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conomic
July/August 1995
Volume 80. Number 4
Federal Reserve
Bank of Atlanta
In This Issue:
deducing Our Ignorance about
Monetary Policy Effects
FYI—Testing the Informativeness of
Regional and Local Retail Sales Data
/cpnomic
/ R e v i e w
July/August 1995, Volume 80, Number 4
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c
feview
Federal Reserve
Bank of Atlanta
President
Robert P. Forrestal
Senior Vice President and
Director of Research
Sheila L. Tschinkel
Research Department
B. Frank King, Vice President and Associate Director of Research
Mary Susan Rosenbaum, Vice President, Macropolicy
Thomas J. Cunningham, Research Officer, Regional
William Roberds, Research Officer, Macropolicy
Larry D. Wall, Research Officer, Financial
Public Affairs
Bobbie H. McCrackin, Vice President
Joycelyn Trigg Woolfolk, Editor
Lynn H. Foley, Managing Editor
Carole L. Starkey, Graphics
Ellen Arth, Circulation
The Economic Review of the Federal Reserve Bank of Atlanta presents analysis of economic
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Contents
Federal Reserve Bank of Atlanta Economic Review
July/August 1995, Volume 80, Number 4
/deducing Our
Ignorance about
Monetary Policy Effects
E r i c M. L e e p e r
39
FYI—Testing the Informativeness of Regional and
Local Retail Sales Data
G u s t a v o A. U c e d a
Business news often gives the impression that the effects of
monetary policy on the macroeconomy are well understood and
predictable. The author of this article, however, believes that, far
from sharing such certainty, policymakers and economists alike
have knowledge limited by difficulties in sorting out causal factors
in economic data. He holds that monetary policy effects are neither
well understood nor easily predicted.
The article presents five models of private and monetary policy
behavior in the United States. Identical policy experiments—an
unanticipated one-time monetary policy contraction—performed
in each model show different qualitative and quantitative effects
of policy from one model to the next. The author considers a variety of methods for ranking the models according to their plausibility
and suggests that because each model has its limitations, it would
be wise for policy advisors to be eclectic in formulating advice.
A large collection of published and unpublished retail sales estimates produced by the U.S. Department of Commerce provides
potentially valuable current and historical estimates and industry
detail for several regions of the country dating back to 1978. Analysts may find these data particularly useful as supplements to published data in monitoring retail spending in some states and
metropolitan statistical areas.
This article examines whether the breadth of detail the data offer can offset such limitations as small sample size and volatility.
The author analyzes the information provided by augmenting published data with unpublished data for its usefulness in predicting
regional employment. The research suggests that regional and
metro retail sales data can aid researchers as well as others in the
business of local economic analysis.
Reducing Our
Ignorance about
Monetary Policy Effects
r
This article was written
while the author was a
research officer in the
macropolicy section of the
Atlanta Fed's research department. He is currently on the
faculty in the department of
economics at Indiana University. The article draws heavily
on work by David R. Gordon
and the author
(1993,1994).
The author thanks Jon Faust,
Dave Gordon, and especially
Will Rohercls and Tao Zha
for helpful
discussions.
Reserve B a n k of Atlanta
DigitizedFederal
for FRASER
Eric M. Leeper
he business pages of leading newspapers give the impression
that the effects of monetary policy on the macroeconomy are
well understood and predictable. Newspapers write with great
certainty that when the Fed raises interest rates it "slows econ o m i c growth, and with it inflation" (Louis Uchitelle 1994),
"bidding down stocks and bonds" (Anthony Ramirez 1994). With equal certainty, press accounts report that monetary policy responds to e c o n o m i c
conditions: "The recent strength of the U.S. economy will continue in the
first quarter, prompting the Federal Reserve to raise short-term interest rates
as a preemptive strike against inflation" (Fred R. Bleakley 1994). With the
economy responding to policy and policy responding to the economy, it is
hard to tell what causes what. Far from the certainty with which economic
journalists write, our knowledge is limited by these difficulties in sorting out
causal factors in the data. Monetary policy effects arc neither well understood nor easily predicted.
Evaluations of how monetary policy influences the economy differ, but
particular e l e m e n t s are c o m m o n to all. Each e m b o d i e s particular v i e w s
about (1) the current stance of monetary policy (whether it is " t i g h t " or
"loose"); (2) how the monetary authority behaves, including what it is trying
to achieve and what it is doing to pursue its goals (its "reaction function");
and (3) how the private sector responds to current and expected future monetary policy (the "propagation m e c h a n i s m of policy"). Pundits frequently
blend these views to arrive at a Goldilocks-like assessment that policy is
Eco n o m ic Revie w 9
"too tight" or "too loose" or "just right"—though the
last assessment is rare. For example, Jerry Jasinowski,
president of the National Association of Manufacturers, declared in September 1994 that "one more rate
increase by the Federal Reserve will drive the economy into a ditch, bringing on a recession" (quoted in
Uchitelle 1994).
Putting these three things together, objective observers of monetary policy form a conclusion about the
extent to which monetary policy has caused current
e c o n o m i c conditions. These observers allocate some
portion of the movements of variables to policy and the
rest to nonpolicy factors. For example, if lower inflation and lower economic growth follow rising shortterm interest rates, observers might conclude that the
monetary authority wanted to slow down the economy
(point 2 above), so it "tightened" policy by raising interest rates (point 1), causing economic activity to decline and easing upward pressure on prices (point 3).
Of course, during this period more than just monetary policy would have been impinging on the economy
and affecting private decisions. Observers implicitly
filter out the i n f l u e n c e s of other f a c t o r s , h o w e v e r ,
leaving only the impacts of monetary policy. How can
the plausibility of such an approach be evaluated? The
process of attributing particular m o v e m e n t s in variables to particular c h a n g e s in e c o n o m i c behavior is
called identification, a process applied—with varying
degrees of sophistication and explicitness—whenever
data are interpreted in terms of e c o n o m i c behavior.
I d e n t i f i c a t i o n can be a c o n t e n t i o u s m a t t e r b e c a u s e
there is no single "correct" view of how the economy
works.
This article illustrates the role that identification
plays in policy analysis. Even though most economists
agree on the qualitative effects of monetary policy, they
disagree on its quantitative importance. The differences
of opinion allow consensus and conflict to coexist, as
the article e x p l a i n s . D e s p i t e the lack of c o n s e n s u s
about monetary policy's quantitative impacts, monetary policy advisors must interpret economic developments and formulate policy advice. O n e approach is to
specify and estimate a model of policy and private behavior. At a m i n i m u m such a model should include
behavior in the market for bank reserves because monetary policy a f f e c t s the e c o n o m y initially t h r o u g h
changes in the supply of reserves. Before turning to
the data, therefore, the article discusses supply-anddemand behavior in the market for reserves.
A central t h e m e of this article is that identifying
monetary policy effects is a tricky business. Different
but s e e m i n g l y r e a s o n a b l e identifications can imply
2
Economic
Review
wildly different policy effects, including perverse ones,
as is shown in the article's presentation of five models
of private and monetary policy behavior in the United
States. The models specified and estimated differ only
in terms of their assumptions about how current economic decisions depend on current variables; dependence on past economic variables is the same across
the models. Identical policy experiments—an unanticipated o n e - t i m e m o n e t a r y policy c o n t r a c t i o n — w e r e
performed in each model, with the results showing different qualitative and q u a n t i t a t i v e e f f e c t s of policy
from one model to the next. A policy advisor's interpretations of economic developments would therefore
differ across models. In practice an advisor must rank
the models according to their plausibility, and this article considers a variety of schemes for ranking them.
The diversity of results presented below might lead
one to conclude that the impacts of monetary policy
are largely u n k n o w n — a n d perhaps unknowable. H o w ever, by combining economic reasoning with careful
data analysis it seems possible to reduce our ignorance
about monetary policy effects.
Consensus and Conflict
A remarkably strong consensus exists among policymakers, business economists, and academic economists
about many of the qualitative effects of a monetary
policy e x p a n s i o n . To p a r a p h r a s e Milton F r i e d m a n
(1968), increasing the quantity of m o n e y at a faster
rate than it had been increasing (a) initially lowers
short-term nominal and real (inflation-adjusted) interest rates (the "liquidity effect"); (b) stimulates spending t h r o u g h the i m p a c t of l o w e r i n t e r e s t r a t e s o n
investment and other spending, which raises income;
(c) increases production and lowers unemployment, at
least temporarily; and (d) raises overall prices. As the
demand for liquidity rises with incomes and as prices
rise, the initial decline in interest rates will be reversed
and rates will return to their initial levels. If m o n e y
growth increases permanently, as people come to expect that prices will continue to rise, borrowers will be
willing to pay and lenders will demand higher nominal
interest rates. The higher rate of monetary growth will
result in higher interest rates (the "expected inflation effect"). This synopsis of monetary policy effects, while
credited to Friedman, accurately reflects the views held
by economists of almost all stripes.
Economists disagree, however, about the quantitative
importance of monetary policy. Some believe that "er-
J u l y / A u g u s t 1995
ratic" monetary policy plays a substantial role in generating business cycle fluctuations. Among writers before
World War II, Irving F i s h e r ( 1 9 3 1 ) , R . G . H a w t r e y
(1934), Friedrich A. Hayek (1934), Ludwig von Mises
(11934J 1980), and Lionel Robbins (1934) were important contributors to this view. Since the war, prominent
examples are Friedman (1960, 1968, 1970), Friedman
and A n n a J. S c h w a r t z (1963), F r i e d m a n and David
Meiselman (1963), Robert E. Lucas, Jr. (1987), and
Christopher A. Sims (1972). Economists like James Tobin (1980) credit policy, including m o n e t a r y policy,
with reducing the amplitude of business cycle fluctuations since World War II. Both assessments embrace the
view that monetary policy has powerful effects.'
O v e r the years other respected e c o n o m i s t s h a v e
staked out the opposite turf, arguing that m o n e t a r y
policy is all but impotent. During the Great Depression m a n y believed that monetary policy was helpless.
If at very low interest rates and high levels of unemp l o y m e n t the d e m a n d for liquidity is insensitive to
changes in interest rates, then monetary policy cannot
affect rates. If in addition consumption and investment
d e m a n d are also insensitive to the interest rate, then
even if monetary policy could change interest rates, it
would do little good. As Friedman described it, this
v i e w held that " m o n e t a r y policy was a string. You
could pull on it to stop inflation but you could not
push on it to halt recession" (1968, 1). In the 1950s and
1960s some theorists emphasized "real" causes of business cycles, relegating monetary policy to a purely passive role. (See examples in Robert Aaron Gordon and
Lawrence R. Klein 1965. 2 ) At the same time there was
much debate about whether monetary or fiscal policy
was the m o r e potent tool. (See, for example, Albert
A n d o and Franco Modigliani 1965, Leonall C. Andersen and Jerry L. Jordan 1968, Friedman and Walter W.
Heller 1969, and Bennett T. McCallum 1986.)
M a n y modern business cycle theorists, following
Finn E. Kydland and Edward C. Prescott (1982), attribute the vast majority of output and e m p l o y m e n t
fluctuations to shifts in technological innovation and
p r o d u c t i v i t y that are u n r e l a t e d to m o n e t a r y policy.
Robert G. King and Charles I. Plosser (1984) identify
correlations between money and economic activity as
arising entirely from a passive response of the monetary sector to real e c o n o m i c activity. The view that
unanticipated changes in monetary policy have had little influence on the macroeconomy has found a modern empirical voice in work by Sims (1980b, 1989)
and Sims and Tao Zha (1994).
O n e r e a s o n that e c o n o m i s t s m i g h t a g r e e on the
qualitative effects of policy while they disagree on its
F e d e r a l R e s e r v e B a n k of Atlanta
quantitative i m p o r t a n c e is that they view e c o n o m i c
data through very different e c o n o m i c lenses. Beliefs
about qualitative effects stem largely f r o m controlled
monetary policy experiments conducted in theoretical
models. A controlled experiment holds everything in
the m o d e l f i x e d e x c e p t m o n e t a r y policy, w h i c h is
changed in some k n o w n way. Policy e f f e c t s are inferred by comparing the model's e c o n o m y before and
after the experiment. A wide variety of traditional theoretical models make similar predictions about policy
effects, and a consensus of opinion has formed around
those predictions.
To formulate a policy recommendation
an
advisor needs a model that both provides
an unambiguous economic
interpretation
of past data and forecasts future data well.
Measuring quantitative effects is a trickier business
as it involves the process of identification referred to
earlier. A set of identifying assumptions a m o u n t s to
using a m o d e l e c o n o m y to interpret the actual economy. In the actual e c o n o m y a n u m b e r of t h i n g s are
c h a n g i n g s i m u l t a n e o u s l y . To h a v e d a t a m i m i c the
theoretical thought experiment, all kinds of identifying a s s u m p t i o n s about b e h a v i o r m u s t be m a d e , assumptions that serve to control for the fact that m a n y
things are c h a n g i n g at once. B e c a u s e private-sector
decisions depend on policy c h o i c e s and vice versa,
there is no universally accepted way to construct the
empirical analog to the controlled policy experiment.
With much room for differing views of how best to
p r o c e e d , t h e r e is m u c h r o o m f o r d i f f e r i n g b e l i e f s
about the quantitative importance of monetary policy.
Intellectual quagmires notwithstanding, policy decisions are made regularly. These decisions are likely
to be most effective if they are based on some internally consistent view of h o w m o n e t a r y policy choices
will affect the economy. Toward that end, this article
considers several different identifications of monetary
policy and private-sector behavior. Because each ident i f i c a t i o n , or m o d e l , m a k e s d i f f e r e n t a s s u m p t i o n s
Eco n o m ic Revie w
3
about behavior, each one conducts the empirical experiment of changing monetary policy, holding all else
fixed, differently. And as a consequence, each identification carries different predictions about the effects of
a monetary policy shift. The models are constructed
with an eye toward developing tools that might be useful in advising monetary policymakers.
71ie Problem Facing a Policy Advisor
Consider the situation facing a monetary policy advisor in the United States in the beginning of the summer
of 1995. Chart 1 reports recent data through May 1995
on reserves m a r k e t variables and variables the Fed
wants to influence. These are the data available to the
advisor as of mid-June. The Fed raised the funds rate
target from 3 percent to 6 percent between February
1994 and March 1995 and brought the annual growth of
reserves from positive double digits to negative rates.
Inflation hovered around 3 percent, as it did in 1992 and
the first half of 1993. Output growth, as measured by
industrial production, fell from its high level the previous year, and unemployment stopped the steady decline
it experienced in 1993 and 1994/ These data, combined
with other available information, may lead the advisor
to believe real G D P growth in the second quarter of
1995 will be sluggish or possibly zero. There is also
some risk that the sluggish growth will persist through
the year. In light of this information, the advisor must
decide whether to recommend that the Federal Open
Market C o m m i t t e e vote to ease conditions in the reserves market and lower the federal funds rate.
Before arriving at a policy recommendation, several more fundamental questions should be answered:
• W h y has the economy slowed?
• W a s the s l o w d o w n p r e d i c t a b l e early last y e a r
when the Fed was considering raising the federal
funds rate, or is the slowdown a surprise, resulting
f r o m unpredictable changes in private or policy
behavior since the funds rate began rising?
• If the slowdown is a surprise, what unanticipated
shifts in behavior account for it?
• Are unanticipated shifts in monetary policy partly
responsible?
• How do surprises in monetary policy affect the
economy?
• If the Fed were to lower the federal f u n d s rate
now, what would the effects be?
• What are the effects of not lowering the f u n d s rate
now?
4
Economic
Review
To address these questions and formulate a policy
recommendation the advisor needs a model that both
provides an unambiguous economic interpretation of
past data and forecasts future data well. The model
should be able to predict the economic consequences
of alternative current and future policy choices. Constructing such a model is difficult. Models with clear
e c o n o m i c interpretations tend to fit the data poorly,
and m o d e l s that forecast well usually are consistent
with a variety of economic interpretations with different p o l i c y i m p l i c a t i o n s . T h e d i c h o t o m y that s o m e
economists maintain between "policy evaluation"
models and "forecasting" models seems false, however. This article emphasizes that for most purposes one
would not be interested in the policy assessments of a
model that forecasts poorly.
.Forecasting and Policy Analysis
T h i s article is an attempt to d e v e l o p f o r e c a s t i n g
models for use in analyzing policy. The models adopt
the perspective that economic time series are generated by shocks w h o s e e f f e c t s on e c o n o m i c decisions
and, therefore, on data can be long-lasting. Shocks are
u n a n t i c i p a t e d e v e n t s that p r o v i d e new i n f o r m a t i o n
about the state of the e c o n o m y — f o r e x a m p l e , bad
(good) weather that produces crop failures (successes),
rapid increases in oil or raw materials prices that drive
up production costs, technological improvements that
make workers more productive, or sudden changes in
social attitudes toward government involvement in the
economy. At each point in time a variety of different
shocks impinge on the economy.
In interpreting data it is important to separate the
shocks that hit the economy from the economic mechanisms that propagate the shocks. Private decisionmakers
respond to shocks by altering their consumption, saving, production, and employment decisions. Policymakers also respond to shocks, changing taxes, government
spending, regulations, the supply of money, or shortterm interest rates. Social arrangements, like contracts,
technological constraints such as the time it takes to
build a new factory, and lags in implementing legislation or recognizing the need to change policy limit the
ability of individuals and policymakers to adjust quickly to shocks. Since these factors evolve slowly over
time, the propagation mechanisms will be fairly stable
and predictable. Shocks are unpredictable by definition.
A n e c o n o m i c m o d e l that s e p a r a t e s s h o c k s f r o m
propagation m e c h a n i s m s posits a set of behavioral
J u l y / A u g u s t 1995
Chart 1
U.S. Data, January 1990-May 1995
Federal Funds Rate
Percent
4
2
1990
1991
1992
1993
1994
1995
1994
1995
1994
1995
Total Reserves Growth
20
15
Annual
Percent
10
5
0
-5
1990
1991
1992
1993
Inflation
Annual
Percent
4
2
1990
1991
1992
1993
Source: Board of Governors of the Federal Reserve System and U.S. Department of Labor, Bureau of Labor Statistics.
Federal
Reserve Bank of Atlanta
Eco n o m ic Revie w 13
relationships for each type of d e c i s i o n m a k e r in the
e c o n o m y — c o n s u m e r s , businesses, and governments.
These relationships, which reflect the stable and predictable aspects of economic behavior, can be used to
forecast the m o d e l ' s e c o n o m i c variables. The differences between actual data and the model's predictions
are the shocks to behavioral relationships. 4 Forecasts
of future e c o n o m i c variables m a y simply reflect the
evolution of the propagation mechanism, assuming all
future shocks are zero. Alternatively, forecasts m a y
c o m b i n e the p r o p a g a t i o n m e c h a n i s m with a s s u m p tions about future shocks and the accompanying shifts
in behavioral relationships.
One convenient way to decompose economic time
series into anticipated and unanticipated components is
the vector autoregression (VAR) model. This model's
predictions are based on estimates of the historical dyn a m i c c o r r e l a t i o n s a m o n g v a r i a b l e s in the m o d e l .
Mechanically, the VAR consists of an equation for each
variable. T h e equations are estimated by regressing
each variable against lagged values of all the variables
in the model. T h e regression error in each equation
represents the change in that variable that cannot be
forecast from past information on all the variables, so
regression errors are forecast errors. Forecast errors average out to zero over time and, on the basis of information up to this period, are expected to be zero in the
next and all future periods. In general, forecast errors
are combinations of the shocks that shift behavioral relationships. An economic model allows the analyst to
interpret statistical forecast errors in terms of the underlying economically meaningful changes in behavior.
There are several ways to use the estimated VAR to
analyze data. As a pure forecasting model, the VAR
can generate predictions of variables beyond the period for which data are available. This is the sort of exercise m a n y c o m m e r c i a l forecasters undertake. T h e
VAR can also be used to break an observed data series
into two parts: (1) its predicted value, given information on actual data up to some date T, and (2) its unpredictable value, which depends on the actual shocks
hitting the economy after date T. The predicted value
reports what would have happened to the variable after date T if the v a r i a b l e e v o l v e d a c c o r d i n g to the
propagation mechanism alone.
This article has the modest goal of quantifying the
effects of unanticipated shifts in monetary policy behavior, so the economic models will be correspondingly modest. All of the models' economic interpretations
center on the behavior of demanders and suppliers in
the market for reserves. N o economic interpretation is
attached to behavior in other markets. Before estimat-
6
Economic
Review
ing the models, however, it is necessary to develop an
understanding of reserves market behavior.
Supply and Demand in the
Reserves Market
A n y empirical analysis of m o n e t a r y policy must
first settle on a particular money market to study. The
traditional analyses of Friedman and Schwartz (1963)
or Phillip Cagan (1972) emphasized relatively broad
monetary aggregates such as M1 or M2, which include
currency in circulation, d e m a n d deposits, and other
sorts of deposits held in financial institutions. To determine the role of money in the economy, it may be
appropriate to focus on such broad aggregates. After
all, households and businesses demand broad monetary aggregates to buy goods and services, so the demand for M1 or M 2 is a "final d e m a n d " representing
the portfolio behavior of only the private sector.
Unfortunately, the supply of broad aggregates has
two influences—Federal Reserve policy and banking
system behavior. When the Federal Reserve increases
reserves through open market operations, it increases
the banking system's ability to extend loans by "creating" deposits and increasing the private sector's liquidity. Of course, it is possible that an increase in the
supply of reserves by the Federal Reserve would elicit
no expansion of lending and deposits by the banking
system, leaving the broader aggregates unchanged. On
the other side, if banks have excess reserves they can
extend additional loans and expand M l or M2 without
any change in behavior by the Fed. Consequently, the
supply of broad aggregates combines the behavior of
the Federal Reserve with the behavior of the banking
system.
The purpose of this study is to isolate the effects of
monetary policy per se rather than the effects of money, so it is essential to focus on a m o n e y market in
which the Federal Reserve has control of the supply.
All the results in this article stem from changes in behavior in the reserves market. In that market banks
trade reserves and the federal f u n d s rate a d j u s t s to
equate the quantity supplied to the quantity demanded. 5 (A more formal description of behavior in the res e r v e s m a r k e t and h o w that m a r k e t is l i n k e d to a
broader money market is contained in Appendix A.)
The D e m a n d for Reserves. B e c a u s e reserves on
deposit at the Federal Reserve earn no interest, it is assumed that banks hold reserves largely because they
are required to. For certain classes of deposits, banks
J u l y / A u g u s t 1995
are required to hold a specified fraction of deposits as
reserves on deposit at the Fed or as vault cash. Consequently, the demand for reserves is a derived demand,
rather than a final demand. O n e way to think of the
derived demand is that reserves serve as an intermediate input in the "production" of loanable funds.
Demanders observe the cost of holding reserves (the
federal f u n d s rate), the prices of the goods they purchase, and their wealth when they make their demand
decisions. T h e quantity d e m a n d e d d e c r e a s e s as the
funds rate rises, and it increases as either the price level
or wealth increases. In principle the derived demand also depends on the prices of the banks' other factors of
production, such as wages of employees and interest
rates on bank assets. These other factor prices are ass u m e d not to be i m p o r t a n t and are e x c l u d e d f r o m
d e m a n d . 6 The d e r i v e d d e m a n d f o r r e s e r v e s c a n be
represented as
TRd = D(R, P, Y, / j) + ed,
(1)
where TRd is the quantity of total reserves demanded.
D(R, P, Y, I_{) is n o t a t i o n that r e p r e s e n t s h o w the
quantity demanded depends systematically on current
and past economic variables. R is the current federal
funds rate, P is a current aggregate price level like the
consumer price index, and Y is current real income or
wealth (in the empirical work industrial production
serves as a proxy). 7 / , reflects past information upon
which demand is also assumed to depend. The term ed
represents a shock that shifts the demand for reserves
unexpectedly. By construction, the shock reflects
changes in the demand for reserves that cannot be attributed to changes in R,P, Y, or past economic conditions.
Just as the supply of broad aggregates c o m b i n e s
policy behavior and bank behavior, so too the demand
for reserves combines the behavior of banks with that
of final money demanders. The comingling of behavior would present a problem if the focus of this study
were on isolating which shifts in demand for reserves
arose from the two sources. To derive the effects of an
unanticipated shift in supply, however, it is sufficient
to estimate a demand for reserves that does not shift in
the experiment of shifting the supply curve. To do so,
all that is needed is a systematic relationship between
the determinants of d e m a n d and the quantity of reserves.
The S u p p l y of Reserves. The supply of total reserves is composed of borrowed reserves plus nonborr o w e d r e s e r v e s . 8 T o m e e t t h e i r l e v e l of r e q u i r e d
reserves, banks in the United States can borrow from
F e d e r a l Reserve B a n k of Atlanta
the Federal R e s e r v e ' s discount window, where they
are charged the discount rate. Typically banks are instructed to try first to obtain reserves f r o m sources
other than the d i s c o u n t w i n d o w , and e a c h R e s e r v e
Bank discount officer must verify that loans are extended only for "appropriate" reasons. 9 A discount officer m a y pressure banks whose access to the window
is deemed inappropriate to pursue other sources of reserves. Thus, discount w i n d o w borrowing carries an
additional implicit cost associated with moral suasion,
making the actual cost to banks the discount rate plus
such nonpecuniary costs.
Nonborrowed reserves are simply the portion of reserves provided to depository institutions through any
means other than the discount window. The most important source of changes in nonborrowed reserves in
the United States is open market operations conducted
by the Fed. Open market operations are purchases or
sales by the Fed of U.S. government securities. When
the F e d b u y s s e c u r i t i e s it p r o v i d e s r e s e r v e s to the
banking system; when it sells securities it extracts reserves f r o m the banking system.
Since the end of 1982 the Fed has followed a policy
of indirectly targeting the federal f u n d s rate, meaning
that it adjusts the supply of reserves to achieve a targeted equilibrium interest rate in the reserves market. 1 0
The Fed changes the target level of the funds rate in response to its expectation about levels of output, unemployment, and inflation—the e c o n o m i c conditions it
cares about. Future economic conditions are forecast
using all available information. Although the Fed eventually sees data on current output, unemployment, and
inflation, when it sets the target funds rate in a given
month it knows the previous month's values of these
variables but not the current m o n t h ' s . B o n d , stock,
commodity, and foreign exchange markets operate almost around the clock, and prices f r o m these markets
are available continuously. From current financial data
and all past data, the Fed tries to glean information on
the future values of the variables it cares about and
hopes to influence.
Combining the indirect targeting of the f u n d s rate
with the timing in which information becomes available
to the monetary authority leads to the specification of the
supply of reserves, or the authority's "reaction function":
TRs = S(R,a,I_l)
+ es,
(2)
where TRS is the quantity supplied of total reserves.
S (R, Q, 1 j) represents the systematic response of supply to past and currently observable economic conditions. R is the funds rate, Q reflects the high-frequency
Eco n o m ic Revie w
7
information the monetary authority observes within
the month, and I , is past information that influences
the supply of reserves. es represents shifts in policy beh a v i o r that are u n a n t i c i p a t e d by the private sector.
Monthly realizations of es are monetary policy shocks
that shift the supply of reserves.
Equation (2) is an abstract representation of policy
behavior. N o monetary authority literally behaves as
equation (2) depicts. The systematic part of the reaction function captures how policy responds on average
to current and past e c o n o m i c conditions. W h e n this
m o n t h ' s f u n d s rate begins to rise above its target level,
the monetary authority injects reserves into the econom y to bring it back to its target. Variables represented
by £2 are informational rather than behavioral: they appear in the supply function because they contain information about current and expected future values of the
variables the monetary authority responds to, not because the authority necessarily wants to influence or
respond to the variables in Q specifically. The monetary authority combines the information contained in
current and past observable data—£2 c o m b i n e d with
/ j—to construct forecasts of the variables important
to its decisions. The response of policy to current and
past information, therefore, can be interpreted as a response to forecasts of the variables that concern the
policy authority.
Chart 2
The Reserves Market—Open Market Purchase
Equilibrium in the Reserves Market. Banks can
be either net suppliers or net demanders of reserves.
Overnight loans of reserves from one bank to another
are called federal funds and bear the overnight federal
funds rate. Arbitrage implies that borrowed and nonborrowed reserves must be perfect substitutes from the
perspective of d e m a n d e r s , so the federal f u n d s rate
m u s t equal the discount rate plus the n o n p e c u n i a r y
costs of borrowing at the discount window. One implication of the assumption that rate-of-retum differences
between borrowed and nonborrowed reserves are arbitraged away is that the federal funds rate changes if and
only if total reserves change: the composition of total
reserves between the two components is irrelevant.
The interaction of supply and d e m a n d in the reserves market is s u m m a r i z e d in Chart 2. 12 An open
market purchase of securities increases the supply of
nonborrowed (and total) reserves, shifting the supply
curve to the right from SQ to SQ'. To induce banks to
hold the higher level of reserves, the cost of doing so
must fall from RQ to / ? r 1 3 The decline in the short-term
interest rate from a monetary policy expansion, dubbed
"the liquidity effect," is the first step in the transmission of monetary policy to the macroeconomy.
Empirical work that seeks to quantify the effects of
monetary policy must find an empirical analog to the
textbook exercise depicted in Chart 2. The thought experiment shifts the supply of reserves, holding the dem a n d curve f i x e d . In the e c o n o m y both c u r v e s are
shifting around, so actual monthly data on the f u n d s
rate and total reserves combine instances in which the
supply curve shifts with ones in which the d e m a n d
curve shifts. If, for example, the correlation between
total reserves and the funds rate is close to zero at least
three inferences are possible: (1) demand is either very
sensitive to interest rates (nearly flat) or very insensitive (nearly vertical), and supply shifts around a stable
demand; (2) supply is very responsive or unresponsive
to interest rates, and d e m a n d shifts around a stable
supply; (3) supply and demand shifts by approximately
NBR = Nonborrowed Reserves
BR = Borrowed Reserves
TR = Total Reserves
8
Economic
Treating the policy reaction function as composed
of a regular, predictable part, S(R,Q.,I_,), and a random, unpredictable part, e\ is necessary to conduct a
thought experiment that shifts supply, holding all else
constant. Along with the specification of private and
policy behavior in the model comes a specification of
the information upon which the economic players base
their decisions. Equation (2) introduces the r a n d o m
term in policy behavior as a tool for describing an environment in which private decisionmakers and polic y m a k e r s interact without certain k n o w l e d g e of the
information and incentives facing each other."
Review
J u l y / A u g u s t 1995
equal amounts, and the negative correlations induced
by supply shifts canceled out the positive ones generated by demand shifts. Each of these inferences makes
identifying assumptions about the behavior that generated the data. After describing the data used to estimate the models, the following section of this article
looks at the data through the lenses of two different,
simple assumptions about supply behavior. The discussion shows that the inferences drawn about the effects of m o n e t a r y policy u n d e r the t w o behavioral
assumptions seem to be inconsistent with widely held
beliefs about the dynamic impacts of monetary policy.
The Data Series
Choosing the sample period requires an unpleasant
trade-off. A longer sample period is likely to be more
informative, as it reflects changes in policy and private
behavior in the face of a wider variety of e c o n o m i c
events. For example, data f r o m 1960 to 1994 would report changes in behavior in response to large increases
in military spending (the Vietnam War), big m o v e ments in relative prices (oil price increases), and dramatic swings in inflation. But the longer the period, the
more likely it is that policy behavior itself displays discrete and unpredictable shifts. F o l l o w i n g the steady
rise in inflation during the 1970s, for example, in October 1979 the Fed shifted policy dramatically by focusing on monetary aggregates and allowing interest rates
to fluctuate more. In late 1982 the Fed moved toward
smoothing interest rates. W h e n monetary policy operating procedures and policy objectives are shifting over
time, it takes a while for the private sector to learn
about policy. Economic models are not very good at
capturing how people learn, and the models produce
unreliable forecasts during the learning process.
This article trades the variety of economic experiences for a stable policy environment. All the results
in the article c o m e f r o m estimating a vector autoregression (VAR) using monthly data f r o m D e c e m b e r
1982 to December 1994. This is a period over which
the Fed indirectly targeted the f u n d s rate (see Marvin
G o o d f r i e n d 1991), the inflation process was stable,
and financial markets had been deregulated, producing
a fairly stable policy environment.
The variables to be included in the estimated model
were chosen to represent the quantity and price in the
reserves market (total reserves and the federal f u n d s
rate), the variables reflecting the goals of m o n e t a r y
policy ( c o n s u m e r prices, industrial p r o d u c t i o n , and
Reserve B a n k of Atlanta
Digitized Federal
for FRASER
u n e m p l o y m e n t ) , and two variables that the Fed can
observe daily that contain information about financial
market participants' expectations of current and future
economic conditions (the ten-year U.S. Treasury bond
yield and a c o m m o d i t y price index). 1 4 The s y m b o l s
used to represent variables in the charts and tables are
reported in Box 1.
.Extreme Assumptions about Policy
Behavior Produce Inconsistencies
When supply and demand are drawn as in Chart 2,
with demand sloping d o w n w a r d and supply sloping
upward, it is difficult to sort supply f r o m demand effects in data on reserves and the funds rate. Shifts in
each of the curves generate changes in both reserves
and the funds rate, so it is untenable to claim that all
changes in reserves or f u n d s rates are due to supply
shifts or, alternatively, that all changes are due to demand shifts. Such straightforward interpretations of
the data are possible only under extreme maintained
assumptions about behavior. This section explores the
implications of two sorts of extreme assumptions commonly made in analyses of monetary policy. The first
is that the supply of reserves is perfectly inelastic with
respect to the interest rate (Chart 3). In this case, the
supply schedule is vertical and all changes in reserves
must arise f r o m shifts in the supply curve. Any correlation between the t w o variables necessarily occurs
because a change in the supply of reserves causes the
change in the funds rate along a fixed demand curve.
The second sort of extreme assumption is that the supply curve is perfectly elastic with respect to the f u n d s
rate ( C h a r t 4). A f l a t s u p p l y c u r v e i m p l i e s that all
changes in the interest rate are due to shifts in the supply
schedule. These shifts induce m o v e m e n t s along the
demand curve and changes in the quantity of reserves
demanded.
Box 1
Notation
TR
R
P
Y
U
RIO
CP
= total reserves
= federal f u n d s rate
= c o n s u m e r price index
= industrial production
= unemployment
= ten-year U.S. Treasury bond yield
= c o m m o d i t y p r i c e i n d e x d e n o m i n a t e d in U . S .
dollars
Eco n o m ic Revie w
9
to past information. The authority's reaction function
can be expressed abstractly as
Chart 3
The Reserves Market with Inelastic Supply—
Open Market Sale
Federal
A shift in the supply of reserves is equivalent to a change in total reserves.
Model T R : A Perfectly Inelastic Supply of Res e r v e s . M u c h traditional e m p i r i c a l w o r k r e g r e s s e s
some variable of interest on current and lagged values
of a money stock and interprets the coefficients as reporting the effects of m o n e y or monetary policy on
that variable. Andersen and Jordan (1968) present one
p r o m i n e n t e x a m p l e of this style of w o r k . T h e y regressed G N P against the m o n e y stock and the fiscal
deficit and interpreted the estimated c o e f f i c i e n t s as
meaning that the effects of monetary policy are bigger,
more predictable, and faster than are the effects of fiscal policy. Cagan's (1972, chap. 7) classic work on the
liquidity effect is another important example. He regressed an interest rate on current and past money and
interpreted the coefficients as measuring the dynamic
effects of money on interest rates. 15
Empirical inferences based on such regressions assume that all changes in m o n e y arise f r o m shifts in
supply, rather than m o v e m e n t s along a fixed supply
curve induced by shifts in demand. In the context of the
reserves market the inferences assume that changes in
reserves are due entirely to shifts in monetary policy,
with no role for changes in policy that accommodate
m o v e m e n t s in demand. In terms of equation (2) and
the VAR model, an inelastic supply implies that the
monetary authority does not respond to the funds rate
or other current information, although it m a y respond
1 0
Economic Review
TRS = 5(/_j) + es.
(2-TR)
The assumption that supply is inelastic is simple
and appealing. It is also one to which many economists
are a c c u s t o m e d , as m o s t t e x t b o o k s about m o n e t a r y
economics also make the simplifying assumption (see,
for example, Don Patinkin 1965, David E.W. Laidler
1985, or Frederic S. Mishkin 1992). It would be convenient if it could be assumed that supply is vertical, because the assumption implies that it is not necessary to
model demand and supply: the quantity is fixed by policy and, given a quantity, the equilibrium interest rate
is completely determined by demand.
B e f o r e p r o c e e d i n g with i n f e r e n c e s based on the
simplifying assumption about policy behavior it is important to check whether the assumption's implications
are reasonable. In order to do so, equation (2-TR) is
e m b e d d e d in a VAR to f o r m Model TR. The model
can be used to estimate the d y n a m i c impacts of an
unanticipated decline in total reserves under the maintained assumption that the supply is inelastic. The reasonableness check is whether the results conform with
consensus views about the qualitative effects of monetary policy that are summarized in points (a)-(d) earlier in the article (on page 2).
M o d e l T R can b e used to m i m i c the theoretical
thought experiment of a one-time unanticipated monetary policy contraction. The model identifies the experiment with a one-period decline in es in equation
(2-TR), holding all else fixed initially, which corresponds to the inward shift in the supply of reserves depicted in Chart 3. The qualitative effects of monetary
policy, according to Model TR, are simply the model's
predictions of the time paths of all the variables following the surprise contraction.
Chart 5 reports the dynamic responses of all seven
variables over thirty-six months to an unanticipated 1
percent decline in reserves. In the absence of the decline in reserves, the variables would lie on the zero axis, so all movements in the variables are attributable to
the unanticipated change in reserves. The solid lines are
point estimates, and the dashed lines are one-standarddeviation bands. When both dashed lines fall above or
below zero, the response of that variable is statistically
significant. 1 6 Many of the responses look reasonable.
Prices, output, and commodity prices fall throughout
the horizon. U n e m p l o y m e n t rises with a lag of six
months, although it falls significantly for one month
near the beginning. Other responses are less plausible.
J u l y / A u g u s t 1995
At impact, the decline in reserves lowers the f u n d s
rate, so there is no liquidity effect. Rates do rise significantly after one month, consistent with a delayed liquidity effect. The brief increase in the long-term bond
yield is consistent with the expected increase in the
short-term interest rate o v e r the s u b s e q u e n t several
months.
This pattern of responses raises doubts about the
identifying assumption that the supply of reserves is
perfectly inelastic. Most economists believe the funds
rate adjusts immediately to clear the reserves market
after a supply shock, with output and prices adjusting
gradually to the lower level of reserves. The results
make it seem that the demand curve is upward sloping. An immediate and significant drop in prices and
output reduces the quantity of reserves d e m a n d e d at
any given funds rate, having the effect of shifting the
demand curve in Chart 3 inward. For both the equilibrium funds rate and the level of reserves to decline, as
they do in Chart 5, demand cannot be downward sloping. Although some responses seem to be consistent
with c o m m o n beliefs about monetary policy effects,
the behavioral implications of the patterns of responses in this chart are implausible.
M o d e l R: A P e r f e c t l y E l a s t i c S u p p l y o f R e serves. Over the past twenty-five years it has been far
more c o m m o n for the Fed to target the federal funds
rate than some measure of reserves. 1 7 If over a period
of a month the monetary authority were to essentially
provide reserves passively to a c c o m m o d a t e shifts in
demand, then the supply of reserves would be perfectly elastic. To accommodate shifts in demand the monetary authority makes the supply of reserves infinitely
responsive to changes in current economic conditions.
Doing so amounts to making the funds rate unresponsive to current information, and the authority's "reaction function," equation (2), becomes
R = S(I_l) + e°.
(2-R)
Under this assumption about policy behavior, every unanticipated change in the f u n d s rate represents
a shift in the supply schedule. A m o n g financial market o b s e r v e r s and b u s i n e s s j o u r n a l i s t s , this view is
widespread, as implicitly every increase in the f u n d s
rate is treated as a monetary policy contraction. Many
researchers have also assumed supply is elastic. Sims
(1980b, 1992) and Ben S. Bernanke and Alan S. Blinder
(1992), for e x a m p l e , interpret m o v e m e n t s in m a c r o
variables f o l l o w i n g an unanticipated increase in the
short-term interest rate as reflecting the dynamic impacts of a contractionary monetary policy shock.
Federal Reserve B a n k of Atlanta
Chart 4
The Reserves Market with Elastic Supply—
O p e n Market Sale
Federal
A shift in the supply of reserves is equivalent to a change in the federal
funds rate.
The abstract representation of policy behavior in
equation (2-R) also comes close to reflecting the Fed's
own views of its behavior. Policy debates are couched
in terms of changes in the f u n d s rate. M a n y of the
models used in the Federal Reserve System to simulate the effects of alternative policy scenarios treat the
f u n d s rate as affecting current private behavior, but
other variables do not affect the f u n d s rate contemporaneously. This is precisely the assumption embedded
in equation (2-R). With financial market participants,
e c o n o m i c journalists, researchers, and the monetary
authority all treating an equation like (2-R) as representing policy behavior, the identifying assumption that
the supply of reserves is perfectly elastic is clearly important as well as widespread. Model R ' s implications
for the dynamic impacts of unanticipated changes in
monetary policy, therefore, are especially interesting.
Unfortunately, treating changes in the f u n d s rate as
shifts in the supply of reserves does not lead to reasonable results. Chart 6 reports responses to a surprise 25
basis point increase in the funds rate. 18 Interpreting the increase as an unanticipated monetary policy contraction
implies some strange policy effects. T h e price level
and output rise strongly for about six months, while
unemployment is significantly lower for a year. Eventually, however, the interest rate increase affects the
economy as most people would predict. The sharp rise
Eco n o m ic Revie w
11
Chart 5
R e s p o n s e s t o U n a n t i c i p a t e d 1 Percent D e c l i n e in Reserves
(Supply Perfectly Inelastic)
Total Reserves
0.4
0
—'
J"*/
-1.2
12
18
24
30
36
130
36
24
30
36
24
30
36
Federal Funds Rate
0.18
Percentage
Points
0
1
12
-0.18
1
1
1
18
1
i-
24
-t
1
Consumer Prices
Percent
12
18
24
Industrial Production
Percent
12
18
Unemployment
0.06
Percentage
Points
y
0
-0.06
-
y
vi
—
*—»-
12
18
Long-Term Bond Yield
0.14
Percentage
Points
^
0
-0.14
-
-
— X
1
1——1——1—— r — — 1
12
1
1
18
1——1
!
24
1
1
1
30
1
36
Commodity Prices
Percent
12
Economic
24
30
36
Months after Shock
Review
July/August 1995
Chart 6
R e s p o n s e s t o U n a n t i c i p a t e d 2 5 Basis P o i n t I n c r e a s e in F u n d s R a t e
( S u p p l y P e r f e c t l y Elastic)
Total Reserves
1.2
Percent
0
i
-1.2
12
18
24
30
36
24
30
36
24
30
36
24
30
36
1—
24
30
36
24
30
36
Federal Funds Rate
0.36
Percentage
Points
q
-0.36
12
18
Consumer Prices
Percent
12
18
24
Industrial Production
Percent
12
18
Unemployment
0.14
Percentage
Points
_
-
o
- 0 . 0 7 r ^ T ^ ^ ^ r ^ v - r - — f -——f——I—
12
18
Long-Term Bond Yield
0.36
dPercentage
„
Points
0.18 —
g
-I
-0.18
Reserve Bank of Atlanta
Digitized Federal
for FRASER
12
18
Commodity Prices
Months after Shock
Eco n o m ic Revie w
13
in long-term interest rates for a f e w months is consistent with the financial press's view that the funds rate
and bond prices m o v e in opposite directions in the
short run. The responses to a f u n d s rate increase are
sharply at odds with most e c o n o m i s t s ' beliefs about
policy effects, though: although most economists believe monetary policy affects economic activity with a
lag, few would argue that the short-run effects are opposite to the longer-run impacts.
In spite of these i n c o n s i s t e n c i e s , c h a n g e s in the
f u n d s rate are widely v i e w e d as indicating shifts in
policy. Thus, conducting a detailed analysis of the implications of Model R is worthwhile. Chart 7 reports
Model R ' s predictions of the effects of monetary policy shocks on the time paths of the funds rate, inflation,
output growth, and unemployment from January 1990
to D e c e m b e r 1994. 1 9 T h e solid lines are the actual
paths of the variables, and the d a s h e d lines are the
paths the v a r i a b l e s w o u l d h a v e f o l l o w e d had there
been no unanticipated changes in the funds rate over
the period. In terms of equation (2-R), the solid lines
correspond to using S(I_,) + es as the path for the f u n d s
rate and the d a s h e d lines c o r r e s p o n d to using only
£ ( / , ) , setting es equal to zero in each period.
This exercise provides one statistically based interpretation of statements that monetary policy is "tight"
or "loose." By this interpretation, policy is tight when
the f u n d s rate is higher than would be predicted on
the basis of past information alone. 2 0 Tight policies
emerge when es is positive. When the actual funds rate
is greater than the rate without funds rate surprises, as
it was in 1990 and throughout 1994, the decomposition suggests that the surprise changes made the funds
rate higher than it would otherwise have been. Under
the maintained assumption that the supply of reserves
is flat, this result coincides with interpreting these as
periods when policy was tight, shifting supply upward
unexpectedly and producing contractionary monetary
p o l i c y s h o c k s . In c o n t r a s t , the p e r i o d f r o m 1992
through 1993 was one when policy was loose and the
funds rate was lower than would have been predicted
using past information alone. Negative values of es
imply loose policy.
The chart lends support to those w h o argue that
tight monetary policy lowers inflation and output and
raises unemployment. According to Chart 6, an unanticipated increase in the f u n d s rate lowers the price
level after two years, lowers output after one year, and
raises unemployment after eighteen months. This timing is borne out by Chart 7. By this analysis, policy
was tight until early 1991, and inflation was lower
than expected until mid-1993; policy was loose begin-
1 4
Economic
Review
ning in 1992, and inflation was higher than expected
in 1994. The patterns show up more strongly in output
growth and unemployment. 2 1
U n d e r the m a i n t a i n e d a s s u m p t i o n that supply is
perfectly elastic, shocks to the monetary authority's reaction function appear to be an important source of
fluctuations in output and unemployment over the entire sample. The first column of Table 1 reports the
percentage of unanticipated fluctuations in variables
attributable to surprise c h a n g e s in the f u n d s rate in
previous periods. This percentage calculates the total
effect of the changes attributable to policy shocks (def i n e d in M o d e l R as surprise c h a n g e s in the f u n d s
rate), including the systematic, predictable response of
private behavior to the policy shocks and of policy behavior to the private sector's response.
By a s s u m p t i o n all u n a n t i c i p a t e d c h a n g e s in the
f u n d s rate are p o l i c y s h o c k s , so in the first m o n t h
those shocks account for 100 percent of the funds rate
fluctuations, as shown in the second panel of the table.
Even one to three years later, past m o n e t a r y policy
shocks continue to account for the majority of f u n d s
rate fluctuations. Taken literally, the result means that
the a s s u m e d elastic supply of reserves implies that
most changes in the funds rate arise from shifts in the
supply function. In contrast, policy shocks account for
a much smaller fraction of fluctuations in the quantity
of reserves: as shown in the TR panel of the table, 0.8
percent in the first month and m o r e than 25 percent
over horizons of a year or more. 2 2 Monetary policy
shocks account for large percentages of long-run fluctuations in o u t p u t , u n e m p l o y m e n t , and c o m m o d i t y
prices but for only a small fraction of the fluctuations
in c o n s u m e r prices. T h e results in the table c o n f i r m
that the close association between policy shocks and
economic activity over the 1990-94 period (reported in
Chart 7) appears to hold over the entire sample.
Chart 7 certainly seems consistent with the views of
policy effects appearing in the press. Under the assumption that supply is flat, policy shocks have important and predictable effects on m a c r o variables. The
effects kick in six months to two years after the surprise shift in policy. To an economist, however, the
perverse results reported in Chart 6 are persuasive that
unanticipated changes in the f u n d s rate do not reflect
surprise shifts in the supply of reserves alone. It appears that unanticipated changes in the funds rate are
not pure monetary policy shocks. It is not hard to think
of plausible assumptions about policy behavior that
imply that u n a n t i c i p a t e d c h a n g e s in the f u n d s rate
stem f r o m a combination of monetary policy shocks
and other behavioral shocks. Suppose that equation
J u l y / A u g u s t 1995
Chart 7
I n f l u e n c e o f U n a n t i c i p a t e d C h a n g e s in F u n d s R a t e
Actual
Less influence of unanticipated
changes in funds rate
Federal Funds Rate
Percent
1990
1991
1992
1993
1994
1993
1994
1993
1994
1993
1994
Inflation
Annual
Percent
1990
1991
1992
Industrial Production Growth
Annual
Percent
1990
1991
1992
Unemployment
Percent
1990
Federal Reserve Bank of Atlanta
1991
1992
Eco n o m ic Revie w
15
Table 1
The Role of Policy Shocks in A c c o u n t i n g for Fluctuations
Percentage of Forecast Error Variance Due to Policy Shock
Variable
Explained
Impose TRS
Perfectly Elastic
Model 1
Model 2
Model 3
TR:
1 st month
1 year
2 years
3 years
0.8
26.1
29.2
27.9
20.5
8.2
9.1
7.7
86.9
17.2
12.8
10.3
0.8
0.9
3.3
4.4
R:
1 st month
1 year
2 years
3 years
100.0
58.4
49.1
51.7
54.2
24.9
19.9
18.0
7.4
11.3
10.4
9.6
0.2
4.1
7.8
5.8
P:
1st month
1 year
2 years
3 years
0.6
2.4
2.3
5.5
0.0
4.8
2.9
3.9
0.0
5.3
5.7
8.1
0.0
2.7
4.8
5.4
V:
1st month
1 year
2 years
3 years
14.6
11.5
26.9
33.3
0.0
17.2
23.3
21.9
0.0
18.2
24.2
20.6
0.0
11.3
7.9
7.2
U:
1st month
1 year
2 years
3 years
3.9
16.5
19.6
31.5
0.0
0.6
4.7
10.3
0.0
1.9
7.6
9.0
0.0
0.9
1.4
1.8
RIO:
1st month
1 year
2 years
3 years
16.7
8.9
10.1
14.8
0.0
4.9
4.5
4.4
1.1
1.4
1.4
1.4
0.5
5.1
5.6
5.0
CP:
1st month
1 year
2 years
3 years
7.4
5.7
21.6
26.2
0.0
13.6
15.2
12.7
0.5
9.7
11.4
9.5
88.5
40.4
25.3
20.8
16
Economic
Review
July/August 1995
(2-R) understates the amount of information upon which
the Fed bases its choice of the funds rate target. Then the
correct specification of the reaction function is
R = S(I_ j, X) + es,
where X represents the information known by the Fed
that is not contained in past values of the variables in
the model. Further suppose that the information contained in X suggests that future inflation m a y rise. The
Fed's response to the news in X might be to contract
the supply of reserves and allow the funds rate to rise.
Such an endogenous response to economic conditions
does not represent the thought experiment of shifting
the supply curve, holding all else fixed. In this example, the news about future inflation violates the "holding all else fixed" assumption. Reaction function (2-R)
then c o n f o u n d s systematic e n d o g e n o u s responses of
policy with shifts in the supply curve that hold all else
fixed, c o n t a m i n a t i n g the policy shock identified by
Model R. 2 3 The story, however, m a y be able to rationalize the perverse short-run responses of prices, output, and unemployment in Chart 6.
The data imply that the only way to maintain the
a s s u m p t i o n that the s u p p l y of reserves is p e r f e c t l y
elastic within a month and reconcile the perverse results in Chart 6 with widely held views of monetary
policy effects is to tell a complicated story. The story
reverses the usual causal ordering, where current policy causes future economic developments. According
to the story, in M o d e l R e x p e c t e d f u t u r e e c o n o m i c
conditions cause current policy shocks. Such a story is
unappealing for two reasons. First, it requires that one
step outside the economic model to interpret the data.
Second, it hinges critically on assumptions about unobservable and untestable notions such as the policy
authority's expectations of future inflation.
Good policy analysis should strive for higher standards than storytelling can hope to meet. It appears that
imposing extreme assumptions on the interest elasticity
of the supply of reserves generates measures of monetary policy shocks that do not do what theory predicts.
To avoid imposing the supply elasticity it is necessary
to build a model of reserves behavior that allows the
supply and demand elasticities to be estimated directly.
With separate estimates of supply and demand it may
be possible to trace out the effects of shifting supply,
holding all else fixed. Once able to make direct connections between current policy actions and future economic developments, the policy advisor can dispense
with telling stories that rely on expected future events
causing current monetary policy.
e dFRASER
e r a l R e s e r v e B a n k of Atlanta
Digitized Ffor
Estimating Behavior in the
Reserves Market
The rest of the article reports results f r o m three other models of the economy based on different assumptions about policy behavior and about the information
upon which financial market participants, who determine bond and commodity prices, base their decisions.
All differences among the models stem f r o m assumptions a b o u t i n t e r a c t i o n s a m o n g v a r i a b l e s w i t h i n a
month. The models m a k e the same assumptions that
Models TR and R did about how current variables depend on the past. As a consequence, the assumptions
underlying all five models differ only in how a monetary policy shock is defined and how that shock can
affect financial variables in the month.
All three remaining models assume that the equilibrium quantity of reserves and level of the f u n d s rate
are determined simultaneously by the interaction of
supply and demand, an advance over Models TR and
R. In addition, all the models build in the assumption
that goods market variables—the price level, output,
and unemployment—are determined in sectors of the
economy that do not respond within the month to policy shocks. This assumption is not very controversial.
Most economists believe that firms do not adjust their
pricing, production, or employment decisions immediately in response to unanticipated changes in monetary
policy. The models assume no response in these sectors within the month, and goods markets' responses
in subsequent m o n t h s are not restricted in any way.
This assumption implies that all e c o n o m i c decisionmakers respond to past information in ways that the
economic model does not restrict.
In terms of the flow of information within the month,
all three models assume that demanders of reserves observe the cost of holding reserves (the funds rate), the
prices of the goods they purchase (the price level), and
their own wealth (output). Within the month the monetary
authority does not observe information about the goods
market variables, the price level, output, and unemployment, which it hopes to influence. Instead, it bases its
supply decision on the current funds rate and current information from financial markets, as assumed in equation
(2). Differences across the models are summarized by
• Model 1: Fed responds to /?, RIO, and CP; financial markets respond to P, F, U.
• M o d e l 2: F e d r e s p o n d s to R and CP; f i n a n c i a l
markets respond to P, Y, U, and R.
• M o d e l 3: Fed r e s p o n d s to R and CP; financial
markets respond to P, Y, U, and R and TR.
Eco n o m ic Revie w
17
Another way to summarize the differences across
the models is that Model 1 treats reserves market variables as determined before financial market variables.
Models 2 and 3 allow reserves market and financial
market variables to be determined simultaneously, but
in slightly different ways.
E a c h of the m o d e l s f r e e l y e s t i m a t e s the interest
elasticity of the supply of reserves. It is possible, therefore, for either of the t w o s c h e m e s that i m p o s e extreme elasticities—Models T R or R — t o end up being
estimated as the model of reserves market behavior.
Table 2
Model 1
Reserves Market
Demand:
137.88 TR? = -2.68/? + 148.53 P+ 75A5Y+
(18.99)
(.89)
(66.79)
(28.11)
Supply: 95.85TR S = 4.91 R(25.82)
(.57)
1 . 9 3 R W - 1 3 . 0 2 C P + es
(.42)
(6.26)
Financial Market Variables
4.67/?70 = 8 9 . 2 6 P + 3 6 . 6 6 V - .79U
(.28)
(66.81) (24.69) (.79)
+eRW
7 1 . 5 6 C P - - 3 . 3 3 P + 8 . 9 4 V - . 6 9 U + . 9 6 R 1 0 + ecp
(4.29)
(4.38) (25.56) (.79)
(.40)
Goods Market Variables
7 7 8 . 9 5 P = .51 V - 1 . 2 5 L / + ep
(46.72) (6.66)
(.74)
290.05 V = - 3 . 5 4 1 7 + e v
(17.40)
(.76)
8.54
(-51)
eu
Log likelihood value = 3283.673
LR test of overidentifying restrictions: x 2 (5) = 13.032,
significance level = .023
LR test with small-sample correction: x 2 (5) = 9.001,
significance level = .109
Akaike criterion = 3237.673
Schwarz criterion = 31 70.180
18
Economic
Review
e
d
(Appendix B provides econometric details about how
the models are estimated.)
Model 1: A "Partial Equilibrium"
View of the Economy
Standard textbook treatments of m o n e t a r y policy
adopt the view that a change in policy affects the rest
of the economy only with a lag. In the context of the
model, this perspective implies that within the month
demanders take prices and output as given, while the
Fed takes financial market variables as given. These
assumptions underlie the partial equilibrium analyses
of reserves market behavior that are taught in college
economics courses.
Table 2 reports the e s t i m a t e d c o e f f i c i e n t s of the
model. 2 4 The elasticity of demand with respect to the
interest rate is negative, and the price and output elasticities are positive, as theory would predict. The estimated supply equation also has appealing properties.
An unanticipated increase in the funds rate brings forth
an increase in the supply of reserves to push the funds
rate back down. This reaction is precisely what one
would expect under a policy that targets the funds rate.
In addition, surprise increases in long-term interest
rates or c o m m o d i t y prices, w h i c h m a y p o r t e n d increases in expected inflation, induce the Fed to contract the supply of reserves.
The estimated demand and supply curves are drawn
in Chart 8. Demand is estimated to be fairly inelastic.
To conduct the experiment of shifting the supply schedule along a fixed demand curve in Chart 8, the shock
in the policy equation, es, is decreased for one month.
The contractionary policy shock shifts supply to the
left. Because monetary policy is assumed to affect the
economy with a one-month lag, total reserves and the
funds rate do not enter the equations for the remaining
f i v e variables. T h e partial e q u i l i b r i u m e x p e r i m e n t ,
therefore, changes only reserves and the f u n d s rate in
the month the shock occurs.
T h e D y n a m i c I m p a c t s of M o n e t a r y P o l i c y
Shocks. The dynamic responses of all seven variables
to a one-time unanticipated contraction in monetary
policy that raises the f u n d s rate initially by 25 basis
points are reported in Chart 9.25 Point estimates appear
as solid lines and one-standard-deviation bands appear
as dashed lines. 26 The leftward shift in supply has the
immediate effect of moving the economy up the initial
demand curve, raising the funds rate, and lowering the
quantity of reserves. This liquidity effect lasts almost a
July/August 1995
year before the funds rate begins to fall significantly.
The price level rises slightly initially, though the increase is substantially smaller and shorter-lived than it
was under the assumption that the supply of reserves
is perfectly elastic (Chart 6). After a couple of months
prices begin to fall and continue to fall over the next
f e w years.
changed for a little over a year after the policy shock,
then it rises significantly. Financial variables, which
are not permitted to react immediately to the policy
shock, decline a month after the shock. These responses are interpretable as consistent with the decline in
the price level and the eventual decline in short-term
interest rates.
Output displays none of the perverse responses appearing in Chart 6. It declines throughout the forecast
horizon and is significantly l o w e r a f t e r about three
months. The sharpest drop in output occurs only five
m o n t h s after the contractionary policy shock. These
results suggest that the lag effects of monetary policy
are substantially shorter than many people believe. 2 7 It
takes only a f e w m o n t h s for policy shocks to affect
p r i c e s and o u t p u t m e a s u r a b l y , w h e r e a s in C h a r t 6
unanticipated funds rate increases do not affect these
variables in the expected ways for twelve to eighteen
months. Thus, the identification of policy shocks influences inferences about the lags with which policy
affects the economy. Unemployment is essentially un-
Past policy shocks have been an important source
of unforecastable changes in output but a surprisingly
unimportant source of m o v e m e n t s in the price level
(Table 1, column 2, panels 3 and 4), according to the
m o d e l . Unanticipated shifts in m o n e t a r y policy account for a fairly large percentage of fluctuations in
commodity prices but not in long-term interest rates.
The model specifies supply-and-demand behavior
in the reserves market only. Lacking a model of the
rest of the economy, it is not possible to infer from the
results exactly how the policy effects are transmitted
into movements in prices, output, and unemployment.
It is possible, however, to take a closer look at the dynamics of the reserves market. Each combination of
Chart 8
Estimated Supply and Demand Schedules in the Three Models
Model 1
R
Model 2
Model 3
12.5
Demand
Supply
Demand
Supply
Demand
Supply
R = Federal Funds Rate (percent)
TR = Total Reserves (billions of dollars)
Federal Reserve Bank of Atlanta
Eco n o m ic Revie w
19
Chart 9
R e s p o n s e s t o U n a n t i c i p a t e d M o n e t a r y Policy C o n t r a c t i o n in M o d e l 1
(Policy s h o c k raises f u n d s rate initially by 2 5 basis points)
Total Reserves
Percent
12
18
24
30
36
24
30
36
24
30
36
24
30
36
Federal Funds Rate
0.36
Percentage
Points
-0.36
12
18
Consumer Prices
Percent
-i
12
18
24
Industrial Production
Percent
12
18
24
Unemployment
Percentage
Points
12
18
24
Long-Term Bond Yield
0.14
Percentage
Points
0-0.14
-0.28 -I
0
1
»
t6
12
18
Commodity Prices
Percent
Economic
20
Months after Shock
Review
July/August 1995
Chart 10
Dynamic Effects of Policy Shock on Reserves Market in Model 1
Federal Funds Rate
Total Reserves (billions of dollars)
Initial monetary policy shock shifts supply from S 0 to 5,',, moving the equilibrium from point A to point B along the initial demand curve,
DQ. Six months later, the supply curve has shifted farther inward to S 6 and the demand curve has shifted inward to D fi , creating a new equilibrium at point C. Over time, the supply and demand curves continue to shift, with their intersections traced out by the curved black line
labeled "dynamic path of reserves and the funds rate." Thirty-six months after the initial policy shock, the equlibrium level of reserves and
the funds rate occurs at point D, where the S.. and D. curves intersect.
reserves and the funds rate reported in the dynamic responses in the first two panels of Chart 9 represents an
equilibrium in the reserves market at a different point
in time. The dynamic sequence of supply and demand
curves associated with Chart 9 are depicted in Chart 10.
SQ and D 0 are the preshock curves, with point A the
initial equilibrium. 2 8 T h e curved line traces out the
e q u i l i b r i u m r e s e r v e s - f u n d s rate path. T h e c o n t r a c tionary policy shock shifts supply to S()', and the econo m y slides up D 0 to a n e w e q u i l i b r i u m at B, which
is associated with the first point in the top t w o panels
of Chart 9. At each point in time the positions of the
supply-and-demand schedules reflect the accumulated
effects of the policy shocks on the variables on which
supply-and-demand behavior depend. After the initial
period the effects of the shock on prices, output, unemployment, long-term interest rates, and commodity
prices serve to shift both curves. Points C and D are
the equilibria six months and three years after the supply shock.
Federal Reserve B a n k of Atlanta
Chart 9 shows that policy shocks have persistent effects on the quantity of reserves. The steady decline in
reserves shows up in Chart 10 as a series of inward
shifts in the supply schedule: even six months after the
shock, supply is shifting inward (S6). Eventually, however, the accumulated effects of lower long rates and
c o m m o d i t y prices dominate supply behavior and the
curve shifts outward toward its initial position, landing
at S36 three years after the original shock. On the demand side, lower prices and output reduce the quantity
of reserves demanded at any given interest rate and shift
the schedule inward (to D 6 in six months and D % in
three years). After three years, the accumulated effect
on the funds rate is close to zero, while that on the level
of reserves is negative. This pattern is wholly consistent
with Friedman's summary of policy effects as presented
in the introduction of this article. After three years the
level of total reserves has fallen but the growth rate is
near zero. Consequently, the level of the funds rate ends
up at the point at which it started. By showing h o w
Eco n o m ic Revie w
21
much policy responds to changes in the economy generated by policy itself, the chart emphasizes that monetary
policy depends strongly on economic conditions.
Policy also responds over time to nonpolicy shocks
emanating from other sectors of the economy. Chart 11
reports the responses of total reserves and the f u n d s
rate to unanticipated changes in nonpolicy variables.
Because these other markets are not modeled economically, it is not possible to infer what underlying beh a v i o r generates the n o n p o l i c y shocks. T h e c h a r t ' s
message is that the model implies that the Fed adjusts
the supply of reserves and allows the f u n d s rate to
change substantially when other disturbances hit the
economy. Unanticipated increases in prices and output, which increase the demand for reserves, appear to
be partially a c c o m m o d a t e d by monetary policy: the
supply of reserves rises initially but not by enough to
avoid an increase in the funds rate designed to squeeze
out the excess demand for reserves. Responses to surprise rises in u n e m p l o y m e n t are consistent with the
casual observation that the Fed pays close attention to
labor market conditions. Higher unemployment generates significant increases in reserves and decreases in
the funds rate, which are consistent with c o m m o n perceptions that m o n e t a r y policy tries to offset shocks
that raise unemployment. 2 9 Finally, the decline in reserves and the increase in the f u n d s rate f o l l o w i n g
unanticipated increases in the long rate and commodity prices are consistent with the view that the Fed may
interpret financial variables as containing news about
higher expected inflation.
These results are confirmed by the second column
of Table 1. Monetary policy shocks in M o d e l 1 account for only 20 percent of the variance of fluctuations in reserves and half of the variance of the funds
rate within the month (see the first two panels of the
second column). These percentages decline over time,
making policy shocks a relatively unimportant source
of unforecastable movements in reserves market variables t w o years out. Most of the fluctuations in these
variables arise from endogenous responses of policy to
nonpolicy shocks, underscoring the strong and consistent dependence of policy on the economy.
Interpreting Recent Economic History. What
does this model tell a policy advisor about the recent
slowdown in economic activity? Contrasting Charts 12
and 7, Model 1 implies that policy was less tight in
1990 and less loose in 1992-93 than it was according to
Model R, which assumed the supply of reserves is perfectly elastic. The differences emerge for straightforward reasons. Chart 7 assumes that all unanticipated
funds rate changes arise from shifts in the supply of re-
Economic
22
Review
serves. Model 1 attributes some of these changes to
shifts in demand that induce the Fed to adjust the quantity of reserves supplied along a fixed upward-sloping
supply curve, some to changes in policy in response to
n e w s c o n t a i n e d in financial variables, and s o m e to
shifts in the supply of reserves that are not associated
with current or past information. Nonetheless, Model 1
implies that policy shocks have had predictable effects
on inflation, output growth, and unemployment over
the period. The dynamic impacts reported in Chart 9
suggest that policy shocks affect prices in about six
months, output in three months, and unemployment after five quarters. Although the effects on inflation in
Chart 12 are small, unanticipated policy shifts map directly into changes in output and unemployment with
the predicted lags.
Chart 12 makes it appear that in recent years monetary policy shocks have had little influence on inflation
but larger effects on output and unemployment. Taken
at face value this implication would concern those who
advocate that the Fed should focus almost exclusively
on price stability (for example, J. Alfred Broaddus, Jr.,
1995). While this literal interpretation may be mistaken, it highlights a pervasive and subtle problem with
estimating the effects of policy. As an extreme example,
suppose that the monetary authority seeks to achieve
absolute price stability and that it has been successful
in achieving this goal. To do so the authority must adj u s t the s u p p l y of r e s e r v e s to o f f s e t any e c o n o m i c
shocks that would otherwise cause the price level to
adjust. Macroeconomic time series would exhibit large
fluctuations in reserves market variables and in output
and employment, but none in prices. Empirical work
w o u l d find no e f f e c t s of policy on prices but likely
would find effects on real activity. Because policy has
been so s u c c e s s f u l at controlling prices, an analyst
without knowledge of the authority's objectives might
mistakenly conclude that policy has only real effects. 3 0
By this interpretation, Model 1 implies that policy has
been fairly successful at avoiding taking actions that
generate price level fluctuations at the cost of producing fluctuations in output and unemployment.
The model may give cause for concern about economic developments in 1995. Policy shocks in 1994
were contractionary, according to the model. If the historic correlations between policy and macro variables
c o n t i n u e to h o l d , the m o d e l predicts l o w e r o u t p u t ,
somewhat lower inflation, and, with a longer lag, higher
unemployment in 1995. 31
However, a model's predictions are only as good as
its behavioral and statistical underpinnings. T h e assumption of Model 1 that financial market participants
J u l y / A u g u s t 1995
C h a r t 11
R e s p o n s e s o f R e s e r v e s M a r k e t V a r i a b l e s t o U n a n t i c i p a t e d I n c r e a s e s in O t h e r V a r i a b l e s
Responses of Funds Rate to
Responses of Reserves to
Percentage Points
0.24
Consumer Prices
Consumer Prices
-0.24
12
18
24
30
36
24
30
36
24
30
36
30
36
Industrial Production
Industrial Production
0.24
-0.24
Unemployment
0
6
12
18
Unemployment
0.24
-0.24
0
6
12
18
Long-Term Bond Yield
Long-Term Bond Yield
Commodity Prices
Commodity Prices
Federal
Reserve Bank of Atlanta
0.24
-0.24
24
30
36
Months after Shock
24
Months after Shock
Eco n o m ic Revie w
23
Chart 1 2
I n f l u e n c e of M o n e t a r y Policy S h o c k s o n M o d e l 1
Actual
Less influence of unanticipated
changes in funds rate
Federal Funds Rate
7.2
Percent
4.8
2.4
1990
1991
1992
1993
1994
1993
1994
Inflation
Annual
Percent
1990
1991
1992
Industrial Production Growth
5 --
/v
-
Annual
Percent
r
/
' s / N *
-5
24
Economic
1
1990
Review
1991
!
1992
1993
1994
July/August 1995
do not react to p o l i c y a c t i o n s within the m o n t h is
grossly at odds with actual behavior. 32 Markets actually react immediately and often strongly to news about
monetary policy. The next two models attempt to address this weakness by allowing reserves market variables and financial market variables to be determined
simultaneously.
Model 2: The Funds Rate Affects Financial Variables Contemporaneously
M o d e l 2 m o d i f i e s M o d e l 1 by allowing reserves
market behavior to affect financial variables within the
month. Whereas Model 1 imposed the rule that financial variables affected the reserves market immediately but not vice versa, Model 2 determines all reserves
market and financial market variables simultaneously.
The model assumes that within the month the Fed responds only to the f u n d s rate and commodity prices
when it sets the supply of reserves. Model 2 also assumes that the behavior of financial m a r k e t participants d e p e n d s on the current f u n d s rate as well as
goods market variables.
The model and its estimated parameters are reported in Table 3. The qualitative features of demand-ands u p p l y b e h a v i o r in the r e s e r v e s m a r k e t are similar
across Models 1 and 2. Demand for reserves continues
to depend negatively on the f u n d s rate and positively
on the price level and output. Supply still rises with
the f u n d s rate and falls with c o m m o d i t y prices. A s
seen in Chart 8, the estimated supply of reserves is
fairly inelastic with respect to the funds rate. A policy
shock in Model 2, therefore, is defined very much as it
was in Model TR, where the maintained assumption
was that supply was perfectly inelastic and every unanticipated change in reserves was interpreted as a monetary policy shock.
With the f u n d s rate and financial variables determined simultaneously, it is possible f r o m the coefficients reported in Table 3 to infer immediately how
s o m e of the d y n a m i c responses to policy shocks in
Model 2 will differ from those reported for Model 1.
A contractionary monetary policy shock shifts the supply of reserves inward and raises the funds rate initially. T h e h i g h e r f u n d s rate in M o d e l 2 i m m e d i a t e l y
increases both the long-term interest rate and c o m modity prices. The higher commodity prices feed back
into the supply equation, shifting it inward and reinforcing the original contraction. By making monetary
policy depend on commodity prices at the same time
Federal
Reserve Bank of Atlanta
that it affects commodity prices, Model 2 changes the
amount by which a given-sized policy shock shifts the
supply schedule.
Chart 13 records the dynamic responses in Model 2
to an unanticipated monetary policy contraction that
raises the funds rate by 25 basis points initially. 33 Policy
shocks continue to have statistically significant effects
on all the variables. Contractionary policy increases the
funds rate in the short run and decreases it in the long
run. The price level no longer increases initially, and it
falls more persistently than in Model 1. Output also falls
for three years after the shock. After a strange one-month
decline, unemployment rises more quickly than it did in
the first model. Long rates rise at impact, consistent
Table 3
Model 2
Reserves Market
Demand:
47.7677?'' = - 5 . 0 1 R + 8 8 . 3 7 P + 1 1 0 . 5 9 V + e<'
(36.57)
(.51)
(72.09)
(23.96)
Supply:
155.3277?*= 1 . 8 3 / ? - 3 . 2 5 C P + e s
(13.77)
(1.08)
(6.46)
Financial Market V a r i a b l e s
5.02/?/0 = 2.10/? + 8 0 . 5 5 P - 1.79 V - .66U + eRW
(.30)
(.45) (66.35) (17.04)
(.76)
7 2 . 9 4 C P = 1 . 0 6 R - 4 . 6 3 P - 8 . 8 6 V - .67U + .61 RIO + eCP
(4.38)
(.51) (42.65) (26.69) (.79)
(.42)
G o o d s Market Variables
7 7 8 . 9 5 P = .52Y(46.72) (2.30)
1.261/ + ep
(.73)
2 9 0 . 0 6 V = - 3 . 5 4 ( 7 + eY
(17.40)
(.76)
8.54 U = e
(.51)
u
Log likelihood value = 3 2 8 5 . 3 5 1
LR test of overidentifying restrictions: x 2 (4) = 9 . 6 7 6 ,
significance level = . 0 4 6
L R test with s m a l l - s a m p l e correction: x 2 (4) = 6 . 6 8 2 ,
significance level = . 1 5 4
A k a i k e criterion = 3 2 3 7 . 3 5 1
S c h w a r z criterion = 3 1 6 6 . 9 2 4
Eco n o m ic Revie w
25
with press accounts of bond market reactions to policy.
In contrast to Model 1, however, long rates never fall
significantly in spite of a steady decline in the price level and lower short-term interest rates in the future. This
is a questionable implication of the model. 3 4
Returning to Table 1, policy shocks in Model 2 are
the primary source of short-run fluctuations in reserves.
This is exactly what the estimated highly inelastic supply of reserves implies. Policy shocks account for relatively small p e r c e n t a g e s of f l u c t u a t i o n s in all the
remaining variables except output. In Model 2, policy
s h o c k s i n f l u e n c e o u t p u t as strongly as they did in
Model 1.
Model 2 supports an interpretation of the 1990-94
period that is qualitatively very similar to that of Model
1 except that unanticipated shifts in policy are quantitatively less important. This point will be discussed later.
Model 2 can be criticized for implicitly assuming
that financial markets view all changes in the f u n d s
rate as created equal. The model forces all changes in
the f u n d s rate, whether from supply shocks, demand
shocks, or e n d o g e n o u s responses of policy to other
behavioral disturbances, to affect financial variables in
the same way. But it is likely to be important to financial
market participants to know why the funds rate changed.
For example, if the impacts of demand shocks tend to be
short-lived, the shocks may affect the f u n d s rate this
month but not contain much useful information about
the funds rate six months from now. Supply shocks, on
the other hand, may have more persistent effects on interest rates, as the Fed has tended to m o v e the f u n d s
rate in the same direction for some time. This article
has argued that to isolate monetary policy shocks it is
essential to construct a model that determines equilibrium price and quantity in the reserves market simultaneously, so treating all changes in the f u n d s rate as
stemming from the same source (for example, shifts in
monetary policy, as Model R does) is misleading. Logically it seems that financial market participants may
need to observe the funds rate and reserves in order to
distinguish the source of the change in the short-term
interest rates. The final model addresses this concern.
Model 3: Reserves and the Funds
Rate Affect Financial Variables
Contemporaneously
The final model is identical to Model 2 except that
total reserves and the funds rate are allowed to affect
long-term interest rates and commodity prices within
Economic
26
Review
the month. This model assumes that financial market
participants base their decisions on information about
the current levels of both reserves and the funds rate.
Table 4 presents the model's estimated parameters.
The critical differences between Models 2 and 3 are apparent immediately. Model 3 implies a huge monetary
policy response to commodity prices. The responsiveness of the supply of reserves to changes in commodity
prices is more than 150 times larger in the third model. 35 The simultaneous determination of financial variables, total reserves, and the funds rate implies that an
unanticipated contraction in policy generates the following sequence of responses within the month: the inward shift in the supply of reserves raises the funds rate;
the lower level of reserves and higher funds rate have
r e i n f o r c i n g e f f e c t s that raise c o m m o d i t y prices; the
higher commodity prices shift the supply of reserves
o u t w a r d , c o u n t e r a c t i n g the initial contraction. T h i s
chain of events eventually implies that the ultimate shift
in reserves due to a reasonably sized policy shock is minuscule.
Qualitatively the dynamic impacts of a policy shock
f r o m M o d e l 3 on goods market variables, shown in
C h a r t 14, are similar to t h o s e f r o m M o d e l 2. 3 6 An
unanticipated policy contraction significantly lowers
p r i c e s a n d o u t p u t and r a i s e s u n e m p l o y m e n t w i t h
s o m e w h a t shorter lags than in p r e v i o u s models. A s
Table 4 reveals, with the funds rate rising and reserves
falling initially, long-term interest rates fall significantly. Long rates continue to fall through most of the
next three years. Commodity prices drop sharply at the
time of the policy shock. The initial drop seems implausibly large.
The most substantive difference between Models 2
and 3 comes f r o m the m o d e l s ' predictions of f u t u r e
policy following an unanticipated contraction. Chart 14
shows that in Model 3 the contraction lasts only a few
months before being reversed. Four months after the
c o n t r a c t i o n , r e s e r v e s h a v e b e g u n to g r o w a n d the
f u n d s rate has begun to decline. This reversal in policy
is strong enough that by the end of three years output
is growing and unemployment is falling. Neither Model 1 nor Model 2 display such a rapid turnaround in
policy behavior.
Table 1 reports that policy shocks in Model 3 have
been a trivial source of fluctuations in all economic
variables except c o m m o d i t y prices. In the short run,
policy disturbances have been the single most important reason that c o m m o d i t y prices m o v e d in unpred i c t a b l e w a y s . T h i s i m p l i c a t i o n , c o u p l e d with the
model's implied rapid reversal of the direction in policy, make Model 3 of dubious usefulness.
July/August 1995
Chart 1 3
R e s p o n s e s t o U n a n t i c i p a t e d M o n e t a r y P o l i c y C o n t r a c t i o n in M o d e l 2
( P o l i c y s h o c k r a i s e s f u n d s r a t e initially b y 2 5 b a s i s p o i n t s )
Total Reserves
1.6
0
Percent
-1.6 +
-3.2
12
0
18
24
30
36
Federal Funds Rate
Percentage
Points
12
18
24
Consumer Prices
0.25
Percent
0
-0.25
- '
—
N
-"*
—
—
—~~—~—HLZT"
—-
--
-0.75
12
24
_
^
30
36
Industrial Production
0.45
0 r
Percent
18
~
-*.
X
-0.45
^
-
-
—
—
-0.90
-1.35
1
-
I
12
- -
-
18
24
-
~
•—
30
36
Unemployment
0.32
Percentage
Points
-0.16
¥—I
1
1
1
1
12
1
1
1
18
1
1
24
1
1
1
30
t
1
36
Long-Term Bond Yield
Percentage
Points
12
18
24
Commodity Prices
2.5
Percent
0
-2.5 +
-5.0
0
Federal Reserve B a n k of Atlanta
12
24
30
36
Months after Shock
Eco n o m ic Revie w 35
Are the Models Believable?
The article has reviewed the monetary policy implications f r o m five sets of behavioral assumptions about
policy and financial markets. Each of the five models
has its flaws, but some flaws are more troubling than
others. The schemes that impose extreme assumptions
on the interest elasticity of the supply of reserves imply dynamic impacts of unanticipated policy shifts that
are sharply at odds with widely held beliefs about policy effects. M o d e l T R can be rejected on this basis.
M o d e l R also implies perverse m o n e t a r y policy e f -
fects, but because it comes close to the way many people identify monetary policy, it deserves closer scrutiny.
Models 1 through 3, which directly estimate supplyand-demand behavior in the reserves market, all make
reasonable assumptions about economic behavior and
produce policy shocks whose impacts are qualitatively
consistent with beliefs. In spite of the similarity of the
dynamic impacts of policy across the three models, the
models have strikingly different implications for how
quantitatively important policy shocks have been in
the data. Model 1 implies that monetary policy shocks
are an important source of fluctuations in the f u n d s
rate and output, Model 2 implies that policy shocks
Table 4
Model 3
Reserves Market
Demand:
70.7677? d = - 4 . 6 8 P + 104.31 P + 1 0 7 . 2 0 V + ed
(133.69)
(2.28) (123.05)
(36.16)
Supply: 2 2 . 1 0 7 / ? = 1.65R - 71.85CP + e5
(20.54)
(.70)
(4.43)
Financial Market Variables
3.44R10 = 9 1 . 0 9 T R - .40R - 2 0 . 1 5 P + 15.71 V - 1.1 3U + eKW
(1.51)
(90.03) (2.27) (135.68) (74.15)
(.80)
11.47CP = 1 1 9 . 8 9 T R - 3 . 1 1 P - 1 6 2 . 3 9 P + 8.91 Y - .45U + 3.81 R10 + e c p
(9.18)
(28.96)
(2.87)
(88.80) (69.36) (.98)
(1.39)
Goods Market Variables
779.02P = .52 V - 1.26U + ep
(46.73) (7.57)
(.74)
290.04 V = - 3 . 5 4 L/ + eY
(17.40)
(.76)
8.54 U = e u
(.51)
Log likelihood value = 3289.800
LR test of overidentifying restrictions: x 2 (2) = .779, significance level = .678
LR test with small-sample correction: x 2 (4) = .538, significance level = .764
Akaike criterion = 3237.800
Schwarz criterion = 3161.503
28
Economic
Review
July/August 1995
Chart 1 4
R e s p o n s e s t o U n a n t i c i p a t e d M o n e t a r y P o l i c y C o n t r a c t i o n in M o d e l 3
( P o l i c y s h o c k r a i s e s f u n d s r a t e initially b y 2 5 b a s i s p o i n t s )
Total Reserves
Percent
12
18
24
Federal Funds Rate
3.2
z'
-
Percentage
Points
q
X
v
-3.2
'
_ —- —
—
12
18
24
30
36
24
30
36
Consumer Prices
\
s
—
\
-3
12
18
Industrial Production
Percent
12
18
24
Unemployment
0.8
0
Percentage
Points _Q g __
1
-0.16
I12
18
24
30
36
Long-Term Bond Yield
1.8
Percentage
- - -
0
-1.8
-3.6
V
— "
\
,
\
r - r
--
—
" 1 - -
- -
-
"
1
1
12
1
(
1
18
1
f
24
1
«
1—
30
36
30
36
Commodity Prices
Percent
Federal
Reserve Bank of Atlanta
24
Months after Shock
Eco n o m ic Revie w 37
influence reserves and output, and Model 3 says that
policy shocks affect only commodity prices.
T h e r e is no s e n s i b l e m e c h a n i c a l w a y to c h o o s e
among the three models. Purely statistical criteria do not
imply that one model clearly dominates the others. 37 A
little c o m m o n s e n s e can help, t h o u g h . To e v a l u a t e
Models R and 1 through 3, it is important to standardize the experiment being conducted. Charts 6, 9, 13,
and 14 were drawn assuming the policy shock was big
enough to unexpectedly change the funds rate initially
by 25 basis points. Because much of a typical monthly
change in the funds rate is anticipated on the basis of
past i n f o r m a t i o n , the shocks underlying those three
c h a r t s w e r e " b i g . " U s i n g the d e f i n i t i o n that a big
shock raises the funds rate on impact by at least 25 basis points, over the sample period f r o m May 1983 to
D e c e m b e r 1994 M o d e l R p r o d u c e d t w e n t y - t w o big
policy shocks and Model 1 produced eleven. Models 2
and 3 produced none. 3 8 On average, therefore, Model R
suggests that o n e should expect 2.6 big shocks per
year, while Model 1 predicts 1.1 per year. An analyst
who treats all unanticipated changes in the funds rate
as surprise shifts in monetary policy may be led to attribute to monetary policy a larger role in determining
economic conditions than would an analyst who views
the economy through Model 1. Armed with Models 2
or 3, h o w e v e r , an analyst might infer that only extremely large unanticipated monetary policy actions
will have discernible effects on the economy.
A twist on this standardized experiment asks how
big an unanticipated change in the funds rate a "typical" policy shock generated in each model. 3 9 The initial impacts of such a shock on the f u n d s rate appear in
Table 5. Models 2 and 3 imply that surprise shifts in
the supply of reserves cause implausibly small unanticipated changes in the f u n d s rate. This implication
alone is grounds for believing that those models have
not a d e q u a t e l y s u m m a r i z e d the e c o n o m i c b e h a v i o r
that generates policy effects. Both Model R and Model 1
Table 5
Unanticipated Change in the Funds Rate
from a "Typical" Policy Shock
{In basis
Model
Model
Model
Model
R
1
2
3
Economic
30
points)
20.3
14.8
5.5
0.9
Review
seem r e a s o n a b l e a l o n g this d i m e n s i o n . T h e c h o i c e
between Models R and 1, therefore, c o m e s down to
h o w plausible the m o d e l s ' implications are for policy
effects. The strange policy impacts that Model R implies, shown in Chart 6, lead one to f a v o r Model 1.
A l t h o u g h reality probably lies closer to M o d e l 1
than to Models 2 or 3, the latter models are instructive.
Almost certainly, financial market participants anticipate policy actions better than Model 1 posits but not
nearly as well as the other two models imply. Models
1 through 3 impose economic structure on information
Hows into the reserves markets but no economic restrictions on f l o w s into financial markets. E c o n o m i c
structure in f i n a n c i a l m a r k e t s w o u l d consist of assumptions about the supply-and-demand behavior that
determines the financial prices. The lack of structure
implies that reserves market variables are permitted to
influence financial variables in arbitrary and economically uninterpretable ways. This influence then feeds
back to the reserves market to shift supply within the
month. As a consequence, Models 2 and 3, which determine the reserves market and financial market variables s i m u l t a n e o u s l y , do too good a j o b predicting
changes in the funds rate induced by shifts in policy.
T h o s e m o d e l s implicitly ascribe to financial market
participants more information about policy moves
than s e e m s p l a u s i b l e . E s s e n t i a l l y , all the s u r p r i s e
movements in the funds rate, which Model 1 attributes
to shifts in policy, get absorbed by the financial variables. It seems unlikely that adding m o r e " i n f o r m a tional v a r i a b l e s " ( s u c h as e x c h a n g e r a t e s or stock
prices) whose determination is not modeled economically will solve this problem, so there is no easy fix.
The lesson f r o m Models 2 and 3 is that the assumptions about h o w the reserves market interacts with other financial m a r k e t s matter for i n f e r e n c e s about
monetary policy effects.
Because each model has its problems, it would be
wise for a policy advisor to be eclectic in formulating
policy advice. It is also important that the advice accurately reflect the fact that it is not based on a single,
universally accepted view of monetary policy's role in
the economy. Even if the advisor chooses to focus on
the implications of a single model, an honest presentation of the model's predictions would include a clear
statement of both the statistical and the economic uncertainties surrounding the predictions. Having said
this, it is nonetheless instructive to push a single model to its limits by assessing its shortcomings and using
it to analyze the current state of the economy and to
predict the outcomes of alternative policy actions. For
this exercise, the focus will be on Model 1.
J u l y / A u g u s t 1995
Where Does All This Leave the
Policy Advisor?
For all of its warts, Model 1 seems fairly reasonable
as a first cut at the problem of isolating and quantifying monetary policy effects. Like any model it has its
limitations. It cannot be used to predict financial market reactions to policy shocks. It is estimated over a
period that was fairly quiescent in terms of shocks that
hit the economy. During the estimation period there
was only one economic downturn, limiting the information content of the data.
On the plus side, the model appears to fit the data
fairly well. It provides a straightforward interpretation
of behavior in the reserves market, where the Fed intervenes to conduct monetary policy. The specification
of policy behavior is in terms of a quantity (reserves)
that the Fed can potentially control. Model 1 also produces m o n e t a r y policy shocks whose estimated impacts conform closely to consensus views about policy
effects.
Finally, the model provides at least first-pass answers to the questions a policy advisor must confront
b e f o r e f o r m u l a t i n g a policy r e c o m m e n d a t i o n to the
Federal O p e n M a r k e t C o m m i t t e e . In the m i d d l e of
June 1995 the advisor could have used the model to
forecast the e c o n o m y given data through May. T h e
forecast provides one prediction of h o w severe and
how long-lasting the slowdown will be. O n e measure
of the role of monetary policy shocks in the slowdown
comes f r o m reproducing Chart 12 for the period, say,
f r o m June 1994 to M a y 1995. This calculation reports
h o w m u c h of the unpredicted s l o w d o w n in activity
can be attributed to unanticipated contractions in monetary policy. T h e m o d e l ' s e s t i m a t e d policy s h o c k s
would give the advisor an idea of whether recent policy has been tight or loose. A sequence of sizable tight-
F e d e r a l R e s e r v e B a n k of Atlanta
ening shocks would lead the advisor to infer that recent monetary policy actions will tend to make future
output and inflation lower and unemployment higher,
based on the results in Chart 9. In that situation a decision not to lower the funds rate would likely generate
further contractions and exacerbate the slowdown.
This is about as far as a policy advisor can go in extracting i n f o r m a t i o n f r o m the m o d e l . T h e m o d e l is
silent on the question of whether contractionary shocks
are " g o o d " or "bad." The model generates predictions
of future economic conditions and economic interpretations of past developments. It can, in principle, be
used to forecast outcomes of contemplated future policy choices. It cannot evaluate the desirability of the
outcomes. Like the Goldilocks assessments that policy
is too tight, an evaluation of the desirability of outcomes carries an implicit statement about preferences
over the outcomes.
There is one further potential use for the model. If a
policymaker feels that Fed behavior over the 1983-94
period has largely achieved the policymaker's objectives, the model can be used to automate the policym a k e r ' s decisions. The model produces a prediction of
what the funds rate would be if there were no shocks
to policy behavior. This path of the f u n d s rate e m b o d ies policy's usual response to economic conditions. If
the p o l i c y m a k e r s e e k s to m i n i m i z e the e c o n o m i c
shocks introduced by policy behavior, the policymaker
would simply vote to i m p l e m e n t the m o d e l ' s f u n d s
rate prediction.
Of course, such a policymaker is rare. More often
policymakers hope to improve upon past policy and
economic performance. In that case the model remains
informative about past economic developments. The
model must be used with great caution, however, in
predicting longer-run outcomes of policy actions that
deviate f r o m past policy behavior.
Economic Review
31
Appendix A
Demand and Supply Analysis of the Reserves Market
This appendix derives the demand and supply functions for reserves and links these behavioral relationships to a broader monetary aggregate like M2. The
linchpin of the models reported in the text is the existence of an integrated market for reserves: the federal
funds market. As a result of this market, demanders of
reserves face a common opportunity cost of both borrowed and nonborrowed reserves, so demanders perceive borrowed and nonborrowed reserves to be perfect
substitutes. The opportunity cost of reserves is the funds
rate. More precisely, the funds rate equals the interest
cost plus the costs of reserves' transactions in the federal funds market and must equal the discount rate plus
any nonpecuniary costs of borrowing from the discount
window. 1
Assuming that the demand for reserves is not completely interest inelastic—an assumption that appears to
be innocuous as long as excess reserves are positive—
the opportunity cost is a function of the total supply of
reserves and is independent of the composition of total
reserves between borrowed and nonborrowed reserves.
Thus, for the purpose of identifying monetary policy
shocks, no distinction is required among open market
operations and discount window operations. 2
As is implicit in much of the earlier work on the reserves market, reserves are treated as a factor of production in intermediating between the M2 market and a
market for less liquid assets. 3 A demand relation is assumed for M2 of the form
MD = D(R,
P,
W),
(A.l)
where R is the cost of holding M2, P is the price level,
and W is a scaling variable. The demand for M2 is the
demand for a joint product comprising a portion that
pays a positive own rate of return and a portion that provides transactions services. Because the interest-bearing
portion is a perfect substitute for other interest-bearing
assets, its demand is infinitely elastic. Demand for the
transactions services provided by M 2 is a decreasing
function of the price of the services. The return determined in the M2 market is the unobserved sum of the
own rate and the marginal value of transactions services.
In equilibrium, the total return to holding M2 must equal
the rate on the alternative asset.
M 2 supply is given by
Ms =
S(R,Rf,RL,...),
(A.2)
where RF is the fed funds rate, RL is the nominal interest
rate on bank assets, and the additional variables reflect
other costs of intermediation.
Economic
32
Review
S ( * ) is d e t e r m i n e d by a g r o u p of i n t e r m e d i a r i e s
viewed as "producing" loanable funds, L, which earn the
rate of return RL, by using the technology
}{L, TR, M\ . . . ) = 0.
(A.3)
Implicitly, the intermediaries are viewed as using the liabilities, M, as an input to the process of producing the
assets, L.
The cost function C(*) of the intermediaries is the solution to
CO) = min Rf • TR + R • Ms + other costs,
{TR,M"\
(A.4)
subject to the technology (A.3), taking L, Rf, and R as
given.
The first-order conditions for the cost-minimization
problem yield the implicit derived demand for total reserves:
RF =
R.
Jtr
(A.5)
ÎMs
where fx denotes the partial derivative of the production
function with respect to .v.
The M2 supply results from solving:
m a x L»RL-
C(L, R, RF,...),
(A.6)
which yields the inverse supply function for loans:
R. = C. (L, R,
Rf,...).
(A.7)
The demand for reserves can be expressed in terms
of the variables Rf, P, and W by using the M2 demand
function (A.l), the supply function for loans (A.7), and
the production function (A.3) to eliminate M, L, and R.
Substituting these results into the derived demand for reserves (A.5), yields a transformed demand for reserves
of the form:
TR = TR-'*(R P, W,Rl, . ..).
(A.8)
The specification of reserves supply abstracts from
any distinctions between open market operations and
borrowing at the discount window. The Federal Reserve
is assumed to respond to the current federal funds rate
and other available information in determining the supply of reserves:
TRS = G(R.,
Qr),
(A.9)
July/August 1995
where Q G is the information set available to the policy
authority.
In a symmetric fashion, the supply of M 2 can b e e x pressed as a function of the variables in the policy rule
(A.9) rather than of the f u n d s rate. T h e reserves supply
f u n c t i o n (A.9), the derived d e m a n d for reserves (A.5),
and the production function (A.3) are solved for TR, RF,
and L. S u b s t i t u t i n g the results into the m o n e y s u p p l y
function (A.2) yields a t r a n s f o r m e d M 2 supply f u n c t i o n :
T h e e m p i r i c a l work f o c u s e s on the e q u i l i b r i u m
relationship:
TRD\RF,
P, W, RL, . . . ) = TR* = G(RF,
Q0).
(A.
11)
Notes
MS = MS*(R,
RL, IG,
...).
(A. 10)
T h e derived d e m a n d for reserves, equation (A.8), is
obtained by c o m b i n i n g the behavior of M 2 d e m a n d e r s
with t h e behavior of t h e financial intermediaries that are
i s s u i n g l o a n s . T h u s , s h i f t s in t h i s f u n c t i o n m a y arise
f r o m either of these t w o behavioral sources. Similarly,
the M 2 supply f u n c t i o n , equation (A. 10), blends the behavior of the policy authority that is supplying reserves
with the behavior of intermediaries that are issuing the
liabilities that m a k e up M 2 . C h a n g e s in the b e h a v i o r of
either the policy authority or i n t e r m e d i a r i e s can c a u s e
shifts in the M 2 supply function.
1. The discount rate can exceed the f u n d s rate either because discount loans are longer term than federal funds
or because the only holders of discount loans face prohibitive risk premiums in the federal funds market.
2. For questions beyond the identification of monetary policy
shocks, the distinction between borrowed and nonborrowed
reserves is of interest. For example, Tinsley and others
(1981) and Bryant (1983) focus on questions about monetary policy operating procedures and the interaction of
the discount window and open market operations.
3. See, for example, Meigs (1962), Morrison (1966), or
Goldfeld and Kane (1966).
Appendix B
Estimating an Identified VAR
T h i s a p p e n d i x p r o v i d e s the e c o n o m e t r i c details f o r
the estimated m o d e l s reported in the text. T h e procedure
f o l l o w s the work of B e r n a n k e (1986), Olivier J. Blanchard and M a r k W . W a t s o n ( 1 9 8 6 ) , and S i m s ( 1 9 8 6 ) .
Let er be an (« X 1) vector of behavioral d i s t u r b a n c e s
and xt be an (n X 1) vector of data o b s e r v e d over periods
/ = 1 , 2 , . . . T. The structural m o d e l is given by
™
t = LGsvt-s
(B.4)
x
5=0
= Q = In.
(B.l)
m(L)xt-m>
where the impulse response matrices do not depend on m.
Writing out ( B . l ) and (B.2) as
A x
0t
= lne, + £
-
¿4rX,-s
5=1
.5=1
A(L)xi = el,Var(e)
H
+
and
T h e V A R for this structure is
X
t
=V
I~
5=1
C(L)xt = vt, C0 = /, Var{v) =
(B.2)
it is clear that if current and past e's and x's span the s a m e
space and the e process is serially independent, then
A s s u m e that ( B . l ) is complete in the sense that current
x's are determined by current and past e's. T h e n
x=A-\L)et,
(B.3)
when the right-hand side of (B.3) is one-sided and convergent, implying that stationary e's imply stationary x ' s .
T h e V A R in (B.2) can be solved to yield the impulse
response matrices for x, G \
Federal
Reserve B a n k of Atlanta
=
(B.5)
= A~oer
(B-6)
hence,
v
l
Substituting (B.5) into (B.4) implies t h e impulse response matrices of the identified V A R , GsA ()' for all s's.
Eco n o m ic Revie w
33
Equation (B.6) is a mapping from the VAR innovations to the behavioral disturbances. The identification
takes the form of assuming that some of the elements of
A{) are zero. An identity covariance matrix for the behavioral disturbances combines a normalization with the
identifying assumption that each shock is associated
with a behaviorally distinct sector of the economy. The
zero restrictions on AQ limit the contemporaneous interactions among variables. Importantly, if the identifying
assumptions restrict only A(j and Q, then they may restrict 2 , but they will not restrict the C and Gs matrices.
Hence, the reduced form for xf is not affected by identifying assumptions of this form. When the model is just
identified, no restrictions are imposed on 2 and the model is one of many observationally equivalent rotations of
the covariance matrix of the unrestricted VAR. Among
these o b s e r v a t i o n a l l y equivalent r o t a t i o n s are t h o s e
orthogonalized using a Choleski decomposition.
The model is fit by treating the estimate of 2 as data
and performing maximum likelihood with respect to the
free parameters in AQ. The log likelihood function of the
sample in terms of the VAR innovations is
in A(). When more than n{n - l)/2 restrictions are imposed on AQ, the model is overidentified. In this case, estimates obtained by maximizing (B.9) are consistent but
not fully efficient.
Four methods of evaluating the models' goodness of
fit are presented in the text. Classical tests of overidentifying restrictions are computed in two ways as follows.
Let k be the number of parameters estimated in AQ so
that r = n(n + l)/2 - k is the number of overidentifying
restrictions. Evaluated at the maximum likelihood estimates, the likelihood value for the unrestricted model is
T ,
Tn
log|2|-y,
(B.10)
and the value for the restricted model is
L= - | l o g | ^ V | - Y ^ o ) The statistic
W/ = 2(LU - L r ) = r ( l o g l ^ ^ ' l +
trfaiAo)
-log|i|-»)
logLoe-IlQglsj-IjviX-V
Z
Z
/=!
(B.7)
Assuming a flat prior distribution over the VAR parameters, and parameterizing 2 by A ^ Q A ^ ' , the posterior
density for AQ and the C matrices is given by
T
logLoc
1
i
'i
logUo^Ao
1
^Tv^r'/V,.
1=l
(B.8)
Integrating out the VAR parameters produces the marginal posterior density for A0:
log L oc r .log\A 0 \ - l o g | Q | -
ocT-\og\A0\~trA0iA'0,
UriT\±A'Q
Review
is distributed as central x 2r- To improve the small-sample
properties of the test statistic, Sims (1980a) has suggested using the statistic
<
=(T-nl-
l)(log l A T ' V l + ^(A) ZAq)
(B.13)
where I is the number of lags in the estimated VAR.
T h e other two fit criteria applied to the estimated
models are Bayesian. Letting L" denote the value of the
maximized likelihood function for a given model, the
Akaike criterion is computed as
AC = L*-2'k,
(B.9)
where the last line of (B.9) is obtained by imposing the
normalization and the identifying restrictions that £2 = / ( .
There are /?(/? + l ) / 2 distinct elements in 2 . From
these it is possible to estimate up to n(n + 1 )/2 elements
Economic
34
(B.12)
— log |±| —w),
1 ^
1
(Bll>
(B.14)
and the Schwarz criterion is computed as
SC = L* -k*
log(T).
(B.15)
July/August 1995
Notes
1. Gottfried Haberler (1965) traces the rise and fall of monetary explanations of economic fluctuations that were put
forth in the first half of this century.
2. The work of Gottfried von Haberler (1938) is an early example of a theory of business cycles in which money plays
no active role.
3. In the chart all growth rates are calculated month-overmonth a year ago.
4. Another way to view the shocks is as movements in economic variables that the posited economic behavior in the
model cannot explain.
5. It may seem more natural to study supply and demand for
the monetary base, which is also under the control of the
Fed. The base is the sum of the Fed's monetary liabilities
(currency in circulation and reserves) and the U.S. Treasury's monetary liabilities (Treasury currency in circulation), with currency making up the vast majority. There are
three reasons not to concentrate on the base. First, much
U.S. currency is held outside the United States and does not
influence American economic conditions directly. Second,
because open market operations affect reserves, the Fed's
policy directive is couched in terms of reserves rather than
the base. Finally, the Federal Reserve has for a long time
maintained a policy of elastically supplying currency, so
changes in the base that are not associated with changes in
reserves are not likely to represent the desired policy experiment.
6. For example, long-term interest rates are excluded from the
demand for reserves, leaving short-term rates, prices, and
output to distinguish between changes in expected inflation
and changes in expected real interest rates. When real rates
are easy to forecast, this exclusion is unlikely to be a bad
approximation. However, when there is much uncertainty
about inflation and real rates, omitting other factor prices
from the derived demand may be overly restrictive.
7. Industrial production is an imperfect proxy for the income
or wealth concept that influences money demand. It is also
an imperfect measure of output, as it ignores the large fraction of output associated with the service sectors of the
economy.
8. Meulendyke (1989) offers an excellent and thorough introduction to the Fed's operating procedures and the reserves
market.
9. See Mengle (1993) for further discussion of the discount
window.
10. See Goodfriend (1991) for a discussion of the operating
procedure.
11. Randomness in policy need not reflect capriciousness or mistakes in policy choices. Without a detailed model of policy
behavior, however, it is not possible to distinguish among
several potential sources of the randomness. Sources may
be imperfect understanding of economic conditions stemming from preliminary data releases or errors in forecasting
or they may be unpredictable shifts in the preferences of
policymakers.
Federal Reserve B a n k of Atlanta
12. The graph is from Goodfriend (1982), which gives a detailed description of how various monetary policy operating
procedures influence the supply of reserves and of broader
monetary aggregates.
13. The chart also shows that the open market purchase, holding the discount rate fixed, decreases the spread between the
funds rate and the discount rate. A smaller spread decreases
the incentive to borrow at the window, so borrowed reserves fall, but by less than the increase in nonborrowed reserves, leaving total reserves higher.
14. The VAR was estimated with six lags and a constant term.
Data from December 1982 to May 1983 were used as initial
conditions. Total reserves, the price level, output, and commodity prices are measured in logs; the federal funds rate,
unemployment, and the long-term bond yield are measured
in percentages. The data were TR = total reserves, seasonally adjusted and adjusted for reserve requirement changes; R
= federal funds rate, average of business day figures; P =
consumer price index, seasonally adjusted; Y = total industrial production, seasonally adjusted; U = civilian unemployment rate, seasonally adjusted, adjusted in 1994 by - 0 . 3
percentage points to account for changes in survey methods;
RIO = yield on ten-year U.S. Treasury bond, constant maturity, average of business day figures; CP = industrial country commodity price index from the International Monetary
Fund International Financial Statistics, line 110, denominated in or converted to U.S. dollars.
15. Leepcr (1992) and Leeper and Gordon (1992) explore Cagan's results in the context of modern time series models.
Recently Pagan and Robertson (1995a, 1995b) have executed careful statistical analyses of existing work on the liquidity effect.
16. The bands are produced using the Bayesian Monte Carlo
procedures in RATS and are based on 10,000 draws from
the posterior distribution of the VAR coefficients.
17. A notable exception was from October 1979 to November
1982 when the Fed targeted nonborrowed reserves.
18. The unanticipated increase in the funds rate holds the level
of reserves fixed in the month, so the positive contemporaneous correlation between the two variables that appears in
Chart 5 is forced to be zero in Chan 6. Because the correlation is small, holding reserves fixed for this experiment does
not alter the results.
19. To compute the historical decompositions, the VAR is estimated over the entire sample period and the model is used
to generate a forecast conditional only on the model's initial
conditions, meaning on actual data available through May
1983.
20. This definition of tight and loose policy emphasizes that
these are relative terms. It employs an information-based
metric of policy that may differ from the basis of comparison others employ.
21. Chart 6 also points to one inteipretation of the "overheating"
view that "too rapid" output growth pushes up inflation. Because output tends to respond to interest rate surprises more
Eco n o m ic Revie w
35
22.
23.
24.
25.
26.
quickly than does inflation, the timing makes it appear that
higher output leads to higher inflation. Of course, in this
case there is no causal relationship between the two, as the
cause of movements in both was the change in the funds
rate.
For these calculations, reserves are not held fixed to compute the correlations of funds rate surprises with other variables.
To word it differently, the unanticipated change in the funds
rate, which Model R identifies as a monetary policy shock,
is not a shock at all because it must be partially predictable
from data outside past values of the seven variables in the
VAR.
The model is normalized to have an identity covariance matrix. The standard errors, reported in parentheses, were
computed from a numerical estimate of the inverse of the
second derivative matrix of the likelihood function evaluated at the maximum likelihood estimates of the parameters.
The full moving average representations for the models are
available from the author.
The errors bands are estimated using the Bayesian Monte
Carlo procedure developed by Sims and Zha (1995). The
method draws directly from the asymptotic distribution of
the restricted model, so it is applicable to models that are
overidentified. The error bands are computed based on
12,000 random draws. Thanks to Tao Zha for providing the
code for the procedure.
27. Industrial production, however, is noted for its cyclical sensitivity, so the speed of its response to policy ought to be interpreted cautiously. A broader measure of output, such as
gross domestic product, which includes services, may not
display such a sharp short-run response.
28. The initial equilibrium is normalized to be the unconditional
sample means of the funds rate and total reserves.
29. Unemployment's response to its own unanticipated increase
turns negative after about eighteen months and then falls significantly, providing corroborating evidence that the Fed's
response effectively reverses the initial increase. (This result is not reported in the chart.)
30. This is an old but frequently overlooked point. The earliest
mention of it known to the author is in Kareken and Solow's
(1963) criticism of Milton Friedman's empirical work.
31. Some readers may be concerned that the introduction of
"sweep" accounts by several large banks in 1994 may distort the results from this model. Sweep accounts transfer a
customer's other checkable deposit account balances in excess of a certain threshold into a money market deposit account. Because money market deposit accounts are not
reservable, sweep accounts benefit banks by reducing their
required reserves. In addition, customers may earn more interest on money market accounts. In general, the more costly
it becomes for banks to hold non-interest-eaming reserves,
the greater is their incentive to exploit sweep accounts. The
use of sweeps should reduce the derived demand for reserves at any given funds rate.
For the sample period used in this study, sweeps affect
the level of total reserves in only a couple of months in
36
Economic
Review
1994, the last year of the data set. For those months. Model 1
accounts for the decline in reserves due to sweeps as part of
the predictable part of the derived demand for reserves, as
theory implies the model should. Thus, it does not appear
that the introduction of sweep accounts affects the inferences drawn from Model 1. Corroborating evidence that
Model 1 adequately explains sweeps' behavior comes from
Gordon and Leeper (1994). The authors estimate a version
of Model 1 using data from December 1982 to April 1992,
a period that predates sweep accounts. The qualitative results from that work parallel those reported in this article.
32. One of the themes of Sims and Zha's (1994) work is the
problems that may arise from this assumption. They argue
that the strong effects of monetary policy shocks reported
by Gordon and Leeper (1994) stem from this assumption.
33. The standard-deviation bands for the impulse response
functions are computed based on 10,824 random draws.
34. If the increase in the funds rate in the short run is sufficiently strong, the expectations theory of the term structure may
hold even though the model appears to have questionable
longer-run implications.
35. To see this, normalize the supply functions in the two models to have ones on TR\ Model 2 implies a coefficient on
commodity prices of .021, and Model 3 implies a coefficient of 3.25.
36. As before, the chart is drawn for a policy shock that raises the
funds rate 25 basis points at impact. The standard-deviation
bands for the impulse response functions are computed
based on 9,664 random draws.
37. As reported in Tables 2 through 4, classical hypothesis tests
reject Model 1 at a 2 percent confidence level and Model 2
at a 5 percent level. Model 3 cannot be rejected. Using
Sims's (1980a) correction to improve the small sample
properties of the test statistic, Models 1 through 3 can never
be rejected at higher than a 10 percent confidence level.
The Akaike criterion for the (just-identified) models that
impose extreme assumptions on interest elasticities of the
supply of reserves—Models TR and R—is 3234.189, while
the Schwarz criterion for these models is 3152.023. Consequently, the Akaike criterion ranks the models in the order:
Model 3, Model 1, Model 2, Models TR and R. The Schwarz
criterion ranks them in the order: Model 1, Model 2, Model 3,
Models TR and R. The Akaike criterion, and the Schwarz
criterion even more strongly, penalize the fit of the model
for requiring many parameters. Because Models TR and R
estimate twenty-eight parameters, Model 1 estimates twentythree, Model 2 estimates twenty-four, and Model 3 estimates twenty-six, it is possible for these alternative model
selection criteria to imply different rankings in terms of
goodness of fit than the straight likelihood criteria.
38. Under the normalization that the shocks have mean 0 and
variance 1, a "big" surprise in the funds rate requires policy
shocks of magnitude at least 1.23 in Model R, 1.69 in Model 1,4.51 in Model 3, and 29.20 in Model 4.
39. A "typical" shock is taken to be 1 standard deviation, which
equals unity in each model.
July/August 1995
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July/August 1995
f 71
Testing the Informativeness
of Regional and Local
Retail Sales Data
Gustavo A. Uceda
mong the potentially useful and informative low-level government data are monthly retail sales data series produced by the
U.S. Department of Commerce. Although part of this large collection of retail sales estimates released to analysts does not meet
Commerce's publication standards because of the small samples
from which the estimates are generally derived, the unpublished data may
still provide valuable historical and industry detail for several U.S. geographic areas dating back to 1978. Analysts monitoring retail spending in states
and metropolitan statistical areas (MSAs) may find them useful supplements
to the Commerce Department's published data.
The author is an economic
analyst in the regional
section of the Atlanta Fed's
research department. He
thanks Irving J. True of the
U.S. Bureau of the Census for
reviewing the article and
especially Frank King, Tom
Cunningham, and Andrew
Kr ike las for valuable
comments on early drafts.
Federal Reserve Bank of Atlanta
Available in both printed and electronic forms, the regional, state, and
metro area data feature detailed accounts of personal consumption expenditures, a measure that accounts for about two-thirds of the nation's gross domestic product (GDP). The data report provides monthly observations on
overall and selected categories of retail sales for the nation and several subnational areas. While the amount of detail is impressive, these estimates
have several limitations that are worth discussing along with the ways in
which the data are useful.
The purpose of this article is to examine whether the range of historical,
geographic, and product information in the retail sales data can offset limitations such as small sample size and volatility. The discussion considers
the usefulness of combining the unpublished with published data, tests its
Economic Review
39
correlation with regional trends, and explores the relationship between the Sixth Federal Reserve District's
retail sales as depicted by this data and measures of
district employment. 1
Published and Unpublished
Monthly Retail Trade Data
Each month the Department of Commerce publishes
a wide variety of retail trade statistics in Monthly Retail
Trade—Sales and Inventories (MRT). MRT series are
also available in electronic f o r m f r o m several dataretrieval information vendors and the C o m m e r c e Department's E c o n o m i c Bulletin Board. The published
data report the dollar value of retail sales in selected categories recorded during the reference month and the
most recent twelve-month period for the nation, four geographic census regions, nine census divisions, nineteen
states, twenty-five metro areas, and nineteen submetro
areas, including the nation's four largest cities. MRT also
provides national estimates of end-of-month inventories
by category of retail trade establishment. For states and
metropolitan areas, the data estimate total retail sales,
sales of nondurable goods, department store sales, and
general merchandise, apparel, or furniture store (GAF)
sales. For the Southeast, published estimates of these
groupings are available for only three states (Florida,
Louisiana, and Tennessee), three metropolitan statistical
areas (Atlanta, Miami-Hialeah, and Tampa-St. PetersburgClearwater), and one consolidated metropolitan statistical area (Miami-Fort Lauderdale). 2
Unpublished estimates differ from the published reports in two ways that add to their importance. First, the
unpublished data provide retail sales estimates for nine
additional states/areas: four from the South (Delaware,
Georgia, Kentucky, and the District of Columbia), three
f r o m the West (Arizona, Colorado, and Washington),
and one each f r o m the Northeast (Connecticut) and
Midwest (Kansas) census regions. Second, the unpublished data include additional information on consumer
spending in states and metropolitan areas. For most
states and MSAs, data for up to fifteen retail categories
(see Table 1 for a list) are available from January 1978
to the present and can be obtained from the Bureau of
the Census, for a fee, in printed form or on computer
diskettes. In releasing these data to the public, however,
the bureau explicitly notes that these unpublished estimates are not nearly as statistically reliable as the more
highly aggregated data series reported in Monthly Retail
Trade—Sales and Inventories.
Economic
40
Review
t/nderstanding the Published Data
In order to be clear about the significance of differences in the published and unpublished data, it is nece s s a r y to k e e p in m i n d that b o t h p r e l i m i n a r y and
revised monthly retail sales figures are derived from a
survey of approximately 12,500 retail establishments
across the nation. 3 Several key concepts and methodologies used in the production of the retail survey and
the published report are important for understanding
the reliability of retail sales as a regional economic indicator. 4
It is crucial that analysts distinguish between preliminary and revised benchmark statistics. The statistics p u b l i s h e d in Monthly Retail Trade—Sales
and
Inventories are compiled f r o m a comprehensive reporting process linked to the C o m m e r c e Department's Annual Retail Trade Survey and its five-year Census of
Retail Trade. Monthly estimates are revised each year
according to b e n c h m a r k s obtained f r o m the A n n u a l
Survey of Retail Trade. With each January release, the
benchmarking operation revises monthly estimates for
several recent years, adjusting twelve monthly estimates for a given year to annual sales figures derived
f r o m the Census of Retail Trade and Annual Retail
Trade Survey.
Analysts interested in greater accuracy and detail
should refer to the most recent Census of Retail Trade,
which is the most complete retail information available
for low-level data. The Census of Retail Trade features
retail sales data compiled from approximately 1.5 million retail establishments throughout the United States,
organized by the fifty states, the District of Columbia,
MSAs, and counties. It includes detailed Standard Industrial Classification (SIC) retail data for most geographic
areas, in addition to retailers' payroll employment data.
Unfortunately, this level of detail is available only with
a considerable time lag; the most recent Census of Retail Trade contains data through 1992.
Although the monthly retail survey results are regularly rebenchmarked to reflect the sales levels recorded
in the m o r e c o m p r e h e n s i v e annual surveys and the
quinquennial censuses of retail trade, the revised retail
sales figures in their final f o r m still contain a great deal
of information from samples. As survey results, therefore, each of the individual series reported in Monthly
Retail Trade—Sales and Inventories are subject to sampling and nonsampling errors, including errors generated by inappropriate stratification of the survey sample
and flaws in the collection and reporting of the data. In
order to provide users with a sense of the size of these
J u l y / A u g u s t 1995
Table 1
C o e f f i c i e n t s of Variations in Percent for M e d i a n Retail Sales Estimates by Kind of Business
(.September
7 994-February
1995)
United
States
South
Region
East-South
Central Division
Florida
Total Retail
0.7
1.3
3.5
3.9
5.6
9.0
Nondurable
0.8
1.2
3.5
3.6
5.7
0.2
1.0
1.0
2.0
1.9
4.2
1.2
4.4
0.7
1.9
2.0
3.6
3.7
5.5
9.2
5.0
3.0
6.5
6.7
9.6
9.6
13.1
13.0
18.8
2.4
8.2
8.5
8.2
7.3
12.0
17.4
7.4
1.2
2.5
6.5
2.3
1.6
1.6
4.5
5.6
3.6
4.8
6.1
0.6
1.3
General Merchandise
Food
Grocery
Gas Service Stations
Apparel
Eating/Drinking
Drug Stores
Other Nondurable
Durable
Building Materials
Automobile Dealers
Furniture
Other Nondurable
GAF
Atlanta
MSA
Miami
CMSA
Tampa
MSA
7.0
7.7
7.6
10.8
8.2
5.8
7.0
8.9
10.1
3.8
10.6
11.0
7.5
7.7
20.6
44.9
12.2
4.1
15.5
16.5
15.6
12.8
26.6
55.9
25.0
3.5
12.9
13.3
16.1
13.7
16.6
20.8
33.5
5.9
15.9
17.2
15.7
9.6
20.4
32.0
6.2 .
5.3
14.0
14.6
15.4
10.8
38.9
37.0
9.2
0.5
21.1
21.9
32.6
7.4
20.2
43.8
10.7
6.4
11.0
15.3
10.7
14.6
10.6
18.9
9.8
9.9
12.6
15.5
18.1
9.6
10.4
10.1
22.0
17.7
23.7
16.6
24.2
19.2
19.5
23.1
21.2
19.0
21.9
22.1
40.0
25.7
23.5
20.8
34.8
12.8
15.5
17.3
34.5
31.0
15.6
23.2
3.5
3.0
7.1
6.2
7.4
6.9
5.7
4.7
Georgia
Louisiana
Tennessee
G e o g r a p h i c areas are census regions. Based on monthly sales estimates not adjusted for seasonal variations, holiday, or trading-day differences. Published estimates in bold type. GAF
sents stores that specialize in department-store types of merchandise (general merchandise, apparel, and furniture).
Source: Monthly
Retail Trade—Sales
and Inventories
and unpublished tables. U.S. Department of C o m m e r c e , Services Division. Bureau of the Census. March 1995.
errors, Appendix B of the MRT includes an estimate of
the coefficient of variation (CV) for each of the series
reported, a statistic that provides a measure of the size
of a one-standard-deviation sampling error for each series. The CV is defined as the standard deviation of the
sample, times 100, divided by the mean of the estimated sample.
Table 1 reports the coefficients of variation for fifteen categories of retail sales in ten census-defined geographic regions. The CV for total retail sales in the
nation is listed as 0.7, which is quite small compared
with some of the other standard errors shown. For example, the C V for total retail sales for the Atlanta M S A
is 7.7 percent while for eating and drinking establishments in Atlanta the standard error increases to more
than 20 percent. This disparity in accuracy is at least
partially a statistical property of the sample size.
The information in this table reveals t w o definite
patterns: (1) the C V s for each retail category are smallest at the national level and grow larger as the geographic areas become more specific, and (2) the CVs
for particular sales categories differ according to geographic area, with some regions producing consistently
larger standard errors than others. Because the C V s for
many of the unpublished series are quite large, it is
easy to understand why the C e n s u s Bureau advises
caution in using these data for analytical purposes.
O n e reason for caution is that the Census Bureau's
sample has been chosen to represent retail stores in the
entire nation rather than the stores located in each of
the geographic areas. In addition, low-level data for local areas and retail groups may have a limitation arising f r o m potential overlap in reporting merchandise
groupings, which can occur because retailers sell an
ever-changing merchandise mix. Merchandise groupings are listed according to the products accounting for
the largest percentage of total sales for each establishment. For example, stores deriving their largest percentage of revenues from the sale of food products are
grouped as food retail stores despite the fact that they
may also gain revenues from sale of a wide range of
nonfood items like housewares, gasoline, and pharmacy products. Analysts should keep in mind that this reporting m e t h o d m a y not accurately represent retail
sales trends of particular lines of merchandise sold in
such establishments.
C l e a r l y , d a t a users m u s t e x e r c i s e c a u t i o n w h e n
drawing conclusions from unpublished monthly lowlevel data. Nonetheless, these data may be a valuable
source of information about retail activity as long as
the analyst takes the d a t a limitations into a c c o u n t .
Those who favor using the unpublished reports point
Economic
4 2
Review
out that the estimates are linked to a consistent methodology designed by the Census Bureau in producing the
annual and five-year estimates.
R e tail Sales Data as an Indicator of
Regional Economic Activity
Analysts use the national retail sales report as a key
e c o n o m i c indicator. Retail j o b s m a k e up about onefifth of the nation's nonfarm employment. The data also
play an important role in deriving personal consumption expenditures. In addition, like n o n f a r m employment, the retail sales data series is a component of the
coincident index of economic activity, an important national indicator designed to confirm the timing of business cycle changes. In short, at the national level retail
sales are "probably the most closely followed indicator
used f o r j u d g i n g the strength of the consumer sector. In
popular analysis, it also tends to be used as a broad
yardstick f o r the health of the e c o n o m y " (R. M a r k
Rogers 1994, 62).
But is the retail sales report an equally useful barometer f o r r e g i o n a l a n a l y s t s ? D o p u b l i s h e d and u n p u b l i s h e d regional retail sales data also contain inf o r m a t i o n u s e f u l in f o r e c a s t i n g regional e c o n o m i c
performance? Chart 1, which compares the data over
time, suggests a clear association between real retail
sales values and m a n u f a c t u r i n g e m p l o y m e n t for the
United States and the district during the 1990-94 period. While this chart is useful for illustrating the linkage
between c o n s u m e r spending and m a n u f a c t u r i n g e m ployment, it tells little about how changes in one variable are associated with changes in the other.
More detailed and sophisticated tests of the regional
retail sales data's u s e f u l n e s s involve using what are
called Granger-causality tests. Simply put, a data series
X (say, retail sales) is said to Granger-cause a series Y
(say, employment) if Y can be better forecast by using
past values of X in addition to past values of Y than it
can be by using past values of Y alone. (See the box on
page 4 6 for a m o r e detailed discussion of Grangercausality and Thomas A. Doan 1992, chap. 6, 10.)
These tests are easily perfonned using a vector autoregression (VAR), which is a set of equations using
simple linear regression techniques. (Details of the
models are discussed below.)
The analysis uses two sets of VARs. The first set
tests bivariate relationships between three different
employment series—total nonfarm, manufacturing,
and retail—and total retail sales. The second set of
J u l y / A u g u s t 1995
Chart 1
Retail Sales and Manufacturing Employment
(Quarterly
year-to-year
Percent C h a n g e
1979
1981
percent
change,
1979.1-1994.4)
United States
1983
1985
1987
1989
1991
1993
District
Source: Federal Reserve Bank of Atlanta and U.S. Department of Commerce. Monthly Retail Trade—Sales and Inventories data converted to
real terms using G D P price deflators for personal consumption expenditures.
Federal Reserve Bank of Atlanta
Eco n o m ic Revie w
43
Granger-causality tests uses multivariate VARs with
two m a j o r retail sales variables along with three key
employment series that likely would be included in a
regional forecasting model.
The data series described are published and unpublished m o n t h l y retail sales estimates for the period
from 1978 to 1994. Data series include unpublished total retail sales for Georgia and published sales and employment data for Florida, Louisiana, Tennessee, the
United States, and the Atlanta MSA.
To address issues like seasonality and the consistency
of nominal retail values, the data were adjusted in several ways. First, the series were subjected to transformations of monthly differencing of year-over-year changes
to cancel seasonality and long-run trends. 5 Second, in
the absence of comparable regional price deflators, G D P
deflators for personal consumption expenditures were
used to convert retail values to real (inflation-adjusted)
terms. Although there may be arguments against using
national deflators for local area retail values, this step
was considered necessary for removing the price factor
from nominal retail values and allowing the computation
of retail series in real terms.
Testing by VAR. Statistical analysis can be used to
assess the degree of correlatedness between these sets
of series. In particular, these tests can be used to investigate whether G e o r g i a ' s unpublished retail data are
correlated with Georgia employment measures in the
same way that published retail sales data are correlated
with employment measures in their respective regions.
The approach is to test the correlation of current and
lagged values of Georgia's total retail sales with current and lagged values of each of three employment
measures and then compare the results with similar relationships in five other geographic areas. These areas
are the United States, Florida, Louisiana, Tennessee,
and the Atlanta MSA.
The test consists of setting up a VAR model, which
basically relates current values of an array of variables
to past values of that vector (see Table 2). That is,
+
X,
,
c
X,
\
ß12"
ß21
ß 221
+
u ,
yt
u ,
, xt.
where Yf is employment at time t, Xt is retail sales at time
t, C is constant,
is the residual term, and the null hypothesis is expressed as // ( 1 : 6, 2 = 0 for all s = 1 , . . . , 6.
The m o d e l estimates the regression c o e f f i c i e n t s
using lag values of a bivariate relationship with an exclusion restriction that enables identification of statisti
44
Economic
Review
cally significant coefficients. In this case, employment
variables (Y) are related to one- to six-month lag values of retail sales (.X) and also by lagged values of the
dependent employment variable. A hypothesis test that
past X is not c o r r e l a t e d w i t h the c u r r e n t Y is then
probed by excluding lag values of the retail sales variable. The F-statistics and their significance levels noted
with asterisks provide evidence to reject the null hypothesis that the variables tested are hardly related or
not related at all.
Table 2 reports the F-statistics in the VAR model
for corrected second differences in total, manufacturing, and retail trade employment variables. Three major conclusions result: (1) Retail sales are significantly
correlated with total and manufacturing employment in
three of the six areas tested—the United States, Georgia, and T e n n e s s e e . H o w e v e r , the R2 v a l u e s corres p o n d i n g to these tests are relatively low f o r total
employment, explaining only about 35 percent of the
variation in employment for the United States and less
than 18 percent for district areas. In addition, the retail
sales variable was not correlated with retail employment in any of the geographic areas tested. (2) Retail
sales variables were more closely correlated with manufacturing employment than total employment for all
areas except Georgia. (3) An overall assessment of the
test results for total and m a n u f a c t u r i n g e m p l o y m e n t
shows that retail sales are closely correlated with employment at the national level. Georgia results are similar to or better than those obtained using published
data from other areas. Measuring the significance of
the retail variable in a bivariate relationship, this test
tells us that important factors besides retail sales account for much of the variation in employment.
As noted, these first VAR models used one- to sixmonth lagged values to estimate the regression parameters. In reality, forecasters generally use all available
information, including the v a r i a b l e s ' c o n t e m p o r a n e ous values. Introducing a variant to the regression described above, using zero- to six-month lags, led to the
following conclusions: (1) Changes in retail sales were
significantly correlated with changes in at least two of
the employment variables in five of the six geographic
areas tested, with Georgia results showing consistency
with those of the United States and other areas. (2) The
R2 values were noticeably stronger in manufacturing
for most areas but particularly for the United States.
The results also indicated that one-fourth of the variation in the nation's retail employment can be predicted
by changes in retail sales.
On the basis of these bivariate tests it seems fair to
say that the use of regional retail sales data, including
J u l y / A u g u s t 1995
Table 2
VAR Tests on Employment Measures
Predicted by Total Sales Data
Employment
Variables by Areas
Retail Sales,
Lagged O n e to Six Months
Retail Sales,
Lagged Zero to Six Months
F-tests
R2
F-tests
R2
United States
Total Nonfarm
Manufacturing
Retail
3.36***
4.18"*
0.84
0.35
0.50
0.09
7.08***
4.77*"
5.64***
0.44
0.52
0.23
Georgia
Total Nonfarm
Manufacturing
Retail
3.03***
2.09**
0.90
0.18
0.15
0.03
4.07***
3.27***
1.78*
0.21
0.19
0.06
Florida
Total Nonfarm
Manufacturing
Retail
0.59
1.52
0.41
0.18
0.39
0.13
3.06'**
2.12*
0.88
0.26
0.41
0.15
Louisiana
Total Nonfarm
Manufacturing
Retail
0.55
0.99
0.52
0.09
0.23
-0.04
2.52***
1.30
0.49
0.15
0.24
-0.05
Tennessee
Total Nonfarm
Manufacturing
Retail
2.93***
2.26"*
0.50
0.13
0.33
-0.02
5.09***
4.35***
1.48
0.20
0.38
0.01
Atlanta MSA
Total Nonfarm
Manufacturing
Retail
1.51
0.26
1.72
0.07
-0.02
0.03
3.14
2.27
2.13
o.13
0.05
0X)5
An F-statistic noted with "** indicates a significance at the 1 percent confidence level. Likewise, ratios marked with *" and * stand for a significant confidence level of 5 and 10 percent, respectively.
Source: Calculated by Federal Reserve Bank of Atlanta using data from the U.S. Department of Commerce and the U.S. Department of Labor, Bureau of Labor Statistics.
unpublished data, can sometimes add information important for forecasting changes in levels of regional
employment. An additional step in exploring these data
relationships would be to test for Granger-causality in
more complex VARs. This research expands the coverage of retail and employment variables by computing
multivariate VARs with three e m p l o y m e n t and two
retail sales variables. These variables are nonmanufacturing, durable manufacturing, and nondurable manu-
Digitized Federal
for FRASER
Reserve Bank of Atlanta
facturing employment and durable and nondurable retail sales. The e m p l o y m e n t variables add up to total
nonfarm employment; the retail sales variables, to total
retail sales.
Together, these five variables provide a partially disaggregated view of employment and total retail sales
in each of the regions examined. Table 3 presents the
results of the s e v e n sets of f i v e - v a r i a b l e G r a n g e r causality tests performed on these data. In each case,
Eco n o m ic Revie w
45
the figures in the cells of the table report the F-statistic
with the c o r r e s p o n d i n g c o n f i d e n c e level associated
with testing the null hypothesis: The column variable
does not Granger-cause the r o w variable. If this hypothesis is rejected one accepts the alternative hypothesis: that the column variable does indeed Granger-cause
the row variable.
The larger the F-statistic the lower the likelihood
that the researcher will make a mistake by incorrectly
rejecting the null hypothesis of no linear relationship.
T h e c o n f i d e n c e levels noted with asterisks state the
probabilities of errors that support such rejection. Observing asterisks in the t w o right-hand c o l u m n s for
each region is a quick way to determine whether the retail sales variables contain information that might be
useful to regional employment forecasters. 6
The tests indicate that retail sales data do contain information useful in predicting e m p l o y m e n t series in
several regional areas, with the correlations existing at
the state and metropolitan area levels. For example, test
results for Florida, Georgia, L o u i s i a n a , the Atlanta
M S A , and the district all indicate that one or both of
the retail sales variables contain information that might
be useful for predicting at least one of the regional employment series. However, these tests also indicate that
retail sales data would be of little value in improving
employment forecasts for Tennessee.
The most interesting findings reported in Table 3 are
the ones contained in the off-diagonal cells of each
The Meaning o
In 1969, C.W. Granger introduced the concept of
causality while examining the underlying assumptions of
an econometric model estimated from time series data.
The Granger test uses the /-"-statistic to examine whether
one variable statistically explains the other. In simple
terms, a series X is said to Granger cause Y if the variable Y can be forecast better by using past values of X in
addition to past values of Y than it can be by using past
values of Y alone. The Granger test consists of running
regressions of Y on itself lagged and on a set of lagged X
values. If the lagged values of X do not contribute a
statistically significant explanation, then X does not
"Granger-cause" Y (see Adrian C. Darnell 1994, 41-43).
Similarly, to examine if Y causes X the procedure is reversed and the results examined by their F-test values,
which in turn determine if the regression coefficients are
sufficient to reject the null hypothesis of no linear relationship. The causality concept can be unidirectional (X
causes Y, but Y does not cause X) or bidirectional (Y and
X cause each other).
4 6
Economic Review
five-variable model, particularly those in the last two
columns. These results indicate that in every geographic region, at least one of the retail sales variables appears to contain information useful for predicting one
or more of the other four variables. For example, in the
nation the results suggest that each of the two retail
sales variables contain information useful for predicting the other sales variable. According to these tests,
though, national retail sales data do not contain any information useful for predicting the three employment
series examined.
One final set of results reported in Table 3 deserves
mention. Tests for each of the seven regions indicate
that at least one of the employment variables contains
information that would improve forecasts of the retail
sales variables. At the national level, only nondurable
manufacturing employment is correlated. However, results for all the regions indicate that employment variables Granger-cause more than one of the retail sales
variables, particularly in Georgia, where nonmanufacturing employment Granger-causes both durable and
nondurable retail sales while nondurable goods manufacturing e m p l o y m e n t Granger-causes sales of nondurable goods. Test results also indicate that for both
Louisiana and the Atlanta MSA, nondurable goods manufacturing e m p l o y m e n t Granger-causes sales of both
durable and nondurable goods. Generally, understanding
temporal causality between these variables can have
practical applications for users of regional data.
mger-Causality
The Granger-causality test is closely related to the
concepts of exogeneity and endogeneity (when a variable
is determined either outside or inside, respectively, a
jointly determined model), which hold that a classical exogenous variable can only be a cause and not an effect
whereas an endogenous variable can be both cause and
effect. In the Granger-causality notion, the premise suggested is that the past can cause the future, the future cannot cause the past, and such temporal ordering is not
sufficient evidence to assert causality. The main concerns
are with temporal ordering and the predictive ability of
variables rather than causality.
The power of the Granger-causality test is greatest
when used for the purpose for which it was designed: to
determine whether one variable might be able to aid in
the forecasting of another. The existence of a temporal
ordering among variables, although insufficient to prove
causality, generally has some value as a predictive tool in
forecasting.
July/August 1995
Table 3
Granger-Causality Tests for Selected Geographic Areas
Variables (X)
Employment Variables
Retail Sales Variables
Durable
Manufacturing
Nondurable
Manufacturing
Durable
Goods
Nondurable
Goods
4.2129'
0.7370
0.4597
1.5263*
0.5952
1.0968
6.4639*
1.6488*
2.1685*
0.8818
1.3630
2.2129*"
2.9811**
0.2540
0.9949
2.3919*
2.8499*
1.7878*
6.4681*
5.2649*
3.0288*
1.3866
0.6604
1.3202
7.5913*
Nonmanufacturing Employment
Durable Manufacturing Employment
Nondurable Manufacturing Employment
Durable Goods Sales
Nondurable Goods Sales
Louisiana
1.8238*
2.1168"
3.6661"
3.3574*
2.2070*
0.7692
2.4488'
1.3662
0.5857
1.0368
1.0707
1.8245"
1.7954"
0.6632
1.4876*
1.4392
0.7801
1.4876*
4.0057*
0.8978
1.4688*
1.0235
1.5931*
5.0384
Nonmanufacturing Employment
Durable Manufacturing Employment
Nondurable Manufacturing Employment
Durable Goods Sales
Nondurable Goods Sales
Tennessee
2.8914*
1.5366*
1.5193*
1.2887
1.0055
0.7628
4.8008
1.9140*
1.0353
0.8977
2.4851"'
0.9178
3.5852*"
1.9225"
1.6010*
1.8432*
2.0697*
2.4018*
5.5501*
3.2594*
1.2295
0.9348
0.9913
1.2589
4.8426*
Nonmanufacturing Employment
Durable Manufacturing Employment
Nondurable Manufacturing Employment
Durable Goods Sales
Nondurable Goods Sales
Atlanta MSA
3.4658*
1.8433*
0.9263
2.1613*
1.1410
0.8638
6.7232*
1.1359
1.1203
0.8215
1.7489"
1.5061*
3.7166"
1.1931
1.3897*
0.7732
0.7635
0.4860
4.0618*
1.0781
0.6623
0.8136
1.1412
2.6553*
4.6289*
Nonmanufacturing Employment
Durable Manufacturing Employment
Nondurable Manufacturing Employment
Durable Goods Sales
Nondurable Goods Sales
District
3.6082*
1.4139
0.8807
1.5477*
0.8437
0.9275
2.7239*
0.9277
1.4471
1.0197
1.9631"
1.6915*
1.9502"
3.0218"*
2.6071"*
1.6523*
1.0909
1.5992*
2.2772*
1.5100*
1.4239
1.4208
0.7312
1.3093
4.8530*
Nonmanufacturing Employment
Durable Manufacturing Employment
Nondurable Manufacturing Employment
Durable Goods Sales
Nondurable Goods Sales
United States
3.5588*
0.9179
1.1177
1.7288*
1.4942*
1.6696*
8.1049*
1.1490
1.0720
0.9683
1.0874
3.3242*"
2.8674*"
0.9791
1.1630
0.8327
1.1350
5.1070*
3.2554*
1.3438
0.7326
1.1040
2.4426*
9.4079*
Nonmanufacturing Employment
Durable Manufacturing Employment
Nondurable Manufacturing Employment
Durable Goods Sales
Nondurable Goods Sales
3.1997"
1.8448*
0.5231
1.3769
1.2943
1.1397
6.2042*
1.2451
0.6829
1.1446
1.4320
4.6311"*
1.7845"
0.5890
1.5985*
0.4816
0.6942
0.8504
2.8196*
2.1102*
1.0514
0.7930
0.3173
1.5444*
12.8229*
Variables (Y)
Florida
Nonmanufacturing Employment
Durable Manufacturing Employment
Nondurable Manufacturing Employment
Durable Goods Sales
Nondurable Goods Sales
Georgia
Nonmanufacturing
1.6208*
1.8010*
Ratios are F-statistics of the test of the null hypothesis that the column variable X d o e s not Granger-cause the raw variable Y. Ratios reported
with " denote the acceptance of an alternative hypothesis that the column variable X d o e s in fact Granger-cause the raw variable Y. An Fstatistic noted with "" indicates a significance at the 1 percent confidence level. Likewise, ratios marked with " and " stand for a significant
confidence level of 5 and 10 percent, respectively.
Source: Calculated by Federal Reserve Bank of Atlanta using data from the U.S. Department of Commerce and the U.S. Department of Labor, Bureau of Labor Statistics.
Federal
Reserve Bank of Atlanta
Eco n o m ic Revie w
47
on the r e f i n e m e n t of e m p l o y m e n t forecasts are in fact
Conclusion
p r o m o t i n g the u s e of p u b l i s h e d and u n p u b l i s h e d retail
sales data a l o n g w i t h an array of e c o n o m i c statistics
available to regional researchers. 7
T h i s article s u g g e s t s that i m p o r t a n t i n f o r m a t i o n is
provided by published and u n p u b l i s h e d retail sales data.
A l t h o u g h the release s c h e d u l e s of the m o n t h l y regional
retail sales report are several w e e k s b e h i n d the m o r e
current e m p l o y m e n t releases, the d a t a ' s u s e f u l n e s s in
a n a l y z i n g a n d f o r e c a s t i n g regional e c o n o m i e s should
not b e totally d i s c o u n t e d . Despite the limitations of unpublished retail data discussed in this article the relev a n t a m o u n t of i n f o r m a t i o n a v a i l a b l e f r o m r e g i o n a l
retail s p e n d i n g d a t a s h o u l d e n c o u r a g e r e s e a r c h e r s to
test f u r t h e r the u s e f u l n e s s of this data. R e c e n t studies
Given the importance of estimating c o n s u m e r strength
in local c o m m u n i t i e s , published a n d u n p u b l i s h e d data
c a n fill a n u m b e r of i n f o r m a t i o n gaps. F o r e x a m p l e , the
c o m p r e h e n s i v e n e s s of retail i n f o r m a t i o n b e i n g reported
t o d a y a l l o w s users to access i m p o r t a n t data such as retail m a r k e t s ' p o t e n t i a l , r e t a i l e r s ' payroll i n c o m e , a n d
other growth indicators related to locally important
c o n s u m e r m a r k e t s . S u c h t y p e s of i n f o r m a t i o n can be
h e l p f u l to retailers, d e v e l o p e r s , a n d o t h e r s in m a k i n g
b u s i n e s s decisions.
Notes
1. The Federal Reserve's Sixth District encompasses six states
in whole or part: Alabama, Florida, Georgia, Louisiana, Mississippi, and Tennessee. In this article, for the purpose of
making consistent comparisons with available data, the term
district also includes the portions of Louisiana, Mississippi,
and Tennessee not in the district and the state of Kentucky.
The derived district conforms to the availability of retail sales
data for the Census' East South Central Division (Alabama,
Mississippi, Tennessee, and Kentucky) plus individually reported data for the states of Florida, Georgia, and Louisiana.
2. The Office of Management and Budget defines MSAs as urban centers with populations of at least 50,000. The terms "primary" and "consolidated" metropolitan areas are defined by
the Office of Management and Budget on the basis of such
factors as commuting patterns, population density, and growth.
Metro areas with a million or more people and identified by
other specific factors may be subdivided into primary
metropolitan statistical areas (PMSAs). When an area is divided into PMSAs, the entire area becomes a consolidated
metropolitan statistical area (CMSA). The CMSA is divided
into PMSAs generally because of the close social and economic links of the PMSAs with each other and with the CMSA nucleus.
3. For a broad overview of the methodology and data issues related to the Survey of Retail Trade see Rogers (1994).
4. See Mason (1992) and Appendixes A and B of the MRT report for detailed discussions of technical concepts like sample
4 8
Economic
Review
selection and methodology for data collection, revisions, and
other issues such as the linkage between monthly and annual
retail estimates, seasonal adjustment, and benchmarks of the
data.
5. The raw data analyzed in these tests were subjected to two
transformations. First, in order to eliminate seasonality in the
data, all series were differenced annually to produce yearover-year changes. Second, these transformed data were subjected to an augmented Dickey-Fuller test. This test indicated
that the majority of the series contained a long-run trend, further suggesting that monthly differencing of the data was appropriate.
6. Readers should note that in the test results presented in Table 3,
the on-diagonal elements of the five-variable regional models
in bold type are in a majority of cases significant at the 1 percent confidence level. However, it is important to recognize
that the results reported in these cells do not represent true
Granger-causality tests but rather tests of the hypothesis that
past values of the row variable contain information useful for
forecasting the row variable itself.
7. Krikelas (1994), for example, argued that the Bureau of Labor
Statistics (BLS) might be able to improve upon its preliminary estimates of total nonfarm payroll employment at both
the state and national level by using additional information
available at the time of the release of those estimates.
July/August 1995
References
Darnell, Adrian C. A Dictionary of Econometrics.
Aldershot,
England: Edward Elgar Publishing Limited, 1994.
Doan, Thomas A. RATS User's Manual. Evanston, 111.: Estima,
1992.
Krikelas, Andrew C. "Revisions to Payroll Employment Data:
Are They Predictable?" Federal Reserve Bank of Atlanta
Economic Review 19 (November/Deccmber 1994): 17-29.
Mason, Joseph R. "A Guide to Monthly Retail Sales Statistics."
Illinois Business Review (Fall 1992): 10-12.
Rogers, R. Mark. Handbook of Key Economic Indicators.
York: Irving Professional Publishing, 1994.
Reserve B a n k of Atlanta
DigitizedFederal
for FRASER
U.S. Department of Commerce. Bureau of the Census. Economics and Statistics Administration. Current Business Reports: Monthly Retail Trade—Sales and Inventories. Various
issues.
U.S. Department of Commerce. Bureau of the Census. Economics and Statistics Administration. 1992 Census of Retail
Trade: Geographic Area Series—United States. RC92-A-52.
November 1994.
New
Eco n o m ic Revie w
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