the supply and demand shocks
in the present model maybe interpreted as combinationsof
domestic and:external shocks.
The structural shocksof model (12) can be recoveredby
first estimating a vector autoregression (VAR) model, and
then exploiting the information from the sample variancecovariance matrix to achieve identification. As discussed
earlier, one of the key identifying assumptions is that
unobservable demand and supply shocks are identified by
assuming that aggregate demand shocks have transitory
effects while aggregate supply shocks have permanent
effects onoutput. The estimation and identification procedures closely resemble those used by Shapiro and Watson (1988) and are discussed more fully in Appendix A. 5
E3t E4/]
+ (1-L)EiL)[E 2t E3tE 4t] .
In the present case, the model is completed by incorporating the processes governing the price level, Pt'
4These polynomials are assumed to have a.bsolutely summable coefficients and roots outside the unit circle (i.e., the dynamics described by
the polynomials are transitory, so the polynomials can be inverted).
Federal Reserve Bank of San Francisco
So,
5 Although the model used in this paper is similar to Shapiro and
Watson's (1988) model, the application differs in two ways: (i) the labor
supply is represented by the labor force, rather than by the total hours
worked by all employed persons; (ii) one equation is used to represent
shocks to demand, ratherthan two equations, as in Shapiro and Watson.
However, Shapiro and Watson do not separately identify the two demand
shocks, but instead use the combined effects of the two shocks in their
analysis.
37
Ill.
DATA ANALYSIS
To estimate the system described by equation (12) I
collected quarterly data for the oil price (0), the Australian
labor force (n), Australian real GDP (y) and the Australian CPI (P). The data and sources are described in Appendix B. Certain properties of the series included in the
model must be checked in order to determine the appropriate specification for estimation purposes. First, it is necessary to determine whether the series are difference- or
trend- stationary. This is done by testing the null hypothesis
that each series included in the model contains a unit root.
If the variables are difference-stationary, it is appropriate to
estimate the VAR model by using the first differences of the
series. If the variables are trend stationary, the VAR model
may be estimated by taking the residuals from a deterministic trend. Second, it is desirable to account for the
possibility of breaks in the deterministic trend. The reason
is that standard (Dickey-Fuller) tests may fail to reject the
unit root null even if the time trend is deterministic, if there
is a largeone-time shift in the intercept or in the trend. 6 To
account for this possibility, I test for breaks in the deterministic trend in each series. If the hypothesis of a trend
break cannot be rejected, I test the unit root null against the
alternative of a broken deterministic trend. Third, if the
variables are difference stationary, it is necessary to establish whether the series in the model share common trends.
If they do not, estimation of a VAR model in first differences is appropriate.
Unit Roots
Totest for unit roots I apply the Augmented Dickey-Fuller
and Phillips-Perron tests for unit roots to the levels and first
differences ofthe series in the system (see Dickey and Fuller
1979, and Schwert 1987). The results ofthe tests, reported
in Table 2, suggest that the labor force and output in
Australia, as well as the oil price, are all differencestationary. The results for the price level are ambiguous.
Both tests indicate that the price level is nonstationary.
However, when inflation is tested the Phillips test rejects the
unit root null, whereas the Augmented Dickey-Fuller test
cannot do so. In what follows, I assume that the price level is
difference stationary.
The unit root test results should be interpreted with
caution. Research has shown that tests for unit roots have
low power (that is, they have low ability to reject the unit
root null when it is false) against plausible local alternatives. Also, the autoregressive models and unit root test
statistics computed for them have been found to be struc>
6See Perron (1989) for the precise conditions.
38
Table 2
Tests for Unit Roots
Log Levels (with
constant and trend)
Variable
First Differences
(with constant)
DickeyFuller
Test
Phillips
Labor Force
-1.39
-1.75
-2.85*
-10.32***
Price (CPI)
-2.89
-2.36
-2.06
-7.83***
Real GDP
-1.92
-1.26
-4.39*** -12.34***
Oil
-1.54
-1.85
- 3.55**
Note:
*
DickeyFuller
Test
Phillips
-6.65***
Reject null hypothesis (unit root) at 10% level.
** Reject null hypothesis at 5% level.
*** Reject null hypothesis at 1% level.
Seasonally adjusted data from 1960.Ql to 1989.Q4, except for Labor
Force, which is 1966.Q3-1989.Q4.
turally unstable under small perturbations, so that small
perturbations in the model lead to large changes in the
distribution theory for the statistics (Cavanagh, undated).
Trend Breaks
Standard tests for trend breaks assume that the date at
which the break occurs is known without using the data
series being tested. In practice, the data are used to find the
break date, so standard critical values for testing the null
hypothesis of no break in the trend cannot be used. To
address this problem I follow a strategy similar to that
adopted by Christiano (1992) and use a bootstrap methodology to calculate the most likely date for a break. As
inspection of the series suggests that trend breaks occurred
in the 1970s, I confine my search for breaksto that period.
The test results, reported in Table 3, indicate that the null
hypothesis of no trend break is rejected for GDP and CPI
(the null of no trend break is not rejected for the oil price
land the labor force, as these results are not reported here).
On this basis, I test the unit root null hypothesis against the
alternative of a deterministic trend with a break for GDP
and CPI, also relying on bootstrap simulations to find the
critical values. As also reported in Table 3, for these two
series, the unit root null cannot be rejected against the
alternative of a broken deterministic trend. 7
7To construct Table 3, 1000 simulated series were generated using the
following bootstrap methodology. The equation lly = JL + {311y was
Economic Review / 1992, Number 3
Table 3
Tests for Break in Trend in the
1970s and for Unit RootNull
against Alternative of Broken
Deterministic Trend
Variable
Most Likely
Break Date
lest for Break
(F Statistic)
lest for
Unit Root
(t Statistic)
Real GDP
1974.Q2
332**
(.03, 64.4)
-2.9
(.76, -3.5)
Price (CPI)
1974.Q2
523**
(.03,96.6)
-2.0
(.92, -3.2)
Note: See Notes to Table 2. Numbers in parentheses are significance
levels and expected values.
Cointegration
While the preceding tests suggest that. the model variables are nonstationary when considered individually, it is
possible that these variables share a common nonstationary
trend. In this case, a stationary linear combination of the
variables may be found, and the variables are said to be
cointegrated. When variables are cointegrated, estimating
a VAR model where the series are expressed in first differences, as proposed above, would be inappropriate. One
reason is that first-differencing would remove important
information about the behavior of the variables contained
in the common trend. 8
A number of tests for cointegration have been developed
in the literature. I use the method proposed by Johansen
(1988) and applied by Johansen and Juselius (1990). Table
4 reports the results of the Johansen's trace and maximum
eigenvalue tests. Based on the critical values reported by
Johansen and Juselius (Table A.2) both tests fail to reject
the null hypothesis that there is no cointegration. In what
follows, I assume that the series in the model are not
cointegrated and that estimation of the VAR model in first
differences is appropriate.
To sum up, conventional tests suggest that all the series
included in the model are difference stationary. There is
evidence of a break in the deterministic trend in GDP and
in the CPI, but the unit root null still cannot be rejected for
these two series when this break is taken into account.
Furthermore, a statistical test cannot reject the null hypothesis that there is no stationary linear combination of the
variables in the model.
In view of the preceding results, the data are transformed
as follows. The first differences of 0, n, y and p were taken
to obtain stationary representations. The differenced seriesAo., dnt were demeaned by subtracting the respective sample means. To account for breaks in the trend rates
Table 4
Johansen Test for Cointegration
Ho:
estimated. Disturbances were randomly drawnfrom the residuals of this
equation with replacement and used to generate 1000 simulated series.
The first sample observation was used as the starting value. To test for a
trend break, equation Yt = a o + a1dr + azt + a3sdumrwas then reestimated using each of the 1000 artificial series for b = bdat + 5 to b
= ldat, The maximum F statistic for b between 1970:Q1 and 1979:Q4
for each of the 1000 artificial series was selected. These 1000 maximum
F -statistics were then ranked in ascending order. The 1 percent critical
value was then given by theF statistic with rank 990(1 percent of the set
of maximum F statistics exceed this F-value), the 5 percent critical value
by the statistic with rank 950, and so on. The expected value is given by
the statistic with rank 500.
To test the unit root null against the alternative of a broken deterf34Yt- J
ministic trend, the equation dYt = 130 + f3J d + f3 zt + f33 d
+ f3 sAYt-J + f36dYt-Z was reestimated using each of the 1000
artificial series used to generate Table 3. For each series, the date b was
set to correspond to the peak of the F statistic computed by the equation
used to find the most likely trend break in Table 3. To find critical
values, the 1000 t-statistics testing the null were collected, and critical values were constructed in a manner analogous to Table 3.
r
Federal Reserve Bank of San Francisco
r+
r~
Trace
95 % critical value
Ho:r=
Maximum eigenvalue
95% critical value
0
44.5
48.4
1
22.1
31.3
2
9.8
17.8
3
2.2
8.1
0
22.4
27.3
1
12.3
21.3
2
7.5
14.6
3
2.2
8.1
Note: Critical values are from Table A.2 of Johansen and Juselius
(1990) which assumes that the nonstationary processes contain linear trends.
8Engle and Granger (1987) show that the appropriate model if the
variables are cointegrated is an error correction model, rather than a
VAR in first differences. Another way of looking at this problem is to
note that a VAR made up of first-differenced variables that are cointegrated involves "overdifferencing." As in the univariate case of "overdifferencing," the vector ARMA system of variables expressed in first
differences will contain noninvertib1e MA terms that cannot be represented by a VAR.
39
of growth and inflation, the differenced seriesAy, ~p
were demeaned by subtracting the appropriate subsample
means, where the subsamples were defined by the break
dates identified using the bootstrap simulation procedure
(1974.Q2 in both cases). The demeaned series were used to
estimate a VAR model. (A similar procedure of subtracting
subs ample means is used by Blanchard and Quah. However, they pick the break date without using a statistical
test.)
IV.
MODEL ESTIMATION RESULTS
The VAR model was estimated over 1966.Q3-1989.Q4
(no earlier data are available forthe Australian labor force).
Using the identifying restrictions discussed in Appendix
A, a structural moving average representation (as in equation (12)) was obtained. This moving average representation allows us to address the three questions posed in the
introduction to this paper.
Impulse Responses
The first question posed in the introduction, concerning
the qualitative responses to supply and demand shocks, can
be addressed by reference to Charts C.l to C.4 in Appendix
C, which illustrate the effects of one standard deviation shocks to the levels of the variables. (By construction,
shocks to the domestic variables have no effect on the oil
price, so the response of the oil price to Australian variables
is not illustrated.) The impulse responses are illustrated for
horizons up to 12 quarters to focus on the short-run
dynamics. In general, the impulse responses are close to the
long-run values at these horizons. Also, the one standard
error bands around the impulse responses in a number of
cases widen sharply at long forecast horizons, as might be
expected for nonstationary series." For these reasons, the
loss of information from truncating the impulse response'
horizons is not very great.
An important test of the plausibility of the model and
identifying procedure adopted in this paper is whether the
responses to supply and demand shocks conform to the predictions of theory. We would expect
9These standard error bands are obtained by using a Monte Carlo
simulation procedure with 300 replications to construct pseudo-impulse
responses and the first and second moments of these impulses. The
pseudo-impulse responses are generated by using draws from the .
Normal and Wishart distributions to modify the variance covariance
matrix and the moving average coefficients of the structural innovations. See Doan (1990). In the charts, a two-standard-error band tends to
disguise the short-run dynamics in the impulse responses, so a onestandard-error band is shown instead.
40
• positive shocks to the oil price to reduce output and
increase the price level in the long-run;
• positive shocks to labor supply and technology to increase output and reduce the price level.in the long-run;
• positive shocks to demand to increase labor and output
temporarily (as a result of the identifying restrictions)
and the price level permanently;
The charts indicate that the responses to shocks in- the
model broadlyconform to these expectations, although the
standard error bands are in some cases quite wide, particularly at horizons exceeding four quarters.
The charts also reveal some interesting dynamics: for
example, GOP rises sharply in response to technology
shock, overshoots its long-run level slightly at about 10
quarters before settling to close to its long-run level of
around % percent above the pre-shock level. This long-run
level is achieved at around 20 quarters and is not shown in
the chart. (The CPI declines with similar, but smoother,
dynamics.) In contrast, Blanchard and Quah (1989), Shapiro and Watson (1988) and Moreno (1992a) indicate a
more pronounced overshooting in the output response to
technology shocks in the U.S. and Japan respectively.
However, these comparisons should be interpreted with
caution because the standard errors in all these models
appear to be quite large.
In addition, some of the impulse response results appear
to be broadly consistent with the characteristics of the
Australian economy discussed in Section I:
Australia does not appear to be vulnerable to oil price
shocks in the very short run, which is consistent with its
status as oil producer and exporter. The impulse responses
indicate that Australian GOP rises temporarily in response
to oil price shocks, followed by a long-run decline. This
suggests that an oil price increase initially stimulates the
economy through Australia's oil sector, but the stimulus is
reversed as the effects of a higher oil price spread to the rest
of the economy.
The effects ofdemand shocks on output die out quickly,
which is consistent with an active countercyclical policy
The charts indicate that the effects of a positive shock
to GOP are fully reversed within one year, which appears to
be relatively fast. In contrast, Blanchard and Quah (1989)
find that the effects of a demand shock on U.S. output take
about six years to be fully reversed. Moreno (1992a) estimates that in Japan, the effects of a demand shock on output
are fully reversed after two years. The rapid reversal of
demand shocks suggests that the countercyclical effects
of fiscal policy and (to the extent applicable) of monetary
policy were quite important in Australia (recall discussion
in Section I). However, it is important to stress that the
Economic Review / 1992, Number 3
rapid reversal in the effects of demand shocks on output is
only an indicator of the possible effects of countercyclical
policy, and that other explanations for this rapid reversal
may be offered. In the model estimated in this paper,
demand shocks reflect the combined effects of private and
public demand, and there is no wayof separating these two
effects.
Australia appears to have a relatively flat short-run
Phillips curve, which is consistent with apparent rigidities
in the labor market. To assess the Phillips curve tradeoff,
I computed the ratio of cumulative GDP growth per unit
of cumulative inflation in response to a one-standarddeviation shock to demand.
A shock to demand yields its greatest output growth
stimulus per unit of inflation in the first quarter, about 208
percent. The cumulative output gain subsequently tapers
off smoothly to 147.50 percent in the second quarter, 100
percent in the third quarter, and to 48 percent in the fourth
quarter. The cumulative output gain is negative and small
at eight and twenty quarters, and is zero at forty quarters.
To provide a benchmark, these results may be compared to
estimates obtained from a similar model for Japan (Moreno
1992a) where labor markets appear to be more flexible than
in Australia: In Japan, the corresponding cumulative increases in output growth per unit of inflation are 93 percent
at one quarter, 43 percent at four quarters, 3 percent at
eight quarters, and close to zero at twenty quarters. Thus,
Australia appears to have a relatively favorable outputinflation tradeoff in the very short run.
Variance Decompositions and the
Importance of Supply Shocks
The impulse response functions illustrate the qualitative
responses of the variables in the system to shocks to supply
and demand. To indicate the relative importance of these
shocks requires a variance decomposition. In order do this,
consider the n-stepahead forecast of a variable based on
information at time t. The variance of the error associated
with such a forecast can be attributed to unforecastable
shocks (or innovations) to each of the variables comprising
the system that occur between t + 1 to t + n.
Table 5 reports the variance decompositions of the
structural forecast errors of the variables in levels, at
horizons up to forty quarters (10 years).
By construction, the variance in the forecast error of the
oil price is attributable entirely to shocks to the oil price
and is not reported. It is also apparent that shocks to the
labor supply are the main determinants of the variance of
the forecast error of the labor force at all horizons. This
result would probably differ if a variable that is more
sensitive to changes in demand in the short-run were used.
Federal Reserve Bank of San Francisco
We can use the variance decompositions for GDP to
assess the empirical importance of demand and supply
shocks, which is the second question posed in the introduction. Demand shocks are most important in the very short
run, accounting for 64 percent of the forecast error onequarter ahead. However, supply shocks soon assume the
dominant role: They account for 74 percent of the forecast
error variance at eight quarters and 95 percent at forty
quarters. Supply shocks arein tum dominated by shocks to
technology.
Three points are worth highlighting. First, the variance
decomposition estimates are relatively imprecise, so the
results of the point estimates should be viewed with some
caution. For example, at the one-quarter horizon for demand shocks, the 95 percent confidence band ranges from
a low of 27 percent to a high of 89 percent.!? However, the
estimates in Table 5 do not appear to be less precise than
estimates reported by Blanchard and Quah (1989) or
Shapiro and Watson (1988), or the estimates in Sims's
(1980) study (see Runkle (1987».
Second, in their study of the U.S. economy, Shapiro and
Watson (1988) found that shocks to labor supply were large
at short horizons (in the neighborhood of 40 percent or
higher). This is surprising because theory and empirical
studies of the U.S. economy suggest an important role for
permanent shocks to labor supply at long forecast horizons, but not at short ones. In the case of Australia, the
contribution of labor supply shocks to the variance of
the forecast error is small. It ranges from 4.5 percent at one
quarter to 13 percent at eight quarters and down to 5 percent at forty quarters. One possible explanation for the relatively small contribution of the labor supply is that the
lO'fhe empirical 95 percent confidence band was constructed by using
a bootstrap simulation procedure with 300 replications to generate
pseudo-variance decompositions, as was done for the impulse responses. However, instead of constructing a symmetric one-standarderror band based on the normal approximation, I define the 95 percent
band as follows. The lower bound is that value such that 2.5 percent of
the pseudo-variance decomposition values are lower. The upper bound is
that value such that 2.5 percent of such values are higher. One advantage
of this approach is that it excludes values below 0 or above 100 and thus
reflects the constraint that the variance decompositions must sum to 100.
The empirical distribution found in this manner is skewed, as the point
estimate of the variance decomposition in a number of cases is close to
the upper or lower boundary of the 95 percent band. A similar bootstrap
procedure is used by Blanchard and Quah (1989) to report asymmetric
empirical one-standard-error bands. Shapiro and Watson (1988) report
one-standard-error bands that appear to be based on the normal approximation. The normal approximation does not take into account the
constraints on the values of the variance decompositions, so the lower
bound of the standard error band may be negative, and the upper bound
may exceed 100. See Runkle (1987) for a discussion of some of these
issues.
41
Table 5
Variance Decompositions
Proportion of Variance Explained by Shock to:
Aggregate Supply
Quarters Ahead
Aggregate Demand
Oil Price
Labor Supply
Technology
Total
0.7
(0.0,12.8)
87.2
(48.0,96.3)
11.7
(0.2,37.6)
99.6
0.4
(0.0,20.7)
4
1.8
(0.7,14.7)
83.4
(47.9,87.3)
13.7
(6.2,30.9)
98.9
1.1
(0.4,15.9)
8
1.2
(0.9,14.2)
88.8
(58.9,90.4)
7.2
(3.6,21.2)
97.2
. 2.8
(1.6,15.2)
12
0.8
(0.9,12.9)
92.7
(58.2,92.9)
4.7
(2.6,23.1)
98.2
1.8
(1.1,16.7)
20
0.6
(0.7,12.5)
95.4
(44.8,95.7)
2.9
(1.7,26.2)
98.9
1.1
(0.7,22.0)
40
0.4
(0.5,16.1)
97.5
(6.1,97.7)
1.5
(0.9,49.6)
99.4
0.5
(0.3,43.5)
2.2
(0.0,19.8)
4.5
(0.1,16.1)
29.6
(3.2,61.7)
36.3.
63.6
(26.7,89.4)
4
1.9
(0.7,20.1)
10.0
(1.3,29.7)
39.6
(16.9,60.1)
51.5
48.5
(24.3,66.3)
8
2.2
(1.9,26.6)
12.9
(2.6,37.9)
58.4
(26.8,69.0)
73.5
26.5
(12.7,43.7)
12
3.7
(2.2,32.4)
9.7
(2.1,36.0)
69.7
(26.9,76.1)
83.1
16.9
(7.5,42.7)
20
5.7
(2.0,42.4)
6.8
(1.6,32.0)
77.1
(23.4,81.1)
89.6
10.4
(4.0,47.9)
40
6.6
(1.2,49.0)
5.0
(0.7,33.0)
83.0
(18.8,88.5)
94.6
5.4
(1.7,47.5)
0.6
(0.0,14.3)
11.6
(1.0,26.8)
62.5
(45.9,73.3)
74.7
25.4
(16.4,33.5)
4
1.5
(0.1,19.8)
15.2
(1.2,36.7)
61.4
(37.4,77.2)
78.1
21.8
(7.3,39.9)
8
5.7
(0.2,37.4)
6.3
(1.0,29.1)
60.4
(30.8,78.7)
72.4
27.6
(7.3,51.1)
12
9.2
(0.3,46.6)
3.3
(0.6,23.9)
58.0
(24.5,78.3)
70.5
29.4
(5.9,52.3)
20
12.2
(0.2,54.6)
1.8
(0.4,27.5)
55.4
(19.8,76.4)
69.4
30.6
(4.9,57.1)
40
13.6
(0.1,61.1)
0.8
(0.2,28.1)
54.4
(17.0,77.5)
68.7
31.2
(4.5,60.2)
Labor Force
1
GDP
1
CPI
1
Note: Empirical 95 percent confidencebands are in parentheses.
42
Economic Review / 1992, Number 3
proxy used for this variable, the labor force, varies relatively little. If total employment-which varies somewhat
more than the labor force-is used instead of the labor
force in the model, labor supply shocks are larger but still
small. They account for 2 percent of the variance of the
forecast error at one quarter, 28 percent at eight quarters
and 29 percent at forty quarters. 11
Third, oil price shocks playa limited role, accounting for
about 2 percent of the variance of the forecast error up to
eight quarters, rising to under 7 percent at forty quarters.
This is somewhat below the short-run results for the U.S.
obtained by Shapiro and Watson (1988) but similar to their
long-run results.
Supply shocks are the most important factor influencing
the short-run behavior of the price level in Australia.
Supply shocks account for 75 percent of the variance of the
one-quarter-ahead forecast error of Australia's CPI, rising
to 78 percent at four quarters, and then falling gradually to
69 percent at forty quarters. Technology shocks are the
main source of supply shocks at all horizons. Shocks to
labor supply have a stronger influence at short horizons
(fewer than twenty quarters), accounting for up to 15 percent. Oil price shocks have a larger influence at longer
horizons (twenty to forty quarters), accounting for about 12
to 14 percent. The oil price has a stronger influence on the
price level than on GDP.
To sum up, both demand and supply shocks have an important effect on output throughout the Australian business
cycle. Demand shocks are dominant in the very short-run,
but their importance tapers off quickly as the forecast horizon is extended. In contrast, supply shocks have a.dominant
influence on the price level at all forecast horizons.
Evidence from Other Studies
The preceding results may be compared to Shapiro and
Watson's (1988) results for the U.S. using a similar model.
The contribution of supply shocks to output in the U.S. is
72 percent at a quarter's horizon and. 80 percent at eight
quarters, which is larger than the 36 percent and 74 percent
found for Australia in Table 5. However, supply shocks
explain 12 percent or less of the variance of the U.S. price
level at horizons up to eight quarters, much lower than the
78 percent found for Australia over similar horizons.P
llShapiro and Watson (1988) use total hours worked by all workers,
which varies even more at business cycle frequencies. Judd and Trehan
(1989) point out that total hours appears to contain a very strong demand
component, so using it as a proxy for labor supply can result in
implausible dynamic responses to shocks.
12Previous studies on the relative importance of supply shocks based on
U.S. data reveal that the estimates are very sensitive to assumptions
Federal Reserve Bank of San Francisco
The results of a study of Scandinavian business cycles by
Gerlach and Klock (1990), which covers Denmark, Norway and Sweden, are closer to those reported here. Gerlach
and Klock estimate a bivariate model of output and price
for each economy using annual data for the period 19501988, and impose the identifying restrictions proposed by
Blanchard and Quah (1989). In general, they find that the
contribution of supply shocks to output for all three countries at a year's horizon is large, ranging from 50 to 75
percent. The contribution to inflation in two of the three
countries is also large, ranging from 66 percent to 83
percent. 13
Patterns. of Cyclical Behavior
Further insights on cyclical behavior can be gained by
examining the pattern of shocks to output during cyclical
downturns, which is the third question posed in the introduction. For this purpose, Chart 1 reports the eight-step
ahead forecast error in output growth and the cumulative
contributions of demand and supply shocks to this error in
Australia. Australia's VAR sample begins in 1966.Q3 (the
starting date for the labor force series) and data points are
used up in setting an eight-quarter forecast horizon. As a
result, Chart 1 begins in 1970 and only five of the eight
recessions reported in Table 1 are included.
The description of recessions offered in Chart 1 differs
from that offered in Table 1. In Table 1, the severity of recessions is measured in terms of deviations from a baseline
rate of growth. In Chart 1, the severity of recessions is
assessed by examining how unforecastable innovations
make output growth deviate from what was anticipated
given the information available eight quarters before.
It is apparent that the first recession indicated in the
chart (which actually begins in 1968.Q4, according to
Table I) is not considered a recession by the VAR model:
about trend behavior, such as whether the series are trend or difference
stationary, or whether there are breaks in the mean rate of drift of output.
For this reason, the present study has attempted to ensure that the
assumptions about trend behavior are reasonable, by testing for unit
roots, trend breaks and cointegration. Also, the comparison with the
U.S. is based on a study which makes very similar assumptions to those
adopted in this paper.
l3In Denmark at a year's horizon, supply shocks account for around 50
percent of the variance of output and around two-thirds of the variance of
inflation. At a five-year horizon, the proportion rises to 75 percent for
output and to 35 percent for inflation. In Norway supply shocks account
for around 98 percent of the variance of output at all horizons, but for
just over 10 percent of the variance of inflation. Finally, in Sweden at a
year's horizon, supply shocks account for 60 percent of the variance of
output and 83 percent of the variance of inflation. At a five-year horizon
the proportion rises to 95 percent for output and falls to 80 percent for
inflation.
43
The forecast errors tend to be positive rather than negative.I" For the remaining four recessions, the forecast errors
are consistently negative, as expected. The discussion that
follows focuses on these last four recessions.
The following features of Australian recessions stand
out. First, negative supply and demand shocks have been a
feature of the four recessions discussed here. Second, the
recessions of 1973.Q4-1975.Q4 and of 1981.Q3-1983.Q2
were more severe than the two intervening recessions
(l976.Q4-1977 .Q4 and 1979.QI-1980.Ql). The two more
severe recessions were associated with larger adverse
supply shocks.
Chart 2 illustrates the eight-step ahead forecast error for
inflation in Australia as well as the cumulative contributions of supply and demand shocks to the forecast error. It
is apparent that recessionary episodes in Australia have
been associated with adverse supply shocks that have
contributed to temporary increases in inflation. With the
exception of the 1982 recession, these inflationary pressures were reinforced by shocks to demand.
l1.
Components of Output Growth Forecast Error
(8 steps)
Total Error
%
3.6
2.4
1.2
0.0
-1.2
-2.4
7071 727374 75 76 77 78 79 8081 82 83 84 85 86 87 88 89
Supply
%
SUMMARY AND CONCLUSIONS
This paper has estimated a small structural vector autoregression model to assess the determinants of business
cycle behavior in Australia. The model sheds light on the
dynamic responses of Australian macroeconomic variables
to demand and supply shocks. In the model, shocks to
technology raise output and lower the price level, while
shocks to demand temporarily raise output and permanently raise the price level. These responses conform to
intuition and theoretical expectations.
The empirical results also shed light on the relative
importance of demand and supply shocks in influencing
output and inflation behavior in Australia. Demand shocks
are dominant in determining fluctuations in Australian
output at a one quarter horizon, but supply shocks assume
the larger role at longer horizons. Supply shocks also
account for most of the fluctuations in the Australian price
level. In contrast, research by Shapiro and Watson (1988),
using a similar model, finds that supply shocks playa larger
short-run role in influencing U.S. output and a very small
role in influencing the U.S. price level. The empirical
results also indicate that supply shocks in Australia are
dominated by shocks to technology, with shocks to the
labor supply or to the oil price playing a smaller role.
14For this episode, the VARresults appears to conform more closely to
the viewsof informed observersthan doesTable 1. In privatecorrespondence, Glenn Stevens of the Reserve Bank of Australia indicates that
1968 is generally not regarded as a recession year in Australia.
44
CHART 1
3.6
2.4
1.2
0.0
-1.2
-2.4
70 71 7273 74 75 76 77 78 79 80 81 8283 84 85 86 87 88 89
Demand
%
3.6
2.4
1.2
0.0
-1.2
-2.4
70 7172 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
Economic Review / 1992, Number 3
CHART 2
Components of Inflation Forecast Error
(8 steps)
Total Error
3
2
o
·1
·2
-3
70 71 72 7374 75 76 7778 79 80 81 82 83 84 85 86 87 88 89
The present paper has used a model that has certain
appealing theoretical features and has the further advantage of being directly comparable to Shapiro and Watson's
(1988) model of the US. However, future research can
extend the model in several ways. First, demand shocks
identified in this paper reflect the combined impact of
private and government actions, and can therefore only
provide indirect insights on the possible role of government
policy in influencing business cycle fluctuations. A larger
model that explicitly identifies monetary and fiscal policy
shocks could be used to analyze the role of government
policy in Australia more directly. Second, other variables,
such as wages and hours worked,may be introduced to
capture the effects of labor markets more fully. Third, the
model could be extended to assess the impact of external
shocks in addition to the oil price. Aside from clarifying the
relative importance of external and domestic shocks, such
an extension could potentially shed light on a number of interesting questions, such as the insulation properties of
alternative exchange rate regimes."
Supply
3
2
o
·1
·2
·3
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 878889
Demand
3
2
o
-1
-2
-3
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 8788 89
Federal Reserve Bank of San Francisco
15Moreno (1992b) assesses insulation under alternative exchange rate
regimes in Korea and Taiwan.
45
ApPENDIX A
IDENTIFYING VARS
Moving Average Representation'
To motivate the general approach to setting up and
identifying VAR models, consider a k x 1vector of endogenous variables z, with a structural moving average representation given by:
(A.I)
where
B(L) = Bo + BIL -I:- B 2U + ... is a k
nomials in the lag operator L
Et
is a k
x k matrix of poly-
x 1 vector of white noise disturbance terms
e, ~ (0, IE) and
IE is diagonal (that is, the structural
shocks are mutually orthogonal)
In order to estimate the response of the elements of Zt to
innovations in the elements of the mutually orthogonal
structural disturbances contained in €t' a procedure is
needed to identify these structural disturbances. The conventional approach is to estimate the VAR representation
of Zt:
where
H(O) = I (that is, no contemporaneous variables enter on
the right hand side of the VAR equations)
u, ~ (0, I u ) ' where I u is not a diagonal matrix (that is, the
residuals are not mutually orthogonal)
If we invert the VAR representation, we obtain,
Zt
= D(L)ut ; D(L) = H(L)-l.
By decomposing the elements of (A.3) using the matrix
B(O) (the matrix that defines the contemporaneous struc-
tural relations) between the variables, we can recover
(A.1):
(A.4)
D(L)u t = D(L)B(O)B(O)<u, = B(L)Et
so we can write
(A.5)
D(L)
= B(L)B(O)-l
and
(A. 6)
"This section draws heavily on the lucid discussion in Hutchison and
Walsh (1992).
46
(A.7)
Equation (A.7) suggests that two conditions must be satisfied in order to identify B(O). First, the number of parameters to be estimated must not exceed the number of unique
elements in the sample covariance matrix I u • Specifically,
there are k2 unknown elements in B(O), and the matrix I u
contains k(k + 1)/2 unique elements. A necessary condition for identification is that k2 - k(k + 1)/2 = k(k - 1)/2
-additional restrictions be imposed. We can think of this as
an order condition.
Second, the system of nonlinear equations resulting
from (A. 7) must have at least one solution. This may fail if
identifying restrictions are imposed in a manner that
prevents equating elements on both sides of the equation.
Bernanke (1986) suggests that this can be thought of as a
rank condition.
Identification
(A. 2)
(A. 3)
Equation (A.6) indicates that an estimate of B(O) is needed
in order to recover the mutually orthogonal structural
disturbances € t from the estimated VAR residuals u..
To motivate the conditions such an estimate must fulfill,
note that (A.6) also implies that the diagonal covariance
matrix of structural disturbances IE is related to the
covariance matrix of the VAR residuals, I u ' by
A number of approaches to identification of a VAR
system have been adopted in the literature. The earliest
approach, pioneered by Sims (1980), assumes that B(O) is
lower triangular. This imposes restrictions on the contemporaneous correlations of shocks to variables that are
equivalent to assuming that the economy described by the
vector Zt has a recursive structure. Under such a structure,
the first variable is unaffected by shocks to the remaining
variables, the second variable is affected by shocks to
the first two variables, but is unaffected by shocks to the
remaining variables, and so on. (The last variable is
affected by shocks to all variables.
The main disadvantage of Sims's approach is that it is
not easily reconciled with economic theory. Twoalternative
approaches have been adopted to address this problem.
First, a number of authors (Bernanke 1986, Sims 1986,
Walsh 1987, Blanchard 1989) have imposed zero restrictions on B(O) to achieve identification. Such contemporaneous restrictions are explicitly motivated by theory and
do not necessarily assume a recursive structure.
Second, other researchers (Blanchard and Quah 1989,
Shapiro and Watson 1988, Judd and Trehan 1989, 1990,
Hutchison, Walsh 1992 and Moreno 1992a) have achieved
identification by imposing zero restrictions on the long-run
multipliers B(1), in a manner that permits the estimation of
Economic Review / 1992, Number 3
B(O). Such restrictions are motivated by the idea that
certain disturbances have no long-run impact on certain
elements of z.
Setting L = 1, (A.4) implies that
(AA')
B(O)
= D(1) -IB(1) = H(1)B(1)
where D(I) is the matrix of long-run multipliers estimated
from the VAR and H(1) is the matrix of sums of coefficients obtained from the estimated VAR. Restrictions on
B(1), along with the restrictions implied by (A.6), can be
used to obtain an estimate of B(O). For higher order VARs,
higher order polynomials are involved in finding a solution, so numerical techniques are needed to estimate B(O).
One such technique is applied by Hutchison and Walsh
(1992).
Estimation
A simple method for recovering the structural disturbances is applied by Shapiro and Watson (1988) in a recent
study of the U. S. economy. Shapiro and Watson estimate a
system that yields the structural disturbances directly from
the VAR representation, that is,
(A.8)
CCL)zt
= Et'
where CCL) = B(L) - I , and B(L) is found in (A. 1) or (12) in
the text.
The structural disturbances are recovered directly from
(A.8) as follows. First, C(O) 4=/ so contemporaneous values of Zt are now allowed to enter on the right hand side of
some of the equations. To obtain consistent estimates,
these equations are estimated using two-stage least
squares, with the exogenous and the predetermined
(lagged) variables as instruments.
Second, the dynamic restrictions on the long-run multipliers (zeros on B(1» are reflected in restrictions on the
sums of coefficients of the appropriate variables (that is, as
zeros on the corresponding elements of C(1».
Third, Shapiro and Watson ensure that the estimated
residuals are mutually orthogonal by estimating each equation in (A.8) sequentially and including the residuals from
previous equations in the estimate of the current equation.
Thus, the residual in the first equation is used in estimating
the second equation, the residuals of the first two equations
are used in estimating the third equation, and so on.
Another way to ensure that the appropriate residuals are
mutually orthogonal is to estimate each equation in (A.8)
without including residuals from the other equations and
then use the Choleski decomposition of the covariance
matrix to obtain the moving average representation. Although the Choleski decomposition is used, the system is
not in this case recursive, because the contemporaneous
Federal Reserve Bank of San Francisco
values of Zt have been included in estimation. (Thus, the
critique of atheoretical recursive methods of VAR identification does not apply here.)
This paper uses Shapiro and Watson's (1988) estimation
technique to recover structural shocks from a VAR system
but relies on the Choleski decomposition to recover orthogonal shocks.
To achieve identification, I impose the following restrictions: First, the oil price depends only on its own lagged
values and is completely unaffected by other variables in
the model. Second, the labor force can be affected by other
variables in the short run; however, the long-run impact of
these other variables is zero (in particular, there are no
wealth effects on the labor supply). Third, the level ofGDP
is permanently affected by shocks to the oil price, the labor
supply, and technology (supply shocks). Shocks to demand
have temporary effects on GDP. No restrictions (except the
lag length) are imposed on the effects of the variables of
the system on the price level. Given such restrictions, the
long-run multipliers in equation (12) in the text satisfy>
(A.9)
b(l)1I
0
0
0
0
b(l)22
0
0
E(l)
b(I)31 b(l)32 b(l)33
0
b(1)41 b(l)42 b(I)43 b(l)44
The zeros in the first and second rows reflect the restriction that oil prices and the labor supply are unaffected by
other variables in the long run. The zero in the third row
reflects the restriction that the demand shock, E4t in equation (12) of the text, has only temporary effects on output.
In a 4-equation system, the variance covariance matrix
contains 10 unique elements, but there are 16 unknown
parameters. Six additional restrictions are needed to identify the system. In equation (A.9), there are seven restrictions, implying that the system is overidentified.
To impose the identifying restrictions discussed previously, the following equations are estimated:
I
(A. 10)
ao, = L
tJ.hll,i0/-i +
ul t
i=1
2For a matrix of polynomials in the lag operator B(L) = B o + BjL +
B2U + ..., the matrix of long-run multipliers is found by setting L = 1.
This yields B(l) = Bo + B, + B 2 + ... or the sum of the moving
average coefficients.
47
(A.ll) an, =
1-1
I
1=0
1=1
L li.2h21, 10H + L h22, lli.nH
1-1
+
L
H
2Y
h 23, lli. t_1 +
I
L h3
1,
I
L li.h 32, InH
.so.,
1=0
+
1=1
I
I-I
1=1
1=0
L h33, lli.Yt-i + L h34, lli.2Pt-i + U3t
I
(A. 13) li.Pt
=
L h41, lli.°
I
H
1=0
+
L li.h 42, Int-I
1=1
I
+
+ U2t
1=0
1=0
(A. 12) li.Yt =
L h24, lli.2PH
I
L h43, lli.Yt_ + L h44, lli.P
1
1=1
H
+ U4t
1=1
where it is assumed that 0, n, Y and P are difference
stationary, and a lag length of five is used in all equations.
Using this lag length yields Q statistics that do not reject
white noise at the 5 percent marginal significance level in
all equations.
Equations (A.lO) and (A.13) are estimated by OLS.
Equations (A.ll) and (A.12) are estimated by two-stage
least squares, with the contempor ineous value of the oil
price and the lagged values of all variables as instruments.
In equations (A. 11) and (A. 12), the restriction that certain
variables have zero effects in the long run is imposed by
expressing these variables in second differences and setting
the maximum number of lags to four for these equations.
The system (A.lO) to (A.l3) incorporates several of the
restrictions implied by (A.9). However, the system does not
exactly correspond to (A.8) because the variance covariance matrix ofthe system (A. 10) to (A.l3) is not diagonal.
That is, the unadjusted residuals u l t ' UZt> u3f' u4 f' are
correlated and are not (necess rily) the same as the uncorrelated structural disturbances in (A.8) or in the moving
average representation of (12) in the text. To identify the
three supply disturbances Elf' EZf' E 3t, and the demand
disturbance E 4t in equation (12) in the text, I select a lowertriangular matrix G such that G-IIuG' -1 = I, where I u
is the variance-covariance matrix of the system (A.lO) to
(A. 13). With such a matrix G, it is possible to define
E t = uG':! and EEtE; = I.
In typical applications, the use of a lower-triangular
matrix G, also known as the Choleski factorization, yields
a recursive system of mutually orthogonal disturbances of
the type proposed by Sims (1980). In the early VAR
literature, this was the sole basis for identification. Since
48
many theoretical models do not imply a recursive economic structure, it is difficult to rely on this approach alone
to distinguish between demand and supply shocks. 3
In the present case, however,the Choleski decomposition
is only one element of the identification procedure, designed to extract mutually orthogonal disturbances. Identification also depends on the specification of the VAR
equations, which incorporate the restrictions proposed by
Blanchard and Quah and satisfy (A. 9) (the Choleski factorization alone cannot guarantee that equation (A.9) will be
satisfied). It may also be noted that since contemporaneous
values of the explanatory variables are included in the
VAR model, the resulting structure of the economy is not
recursive.
ApPENDIXB
DATA DESCRIPTION AND SOURCES
Australia, quarterly
Real Gross Domestic Product. Millions of 1984-85 Australian dollars (A$), seasonally adjusted.
Source: OECD Main Economic Indicators.
ConsumerPrice Index. 1985 = 100.
Source: International Financial Statistics, International
Monetary Fund.
Labor Force. Total labor force, thousands of persons.
Source: Reserve Bank of Australia, Australia Reserve
Bulletin.
International
Oil. Crude petroleum componentofD.S. PPI, 1982 = 100,
quarterly average of monthly data.
Source: Citibase.
3However,a recursive structure may suffice if detailed knowMdge of the
economy is not required. For example, Moreno (1992b) uses a Choleski
factorization to identify mutually orthogonal domestic and external
shocks, and to measure the vulnerability of an economy to these external shocks under alternative exchange rate regimes.
Economic Review / 1992, Number 3
ApPEND/XC
IMPULSE RESPONSES
CHART C.1
RESPONSE TO OIL PRICE SHOCK
Labor Force
Oil
logs
logs
0.20
0.0020
0.18
0.0015
0.0010
0.16
0.0005
0.14
0.0000
0.12
I--~:--_-----------
-0.0005
0.10
-0.0010
-0.0015
2
3
4
5
6
7
8
9
10
11
'--..L..-......l---I-----'-_'--...L-......l---I-----'-_'--...L--J
12
2
3
4
5
6
GOP
7
8
9
10
11
12
8
9
10
11
12
CPI
logs
logs
0.006
0.0175
0.004
0.0150
0.0125
0.002
0.0100
0.000
0.0075
-0.002
0.0050
-0.004
0.0025
-0.006
-0.008
0.0000
2
3
4
5
6
7
8
9
10
11
12
-0.0025
2
3
4
5
6
7
NOTE: Shock Is one standard deviation.
Federal Reserve Bank of San Francisco
49
CHART C.2
CHART C.3
RESPONSE TO LABOR SUPPLY SHOCK
RESPONSE TO TECHNOLOGY SHOCK
Labor Force
Labor Force
logs
logs
0.0072
0.002
0.0064
0.001
0.0056
0.000
0.0048
-0.001
0.0040
-0.002
0.0032
0.0024
2
3
4
5
7
6
8
9
10 11
12
-0.003
2
3
4
5
GOP
10 11
12
7
8
9
1011
12
7
8
9
10
12
logs
0.0150
0.007
0.006
0.0125
0.005
0.004
0.0100
0.003
0.0075
0.002
0.001
0.0050
0.000
0.0025
-0.001
-0.002
2
3
4
5
7
6
8
9
10
11
12
0.0000
2
3
4
5
6
CPI
CPI
logs
logs
0.008
-0.0050
0.006
-0.0075
0.004
-0.0100
0.002
-0.0125
0.000
-0.0150
-0.002
-0.0175
-0.004
-0.0200
-0.006
-0.0225
2
3
4
5
6
7
NOTE: Shock is one standard deviation.
50
9
7
GOP
logs
-0.008
8
6
8
9
10
11
12
-0.0250
2
3
4
5
6
11
NOTE: Shock is one standard deviation.
Economic Review I 1992, Number 3
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Blanchard, Olivier Jean. 1989. "A Traditional.Interpretation of Macroeconomic Fluctuations." American Economic Review (September)
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_ _ _ _ , and Danny Quah. 1989. "The Dynamic Effects of
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Federal Reserve Bank of San Francisco.
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Schwert, G. William. 1987. "Effects of Model Specification on Tests
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Basin Monetary and Economic Studies, Economic Research Department, Federal Reserve Bank of San Francisco.
52
Economic Review / 1992, Number 3
Bank Holding Company Stock Risk
and the Composition of Bank Asset Portfolios
Jonathan A. Neuberger
Economist, Federal Reserve Bank of San Francisco. The
author acknowledges the helpful comments of Jim Booth,
Frederick Furlong, Sun Bae Kim, and Adrian Throop.
Karen Trenholme provided excellent, and patient, research assistance.
In this paper, I conduct an empirical analysis of the
behavior of bank holding company stock returns with the
goal ofidentifying the effect ofportfolio composition on the
risks embodied in those returns. Using a modified arbitrage pricing theory model, I testfor significant balance
sheet effects on both the market and nonmarket components of bank stock systematic risk. I find that several
categories ofbank assets are significant in explaining bank
stock risk profiles. Among other things, I discuss the
importance of these findings in light of the risk-based
capital standards and suggest that noncredit types ofrisk
may need to be incorporated into bank capital standards if
capital levels are to reflect risk accurately.
Federal Reserve Bank of San Francisco
A common theme in recent discussions of U.S. banks
and banking markets is the evaluation of risk. While it is
widely accepted that banks are in the business of taking
and managing risks, the question arises why some banks
are riskier than others, even in the face of similar economic
conditions. This theme has been echoed in the press, in
academic studies, and in speeches given by government
officials and bank regulators. The importance of understanding the determinants of bank risk has been heightened
by the recent poor performance of U.S. banks as well as by
the ongoing incidence of bank failures. Moreover, the issue
becomes a public policy concern each time another banking organization fails, thus requiring the FDIC to step in
and spend funds out of its already diminished reserves.
In recent months, much of the discussion relating to
bank risk has involved the risk-based capital standards
being phased in among the Group of 10 countries in
Europe, North America, and Asia. These standards require
banks holding riskier assets to maintain a larger capital
cushion against losses, thereby reducing the likelihood that
losses will deplete bank capital and lead to failure. Unlike
traditional capital regulations that establish a fixed amount
of capital (relative to assets) for all institutions, the riskbased standards set a variable capital cushion based on the
perceived credit risk of the bank's underlying assets.
In setting the appropriate amount of capital an institution must hold, the risk-based capital standards assign
bank assets to a small number of categories, each with its
own apparent degree of riskiness and, thus, its own risk
weight. The categories (and the weights) were determined
based on assessments of the credit risk associated with
different classes of bank assets. Some critics of the riskbased capital requirements argue that the categories are too
crude to be meaningful, that is, they ignore important
information relevant to determining the risk of bank assets
in order to streamline the standards and make them easier
to implement. Others criticize the standards for failing to
address non-credit types of risk, such as interest rate risk
and asset concentration risk.
In the current study, I attempt to identify some of the
determinants of bank risk by evaluating the influence of
53
bank portfolio composition on the behavior of bank holding company stock returns. In an earlier study (Neuberger
1991), I estimated the sensitivity of bank stocks to overall
stock market conditions and to changes in interest rates. I
showed that these sensitivities have varied considerably
over time and that significant differences exist among
banks in the sensitivities their stocks display to these two
factors. Starting from a similar perspective in the current
work, I relate the observed sensitivity of bank stock returns
to the composition of bank asset portfolios. If bank risk is
explained at least partially by the decisions banks make in
allocating funds among different assets, then we should
observe systematic variations in bank stock sensitivity
based on the profile of their asset portfolios.
A related goal of the current work is to evaluate bank
stock risk in light of the risk-based capital standards. More
specifically, I attempt to determine if some of the classes of
assets consideredeess risky under the risk-based standards
actually do exert less of an impact on the risk of bank
stocks. For example, are single-family mortgage loans a
"safer" investment than loans to private businesses? The
risk-based capital standards assert that they are by requiring banks to hold half as much capital in support of a
residential mortgage than a commercial and industrial
loan. The analysis below sheds some light on whether such
distinctions are empirically important by estimating the
effect these different classes of assets have on bank stock
risk.
I.
BANK STOCK RISK AND BANK PORTFOLIOS
In order to address the role of portfolio composition on
bank stock risk, I need an appropriate model of bank stock
returns. One basic model of asset returns is the Capital
Asset Pricing Model (CAPM), developed by Sharpe (1964)
and Lintner (1965). In this model, the return on a company's equity shares over and above the return on a riskless
asset is explained solely as a function of the return on the
"market portfolio," a perfectly diversified portfolio of all
assets. In practical applications of the CAPM, a broadbased stock market measure, such as the return index on
the S&P 500, is used as a proxy for the return on the market
portfolio, and the risk-free rate of return often is ignored.
This model segregates asset risk into two broad categories:
risk that is related to the return on the market portfolio,
called market or systematic risk, and risk that is unrelated
to the market return, so-called nonsystematic or residual
risk.
The "market model" can be summarized by the
equation:
where Rj t is the return on asset j in period t, RM t is the
return on the market portfolio of stocks, f3j is an estimated
coefficient that represents the sensitivity of the return on
asset j to overall stock market returns, u j is an estimated
constant term, and Ej t is a residual.
The estimated beta value from equation (1) measures the
covariance of the individual asset's return with the return
on the overall stock market. If the asset return moves in
proportion to changes in the overall market's return, then
the estimated value of f3j will be close to 1. Such assets are
said to have average market-related risk. An asset with f3j
greater than 1 .carries above average market risk and
typically must provide an above average expected return in
order to induce investors to hold it. The equity shares of
banks holding well-diversified portfolios of assets are
likely to exhibit about average market risk.
Despite the theoretical appeal of the CAPM, it often has
been found wanting in empirical applications. More specifically, factors in addition to the return on the market
portfolio have been found to be significant in explaining the
returns on individual assets. For example, Stone (1974)
suggested an extension of the basic CAPM formulation.
He reasoned that asset returns ought to depend not only on
the return on the market portfolio of stocks, but also on the
return on an alternative debt instrument. This "two-index
model" identifies two sources of systematic risk for asset
returns: The first is equivalent to the systematic risk of
the CAPM and is the risk associated with the return on the
market portfolio; the second is related to returns on debt
securities and is sometimes referred to as interest rate risk.
Residual risk in this model is any risk that is unrelated
either to the market return or to interest rates. 1
It is notable that the stock returns of most companies do
not exhibit any significant sensitivity to the debt return
variable of the two-index model. However, the asset and
liability characteristics of financial intermediaries would
seem to make them likely candidates for significant sensitivity to interest rate changes. Bank and thrift holding
company stock returns thus have been a frequent object of
study by financial economists. The evidence on the interest
rate sensitivity of financial intermediaries, however, is
mixed. Chance and Lane (1980) and Sweeney and Warga
(1986) found that financial institutions tended not to have
consistent or significant sensitivity to changes in interest
rates. They showed, instead, that the stocks of utilities as a
group exhibited more pronounced interest rate risk than
(1)
'Stone (1974) originally proposed the two-factor model by appealing to
an intuitive argument that asset returns ought to depend on alternative
investments in the stock and bond markets. However, the model has a
sound theoretical basis since it can be derived from Merton's intertemporal CAPM (1973).
S4
Economic Review I 1992, Number 3
any other industry grouping. In contrast, a number of other
studies have shown that the stock returns of financial
intermediaries do exhibit significant, though not necessarily stable, interest rate risk. Among the studies finding
significant interest rate sensitivity at banks and thrifts are
those conducted by Martin and Keown (1977), Lloyd and
Schick (1977), Lynge and Zumwalt (1980), Beebe (1983),
Flannery and James (1984a, 1984b), Booth and Officer
(1985), Kane and Unal (1988), and Neuberger (1991).
Some authors have attempted to explain the market and
interest rate sensitivity of bank stock returns by looking at
bank operations, portfolio composition, or other market
conditions. Rosenberg and Perry (1981) conduct such a
study using the CAPM framework, while Dietrich (1986)
uses a two-index approach to explain the risk sensitivity of
bank stocks as a function of bank balance sheet composition. Both of these studies find some evidence that individual bank characteristics affect the risk of bank stock
returns. Moreover, as these characteristics change over
time, the risks of bank stocks also change.
Several studies of bank stock returns have focused
specifically on their interest rate sensitivity. Some of this
research arose over concerns that maturity mismatches by
financial intermediaries may have left them dangerously
exposed to interest rate swings. This may have been
particularly important for thrift institutions in the early
1980s. Flannery and James (1984a), for example, derive a
measure of maturity mismatch between bank assets and
liabilities. After estimating a two-index model on a cross
section of intermediary stock returns, they relate the estimated interest rate coefficients from this regression to their
duration gap measure. They find that the maturity mismatch is significantly related to the observed interest rate
risk of the bank and thrift stocks they study.
Both the CAPM and the two-index model can be considered special cases of a more general asset pricing framework, known as the arbitrage pricing theory (APT, Ross
1976). In this framework, asset returns are explained by
their relationship to a number of common factors. The
return on the market portfolio of stocks may be one such
factor; changes in interest rates could be another. However,
this more general framework allows for many other influences to affect asset returns in a systematic way. In its most
general terms, the APT suggests that asset returns can be
represented by the following process:
(2)
returns. By itself, it says nothing about how financial assets
should be priced in equilibrium. Nevertheless, the APT is
an equilibrium asset pricing model. Like the CAPM, this
model argues that only systematic risk matters for the
pricing of assets. It ignores nonsystematic risk because
such risk can be diversified away. In the APT, the systematic risk of any asset is characterized by the vector of bs from
equation (2). This vector can be thought of as a multidimensional version of the market beta from the CAPM.
According to the APT, assets that exhibit the same systematic risks must be priced in equilibrium to offer the
same rate of return. If not, then investors could buy and sell
the different assets and risklessly profit from the transaction. Opportunities for such riskless arbitrage prevent
assets from selling at anything but their equilibrium prices.
The vector of bs from equation (2) summarizes the systematic risk of an asset and, according to the APT, is the primary determinant of the asset's price. This implies that the
expected return on any asset can be described as a function
of its vector of factor loadings. The theory also implies that
each of these factor loadings should be "priced" in equilibrium. This means that every b should be associated with a
risk premium. These risk premia measure the increased
return that an investor receives for bearing the systematic
risk associated with the corresponding factors and can be
estimated using the equation:
(3) E(R) = AO + Albjl + A2bj2 + ... + Anbjn,
where Ai is the risk premium that measures the increase in
expected return for a one-unit increase in the ith factor
loading. 2
The APT predicts that all assets are affected by the same
set of systematic factors. Unfortunately, the model provides no guidance as to which factors are important in
explaining asset returns. A number of studies have attempted to identify possible sets of factors that are common
across broad portfolios of assets (see, for example, Chen,
Roll, and Ross 1986). In contrast to the factors, the APT
predicts that asset risk profiles (that is, the set of factor
loadings) differ across assets and likely depend on characteristics that are specific to each asset. Little empirical
work has been done to investigate the characteristics of
individual assets that are important in explaining their risk
profiles.
Rj = aj + bjlIl + bj2I 2 + .. , + bjnIn + ej ,
where the Is are the common factors or indexes that
systematically affect asset returns and the bs (also called
factor loadings in APT parlance) represent the sensitivity
of the asset to the different indexes.
Equation (2) describes the process that generates asset
Federal Reserve Bank of San Francisco
2In applications of the APT, equation (2) is sometimes estimated for a
sample of assets (or portfolios of assets) over a particular time period.
The estimated vector of bs is extracted from these estimates, and then is
used to estimate equation (3) over a different time period. This two-step
procedure yields estimates of the risk premia associated with the
different factors.
55
It is reasonable to assume that these risk profiles (the bs
from equation (3)) depend on some distinguishing characteristics of each asset. In the case of banks, recent developments in capital regulation suggest that regulators view the
composition of bank asset portfolios as an important
determinant of bank risk. The risk-based capital guidelines
set different required levels of capital for each of a number
of categories of bank assets. These asset categories were
established based on perceptions of the relative credit risks
of the different assets. Box 1 provides some detail on the
risk weights of several broad groupings of bank assets. In
this paper, I use a modified APT model to test whether the
stock market confirms this regulatory view that portfolio
allocations are significant in explaining the risk of bank
holding company stock returns.
Box 1
Selected Asset Categories
and Risk Weights under the
Risk-Based Capital Standards
Asset Category
Risk Weight
Treasury and Government Agency securities
(includes GNMA mortgage-backed securities)
a percent
FNMA and FHLMC mortgage-backed securities
20 percent
Privately issued mortgage-backed securities and
residential mortgage loans
50 percent
Commercial & industrial loans and loans to
individuals
100 percent
The risk-based capital standards set minimum capital ratios at 8
percent of risk-weighted assets. More specifically, the standards call
for Tier 1 capital (mostly equity) of at least 4 percent, and sufficient
Tier 2 capital to bring the total to 8 percent. Risk-weighted assets are
determined as the book value of assets in each of the different
categories multiplied by the corresponding risk weight. In effect,
this means that banks must hold the full 8 percent of capital against
assets in the 100 percent risk weight category, 4 percent against the
50 percent risk-weighted items, and no capital against zero riskweight assets like Treasury securities.
The risk-based capital standards also establish required levels of
capital to support off-balance sheet activities, such as interest rate
and foreign exchange swaps and options. The required amounts of
capital for these activities generally depend on the type and maturity
of the contract and the cost of replacing an existing contract with a
new one. These capital requirements are intended to reflect the credit
risk associated with these activities and do not currently incorporate
any hedging effects they may have on the interest rate or foreign
exchange risk of the bank.
In this model, I assume there is one common factor for
all bank stocks, namely, the return on the market portfolio.
I then hypothesize that the proportion of bank portfolios
allocated to different assets represents a set of characteristics that are important determinants of their risk profile and
thus are significant in explaining bank stock returns.
Defining Ij; as the proportion of the ith asset (relative to
total assets) in the portfolio of bank j, this model can be
expressed as
(4)
Rjt
= a j + f3 j R Mt +
2,)\j;Ijit
+
Ejt·
While equation (4) captures the direct effects of portfolio composition on bank stock returns, these asset shares
also may exert an indirect influence by altering the market
risk of bank stock returns. The original market model
views an individual asset's beta as constant over time.
However, subsequent research confirms that the sensitivity
of bank stocks to the market portfolio (as well as to other
systematic factors) is not constant (Kane and Unal1988,
Kwan 1991, Neuberger 1991). One interpretation of the
market beta is that it represents an average of the market
risks associated with each of the assets in the bank's
portfolio. Changes in the bank's asset mix, therefore,
will change the overall market risk of the bank's stock
returns. I test for these indirect effects by allowing the
estimated coefficient f3j to depend (at least partially) on the
proportion of the bank's assets allocated to different asset
categories. 3 This dependence changes somewhat the interpretation of the direct effects: The estimated A coefficients
from equation (4) reflect the influence of portfolio composition on the nonmarket component of systematic risk.
I assume that the relationship between asset allocations
and estimated beta values is additive. Thus, the hypothesis
that market risk is variable and depends on portfolio
composition can be expressed as
(5)
where each coefficient 'Yj; represents the impact of asset
share i on the stock market sensitivity of bank j's equity,
and 'YjO is the portion of market risk that is unrelated to the
bank's asset allocations. If portfolio composition affects
the market risk of bank stocks, then the estimated values of
'Yj; should differ significantly from zero. The sign of these
coefficients will determine whether the specific asset categories increase or decrease the sensitivity of the bank's
stock return to the overall stock market.
These relationships can be expressed in a single equation by substituting equation (5) into equation (4):
"This dependence also means that the estimated coefficient varies over
time and thus requires a time subscript in the subsequent equation.
56
Economic Review / 1992, Number 3
+
2i (~iPjit) + vjt,
where v,jt is a combination of the error terms from equations
(4) and (5). The dependence of the stock market beta on the
composition of the bank's balance sheet adds. several
"interacted" variables to the empirical model. The mteractions are between the return on the market portfolio of
stocks and the asset share variables from the bank's portfolio. The coefficients on these interaction terms measure the
indirect effects of portfolio composition on the estimated
market risk of bank stocks.
An additional bank characteristic that may influence
bank stock returns is the financial leverage of the bank.
Since banks are subject to capital regulation, there are regulatory limits on the extent to which banking firms can leverage their operations. Nevertheless, many banks choose
to hold more (sometimes significantly more) than the
required minimum level of capital. Option-based models
of bank risk take explicit account of leverage. In the market
model approach, leverage effects are implicitly assumed to
affect the market beta. In order to isolate these leveragerelated differences in risk, I interact bank leverage with
the return on the market portfolio. The empirical model
becomes
(7)
Rjt
=
a}
+
'YjORMt
+ 8j LE~t • R Mt
+ 2i ('YjiPjit) • R Mt + 2i Ol.jiPjit) + vjP
where LEVt is the book value of assets divided by the
market val~e of bank equity, and 8j is an estimated coefficient that reflects the influence of bank leverage on the
market risk of bank stock returns.
I make one final adjustment to the model based on
econometric considerations. Equation (7) estimated on a
time series, cross-section of banking firms constrains the
estimated constant term (a in the equation) to be identical
across all banks in the sample and over the estimation
interval. This constraint may not be appropriate and may
bias the estimation results. To account for time-specific
effects that may affect all banks in the same way, I add time
dummy variables (omitting the first period) to all of the
regressions.t I do not account for differences in the constant term across banks because I expect that most of the
4 An
alternative method for incorporating the influence of time-specific
factors on stock returns is to include a time trend variable in the
regressions. This procedure, however, imposes a particul~ stru~ture ~n
the impact of time on the banks in the sample, namely, it r~q~lfes t~iS
effect to be linear. The procedure used here avoids that restriction while
still capturing the impact of time-specific events that influence all banks
in a similar way.
Federal Reserve Bank of San francisco
cross-sectional variation in the sample will be captured
by the balance sheet variables. Since there ~s no e~o
nomic significance to the coefficients on these time penod
dummy variables, I do not report them in the next section.
In evaluating the results presented below, it is important
to recognize that bank stock returns may not be the ideal
vehicle for identifying the determinants of risk that may be
of interest to bank depositors or regulators. Ideally, it
would be preferable to obtain a direct measure of bank
asset or portfolio risk, and then search for the determinants
of that measure of risk. Unfortunately, such direct measures typically are not available. One way around this
problem is to use an option pricing framework to evaluate
bank risk. This modeling approach provides an indirect
measure of bank asset risk based on the behavior of bank
stock and option prices. Examples of option-based models
of bank risk include studies by Levonian (1991), and
Cordell and King (1992).
In contrast to either direct or indirect measures of bank
asset risk, the risk of bank holding company stock returns
reflects the market's perception of an amalgam of risks
associated with operating a bank. These include asset risk,
default risk, deposit insurance risk, charter value risk, etc.
Focusing on the risks of holding bank stocks does not
provide specific evidence regarding bank asset risk. For
example, an increase in bank asset risk will have a positive
effect on bank stock risk, but the risk of holding bank
stocks could rise for reasons other than an increase in asset
risk. Nevertheless, the work presented here does provide
important insights into how bank portfolio allocation decisions influence the market's perception of the combination
of risks incorporated in bank stocks.
II.
EMPIRICAL RESULTS ON BANK PORTFOLIO
COMPOSITION AND BANK STOCK RISK
In this section, I present the results from estimating
equation (7) on a sample of 119 bank holding company
stock returns over the quarterly interval from 1988 to 1990.
The data for (monthly) bank stock returns are drawn from
the Compustat bank tapes, are adjusted for dividends and
splits, and then are summed to a quarterly frequency. The
balance sheet data are taken from quarterly Reports of
Condition (Call Reports).
Having two different sources of data for stock returns
and balance sheets poses an interesting problem for the
empirical work. The stock return data are for bank holding
companies. The balance sheet data are for individual
banks. The problem is that many of the larger bank holding
companies from the Compustat database own or control
multiple banks. In combining balance sheet data with the
holding company stock returns, it is desirable to have
57
accounting data that accurately represent the balance sheet
of the holding company. One solution used in previous
work (e.g., Flannery and James 1984aandKwan 1991) is to
use accounting data from the largest bank subsidiary of the
holding company and to limit the sample to those lead
banks that hold at least, say, 75 percent of total holding
company assets. For the current project, 1 summed individual bank data from the Call Reports, thereby building
up more complete balance sheets for holding companies
with multiple bank subsidiaries. The combined balance
sheet data used in this study average well over 90 percent of
holding company assets during the four-yearestimation interval, considerably higher than in previous studies. The
database also includes significant changes in bank structure during this period, as it was necessary to keep track
of subsidiary sales and purchases, bank mergers and acquisitions, as well as failures and other resolution procedures.
The result of this extensive data project is a consistent
sample of 119 of the largest bank holding companies in
the U.S. over the 12-quarter interval from 1988.Ql to
1990.Q4. 5
All of the reported results are from pooled regressions;
no individual bank estimates are reported. Thus, the
coefficients represent average estimated coefficients for
the banks in the sample. The asterisks in the table reflect
the degree of statistical significance of the estimated
coefficients. The coefficient for RM is tested against a null
hypothesis that the group of stocks exhibits average market
risk, that is, that the value of beta is one. All other tests are
performed against a null hypothesis that the estimated
coefficient is equal to zero.
Finally, in pooled cross-section regressions of the type
presented here, heteroskedasticity is a common problem
that can bias estimated standard errors and thus measures
of statistical significance. A frequently used procedure to
obtain consistent estimates of the covariance matrix and
coefficient standard errors is that proposed by White
(1980). In all of the regressions reported in this paper, I
have employed White's technique to obtain consistent
estimates of standard errors. 6
In Table 1, I present the regression results from the
model of bank holding company stock returns using several non-overlapping categories of securities and loans.
5 Although I originally collected data for the four quarters of 1987, preliminary regressions indicated that the 1987 data contained a number of
anomalies. I therefore restrict the estimation interval to the 1988 to 1990
period.
6White's methodology may not be necessary if there is no evidence of
heteroskedasticity in the sample. Tests for the existence of heteroskedasticity showed that it did exist in the current data set and that
White's procedure was therefore appropriate.
S8
These asset groups comprise on average about 60 percent
of the assets of the banks in the sample. In addition to the
on-balance sheet assets, I also include in column (8) of the
table the sum of two of the largest categories of off-balance
sheet activities: foreign currency and interest rate swaps,
options, and other contracts.
In each succeeding column of Table 1, I include in the
regression one more asset share variable. In this way, I can
determine if an additional asset alters the previous estimates, thereby indicating the presence of multicollinearity
among the different asset categories. As the results in the
table indicate, the estimated coefficients are fairly stable
across the different regressions. Most of the coefficients
that are significant in one regression remain so in succeeding columns. Some point estimates do vary across the
regressions, and there is a tendency for standard errors to
rise somewhat, reducing the significance levels for some
coefficients as more balance sheet variables are added.
The estimated value of the market beta ranges between
2.7 and 3.4, suggesting that the banks in the sample
exhibited significantly higher than average market risk
during this period." Clearly this was an extremely volatile
period for bank stock returns relative to the market portfolio of stocks. The leverage variable interacted with the
return on the market portfolio is not statistically significant
in any of the regressions. This means that differences in
bank leverage appear to have no identifiable impact on the
market risk of bank holding company stock returns, at least
during the period of analysis used in this study.
Among the different categories of assets, the interacted
term for the sum of Treasury and government agency
securities has a negative coefficient that is statistically
significant in all of the regressions. This category encompasses assets with the most favorable risk' weights under
the risk-based capital guidelines. This includes Treasury
securities that require no capital support and mortgagebacked securities issued by FNMA and FHLMC that receive a risk weight of 20 percent. These results provide
evidence that holdings of government securities exert a
negative impact on the market risk of bank stocks. Banks
with a greater proportion of Treasury and agency securities
in their portfolios exhibit less stock return volatility with
respect to overall movements in the stock market than
banks holding a smaller proportion of these assets. This
7 As in most empirical estimates of market-based models, the value of
the market beta depends crucially on the selected time period. Estimated beta values have shown considerable volatility in previous studies (for
example, Neuberger 1991). Estimates of the current model that included
1987 showed significantly lower estimated betas. Notably, the other
estimated coefficients were relatively stable and quite close to those
reported here.
Economic Review. / 1992, Number 3
~
Q.
.,
~
a
'='
I
Table 1
Regression Results: Bank Holding Company Stock Returns
as a Function of Portfolio Composition, 1988-1990.
~
'"
.,
~
~
I:C
I:ll
:s
Inde pendent Variable
~
0
-,
RM
r.n
:s
RM
I:ll
(Treasury
(;i"
RM
0
Private Mortgage Securities!Assets
I:ll
.,""l
:s
n
n
RM
•
•
•
Leverage
+ Govt. Agency Securities)! Assets
(Treas.
+ Govt. Agency Secs.! Assets)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
2.730 ***
2.758** *
2.974 ***
3. 101** *
3.126 ***
3.400 ***
3.455** *
3.445 * **
- 0.001
-0 .003
•
- 0.003
-0.003
- 0.003
- 0.003
- 0.003
0.049
0.049
0.014
0.08 1*
0.085 *
0.081*
0.084*
0.087*
-3 .656* **
- 3.045 ***
- 3.037** *
-3 .172* **
-3 .273** *
- 3.006 ***
- 3.022** *
- 2.43 1***
- 2.660**
- 2.749**
-2 .983* *
- 3.005**
- 2.957* *
- 2.960 * *
-2.870**
13.5 11
(Private Mortgage Securities! Assets)
13.619
- 0 .264***
Commercial Real Estate Loans! Assets
RM
- 0.003
1.281
(Coml. Real Estate Loans!Assets)
19.459
20.442
19.977
20.236
18.703
- 0.268 ** *
- 0.261***
- 0.266** *
- 0.264***
- 0.30 1***
2.221*
2.827**
2.798**
2.742**
3.377**
0.009
0.009
- 1.920**
- 0.006
-0.006
- 0.028
-1.938**
- 1.822* *
- 1.779**
- 1.424
Multifamily Residential Loans!Assets
-0.048
- 0.169
- 0.159
- 0.20 1
RM
-9.771
- 8.810
- 9.035
- 8 .269
- 0.098
- 0.09 1
- 0.102
0.604
0.408
0.594
0.014
- 0.006
- 0.526
- 0.202
1-4 Family Residential Loans!Assets
RM
•
•
(1-4 Family Residential Loans! Assets)
(Mu ltifamily Res. Loans! Assets)
Commerci al & Industrial Loans!Assets
RM
•
(C & I Loans/ Assets)
Loans to Individuals / Assets
RM
•
(Loans to Individuals/A ssets)
- 0.004
Currency & Interest Rate Contracts/ Assets
RM
•
0.070*
(Curr. & Int. Rate Contracts!Assets)
R2
0.460
0.470
0.472
0.473
0.473
0.473
0.472
0.472
Number of Observations
1428
1428
1428
1428
1428
1428
1428
1428
Note: Sample includes 119 banks. Test for RM is against null hypothesis that coefficient is equal to 1.0; all other tests are-against null hypothesis that coefficients equal zero.
Regressions also include dummy variables for each time period (except 1988.Ql); coefficients on these variables are not reported .
= 10 percent level
Significance: *
** = 5 percent level
*** = I percent level
I
til
'C
result is sensible in light of the relative safety of government securities with respect to default risk. Of course, such
securities may expose banks to interest rate risk. The
regressions provide some modest support for the existence
of significant nonmarket risk associated with these securities. The first five columns show a positive coefficient
on the noninteracted government securities variable that is
significant at the 10 percent level. The significance of this
coefficient disappears in the subsequent regressions, suggesting that the stock market may not price the extramarket
risk of these securities in bank portfolios.
For the other category of securities, privately issued
mortgage-backed securities, the interacted coefficient is
not statistically different from zero in any regression.
These securities do not exert any statistically significant
impact on the market risk of bank stock returns. However,
this asset category does have a stable and significant
negative noninteracted coefficient. Larger portfolio shares
of private mortgage securities are associated with lower
bank stock returns. The stock market in effect imposes a
"negative risk premium" on banks with proportionately
higher exposure to the nonmarket systematic risks of
holding these securities. Apparently, the market considers
this exposure to be relatively "safe" for banks, and thus
they receive a lower stock return for assuming it.
Among the different loan categories in Table 1, commercial real estate loans exhibit the strongest effect on bank
stock returns. The estimated coefficient on this interacted
variable is significantly positive in all but the first regression, indicating that these loans increase bank marketrelated risk. Stock returns of banks with a greater proportion of their assets in commercial real estate loans exhibit
greater sensitivity to changes in the overall stock market.
At the same time, the noninteracted variable for these loans
has a significant and negative coefficient. This suggests
that the nonmarket risk of these loans may actually be
negative.
The only other loan category to exhibit any significant
effect on bank stock returns is the interacted term for oneto-four family residential loans. The estimated coefficient
on this variable is negative in all of the regressions and is
significant in all but the last column. These results provide
support for the notion that home mortgages may reduce the
market risk of bank stock returns.
Finally, I consider in column (8) the influence of offbalance sheet activities on bank stock risk and return.
These activities have grown rapidly in recent years, especially at larger banks. Some critics suggest that the explosive growth of these activities has increased bank risk in
significant, though difficult to measure, ways. Banks defend the use of these instruments by claiming that they
provide a hedge against currency and interest rate risk. The
60
risk-based capital standards require some capital support
for off-balance sheet activities, recognizing that they entail
some credit risk. However, the capital guidelines ignore
any risk-reducing effects that such activities may have on
currency or interest rate risk.
As the results in column (8) indicate, the off-balance
sheet category has a positive and marginally significant
estimated coefficient on the interacted variable, suggesting
that these activities are associated with greater market risk
for bank stock returns:" This finding provides some support for including off-balance sheet activities in the riskbased capital regulations and suggests that more work is
needed to understand this rapidly growing market. Perhaps
more important, the off-balance sheet activities do not
show any statistically significant nonmarket risk effects.
At least for the banks in the sample, it does not appear that
off-balance sheet activities have reduced the extra-market
risk of bank stockreturns.
Interpretation ofResults
The findings presented here highlight a number of
interesting aspects regarding the risk of bank stock returns.
First, portfolio composition appears to affect both the
market and nonmarket systematic risks of bank stock
returns." Several categories of assets exert a statistically
significant effect on bank market risk through the balance
sheet variables interacted with the market return. In addition, several asset categories exert an impact on bank stock
returns independent of market risk. In terms of the APT
model, this latter finding suggests that the composition of a
bank's asset portfoliomay represent a set of characteristics
that are significant determinants of its (nonmarket) systematic risk profile.
Second, the significant results among the interacted variables provide some interesting empirical evidence regarding the risk hierarchy ofthe risk-based capital guidelines.
Holdings of government securities, for example, appear to
8When the two types of off-balance sheet activities were included
separatelyin the regressions, each showed the samestatistically significant positive interacted coefficient and no significance for the noninteracted coefficient. However, putting both types of off-balance sheet
activitiesin the sameregression producedevidence of multicollinearity.
Apparently, the samebanksthat use interestrate contracts arealso those
most heavily involved in foreigncurrencycontracts. By combining the
two categories into one, theircombinedeffectcan be estimatedwithout
any statistical problems arising from multicollinearity.
9 As in all studies of this type, any hypothesis tests are tests of the joint
hypothesis that (a) the modified APT modelis correct,and (b) portfolio
composition is an appropriateset of bank characteristics affecting bank
stock returns.
Economic Review / 1992, Number3
reduce the. market risk of bank stocks. This finding provides support for the preferential treatment given to Treasury and other government agency securities in the riskbased capital standards. The absence of credit risk inherent
in these securities provides banks with a "safe haven" that
is reflected in the reduced market risk of bank stock
retums. The weak evidence on the nonmarket risks of
government securities also may raise questions regarding
the empirical importance of any interest rate risk associated with holding them.
Among several broad categories of bank loans, neither
commercial and industrial loans nor loans to individuals
have any significant effect on the market risk of bank stock
returns. This finding is notable because these two categories of loans receive the highest risk weight under the riskbased capital standards and yet they do not appear to
increase the market risk of bank stock returns. This result
may raise some doubts as to whether the highest risk weight
is appropriate for these categories of loans. In contrast, the
results presented here support the preferential treatment
given to residential mortgages under the risk-based capital
rules. The regressions confirm that residential real estate
loans exhibit a significant risk-reducing influence on the
market risk of bank stock returns.
An additional interesting finding among the loan categories is the result for commercial real estate loans. These
loans exert a strong positive effect on the market risk of
bank stock returns. This finding highlights the real source
of risk for banks making real estate loans. Even prior to the
recent "real estate recession," the risky area of real estate
lending for banks has been for commercial projects.
Turning to the noninteracted balance sheet variables,
several significant direct coefficients suggest that the corresponding assets are important in explaining nonmarket
systematic bank stock risk. Among these assets, government securities have a marginally significant positive risk
premium associated with them, while private mortgage
securities and commercial real estate loans are associated
in the sample with significant negative risk premia.
However, the interpretation of these direct coefficients is
somewhat uncertain. The regression model relates portfolio allocations to realized returns rather than expected
returns. as the theory suggests. A significant estimated
noninteracted coefficient, therefore, could represent a fundamental relationship between bank stock returns and
portfolio composition or it could be indicative of (good or
bad) luck on the part of the bank in holding the particular
asset during the estimation interval. This is particularly
true given the relatively short time period over which the
model is estimated. It is thus unclear, for example, whether
commercial real estate loans systematically affect the
nonmarket risk profile of bank stock returns or whether
Federal Reserve Bank of San Francisco
banks that made these loans in the 1988 to 1990period were
the victims of poor performance by these assets.
This same uncertainty should not affect the interacted
coefficients in the regressions. These coefficients represent the influence on market risk of the particular asset
category relative to the average market beta of the banks in
the sample. Each asset in banks' portfolios may be considered to have its own associated market beta value. Thus,
there may exist a "beta" for making residential mortgage
loans or a similar measure for holding government securities. The aggregate beta that a bank exhibits thus will
be a weighted average of the individual betas associated
with the different assets in its portfolio. As the asset mix
changes, so will the bank's market risk. If the market
model is an appropriate representation of asset returns,
then these interacted effects may be stable over time.
III.
CONCLUSION
In the current paper, I conduct an empirical analysis of
the behavior of bank holding company stock returns with
the goal of identifying the effect of portfolio composition
on the risks embodied in those returns. I find that several
categories of assets in bank securities and loan portfolios
do alter the risk profile of bank stock returns. Among other
things, I discuss the importance ofthese findings in light
of the risk-based capital standards and the different risk
weight categories that those standards use. The risk-based
capital guidelines are an important step in establishing
regulations that measure bank risk more accurately. However, these standards may need to be modified as new
evidence is uncovered about the risk effects ofdifferent
bank activities. Moreover, as banks respond to a changing
economic and regulatory environment, their asset mix may
change and alter the risk profile of their portfolios. This
undoubtedly has happened, for example, with respect to
off-balance sheet activities. Capital regulation may need to
respond as well to these changing realities if required
capital levels are to reflect bank risk accurately.
61
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Economic Review I 1992, Number 3
@FedFRASER