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1996 Quarter 1
Practical Issues in
Monetary Policy Targeting
2
by Stephen G. Cecchetti
The Reduced Form as an
Empirical Tool: A Cautionary
Tale from the Financial Veil
16
by Ben Craig and Christopher A. Richardson
Predicting Real Growth
Using the Yield Curve
by Joseph G. Haubrich and Ann M. Dombrosky
FEDERAL RESERVE BANK
OF CLEVELAND
26
http://clevelandfed.org/research/review
Economic Review 1996 Q1
1
ECONOMIC REVIEW
1996 Quarter 1
Vol. 32, No. 1
Practical Issues
in Monetary Policy Targeting
2
by Stephen G. Cecchetti
This paper outlines the considerable information requirements faced by
monetary policymakers and looks at the data to see what we actually know
and how well we know it. The author’s main conclusion is that our forecasting ability is very poor, which creates uncertainty that leads to cautious
policymaking. At a more practical level, he finds that nominal-income targeting rules are more robust than price-targeting rules in the sense that
someone who cares about the aggregate price path loses little by targeting
nominal income, but someone who cares about nominal income is made
much worse off by moving to a price-level target, which substantially
destabilizes real output.
The Reduced Form as an
Empirical Tool: A Cautionary
Tale from the Financial Veil
16
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by Ben Craig and Christopher A. Richardson
The reduced-form empirical strategy has been used for more than 30 years
to test the Modigliani–Miller model of corporate financial structure. Curiously, the early tests almost always accepted the model, whereas subsequent tests almost always reject it. This paper considers the limitations of
the reduced-form strategy that led to the early, spurious results, and
demonstrates why an empirical strategy that is not closely tied to an underlying economic theory of behavior will usually yield estimates that are too
imprecise or too unreliable to form a basis for policy.
Predicting Real Growth
Using the Yield Curve
26
by Joseph G. Haubrich and Ann M. Dombrosky
The yield curve, which relates interest rates to notes and bonds of various
maturities, is often used by economists and business analysts to predict
future economic growth. But how reliable is it? This article uses out-ofsample regressions to determine how well the 10-year, three-month yield
spread predicts future real GDP growth. The authors show that although
the yield curve is a good predictor over the entire 30-year sample period,
it has become much less accurate over the last decade.
Editorial Board:
Charles T. Carlstrom
Ben Craig
Kevin J. Lansing
William P. Osterberg
Editors: Tess Ferg
Michele Lachman
Robin Ratliff
Design: Michael Galka
Typography: Liz Hanna
Opinions stated in Economic Review are those of the authors and
not necessarily those of the Federal Reserve Bank of Cleveland or
of the Board of Governors of the
Federal Reserve System.
Material may be reprinted provided that the source is credited.
Please send copies of reprinted
material to the editors.
ISSN 0013-0281
2
Practical Issues
in Monetary Policy
Targeting
by Stephen G. Cecchetti
Introduction
What do monetary policymakers need to know
and when do they need to know it? Textbook
descriptions and academic discussions of
policymaking usually ignore the practical problems faced by those who make the decisions
and take the actions. While most economists
would agree that monetary policy has real
short-run effects and is most likely neutral in
the long run, they could provide no more than
informed speculation in helping decide at what
level to set the target for a policy instrument
and when to change it.
This paper’s purpose is to outline the type
of information monetary policymakers need in
practice, and to examine the data to see what
we actually know.1 Any policy rule must be formulated in several clearly defined steps. First,
one must identify an operational instrument,
best thought of as something policymakers can
control precisely, like the federal funds rate or
the monetary base. Next, there must be a target.
Many central banks have stated that price stability is their goal, but an obvious alternative to
targeting the aggregate price level is targeting
nominal income.2 In addition to choosing the
target variable itself, formulating policy necessi-
Stephen G. Cecchetti is a professor
of economics at Ohio State University and a research associate at the
National Bureau of Economic
Research and the Federal Reserve
Bank of Cleveland. The author
thanks Charles T. Carlstrom for his
helpful comments on this article.
tates specifying a loss function: What is the relative importance of large and small, or positive
and negative, deviations of aggregate prices
from their target path? One might also assign a
cost to large movements in the target variable.
For example, it might be important for the Federal Reserve to have a reputation for changing
the federal funds rate target smoothly, without
large movements or sudden reversals, to avoid
creating uncertainty in financial markets.
The next stage in devising a monetary rule is
to link the operating instrument with the target.
This requires specification and estimation of a
macroeconomic model. One needs quantitative
answers to questions of the form “If the federal
funds rate is moved by one percentage point,
what will be the path of the aggregate price
level and real output over the following three
years?’’ Not only do we require a point estimate
of this response function, but it is also crucial
that we know how precise our knowledge is in
a statistical sense.
■ 1 This work is based on Cecchetti (1995).
■ 2 I will not discuss the difference between price-level and inflation
targeting. While this is a potentially important practical distinction, it is
beyond the scope of this paper.
3
Finally, policymakers need a timely estimate
of their target variable’s future pathin the absence of any policy actions. In other words,
they must know when external shocks hit the
economy, how large they are, and what their
impact on the time path of aggregate prices
and real output will be.
The next section offers a detailed discussion
of the modeling issue: How do we formulate
and estimate the necessary simple, dynamic,
empirical macroeconomic model? The section’s
first major part looks at econometric identification. What must we assume in order to disentangle the fluctuations in output and prices into
their various components? How might we actually estimate the impact of monetary policy on
macroeconomic quantities of interest?
The section’s second major part discusses
the issue of structural stability. Monetary policymakers change their emphasis fairly frequently,
focusing on one indicator one year and another
the next. How does this affect our attempt to
estimate the relationship between the variables
that policymakers control (like the federal
funds rate) and the things we care about? Can
we estimate a stable relationship between output, prices, and interest rates over any reasonable period?
The methodological discussion of modeling
issues is followed by section II, in which I present a particular model and examine its properties. Several different types of results are
included. First, I look at the impact of different
sources of shocks on the variables of interest.
Besides allowing answers to questions like “If
the federal funds rate were to rise by 100 basis
points, how much would output change over
the next three years?” this approach makes it
possible to examine the sources of fluctuations
in output and prices. For example, has monetary policy been responsible for a significant
share of output variation over the past decade?
Section III discusses how a policy rule can
be formulated. The first step is to specify an
objective function: What do policymakers actually want to stabilize? This discussion emphasizes the need for taking account of imprecision
when forming a policy rule. We are uncertain
how changes in the interest rate affect the size
and timing of output and price movements.
This means we cannot confidently predict policy actions’ impact on target variables, so that
policy actions differ from what they would be
if we had perfect knowledge. From the theoretical discussion, I move on to examine several
possible objective functions of policy and the
interest rate paths implied by the combination
of each rule and the estimated model. I focus
throughout on the importance of employing
rules that recognize the imprecision of our
knowledge regarding the size of the linkages
we need to estimate.
I reach three significant conclusions: First,
since prices take time to respond to all types of
economic shocks, the objective of price stability
implies raising the federal funds rate immediately after a shock, instead of waiting for prices
to rise. Second, and more important, comparing
the results of price-level targeting with those of
nominal-income targeting implies that the difficulties inherent in forecasting and controlling
the former provide an argument for concentrating on the latter. Finally, it is possible to use
policy rules to see how closely recent movements in the federal funds rate conform to
those implied by either price-level or nominalincome targeting rules. The results show that
the policy that is optimal in this limited sense
involves faster, bigger movements than those
shown by the actual federal funds rate path.
This suggests that policymakers’ actions have
been based on something akin to nominalincome targeting, but with costs attached to
interest rate movements.
I. Modeling Issues
The single biggest problem in formulating monetary policy rules is how to construct an empirical macroeconomic model that describes the
critical aspects of the economy. It is important
that the model be dynamic, summarizing the
impacts of shocks to the economy—as well as
those of intended policy actions—over time.
The standard response to this challenge has
been to construct various forms of vector
autoregressions (VAR). A VAR can answer a
question of the following type: “If the federal
funds rate moves, when and by how much
does the price level change?” Policymakers
require quantitative answers to exactly these
kinds of questions.
To construct any usable empirical model, a
researcher must make a number of choices. I
will describe four of these: 1) Which variables
should be included in the model? 2) What is
the appropriate measure of monetary policy?
3) How can the model be identified econometrically? and 4) Over what sample period should
the model be estimated?
4
Variable Inclusion
Identification
When trying to discern the relationship between
A model builder’s most complex decision is formulating a set of “identifying assumptions.”
This is also the subtlest issue and the one that
has generated the most discussion in the literature. It is like the textbook question about estimating supply and demand curves: There, if
data on the price and quantity of a good in a
market both move, we cannot tell whether the
root cause of the change was a shift in supply
or a shift in demand. Here, things are a bit less
transparent, because there are no clearly defined supply and demand curves in the standard microeconomic sense. Instead, it is necessary to distinguish whether prices, output, and
interest rates moved as a result of policy shifts,
or because of factors like changes in the price
of oil (an aggregate supply shock) or in the demand for money (an aggregate demand shock).
To understand the problem and its solution
more fully, we can begin by writing down a
dynamic structural model in its moving-average
form:
inflation, output, and monetary policy, should
we include other variables in the model? Our
answer is guided by the findings of Sims (1992),
who estimates a model with prices, output, and
an interest rate for several countries. His robust
overall conclusion is that with this specification,
increases in the interest rate (which should signal policy contractions) lead to prices that are
higher than otherwise expected, not lower. This
problem, which came to be known as the “price
puzzle,” can be eliminated by including commodity prices in the model. The reasoning is
that the policymaker has additional knowledge
about prices’ future path that the three-variable
model does not adequately summarize. Policy
contractions, being based on this omitted information, signal that these other indicators are
pointing toward higher prices.
More recent research, like that of Christiano,
Eichenbaum, and Evans (1996a, 1996b), has
shown that including commodity prices eliminates the puzzle. They suggest that higher commodity prices mean higher future overall
prices, and that policymakers respond to this.
In other words, an upward move in commodity
prices precedes both a rise in the price level
and a tightening of policy in the form of an
increase in the federal funds rate. The omission
of this information from the original Sims formulation led to a bias in which contractionary
policy predicts higher aggregate prices. This is
not a policy change, but simply a reaction to
external events. The models of Christiano,
Eichenbaum, and Evans do have the following
property: Moving toward a more contractionary
monetary policy drives prices down (relative to
the trajectory they would follow without the
policy change).
Choice of Policy
Instrument
Beyond the question of which variables the
model should include, it is necessary to specify
a monetary policy instrument. Should one
assume that policymakers are focusing on the
federal funds rate itself (or behaving as if they
were), or would it be more realistic to use nonborrowed reserves as the instrument? The literature takes up this issue in some detail.3 Because
events of the past 15 years suggest that the primary focus has been on the federal funds rate, I
will assume that it contains the information
necessary to gauge policy actions.4
(1)
pt = A11(L)ept + A12(L)ect
+ A13(L)eyt + A14(L)u t
(2)
p tc = A21(L)ept + A22(L)ect
+ A23(L)eyt + A24(L)u t
(3)
yt = A31(L)ept + A32(L)ect
+ A33(L)eyt + A34(L)u t
(4)
rt = A41(L)ept + A42(L)ect
+ A43(L)eyt + A44(L)u t ,
where pt , p tc, and yt are the logs of the aggregate price level, commodity prices, and output,
respectively, rt is the policy indicator, the e’s
are exogenous shocks, and u is the policy
innovation. Equations (1) – (4) summarize the
impact of all the shocks to the economy. The
Aij (L)’s are lag polynomials in the lag operator
L. For example,
¥
A11(L)ept = S a11i Li ept
i=0
= a110 ept + a111ept – 1+ .... .
■ 3 See, for example, discussions in Christiano, Eichenbaum, and
Evans (1996a, 1996b) and Bernanke and Mihov (1995).
■ 4 Most results are unaffected by the substitution of nonborrowed
reserves, suggesting that the funds rate elasticity of reserve demand is
relatively stable.
5
Because we do not observe the shocks, it is
not possible to estimate the model (1)–(4) directly. Instead, we estimate the more familiar
VAR form and place restrictions on the coefficients (the ai j k ’s) in order to recover estimates
of the shocks.
Identification entails determining the errors
in this four-equation system, that is, the actual
sources of disturbances that lead to variation
in prices, output, and interest rates. As the appendix to this paper describes, when there are
four endogenous variables, six restrictions are
required for complete identification.
All identification schemes involve assumptions about how these sources of variation are
correlated. Researchers use two types of restrictions for this purpose. The first, based on the
pioneering work of Sims (1980), is what I will
call a “triangular identification,” which assumes
that a shock does not affect a variable contemporaneously, and so one or more of the aij 0’s
are zero. For example, it is commonly assumed
that no variable other than policy itself responds
to monetary shocks immediately, and so a 140 =
a 240 = a 340 = 0.
A more formal description of a triangular
identification begins by writing the matrix A(0)
that is composed of all the coefficients of the
Aij (0)’s—that is, all the aij 0’s. Triangular identification means assuming that six of these aij 0’s
are zero, and so
(5)
a 110
a
A(0) = 210
a 310
a 410
0
a 220
a 320
a 420
0
0
a 330
a 430
0
0
.
0
a 440
In other words, triangular identification
means that the monetary policy shock ut is
identified by assuming that no variable other
than the federal funds rate responds to it contemporaneously. The output shock, eyt , is identified by assuming that it is the portion of the
error in the output equation that is orthogonal
to the policy shock, while the commodity price
shock, ect , is the portion of the error in the
commodity price equation that is orthogonal to
these. The final part of the residual in the aggregate price equation that is orthogonal to all
three of these is the aggregate price shock, ept .
There are many other ways to constrain
the four-variable VAR and achieve identification. One, based on the work of Galí (1992),
combines two types of restrictions. The first are
contemporaneous and resemble those used in
the triangular method. The second, following
Blanchard and Quah (1989), assume that some
shocks have temporary, but not permanent, effects on some variables. For example, we might
claim that monetary shocks have no long-run
effects on real output, and so the impact of u t
on y t dies out. Formally, this involves assuming
¥
that the a34k ’s sum to zero: kS= 0 a 34k = 0.
Recalling that we need six restrictions, the
Galí-style procedure begins with two contemporaneous restrictions based on the logic of
data availability and the time people in the
economy take to act. The first constraint is that
monetary policy does not affect real output
contemporaneously (within the month). In the
notation used above, the assumption is that
a 340 = 0. This seems sensible, since production
planning is unlikely to change suddenly after a
policy innovation. The second constraint is that
the aggregate price level does not enter the
money supply rule. This also seems sensible,
because the Bureau of Labor Statistics does not
publicly release the Consumer Price Index
(CPI) until the month following its price survey.
The Galí-style, long-run restrictions, based
on Blanchard and Quah (1989), amount to
assumptions that neither monetary policy nor
aggregate price (other aggregate demand)
shocks permanently affect real output or the
real commodity price level.
Together, the two contemporaneous and
four long-run restrictions allow us to estimate
the impact of monetary policy shocks on prices
and output.
Structural Stability
Variable inclusion and identification are related.
The way in which we name various estimated
shocks in a model obviously depends on the
quantities being modeled in the first place.
While connected to the other choices, the final,
more general issue concerns the period over
which the empirical model is estimated. The
problem is that the reduced-form relationships
in the data are unlikely to be stable over any
reasonable sample.5 The problem, known
widely as the Lucas (1976) critique, is that policy rule changes alter the relationship among
endogenous variables in the economy.
It is easy to see why this might happen.
For the sake of discussion, assume that inflation
is actually determined by the following structural model:
(6)
pt + 1 = art + b1X1t + b2 X2t + w t + 1,
■ 5 For a more detailed discussion, see section 4 of Cecchetti (1995).
6
where rt is policy, w t + 1 is a random variable,
and X1t and X2t are measures of general economic conditions, like things that influence aggregate supply and money demand.
Next, assume that we can write down a
reaction function whereby policymakers automatically change their policy control variable
when economic conditions change:
(7)
rt = g1X1t + g2 X2t + nt .
The policymaker’s role is to choose g1 and g2,
the reaction of rt to X1t and X2t . Since the g’s
can be zero, a policy regime need not react to
the X ’s. The term nt is a measure of the random
component in the policy rule.
Now, consider the reduced-form regression:
(8)
pt + 1 = f1X1t + f2 X2t + xt .
Since fi = a gi + bi , changes in policy, which
are changes in the g’s, will alter the correlation
between the X’ s and p. In effect, the reducedform inflation regression subsumes the
monetary-policy reaction function (7), so that a
change in the monetary authorities’ policy
rule—which may be a change in the relative
weight placed on various indicators—will
cause changes in (8).
As a practical matter, there are several ways
to deal with the instability that may be caused
by changes in monetary policy rules. First, one
can use institutional information to restrict the
data to a period when there were no large
changes in policy procedure. Second, one can
try to estimate the timing of structural breaks.6
Alternatively, one can use time-varying parameter models, as Sims (1992) suggests. It is also
possible to simply ignore the problem and use
all of the available data.
Following my earlier work, I use only the
past decade’s data, beginning in 1984. Excepting the truncated sample period, I will ignore
the problems created by the Lucas critique in all
of the calculations that follow. This is an unfortunate necessity if any progress is to be made.
Commerce index of industrial materials prices,
and the federal funds rate, along with the triangular identification in equation (5), straightforward procedures yield estimates of the aijk ’s,
as well as a covariance matrix for these estimates. These are the time path of the impact of
innovations on the model’s endogenous variables. They tell us how any one of the four
shocks will affect any of the four variables initially—and after several months.
It is easiest to present these results in a
series of figures. Figure 1 shows estimates of 16
impulse response functions, plotted with two
standard-error bands.7 These are the response
of output, aggregate prices, commodity prices,
and the federal funds rate to a unit innovation
to each of the four shocks.
The impulse response functions are straightforward and easy to understand. Taking the policy innovation as an example, the last column
of figure 1 shows the result of an unanticipated
100-basis-point change in the federal funds rate
for one month on yt , pt , p ct , and rt over the next
three years. For example, the fourth plot in the
third row shows the impact of monetary policy
shocks (ut ) on the aggregate price level (pt ).
The estimates suggest that a one-time policy
tightening—an increase in the federal funds
rate—causes prices to rise slightly initially, then
to fall below their original level after about six
months. Over the next 30 months, the price
level continues to fall. The standard-error bands
on this figure imply that we are actually very
unsure of the response. The data indicate a
strong possibility that the policy tightening will
result in a price-level increase.
Several additional features of figure 1 are
worth noting. First, in all cases, commodity
prices (second row) respond more quickly and
in the same direction as aggregate prices (third
row). Second, for the three e shocks, the output
response seems to be more precisely estimated
■ 6 This is the technique used in Cecchetti (1995).
II. Results from
Estimating
the Model
Impulse Response
Functions
Using monthly industrial production data for
January 1984–November 1995, the CPI for
urban wage earners (CPI-U), the Journal of
■ 7 The standard-error bands in the figure are constructed using the
simple Taylor-series approximation:
^ ~
^ – b),
~ F (b) + dF (b)
F ( b)
^ (b
db b= b
^ follows
where F is any differentiable function. The variance of F ( b)
immediately as
^ – F (b) 2 ~
^
E [F ( b)
] ~ dFd b(b) b = b^ 2 Var ( b).
^
Here, we can think of the estimated impulse response functions, the Aij’ s,
as functions of the estimated reduced-form VAR coefficients, the elements
^
of R(L). Given the estimated variance of these coefficient estimates, the
^
variance of the Aij ’s can be computed by numerical differentiation.
|
[
| ]
7
F I G U R E 1
Impulse Response Functions:
Triangular Identificationa
a. Estimated response, with two standard-error bands.
NOTE: Horizontal axes are in months; vertical axes are in the change in the log per month.
SOURCE: Author’s calculations.
8
than the aggregate price response. This second
conclusion is consistent with Cochrane’s (1994)
observation that real output is forecastable with
high R 2 at horizons of several years, and with
my finding (see Cecchetti [1995]) that inflation
is difficult to forecast at horizons longer than a
single quarter.
It is very tempting to seek a correspondence
between the shocks in this four-variable VAR
and those discussed in macroeconomics textbooks. In a simple model, the basic result is
that aggregate supply shocks move prices and
output in opposite directions, while aggregate
demand shocks move them in the same direction. With this categorization, the impulse responses shown in figure 1 suggest that all of the
shocks in this model come from the demand
side. While this makes intuitive sense for the
monetary policy shock, it renders the other
classifications unsatisfactory.
One can either accept this at face value or
ask whether it might result from the identification used to generate the estimates. Taking the
second possibility seriously leads to examination of an alternative identification—the one
proposed by Galí being a natural choice. Figure 2 plots the impulse response functions from
such a model, estimated using exactly the same
data. Because of the technical difficulty associated with their construction, I do not include
standard-error bands. Here, the results differ
markedly. It now appears that the output shock,
eyt , behaves like an aggregate supply shock,
while the three remaining shocks, representing
the aggregate price-level shock, the raw material price shock, and the monetary policy shock,
lead to reactions consistent with those expected
from aggregate demand shocks.
However, we can draw an important positive
conclusion by comparing these two sets of
identifying restrictions: The impulse response
functions of the monetary policy shock are robust to changes in the identification procedure.
Policy’s impact on output and prices seems
fairly robust to the exact methods used in estimation. Since they are easier to compute, I will
now proceed using only the estimates obtained
with the simpler triangular identification.
Historical
Decompositions
While the ultimate goal is to use the estimated
dynamic model to construct policy rules, the
impulse response functions and structural innovations also allow us to compute the quantities
known as “historical forecast decompositions.”
These allocate output and price movements
into the portions accounted for by each of the
structural shocks. It is easy to understand how
these estimates are constructed from the structural model’s equations (1)–(4):
Define the impact of the monetary policy
shock on output as Hyu (t). From equation (3),
this is just
¥
(9)
Hyu (t) = Sa 34i ut – i ,
i
and analogously for the other shocks. Its estimated value, constructed from the parameter
estimates, is
(10)
^
¥
Hyu (t) = S a^ 34i u^ t – i ,
i
^
where ut is the estimated monetary policy
innovation.
Figure 3 plots the decomposition of the
movements in real output and aggregate prices
into the components attributable to monetary
and nonmonetary shocks. In constructing these,
I have truncated the sum in (9) at 60 months.
Because of the difficulty in identifying innovations from nonmonetary sources, it seems prudent to simply sum them together. That is, I plot
the fluctuations in yt and pt attributable to ut ,
^
^
Hyu (t), and Hpu (t), and the portion not attribut^
^
able to policy, [yt – Hyu (t)] and [pt – Hpu (t)].
The results show that, for the past seven
years, important movements in both output
and prices are largely accounted for by innovations other than those coming from mone^
tary policy. The blue line representing Hyu (t)
^
and Hpu (t) in the figure’s two panels has much
less variation than the green line representing
the fluctuations in yt and pt that are attributable to nonmonetary policy shocks. This result
is particularly striking for prices, where variation seems to be driven by innovations to output, raw materials prices, and the aggregate
price level itself. Aggregate supply shocks and
nonmonetary aggregate demand shocks account for most of the recent movements in
key macroeconomic variables.
III. Formulating
a Policy Rule
Issues
The main use of the empirical model described
in section I and estimated in section II is to provide quantitative answers to the questions required for implementing a policy rule. To see
9
F I G U R E
2
Impulse Response Functions:
Galí Identificationa
a. Estimated response.
NOTE: Horizontal axes are in months; vertical axes are in the change in the log per month.
SOURCE: Author’s calculations.
10
F I G U R E 3
Forecast Error Attributable
to Various Innovations
functions. Mankiw (1994) includes several papers that deal with this topic explicitly. There
are two primary candidates: price-level targets
and nominal-income targets. One version of
these involves setting the policy instrument—
the ut ’s in the model—to minimize the average
expected mean square error (MSE) of either
inflation or nominal-income growth over some
future horizon. In the inflation case, the objective function can be written as
(13)
1
min h
{u i }
where po is the log of the base-period price
level and h is the policymaker’s horizon. The
expectation in (13) is over the sampling distrib^ which is related to the covariance
ution of p,
matrix of the estimated coefficients in equation
(11). Nominal-income targeting simply replaces
the log price level in (13) with the sum of pt
and yt .
One important distinction between the objective function (13) and more standard formulations is the treatment of parameter uncertainty.
As the results in figure 1 clearly show, we are
very unsure about the size and timing of price
movements following innovations to the federal
funds rate. When constructing a policy rule, it
seems prudent to account for this lack of
knowledge.
As Brainard (1967) originally pointed out, the
presence of uncertainty has important implications. This is easily demonstrated in the present
context. Consider a simplified version of the
structural price and interest rate equations
SOURCE: Author’s calculations.
how this is done, first note that the model
implies estimated values for the aggregate price
level and real output:
(11)
h
E ( p^i – po )2,
S
i=1
p^ t = A^11 (L) ^ept + A^12 (L) ^ect
+ A^13 (L) ^eyt + A^14 (L)ut ,
(14)
pt = ept + gut
(15)
rt = ut ,
where g is a parameter. Next, take the horizon
in (13) to be one period (h = 1), and the initial
log price level to be zero, po = 0. The policy
control problem then reduces to
(16)
^
min E [p i2 ].
{u i }
(12)
y^t
=
A^31 (L) ^ept + A^32 (L) ^ect
+ A^33 (L) ^eyt + A^34 (L)ut .
A policy rule is a sequence of ut ’s that is
constructed to meet some objective. In other
words, the policymaker is allowed to pick the
path of the federal funds rate to meet a particular objective.8
The monetary policy literature includes many
discussions of the efficacy of various objective
Substituting in the expression for pt , this is
simply
(17)
^
min E [epi + g
ui ]2.
{u i }
■ 8 Feldstein and Stock (1994) examine an identical experiment, but
without parameter uncertainty.
11
If we ignore that g is estimated, then it is trivial
to generate the policy rule. It is just
(18) ui* = – 1^ epi .
g
Taking account of uncertainty in the estimate of
g, but continuing to assume that ept is known,
the minimization problem yields
(19)
ui* =
–
^
g
^2
^ epi .
[g
+ Var (g
)]
For a given ept , this leads to an unambiguously smaller response. In other words, imprecision creates caution, with policy reactions being muted in the face of uncertainty.
Reactions are further attenuated if policymakers attach a cost to the movement in instrument. Taking the same simple setup, imagine
the modified objective function
^
(20) min E [p i2 + a r^ 2t ].
{u i }
This produces the reaction function
(21)
u i* = –
^
g
e ,
^2
^
[g
+ Var (g
) + a ] pi
which will yield an even smoother path for the
interest rate than does (19).
Results
I examine results based on several policy objectives. It is worth noting that the exercise described here appears to be a gross violation of
the Lucas critique. That is to say, contrary to the
implications of the discussion in section I, I assume that the reduced-form correlations among
output, prices, and interest rates described by
equations (11) and (12) are unaffected by the
change in the policymaker’s reaction function.
There are two ways to defend the procedure.
The first is to take the view of Sims (1982)—
that parameters in these models evolve slowly
enough to make Lucas-critique considerations
quantitatively unimportant. The second defense
is to reinterpret the exercise as an attempt to
recover the objective function that policymakers were implicitly using, by trying to match the
actual federal funds rate path with that implied
by an optimal rule.
I report results for three different policy
rules. The first, which might be termed passive,
holds the federal funds rate fixed in the face of
the shock. (The model makes it clear that this
is not really a passive policy, since it involves
shocks to overcome the estimated reaction func-
tion.) The other two, which I will call active,
minimize the average MSE of either the log of
the price level or the log of nominal output
over a 36-month horizon (h = 36).9 For each
rule, I examine three experiments—one for
each structural shock. In each of the nine resulting cases, ejo = 1 and elk = 0 for l =/ j and
k =/ 0. In other words, there is a unit innovation
to one of the structural disturbances in the base
period, and that is all. I then construct individual estimates for the optimal response of interest rates to each of the shocks.
Figure 4 reports the implied path of the
federal funds rate, aggregate prices, and industrial production for each policy objective in
response to each of the three structural shocks.
The fixed federal funds rate policy results in
consistently higher output and prices than does
either of the other two polices. The activist
policies both have the same profile, whatever
the source of the shock. Output and prices
both rise initially, and then fall, with output
dropping more than prices.
Interestingly, both of the activist policies involve raising the funds rate immediately and
then lowering it slowly. This follows directly
from the fact that prices respond slowly to policy innovations (see the third row of figure 1).
The implication is that a policymaker who
wishes to stabilize prices must respond to exogenous shocks quickly, in order to ensure that
future price movements are minimized. That is
the argument for the Federal Reserve’s tightening up at the first sign of upward price pressure.
Comparing Targeting
Objectives
These calculations have direct implications for
the debate between advocates of price-level targeting and those who favor targeting nominal
GDP. To see why, I have computed the implied
root-mean-square error (RMSE) for inflation and
nominal income for each policy. For the pricetargeting case, these are the square root of the
minimized objective function (13).
Table 1 shows the results. The computations
suggest that nominal-income targeting has a
certain robustness, since inclusion of real output in the objective function increases the
RMSE for inflation only slightly. For the case of
an output shock, the increase is from 0.24 to
0.61. However, when the output shock is the
■ 9 Because the model is estimated in logs, the minimum MSE of the
nominal-income policy minimized the MSE of the sum of the log of industrial production and the log of the CPI.
12
F I G U R E
4
Interest Rate, Output, and
Price Paths following Shocks,
and the Policy Response
ε
ε
ε
ε
ε
ε
ε
ε
ε
.
Min MSE (p) policy
Fixed interest rate policy
Min MSE (p + y )
NOTE: Horizontal axes are in months; vertical axes are in the change in the log per month.
SOURCE: Author’s calculations.
13
T A B L E
source of the instability, the move from pricelevel targeting to nominal-income targeting
decreases the RMSE of nominal income substantially—from 4.12 to 0.69. In other words,
the inability to estimate precisely either the
impact of shocks on prices or prices’ response
to policy innovations argues strongly for including real variables in the objective function.
1
Comparison of Policy Responses
A v e r a g e R M S E of Inflation over a 36-Month Horizon
Source of Shock
Aggregate Commodity
Price
Price
Policy Rule
Fixed interest rate
.
Min MSE (p + y )
Min MSE (p)
2.35
2.15
0.99
1.98
1.50
0.51
Output
1.14
0.61
0.24
Comparing Actual
and Implied Interest
Rate Paths
A v e r a g e R M S E of Nominal Income over a 36-Month Horizon
Finally, one might ask how closely recent pol-
Source of Shock
Policy Rule
Aggregate
Price
Commodity
Price
Output
1.86
0.32
0.99
4.89
0.35
10.85
6.19
0.69
4.12
Fixed interest rate
.
Min MSE (p + y )
Min MSE (p)
SOURCE: Author’s calculations.
F I G U R E
5
Comparison of Optimal and Actual
Federal Funds Rate Pathsa
0
200
400
600
800
1000
1200
1400
1600
1800
π
π
a. Monthly data, June 1987 to November 1995.
SOURCES: Author’s calculations; and Board of Governors of the Federal
Reserve System.
2000
icy conforms to what would have been implied
by either the price-level or nominal-income targeting rules plotted in figure 5. A simulated
interest-rate path can be calculated by taking
the estimated structural innovations, the ^ejt ’s,
and then computing the optimal policy responses implied by each rule before substituting the result into the equation for the federal
funds rate, which is the equivalent of (11).10
Figure 5 compares the actual path of the federal funds rate with that implied by the estimated price-level and nominal-income targeting
policies. When we examine the figure, several
findings emerge. First, targeting the price level
alone yields larger swings, as the funds rate
reaches both higher and lower extremes. The
actual funds rate is the least variable, looking
like a smoothed version of the two simulated
paths, but the general character of the plot suggests that the optimal policy response simply
involves faster, bigger movements than those
on the actual path.11
Figure 5, however, allows an even more
interesting conclusion. From its results, it is
possible to infer something about the procedures policymakers were actually following.
Such a calculation does not violate the Lucas
critique, since it is an attempt to recover the
loss function implicit in the policy actions we
actually observed.
The estimates imply that the actual fundsrate path was very similar to one that would
■ 10 Performing the calculations in this way ignores a number of elements. In particular, there is no guarantee that the policy rules generated
from the artificial experiment of one unit shock in one ejk at a time will be
robust to sequences of shocks in all the ejk ’s simultaneously. One clear
reason for this is that it ignores the covariance of estimated coefficients
both within and across the elements of the A^ij (L)’s.
■ 11 As one would expect, these large policy innovations result in less
stable real output, highlighting that the ultimate issue in policymaking is
still the relative weight of prices and output in the objective function.
14
have been implied by a nominal-income targeting procedure, only smoother. It is as if, over
the past decade or so, the federal funds rate
had been set to conform to a nominal-income
targeting regime, but with policymakers attaching a cost to actually moving the funds rate.
That is, the objective function that we can construct from the actual path of interest rates
would minimize the sum of squared deviations
in nominal income from a target path and
squared movements in the federal funds rate,
over a horizon of about three years.
Appendix:
Identification
To understand the more general issues of identification, it is useful to rewrite the four-equation
model [(1)–(4)] in a more compact form:
(A1)
where x t and e t are now vectors, and A (L ) is a
matrix of lag polynomials. We can also write the
model in its more familiar VAR reduced form as
(A2)
IV. Summary
The information requirements for any policy
rule are daunting. Not only do policymakers
need timely information about current economic conditions, they also need forecasts of
the future path of the variables they wish to
control (aggregate prices and real output) and
quantitative estimates of how their actions will
affect these objectives.
This paper’s purpose is to suggest that much
of our knowledge is very inexact, and that our
inability to precisely forecast the results of policy changes should make us cautious. Even
more important, the fact that we have a much
better understanding of the impact of our policies on real output than on prices suggests that
nominal-income targeting rules are more robust
than price targeting rules. From a purely pragmatic viewpoint, someone who cares about
nominal income is made substantially worse off
by moving to a price-level target, which destabilizes real output considerably. Thus, practical
issues make a strong argument for nominalincome targeting.
In addition, we have seen that the actual
path of interest rates over the past decade is
very similar to that implied by a nominalincome targeting rule, albeit one in which interest rate movements are viewed as costly. By
comparing the actual interest-rate path with the
path implied by the nominal-income targeting
rule, we see that policymakers have smoothed
interest rate movements more than the rule
would have dictated, but not by much.
x t = A (L )e t ,
R (L )x t = ht ,
where R (0) = I, the ht ’s are i.i.d. (implying that
they are orthogonal to the lagged x t’ s), and
E (hh ¢) = S. It immediately follows that A(L)et
= R(L)–1ht . This allows us to write A(0)et = ht ,
and A(L) = R(L)–1A(0). As a result, given estimates of A(0), R(L), and h, we can recover
estimates of both the structural innovations—
the et ’s—and the structural parameters—the
components of A(L).
The issue of identification is the problem of
estimating A(0). To show how this is done,
note that A(0)E (ee ¢)A(0)¢= S, where E (ee ¢) is
diagonal by construction. Normalizing E (ee ¢) =
I, we obtain the result that A(0)A(0)¢= S. In a
system with n variables, S has [n (n + 1) ] unique
2
elements, and so complete identification requires an additional [n (n – 1) ] restrictions. In a
2
four-variable model, six more restrictions are
needed. This is a necessary but not sufficient
condition for identification. Sufficiency can
be established by proving that the restrictions
lead to construction of an A(0) matrix that is
invertible.
The long-run restrictions of the Galí-style
identification can be understood by defining
A(1) as the matrix of long-run effects computed
by summing the coefficients in A(L). That is,
the (i,j ) element of A(1) is
¥
Aij (1) = S aijk .
k=0
There are two long-run restrictions. The first
is that the impact of ept and ut on yt is transitory, and so A31(1) = A34(1) = 0. The second is
that ept and ut have no permanent impact on
the relative price of commodities, ( pct – pt ), that
is, A11(1) – A21(1) = A14(1) – A24(1) = 0.
15
References
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of San Francisco, Working Paper No. 95-09,
March 1995.
Blanchard, O. J., and D. Quah. “The
Dynamic Effects of Aggregate Demand and
Supply Disturbances,” American Economic
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655–73.
Lucas, R. E., J r . “Econometric Policy Evaluation:
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vol. 1, no. 2 (Supplementary Series 1976),
pp. 19–46.
Mankiw, N. G., ed. Monetary Policy.
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S i m s , C. A. “Macroeconomics and Reality,”
Econometrica, vol. 48, no. 1 (January 1980),
pp. 1–48.
Brainard, W. C. “Uncertainty and the Effectiveness of Policy,” American Economic Review, vol. 57, no. 2 (May 1967), pp. 411–25.
. “Policy Analysis with Econometric
Models,” Brookings Papers on Economic
Activity, no. 1 (1982), pp. 107–52.
Cecchetti, S. G. “Inflation Indicators and
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Rotemberg, eds., NBER Macroeconomics
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1995, pp. 189–219.
. “A Nine Variable Probabilistic Macroeconomic Forecasting Model,” Cowles Foundation for Research in Economics at Yale
University, Discussion Paper No. 1034,
June 1992.
Christiano, L. J., M. Eichenbaum, and
C . L . E v a n s . “The Effects of Monetary Policy Shocks: Evidence from the Flow of
Funds,” Review of Economics and Statistics,
vol. 78, no. 1 (February 1996a), pp. 16–34.
,
, and
. “Identification and the Effects of Monetary Policy
Shocks,” in M.I. Blejer et al., eds., Financial
Factors in Economic Stabilization and
Growth. New York: Cambridge University
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pp. 36–74.
Cochrane, J. H. “Shocks,”
Carnegie–Rochester Conference Series on
Public Policy, vol. 41 (December 1994), pp.
295–364.
Feldstein, M., and J. H. Stock. “The Use
of a Monetary Aggregate to Target Nominal
GDP,” in N.G. Mankiw, ed., Monetary Policy.
Chicago: University of Chicago Press, 1994,
pp. 7–70.
G a l í, J . “How Well Does the IS-LM Model Fit
Postwar U.S. Data?” Quarterly Journal of
Economics, vol. 107, no. 2 (May 1992),
pp. 709–38.
16
The Reduced Form
as an Empirical Tool:
A Cautionary Tale
from the Financial Veil
by Ben Craig and Christopher A. Richardson
Introduction
Economic data usually influence policy through
a reduced-form analysis. Using such an analysis, the researcher generally poses an empirical
relationship between an outcome variable, such
as a firm’s total investment, and a policy variable, such as the design of a particular tax. This
relationship serves as a point of departure in
the analysis. Explicit assumptions about behavior that underlie the relationship are not emphasized; rather, the researcher asserts that
the “data do the talking.” Policy implications,
where they exist, are directly observed in the
pattern estimated in the data. Most empirical
analyses of policy questions follow a reducedform strategy.1
It is easy to understand why a reduced-form
approach might, at first glance, appear to be the
best way to analyze policy. It is a simple methodology, and thus can more easily keep track of
what is happening during the complicated process of analyzing data. One does not need to
specify a sophisticated and consistent model of
behavior to use this approach. Further, the answers embodied in the model estimates may
accord with a wide variety of behaviors that
could be true of the firm.
Ben Craig is an economist at the
Federal Reserve Bank of Cleveland,
and Christopher A. Richardson is
a graduate student of economics
at Indiana University. The authors
have benefited from the generous
help and advice of Charles Carlstrom.
A different approach to estimating the effect
of taxes would be to specify a model of optimizing behavior on the part of the firm and to
model the tax policy as a set of constraints on
this optimizing behavior. A simplistic reason for
preferring the reduced-form approach is that
economists are interested only in the overall
effect of a proposed tax policy on investment.
Why should we care about the intermediate
steps by which a tax will affect the firm?
How successful is the reduced-form approach at testing a behavior or measuring a
policy effect? Given that we are never shown
the truth behind the mystery, this paper will
examine the history of an economic question
that has been subjected to 35 years of intense
scrutiny: Does corporate financial structure affect real investment? The empirical answer to
this question, which lies at the heart of corporate financial economics, has heavily influenced every tax reform bill since the 1960s.
■
1 Reduced form has a different meaning here than in simultaneous
equations estimation, where a reduced form is estimated by regressing an
endogenous variable on all of the exogenous variables in a system of
equations. We use the term in a wider context, where the pattern in the
data—not an assumed behavioral structure—forms the point of departure for estimation.
17
The initial econometric strategy was to follow a
pure reduced-form approach. How well have
the results of this research program held up to
further scrutiny?
Modigliani and Miller (1958) provide the
first theoretical model showing the influence
of corporate debt structure on investment. In
the world they portray, perfect capital markets,
coupled with symmetric information about the
investment prospects of the firm, the investors,
and the lenders, mean that the firm’s debt level
is irrelevant to the amount of investment it
undertakes.
One reduced-form approach would be to
directly examine the empirical relevance of the
Modigliani–Miller (hereafter “MM”) hypothesis
that with perfect capital markets, no taxes, and
a given investment policy, capital structure is
irrelevant to firm value. As a consequence, neither capital structure nor dividends should
affect investment behavior. The MM propositions provide the following broad empirical
prediction: In a properly specified regression of
investment on the debt/equity ratio, dividends,
and other covariates, the coefficients of debt/
equity and dividends should equal zero. A
reduced-form estimating strategy uses this prediction as the point of departure.
The following two sections discuss the history of tests of this hypothesis from both a
cross-section and a time-series perspective.
Next, we step back and explore the reasons for
the pattern in the early reduced-form estimates
through a simple structural model. We then
look at what we have learned about whether a
tax policy can affect investment through its
influence on a company’s financial structure.
We conclude with the object lessons that accompany 35 years of intensive research on this
topic—lessons that could be applied to other
situations where the reduced form is used to
help shape policy. What did we first believe the
data were telling us, and how did these beliefs
change under close scrutiny? After all this time
spent researching a single hypothesis, what limitations in our knowledge may be embedded in
the reduced-form approach?
I. Cross-Section
Regression Tests of
the MM Hypothesis
The clear and simple MM hypothesis that there
is no relationship between financing and real
capital investment seems to lend itself easily to
cross-section regressions. The early reducedform models assume away the importance of
differential corporate and personal income
taxes, which are a clear violation of the original
MM statement. Thus, they jointly test the MM
model and the hypothesis that the income tax
structure is irrelevant to the effect of financial
structure on real investment. We will treat the
two tests separately later in this paper. The test
of the joint hypothesis measures the statistical
significance of financial variables in an investment equation where the dependent variable is
capital investment and the independent variables are measures of a firm’s financial position,
which may include its debt/equity ratio, cash
flow, and dividends. The hypothesis of no relationship between financing and investment is
rejected if the coefficients of the debt/equity
ratio and dividends are statistically close to
zero. A simple regression is not adequate here
because both dividend payments and the firm’s
debt are endogenous. Thus, absence of a correlation between the debt/equity ratio and investment is not necessarily evidence that the MM
hypothesis holds.
To alleviate this problem, early cross-section
studies specified instruments in a system that
estimated investment (I ), dividends (D), and
new debt (ND) equations of the general form
Iit
= a0 + a1Dit + a2NDit + a3Xit + eI
Dit = b0 + b1Iit + b2NDit + b3Yit + eD
NDit = g0 + g1Iit + g2Dit + g3Zit + eND ,
where i and t are firm and time subscripts, the
e’s are statistical error terms, and X, Y, and Z are
vectors of exogenous explanatory variables. For
the investment equation to be identified (so that
we are estimating a separate equation for investment, not a hodgepodge of all three equations),
the vectors Y and Z must contain variables that
are not included in X. It is this process of identification that proved so problematic in the early
reduced-form studies. What exogenous variable
affects dividends and debt levels but does not
influence investment behavior?
It is important to note here that the MM
hypothesis is not a theory of investment, but of
why a firm’s financial structure does not influence investment. The estimating system of
equations that test the MM hypothesis must include a theory of investment (even if it is implicit) to control for its endogeneity. Thus, the
reduced form is a joint test of both the MM
hypothesis and an underlying theory of investment. For example, if the researcher holds investment opportunities constant through using
a measure of Tobin’s q, then the test of the MM
18
hypothesis also tests whether Tobin’s q is an
empirically useful model of investment behavior.2 Hence, the test is only as good as the
theory of investment.
The early studies used identifying instruments 3 that included profits, proxies for firm
size and taxes, and firm and industry dummy
variables to allow for fixed firm and industry
effects.4 (See, for example, Dhrymes and Kurz
[1967], McDonald, Jacquillat, and Nussenbaum
[1975], and McCabe [1979].) These studies, like
so many modern consulting reports, argue by
assertion—for example, the profit level should
affect dividends but not investment. Unfortunately, a researcher’s assertion that a variable is
an instrument does not necessarily make it so.
A reduced form offers few checks as to whether
the assertion reflects reality.
Empirical tests of the MM irrelevance hypothesis during the 1970s and early 1980s, though
more advanced econometrically, still came up
short in modeling differences in the financial
environment firms face. Although the studies
varied in their conclusions, all suffered from the
lack of a convincing instrument that would
control for a firm’s investment opportunities.
Again, the studies could not adequately address
the fact that firms with better investment opportunities might choose higher levels of debt.
McDonald, Jacquillat, and Nussenbaum estimate cross-section models using ordinary least
squares (OLS) and two-stage least squares
(2SLS), as does McCabe, but their conclusions
differ. McDonald et al. find support for the MM
propositions, while McCabe does not. Because
investment opportunities surely vary across
firms and certainly affect investment independently of financial structure, these early studies
were never conclusive tests of the MM irrelevance hypothesis.
Another reason for conflicting conclusions
among the early empirical studies seems to lie
in the differences in equation specification.
McDonald et al., like many other researchers
before McCabe, estimate investment as a function of contemporaneous variables only.
Because it is likely that the decision to invest
today will depend in part on financial decisions
made previously, excluding lagged financing
and dividend variables from an investment
equation results in a misspecification.
How was one to choose between these early
studies? If they had been structural, a researcher
could affirm that a particular study was the most
convincing if it had more believable parameter
estimates (for example, if it generated rate-ofreturn estimates of the same general magnitude
as the interest rate). A classic indication that a
system is identified improperly (that is, by false
assumptions) is that estimates of the individual
equations yield parameters that make little sense
economically. One reason the earliest tests of
the MM hypothesis seemed, on balance, to support the theory was that the estimates which
rejected MM had the “wrong” expected sign for
the dividend equation. This seemed to indicate
that the studies which did not reject the hypothesis used more convincing instruments. One pitfall of a simple reduced-form strategy is that it
yields so few checks of whether an estimated
parameter makes economic sense.
Subsequent cross-section studies made significant improvements over previous work. For
example, Peterson and Benesh (1983) estimate
a system of three equations similar to that used
in earlier studies (adding a lagged profit variable to the investment equation and a lagged
dividend variable to the dividend equation),
but in addition to estimating the standard OLS,
2SLS, and 3SLS models, they also conduct MM
hypothesis tests on the reduced-form equations
by estimating a seemingly unrelated regressions
(SUR) model. Their SUR results corroborate the
2SLS and 3SLS findings, which reject the null
hypothesis that financing and investment decisions are independent. The lagged profit variable serves as a proxy (albeit an imperfect one)
for investment opportunities, which makes the
rejection of the MM irrelevance hypothesis
somewhat more convincing.
The use of lagged profits suffers from a problem common to all studies that rely on lagged
variables for identifying instruments. Although it
is true that lagged profits are approximate measures of investment opportunities, they may also
affect both dividends and debt in the same
ways that these variables were correlated with
the original contemporaneous error term. It is
not clear that simply including the lagged profit
term will correct the original statistical bias.
Most recent reduced-form cross-section models reject the MM hypothesis. (See, for example,
Gilchrist and Himmelberg [1995].) However,
■
2 Tobin’s q is defined as the ratio of the market value of capital to
the replacement cost of capital.
■ 3 An instrument is a variable that is correlated with a variable on the
right-hand side of the equation (in this case, corporate debt or dividends)
without being correlated with the statistical error term. An identifying
instrument in this case is one that is correlated with the right-hand variables without being included as a right-hand variable. Thus, it may be
included in the equation where dividends or debt are left-side variables,
but it must be excluded from the original investment equation.
■
4 In some cases, X, Y, and Z contain the same variables.
19
these models often suffer a distressing lack of
robustness to econometric specification. This
makes precise determination of the estimated
reduced-form parameters problematic. Further,
the reduced-form approach does not present us
with an easy point of departure for determining
the correct econometric specification through
convincing tests. We also lack a consensus on
parameter estimates that are specific and precise
enough to be more useful in a policy context
than are cross-section reduced-form models.
Can we glean additional evidence on the empirical validity of the MM irrelevance hypothesis
from time-series patterns in the data?
II. Granger
Causality Tests
Given the difficulty of pinning down a convincing set of instruments to tease out that part
of the correlation of debt and investment stemming from debt’s possible impact on investment, some researchers have tried to determine the causality by studying the timing of
debt and investment. Thus, if investment precedes debt, the correlation may be spurious
because the firm, seizing its more potent
investment opportunities, creates more debt,
whereas the less fortunate firms do not have as
much debt. This would be the case when the
higher debt level was due to more investment
opportunities for the high-debt firm. The test of
a causal relationship between the variables proposed by Granger (1969) says that if a variable
or event X (a change in a financial variable)
causes another variable or event Y (a change
in investment), then X should precede Y. The
test involves measuring the power of lagged
values of X in predicting Y. A test of whether
debt affects investment is connected to whether
corporate debt “Granger causes” investment.
Smirlock and Marshall (1983) perform
Granger causality tests on a sample of 194 firms
from 1958 to 1977. Using annual data on dividends and investment, they fail to reject the null
hypothesis of no Granger causality for the aggregate sample of firms. Causality tests on each
of the 194 firms’ series do not reject the null any
more often than would be expected by chance,
leading the authors to conclude that their results
support the MM irrelevance hypothesis.
True to the pattern of cross-section tests of
the MM hypothesis, the early test did not hold
up to later scrutiny. It is imperative that enough
variables be included in a Granger causality
study so that nearly identical firms are being
compared. For example, Smirlock and Marshall
omit a financing variable, so that the analysis
compares noncomparable firms that differ in
precisely that dimension which the causality test
requires to be the same. Mougoue and Mukherjee (1994) address this issue by including a
long-term debt-financing variable in their
causality tests. They find that dividend and
investment growth rates Granger cause each
other negatively, long-term debt and investment
growth rates Granger cause each other positively, and debt and dividends Granger cause
each other positively, thus rejecting the MM
irrelevance principle.5 If the reduced-form test is
to be appropriate, some sort of implicit structure
must underlie it. In this case, the researchers
had to have an idea about which financing variables were important so that the Granger
causality could test comparable firms.
Although Mougoue and Mukherjee’s Granger
causality tests can detect significant interactions
among investment, debt, and dividend variables, they do not tell us much else. That dividends and investment Granger cause each other
simply means that a motion in one precedes a
motion in the other. Which comes first, the
investment chicken or the dividend egg?
Moreover, it is somewhat ironic that
Mougoue and Mukherjee’s causality tests may
also suffer from a misspecification bias due to
the omission of a proxy for investment opportunities, such as cash flow. If internal funds are
omitted from the system of equations, the observed negative causality from dividends to
investment may actually stem from a negative
causality from dividends to retained earnings
and a negative causality from retained earnings
to investment. The MM irrelevance hypothesis
would still be rejected, but for different reasons.
Although more properly specified equation systems may be useful in illustrating the existence
of causal relationships, it appears that Granger
causality tests have only limited utility in distinguishing among the different hypotheses of
how, why, and to what degree financing and
real investment decisions interact.
In addition, Granger causality tests suffer
from a difficulty related to the forming of
expectations. If debt Granger causes investment, the interpretation is that the corporate
structure effects a change in investment behavior. However, expectations about investment
■ 5 It is assumed here that firms use borrowed funds to finance future
investment or to increase dividend payments. Because the variables are
expressed as changes in logarithms (growth rates), positive bidirectional
causality between debt and investment does not support or refute the presence of financing constraints, as it might if debt and investment were
expressed in levels.
20
opportunities could just as well influence both
investment and corporate debt levels, but affect
debt sooner because debt levels adjust more
quickly. Tests that center on the timing of debt
and investment thus provide weak evidence on
the relevance of the MM hypothesis.
Interestingly, the pattern of evidence in the
Granger causality tests is the same as the pattern in the cross-section regression results. Initially, the evidence seemed to support the MM
hypothesis. However, closer scrutiny and
clearer identifying assumptions tend to reject
the hypothesis. Even current studies are unable
to provide more information than a crude rejection of the hypothesis. Precise parameter estimates needed for policy prediction seem to
require a different estimation strategy. Why do
we observe this pattern in the reduced-form
estimates? It is not clear which part of the joint
hypothesis—perfect capital markets or the
empirical irrelevance of the personal and corporate income tax structure—is being rejected
by the above tests. To further define the two
hypotheses, a simple heuristic model is needed.
III. A MM
Structural Model
In this section, we explore a model in which
the underlying behavior of firms generates the
data. A simple statement of the model will clarify the measurement problems inherent in testing the MM hypothesis with cross-section or
time-series data. A MM firm chooses the levels
of investment, I 0, in a project that will pay F (I 0)
dollars for each period in the future, F ¢(I 0 ) > 0,
F ²(I 0 ) < 0, so that the firm receives
(1)
¥
S F (I 0)
t = 1 (1 + r)t
=
F (I 0)
r
from the investment, where r represents the
interest rate.6 The firm starts with a predetermined amount of cash, C, and must decide
how much of this cash to pay out in dividends,
Cd , and how much to reinvest, CI (C = Cd + CI ).
The firm can also issue debt, D, to finance the
investment. A tax rate is imposed on a corporation at rate tc and on individuals at rate tp.
MM’s first observation is that the market
value of the shares, S, is just a tax-adjusted
value of the investment payoffs (including the
corporate cash paid out today, Cd ) minus the
value of debt, or
(2)
S = (1 – tp )Cd + (1 – tc )
[ F r(I ) – D].
0
The firm maximizes S with respect to the
amount of investment subject to the financing
constraints I 0 = CI + D and C = Cd + CI. A simple substitution gives
(3) S = (1 – tp ) (C – CI ) + (1 – tc )
[F (C r+ D) – D],
I
with first-order conditions
(4) F ¢ = r
and
(5) F ¢ = r (1 – tp ) ,
(1 – tc )
corresponding to investment financed out of
debt and cash, respectively.
If the personal tax rate is equal to the corporate tax rate (or tp = tc , which nests the special
case of MM’s no-tax scenario), the first-order
conditions make it apparent that the expense of
an additional dollar of investment is the same
however it is financed, and that the firm finances from either debt or retained earnings until the marginal benefit from investment is equal
to the outside rate of return (or F ¢[I 0 ] = r).
It is important to note that the first-order
condition in this case simultaneously says two
things about the firm’s behavior. First, a firm’s
decision to finance a given level of investment
out of debt or retained earnings is irrelevant:
The firm is indifferent between the two. Second, the investment level is determined by the
rule that the firm invests until the marginal benefit of investment is equal to the interest rate.7
The level of debt says nothing about the value
of the firm except that it has traded debt for
dividends at a rate of one for one. Investors
who are paying for a share of the company and
who might prefer a higher level of debt in their
portfolio can continue holding shares of this
firm, but elect to borrow more on the outside
market to increase the debt level within their
own portfolios. This and other similar possible
arbitrages force the share value to treat debt
and retained earnings symmetrically.
In a world where the corporate tax rate is
higher than the personal tax rate, tc > tp , the
firm’s rule is to finance until the return on
■ 6 The MM results do not depend on risk neutrality, a constant
stream of benefits, or a constant discount rate. These are assumed here
for expositional convenience.
■ 7 In the MM exposition, the firm invests until the marginal benefit
equals the rate of return for the firm’s risk class. The theory also shows
that investment financed out of new equity issues is equivalent to investment financed out of retained earnings or debt.
21
investment is equal to r. The investment is financed entirely out of debt and all of the cash
appears as a dividend. Financing out of debt
rather than retained earnings costs less
because debt payments are fully deductible.
MM (1963) makes the point that the tax advantages of debt financing (interest payments
are deductible as a cost in calculating corporate taxes) imply that investment should never
be financed out of retained earnings in a pure
example of their model. Indeed, because of
the tax advantages, the firm prefers to borrow
more than its investment amount to finance a
larger dividend. Clearly, a more complicated
model is needed to explain why a corporation
chooses one method of financing over another.
However, the simpler model may still be adequate to explain the level of investment if the
data show no relationship between that level
and corporate financial structure.
If the corporate tax rate is less than the personal tax rate, then cash is the relatively less
expensive investment source. The firm will use
only cash to finance investment unless the
marginal return on investment after all of the
cash is used (and the dividend is zero) exceeds
the cost of financing additional investment out
of debt (or F ¢[C ] > r). At this point, debt becomes the marginal investment source, with
the first-order condition given by equation (4).
If F ¢(C ) < r, then debt will equal zero, and
only cash will be used to finance investment,
until equation (5) is satisfied.
The top federal individual tax rate and the
top federal corporate tax rate are currently
about the same (39.6 percent versus 38 percent). However, in many states, the top corporate rate is higher than the top individual rate
(in Ohio, the respective figures are 8.1 percent
and 4.1 percent). Based on the above analysis,
one would expect to find corporations financing
investment entirely out of debt and never using
retained earnings for this purpose. Clearly, this
is not the case, as firms use both debt and
equity financing. One reason companies do not
rely solely on debt is that outside credit constraints (or the costs of bankruptcy) may make
the marginal cost of debt rise as the total level
of debt increases. In other words, the market
value of debt may decrease the firm’s value
faster at higher debt levels because high debt
may alert the capital markets that the firm is less
likely to survive, or because lenders become
less willing to lend to firms that could be hit
with bankruptcy costs. In this world, the value
of the shares might be written as
(6)
S = (1 – tp ) (C – CI )
+ (1 – tc )
[F (Ir ) – [D + d(D)]] .
0
The parameter d is the increasing cost of
debt not captured in the interest rate, where
d(0) = 0, d¢ > 0, and d¢¢ > 0. The new rule for
debt-financed investment is
(7)
F ¢(I 0 ) = r [1 + d¢(D)].
The first-order condition for investment financed out of equity is the same as in equation
(5). The rule for investment explicitly makes
the amount of investment a decreasing function
of the firm’s debt level if the firm finances out
of debt. Similar to the MM model, the first-order
conditions can generate corner solutions in
which the firm finances investment either completely out of debt or completely out of cash.
For example, if tc < tp , the firm will finance up
to its total cash holdings out of equity, then
finance out of debt only if the marginal return
on investment at that point is greater than or
equal to r. If the corporate tax rate is greater
than the personal tax rate (as it is for most U.S.
corporations), then the investment rule is more
complicated. The firm will finance out of debt
only if [1 + d¢(D)] < (1 – tp )/(1 – tc ); that is, if
the marginal cost of increasing the firm’s debt
burden is small enough. If this is not the case,
firms will use both debt and cash to finance
their investment projects. First-order conditions
for investment financed out of cash remain the
same (equation [5]), so that the equation determining the debt level, if both debt and cash are
used to finance investment, is
[1 + d¢(D)] = (1 – tp ).
(1 – tc )
It is important for policymakers to know
whether a world represented by MM or an
environment of substantially increasing marginal cost of debt, crudely represented by equation (6), best reflects investment behavior. One
easy reduced-form test of the MM assumptions
in the earlier cross-section studies was to examine whether investment was negatively correlated with debt. If the study detected no negative relationship, then the conclusion might be
that equation (6) did not make empirical sense.
However, as the following example illustrates,
lack of correlation between debt and equity
might occur in a world that is very non-MM.
Suppose our sample consists of two types of
firms that differ only in their set of investment
opportunities. Each type faces an investment
(8)
22
payoff of ai F (I ), where a1 > a 2. The empirical
researcher observes only the debt and investment outcomes of the two firms. The firms face
a very non-MM world, one in which increasing
debt discourages investment, represented by
equation (6). We further assume that both debt
and equity are used to finance investment, so
that equation (8) holds. First-order conditions
for the two firms are F ¢(I 0) = ar [1 + d¢(D)] =
i
r(1 – tp )/ai (1 – tc ). The behavior rule gives the
following outcome: I1 > I2 and, if both firms finance investment out of some of their retained
earnings, D1 = D2.8 A simple regression of investment on the firm’s debt level would lend
support to the MM hypothesis of the irrelevance
of debt for the level of investment, even though
the data are generated by a behavior where the
debt level, ceteris paribus, discourages investment. Clearly, lack of a simple correlation between debt and investment is not enough to test
the appropriateness of the theory. If the potential cash available to the individual firms, C, is
unobserved by the empirical researcher (as is
likely), then the dividend amount may also be
uncorrelated with the investment level. The
problem is that the corporate financial instruments are behavior variables chosen by the
agents, not experimental variables applied by
the researcher.
Any estimation must take into account that
both investment and corporate financial structure are caused by the environment facing the
firm, and that the available data contain very little of the information needed to reconstruct the
decision process for each firm’s investment and
corporate financial structure, even if all of the
correct variables are included. The key to the
earlier studies lay in finding sufficient instruments to control for the different investment
opportunities represented by ai and for the fact
that debt was a behavioral variable chosen by
the firm. Poor instrument choice was bound to
lead to poor estimates. In this estimating context, the underlying structure of behavior and a
clear notion of what is generating differences
across observations are needed to formulate a
useful reduced form.
The problems with reduced-form analysis are
clear from this example, yet researchers do not
necessarily have the data to conduct a fullblown structural estimation. Despite these limitations, we can profit from structural models by
using them to devise a test that can help uncover some of the important factors driving
firms’ investment decisions.
IV. Tax Effects
and the Investment/
Financing
Relationship
Early reduced-form empirical work on the tax
effects of the investment/financing relationship,
such as Long and Malitz (1985), Titman and
Wessels (1988), and Fischer, Heinkel, and
Zechner (1989), failed to find economically or
statistically significant effects, just as early
reduced-form studies failed to find a link between corporate financial structure and investment. These early nonstructural studies had an
important influence on the policy debate, particularly when federal tax reform was discussed.
For example, when the Economic Recovery
Tax Act of 1981 (ERTA) was being debated, it
was theoretically understood that in a creditconstrained world, the investment tax credit
might yield a strong substitution effect as firms
changed their investment funding from debt financing to retained earnings. This was not considered important because the early reducedform estimates indicated that the effect of taxes
on corporate financial structure was negligible.9
Subsequent, more careful work has generally
found evidence of a significant tax effect. For
example, MacKie-Mason (1990) states that earlier
studies suffered from a failure to fully consider
the impact of a firm’s tax shields (tax deductions
or investment tax credits) on its effective marginal tax rate. He notes that if a firm has no
taxable income, any additional tax shields it
receives will have no impact on its marginal tax
rate. The marginal rate will be affected only if
tax shields lower taxable income to zero. By taking this point into account and investigating
incremental financing decisions using discretechoice models instead of debt/equity ratios,
MacKie-Mason finds evidence that firms with
high tax-loss carryforwards are less likely to rely
on debt. This is certainly consistent with both
the theoretical models of MM and the debtconstraint model, which predict that as the corporate tax rate decreases, debt should shrink.
This more recent finding of a significant tax
effect forces the reduced-form research to be
more careful in defining its hypotheses. How
do taxes influence investment? They could
( 1 – tp )
= 1 + d¢(D ).
( 1 – tc )
■ 9 See Trezevant (1994), which discusses the contemporary debate
surrounding ERTA. The author finds a significant substitution effect in taxes.
■
8 This follows directly from the relation
23
affect it directly through a change in the posttax price of real investment, or indirectly
through a change in corporate financial structure, as demonstrated in the previous section.
The indirect influence is the one of interest to
corporate finance. Separation of the indirect
financial effect from the direct real-price effect
requires a clarity that makes reduced-form estimation look more like structural estimation.
This clarity is seen in more recent research
that concentrates on the impact of taxes on
corporate financial structure. Givoly et al.
(1992) and Cummins, Hassett, and Hubbard
(1994) find evidence of a relationship between
debt and taxes. The Givoly study empirically
examines the response of business firms to the
Tax Reform Act of 1986 (TRA). The authors
find evidence of a substitution effect between
debt and nondebt tax shields, as hypothesized
by DeAngelo and Masulis (1980). In addition,
both corporate and personal tax rates appear
to affect leverage decisions.
Givoly et al. provide a good example of how
forming an implicit structure about the effect of
taxes provides a precise hypothesis for testing
with a reduced-form estimation strategy. Consider how they use their structure and their
knowledge of TRA specifics to develop simple
statistical hypotheses. For example, they use
only 1987 data to describe TRA’s effect, because
they assert that the Act was surrounded by
uncertainty until its actual passage by the Senate. Their test year was 1987, and their control
years were 1984 and 1985, before any tax reform legislation was introduced. Although firms
might have behaved in anticipation of a new tax
structure, it is unlikely that this Lucas effect
would be of overriding importance in the statistical results.
Givoly et al. test their hypotheses involving
tax code changes by estimating standard crosssection OLS regressions of the change in leverage on the firm’s effective tax rate, nondebt tax
shields, dividend yield, Tobin’s q, firm size,
business risk, and changes in depreciation and
investment tax credits.10 The authors are able to
reach definitive conclusions about the effect of
the TRA using cross-section analysis because
they state their hypotheses carefully. For example, the TRA greatly reduced the statutory corporate tax rates, so that firms faced more similar
■ 10 In Givoly et al., Tobin’s q proxies for bankruptcy costs and the
collateral value of the firm when bankrupt. Business risk is proxied by the
coefficient of variation in operating income (minus depreciation) over the
firm’s last 10 years.
rates. Thus, their Hypothesis 1 states that in response to the decline in the statutory corporate
tax rate, firms with a high marginal effective rate
will decrease their leverage more than will firms
with a low marginal effective rate. In other
words, the decline in the effective corporate tax
rate will have a greater impact on firms with
high marginal tax burdens. Low effective tax
rates imply a low tax advantage of debt and result in a smaller decrease in leverage stemming
from a cut in the statutory tax rate. Hence, the
relationship between the effective tax rate and
changes in leverage should be inverse.
Notice how the hypothesis embodies a solid
underlying structure of how the firm reacts to a
tax change. This structure gives the hypothesis
a clarity and specificity that provide the necessary power for a reduced-form test. The hypothesis also illustrates a clear understanding of
the workings of the tax code. Although tax
laws specify the marginal statutory corporate
tax rate, corporate decisions are based on the
marginal effective tax rate, which is the present
value of future tax payments resulting from an
additional dollar of taxable income. The statutory rate is the same for all firms, but the effective rate differs from firm to firm above a
certain dollar amount. Tax shields such as investment tax credits, tax-loss carryforwards,
depreciation allowances, and interest expenses
lower the effective tax rate.
The Givoly results support all of their hypotheses: Each of the relevant coefficients is statistically significant and has the proper sign for
1987, the first year the TRA was in effect. The
hypotheses appear to be of moderate economic
significance. For example, a firm with an effective tax rate 10 percent above that of another
firm would have lowered its debt/equity ratio
1.15 percent more in response to the TRA.
Givoly and others provide only part of the
answer regarding the effect of financial structure on real input decisions. By showing that
taxes influence financial structure, the studies
have shown that capital markets are imperfect,
thus providing an important clue as to why the
MM propositions are not supported by the data.
However, they have not clearly shown how
these financial decisions impact real input decisions. Furthermore, the magnitude of the effect
is far from certain. Thus, the latest findings
point out one link of the chain of indirect tax
effects through capital structure by showing
how taxes influence corporate finance. However, the complete change still suffers from lack
of information on the magnitude of the effect
of corporate financial structure on real investment decisions.
24
Although earlier empirical work found no
significant tax effects, more recent studies have
addressed the inherent empirical problems and
have produced evidence that supports the
importance of taxes on financing decisions.
Hence, one link between policy and real investment behavior has been established, but only
after very clear statements about the firm’s
underlying structural behavior were used to
define relevant variables and identifying assumptions. These are formulations that require a
careful, informed analysis. Even so, only a fully
structural model can provide policymakers with
an accurate measure of how changes in tax policy influence real investment. Without parameter estimates from such a model, the short- and
long-term effects of tax policy changes on real
investment remain uncertain.
V. Conclusion
Simply estimating a structural model without
first determining and reporting general directions in the data is a recipe for disaster.
However, the reduced-form strategy, when
used without accompanying structural estimates, is distinguished by what it has not
done. We do not have precise estimates of the
magnitude of the effects. Because the estimating equations are formulated without an
explicit structure, the resulting parameters are
subject to fewer “reality checks” to determine
whether they make economic sense. In addition, fewer comparisons can be made to
related empirical literatures to determine the
appropriateness of the estimating equations’
specifications. Is this or that estimated parameter comparable to a risk-aversion parameter
estimated in the portfolio-balance literature?
We cannot tell from a reduced-form estimate
because the reduced form resists a structural
interpretation that will allow comparison.
What have we learned from examining 35 years
of research? In each case—the direct test of the
MM hypothesis through cross-section regressions, the test of the timing of investment
through Granger causality, and the test of
whether taxes should matter to corporate financial structure—the findings exhibit the same
pattern. Early research often failed to reveal statistical significance in the relationship between
corporate real investment and the explanatory
variable, be it financial structure or taxes. This
seemed to provide prima facie support for the
empirical relevance of MM’s assertions.
Our present knowledge of corporate financial structure through reduced-form estimation
is typical of what a more careful reduced-form
strategy can do. The weight of the current evidence seems to reject the MM neutrality hypothesis. Financial structure does matter to a firm’s
investment decisions, and taxes do influence
these decisions through their effect on financial
structure. These are important statements to
bear in mind both when deciding on policy and
when formulating new theory with which to
guide policy.
Our cautionary tale does not say that the reduced form is an unwise estimation strategy.
Rather, it notes what conditions are necessary if
a reduced form is to yield accurate results. In all
cases, an underlying structure of behavior (even
when not used explicitly in a structural estimation model) guided the research through the
crucial steps of data definition and formulating
the correct econometric test. It is also important
to note that a reduced-form analysis is a critical
step in any empirical study of a policy question.
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DeAngelo, H., and R. Masulis. “Optimal Capital
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Fischer, E., R. Heinkel, and J. Zechner.
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“Taxes and Capital Structure: Evidence from
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1986,” Review of Financial Studies, vol. 5,
no. 2 (1992), pp. 331–55.
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Granger, C. “Investigating Causal Relations by
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26
Predicting Real Growth
Using the Yield Curve
by Joseph G. Haubrich and Ann M. Dombrosky
Introduction
The yield curve, which plots the yield of Treasury bonds against their maturity, is one of the
most closely watched financial indicators.1
Many market observers carefully track the yield
curve’s shape, which is typically upward sloping and somewhat convex. At times, however,
it becomes flat or slopes downward (“inverts,”
in Wall Street parlance), configurations that
many business economists, financial analysts,
and other practitioners regard as harbingers of
recession (see figure 1).
A recent article in Fortune labeled the yield
curve “a near-perfect tool for economic forecasting” (see Clark [1996]). In fact, forecasting with
the yield curve does have a number of advantages. Financial market participants truly value
accurate forecasts, since they can mean the difference between a large profit and a large loss.
Financial data are also available more frequently
than other statistics (on a minute-to-minute
basis if one has a computer terminal), and such
a simple test as an inversion does not require
a sophisticated analysis.
In this Review, we examine the yield curve’s
ability to predict recessions and, more generally,
future economic activity. After comparing the
Joseph G. Haubrich is a consultant and economist and Ann M.
Dombrosky is a financial reports
analyst at the Federal Reserve
Bank of Cleveland.
curve’s forecasts with the historical record, we
judge its accuracy against other predictions,
including naive forecasts, traditional leading
indicators, and sophisticated professional projections. This article builds on a wide range of
previous research, but, taking an eclectic approach, differs from the earlier work in a variety
of ways. These differences show up mainly in
the way we judge forecast performance.
Like the important early work of Harvey
(1989, 1991, 1993) and Hu (1993), we use outof-sample forecasts and compare yield curve
forecasts with other predictions (including professional forecasts), but we extend our data set
to the mid-1990s. In addition, we consider how
adding the yield curve improves (or reduces)
the accuracy of other forecasts. In this, we follow Estrella and Hardouvelis (1991), who do
not, however, use out-of-sample forecasts.
Finally, building on the recent work of Estrella
and Mishkin (1995, 1996), we consider how
well the yield curve predicts the severity of recessions, not just their probability, and compare
the forecasts with a wider range of alternatives.
■ 1 Yield curve reports appear in the “Credit Markets” section of The
Wall Street Journal and the “Business Day” section of The New York Times.
27
F I G U R E
1
Yield Curvesa
provides some insight into market sentiment.
Of course, it’s always a good idea to check
whether the expensive and complicated forecasts actually do perform better.
After first reviewing some basics about the
yield curve and the reasons it might predict
future growth, we look at the actual relationship and compare predictions from the yield
curve to those generated by naive statistical
models, traditional indicators, professional forecasters, and an econometric model.
I. Interest Rates
and Real Economic
Activity
While our main goal is a rather atheoretical
a. Three-month and six-month instruments are quoted from the secondary
market on a yield basis; all other instruments are constant-maturity series.
SOURCE: Board of Governors of the Federal Reserve System.
The most distinguishing feature of this paper, however, is that it documents the decline
in the yield curve’s predictive ability over the
past decade (1985–95) and discusses possible
reasons for this phenomenon. By some measures, the yield curve should be an even better
predictor now than it has been in the past.
Widespread use of the yield curve makes
assessing its accuracy a worthwhile exercise for
economists. But policymakers, too, need an accurate and timely predictor of future economic
growth. The ready availability of term-structure
data (as opposed to, say, quarterly GDP numbers) ensures a timely prediction, but accuracy
is another question. Central bankers have an
added incentive to understand the yield curve,
since the federal funds rate and the discount
rate are themselves interest rates. Uncovering
the “stylized facts” about the curve can help the
Federal Reserve to understand the market in
which it operates.
With sophisticated macroeconometric models
and highly paid professional forecasters, is there
any place for a simple indicator like the yield
curve? Aside from the knowledge gained about
the curve itself, there are several reasons to
answer that question affirmatively. Simple predictions may serve as a check on more complex
models, perhaps highlighting when assumptions
or relationships need rethinking. Agreement
between predictions increases confidence in the
results, while disagreement signals the need for
a second look. A simple, popular indicator also
assessment of the yield curve’s predictive power, forecasts based on the yield curve are on a
sounder economic footing than those based on
hemlines or Superbowl victories. The best way
to see this is to start with a simple theory of
the term structure, called the expectations
hypothesis.
Under this theory, long-term interest rates
are the average of expected future short-term
rates. If today’s one-year rate is 5 percent and
next year’s one-year rate is expected to be 7
percent, the two-year rate should be 6 percent
([7 + 5] –.. 2 = 6). More generally, the expectations hypothesis equates the yield (at time t) on
an n-period bond, Ynt , and a sequence of oneperiod bonds:2
Ynt = Et (Y1, t Y1, t + 1Y1, t + 2 ...Y1, t + n – 1).
If low interest rates are associated with recessions, then an inverted term structure—implying that upcoming rates will be lower—predicts a recession.3
One possible reason for expecting low interest rates in recessions might be termed the
policy anticipations hypothesis. If policymakers
act to reduce short-term interest rates in recessions, market participants who expect a recession would also expect low rates. The yield
curve picks up the financial market’s estimate of
future policy.4
■ 2 See chapter 7 of Mishkin (1989) for a fuller treatment of this issue.
Mishkin also points out the main flaw in the expectations hypothesis: The
term structure normally slopes up, but interest rates do not trend up over
time. Campbell (1995) offers a useful discussion of related points.
■ 3
For a classic documentation of this pattern, see Kessel (1965).
■ 4 Rudebusch (1995) takes this approach.
28
Another possibility is that current monetary
policy may shift both the yield curve and future
output. For example, tight monetary policy
might raise short-term interest rates, flattening
the yield curve and leading to slower future
growth. Conversely, easy policy could reduce
short-term interest rates, steepen the yield
curve, and stimulate future growth. The yield
curve predicts future output because each of
these shifts follows from the same underlying
cause: monetary policy. Taking this logic one
step further, monetary policy may react to output, so that the yield curve picks up a complex
intermingling of policy actions, reactions, and
real effects.
In these explanations, the yield curve reflects future output indirectly, by predicting
future interest rates or future monetary policy.
It may also reflect future output directly, because the 10-year interest rate may depend on
the market’s guess of output in 10 years.
The expectations hypothesis certainly marks
the beginning of wisdom about the yield curve,
but only the beginning. The 30-year bond may
have a high interest rate not because people
expect interest rates to rise, but because such
a bond must offer a high return to get people
to hold it in the first place. (This is commonly
called the risk premium, though for some theories that may be a misnomer.) Investors may dislike wide swings in prices as market expectations about the distant future change over time.
Conversely, there may be reasons why some
people would rather hold a 30-year bond than
a one-year bond. For example, they may be
saving for retirement and prefer the certain payoff on the longer-term note (this is sometimes
called the preferred habitat hypothesis).
The risk premium provides another reason
why the yield curve may be a useful predictor:
The premium itself holds information. As a
simple example, consider that recessions may
make people uncertain about future income
and employment, or even about future interest
rates. The risk premium on a longer-term bond
reflects this. In conjunction with changes working through the expectations hypothesis, the
yield curve may take some very strange twists
indeed, becoming inverted, humped, or even
u-shaped.5
These explanations provide an additional
motivation for investigating yield curve predictions. They also hint at the many important issues that transcend the yield curve’s predictive
power. It matters, for instance, if the curve reacts to future policy, to movements in output, or
to some combination of the two. But these considerations fall by the wayside if the yield curve
is not an accurate predictor of future economic
activity. In this article, we concentrate on that
more basic issue, leaving determination of the
underlying causes for another day.
II. Data and
Computation
There are many ways of using the yield curve
to predict future real activity. One common
method uses inversions (when short rates exceed long rates) as recession indicators. Is it
possible, however, to predict the magnitude as
well as the direction of future growth? Does a
large inversion predict a severe recession? Does
a steep yield curve predict a strong recovery? 6
Operationally, this means relating a particular
measure of yield curve “steepness” to future
real growth. In taking this route, we follow and
build on the related work of Estrella and
Hardouvelis (1991).
Obtaining predictions from the yield curve
requires much preliminary work. Three principles guided us through the many decisions that
were required: Keep the process simple, preserve comparability with previous work, and
avoid data snooping. Thus, we avoided both
complicated nonlinear specifications and a
detailed search for the “best” predictor.
To begin with, there is no unambiguous
measure of yield curve steepness. A yield curve
may be flat at the short end and steep at the
long end. The standard solution uses a spread,
or the difference between two rates (in effect, a
simple linear approximation of the nonlinear
yield curve).7 This means choosing a particular
spread, in itself no trivial matter. Among the 10
most commonly watched interest rates (the federal funds rate and the three-month, six-month,
and one-, two-, three-, five-, seven-, 10-, and 30year Treasury rates), 45 possible spreads exist.8
An additional problem is that there are several types of yield curves or term structures. In
fact, it sometimes helps to draw a distinction
between the yield curve and the term structure.
The yield curve is the relation between the
■ 5 Stambaugh (1988) makes this point. For a less technical
description, see Haubrich (1991).
■ 6 Other approaches also exist. For example, Harvey (1988) examines whether the term structure predicts changes in consumption.
■ 7 Frankel and Lown (1994) is one of the few papers that considers
nonlinear measures of steepness.
■ 8 If there are n rates, there are n/2 (n –1) spreads. This is the
classic formula for combinations. See Niven (1965), chapter 2.
29
yield on Treasury securities and their maturity.
The term structure is a particular yield curve—
that for zero-coupon Treasury securities. The
term structure is theoretically more interesting.
It answers the question, “How much would I
pay for one dollar delivered 10 years from today?” The problem is that a zero-coupon Treasury security rarely matures in exactly 10 years.
What we actually observe in the market are
prices (and thus yields) on existing Treasury
securities. These may not mature in precisely
10 years (or whatever maturity you choose),
and they often have coupon payments. That is,
a 10-year Treasury note pays interest semiannually at a specified coupon rate, so its yield is
not the yield called for in the term structure.
Finding the desired interest rate almost always involves estimation of some kind. Calculating the theoretically pure term structure is
often quite difficult, as it must be estimated
from coupon bonds of the wrong maturity, all
subject to taxation. (Using zero-coupon bonds
may help, but this approach introduces problems of its own, as the market is thinner and
the tax treatment of coupons and principal differs.) This means that the pure term structure is
not available in real time, when the Federal
Reserve must attempt to discern the course of
the economy. To avoid stale data, we must turn
to the more “rough-and-ready” yield curve.
Even here, the problem of matching maturities
arises. Fortunately, the Treasury Department
publishes a “constant-maturity” series, where
market data are used to estimate today’s yield
on a 10-year Treasury note, even though no
such note exists.9
For our study, we use data from the Federal Reserve’s weekly H.15 statistical release
(“Selected Interest Rates”), which compiles
interest rates from various sources. For the
spread, we chose the 10-year CMT rate minus
the secondary-market three-month Treasury bill
rate. In addition to allowing a comparison with
the work of Estrella and Hardouvelis (1991),
Harvey (1989, 1993), and Estrella and Mishkin
(1995, 1996), choosing only one spread enables
us to minimize the problems of data snooping
(Lo and MacKinlay [1990]) and the associated
spuriously good results.10 That is, trying every
single spread would produce something that
looked like a good predictor, but it very likely
would be a statistical fluke akin to Superbowl
victories and hemlines. We then convert the bill
rate, which is published on a discount rate
basis, to a coupon-equivalent yield so that it is
on the same basis as the 10-year rate.11
Also following Estrella and Hardouvelis, we
use quarterly averages for the spread. This
smoothes the anomalous rates that appear at
the turn of each month.12 A priori there is no
presumption that GDP should correlate better
with a particular date’s spread than with the
quarterly average.13
As our measure of real growth, we use the
four-quarter percent change in real (fixedweight) GDP. GDP is, of course, the standard
measure of aggregate economic activity, and
the four-quarter forecast horizon answers the
“what-happens-next-year” type of question
without embroiling us in data snooping issues
regarding the optimal horizon choice.
Our sample period runs from 1961:IQ
through 1995:IIIQ. This covers various inflationary experiences, episodes of monetary policy
tightening and easing, and several business
cycles and recessions. Included are five recessions, inflation rates from 1 percent to more
than 13 percent, and a federal funds rate ranging from under 3 percent to over 19 percent.
Our basic model, then, is designed to predict
real GDP growth four quarters into the future
based on the current yield spread. Operationally, we accomplish this by running a series of
regressions (detailed below) using real GDP
growth and the interest rate spread lagged four
quarters (for example, the interest rate spread
used for 1961:IQ is actually from 1960:IQ).
The next step involves comparing the yield
curve forecasts with a sequence of increasingly
sophisticated predictions using other techniques. We start with a naive (but surprisingly
effective) technique which assumes that GDP
growth over the next four quarters will be the
same as it was over the last four. (That is, the
growth rate is a random walk.) We then regress
real GDP growth against the index of leading
economic indicators (lagged four quarters). This
enables us to make a comparison with another
simple and popular forecasting technique.
■ 9 See Smithson (1995) for a good description of constant-maturity
Treasuries (CMTs).
■ 10 Work by Knez, Litterman, and Scheinkman (1994) suggests
that using more or different rates would not capture much additional
information.
■ 11 The three-month CMT rate was not published before May
1995. To keep the data consistent, we use the secondary-market threemonth Treasury bill rate throughout. For such a short rate, the differences
are minimal.
■ 12 Park and Reinganum (1986) document this calendar effect.
■ 13 We also reworked the results using data for the last week of
each quarter for the 1963–95 period. The findings were comparable,
although the predictive power of the spread decreased somewhat.
30
B O X
1
Forecasting Equations
Yield spread: in-sample
RGDPt + 4 – RGDPt
Yield spread: out-of-sample
RGDPt + 4 – RGDPt
Naive
RGDPt + 4 – RGDPt
Leading indicators
RGDPt + 4 – RGDPt
Lagged GDP
RGDPt + 4 – RGDPt
RGDPt
RGDPt
RGDPt
Lagged GDP plus yield spread
RGDPt
RGDPt
RGDPt + 4 – RGDPt
RGDPt
=
a + b spreadt
=
a + b spreadt
=
RGDPt – RGDPt – 4
RGDPt
=
a + b indext
=
a+b
=
a+b
We next look at two additional forecasts
generated by statistical procedures. We regress
real GDP growth against its own lag (again,
four quarters) and against its own lag and the
10-year, three-month spread.
The final, and most sophisticated, alternative
forecasts we consider come from the Blue Chip
organization and DRI/McGraw–Hill (hereafter
referred to simply as DRI). We first compare the
results of our model with forecasts from Blue
Chip Economic Indicators, beginning with the
July 1984 issue.14 We use the one-year-ahead
Blue Chip consensus forecasts for real GDP (or
real GNP when GDP forecasts are unavailable),
labeled “percent change from same quarter in
prior year.” These forecasts are taken from the
Blue Chip newsletters corresponding to the first
month of each quarter.
We next compare our results with predictions from DRI, reported in various issues of its
Review of the U.S. Economy. DRI generates
these forecasts from an econometric model.
Although we tried to collect forecasts for the
same period as our Blue Chip forecasts (that is,
from issues corresponding to the first month of
each quarter), our DRI data set is missing two
points: 1985:IIIQ and 1987:IIQ. We use forecasts for real GDP (or real GNP when GDP
forecasts are unavailable) one year ahead.
Box 1 summarizes the regressions used to
forecast future real GDP growth.
RGDPt – RGDPt – 4
RGDPt
RGDPt – RGDPt – 4
RGDPt
+ g spreadt
III. Forecast Results
Does the yield curve accurately predict future
GDP? First, look directly at the data. Figure 2
shows the growth of real GDP and the lagged
spread between the 10-year and three-month
Treasury yields. A decline in the growth of real
GDP is usually preceded by a decrease in the
yield spread, and a narrowing yield spread
often signals a decrease in real GDP growth. A
negative yield spread (inverted yield curve)
usually precedes recessions, but not always.
For example, the yield spread turned negative
in the third and fourth quarters of 1966, but no
recession occurred for the next three years.
(The recession that began in late 1969 was preceded by two quarters of a negative yield
spread.) The latest recession, which occurred in
1990–91, was preceded by a yield curve more
accurately described as flat than inverted.
Figure 3 plots the same data in a different
form. It shows a scatterplot, with each point
representing a particular combination of real
■ 14 Blue Chip Economic Indicators is a monthly collection of economic forecasts by a panel of economists from some of the top firms in the
United States (the so-called Blue Chip companies). The Blue Chip consensus forecast for real GDP is the average of about 50 individual forecasts. See Zarnowitz and Lambros (1987) for evidence that the consensus
forecast predicts much better than individual forecasts, and Lamont (1994)
for a possible explanation.
31
F I G U R E
2
Real GDP Growth and
Lagged Yield Spread
generate the GDP predictions, we ran an insample regression, using the entire sample to
generate each predicted data point. This is the
sort of comparison Estrella and Hardouvelis
(1991) make, and our results, presented below,
confirm their assessment that the 10-year, threemonth spread has significant predictive power
for real GDP growth:15
Real GDP growth = 1.8399 + 0.9791spread
(3.89)
(4.50)
R 2 = 0.291, D – W = 0.352.
a. Four-quarter percent change.
b. Lagged four quarters.
NOTE: Shaded areas indicate recessions.
SOURCES: Board of Governors of the Federal Reserve System; and U.S.
Department of Commerce, Bureau of Economic Analysis.
F I G U R E
3
Scatterplot of Real GDP
Growth and Lagged Yield Spread
a. Four-quarter percent change.
b. Lagged four quarters.
SOURCES: Board of Governors of the Federal Reserve System; and U.S.
Department of Commerce, Bureau of Economic Analysis.
GDP growth and the lagged yield spread. Even
a casual look at the results reveals that the relationship between the two variables is usually
positive; that is, positive real GDP growth is
associated with a positive lagged yield spread,
and vice versa.
Plotting the data gives a strong, albeit qualitative, impression that the yield spread predicts
future real activity. We desire a more quantitative prediction, one that says more than “The
yield curve is steep; looks like good times.” To
The yield spread emerges as statistically and
economically significant, translating almost one
for one into expected future growth. Thus, a
spread of 100 basis points (1 percent) implies
future growth of 2.8 percent (we derive this as
1.8 + 0.98 x 1). The R 2 indicates that much variation remains to be explained. Figure 4 plots
our in-sample real GDP predictions versus
actual real GDP growth.
The in-sample results are somewhat misleading, as the coefficients depend on information
not available early in the sample. Figure 5 plots
another series of predicted real GDP growth,
this time generated from an out-of-sample regression. Each data point in this chart is based
on a regression using only the data (yield
spreads) before the predicted data point. That
is, the predicted GDP growth rate for, say,
1980:IQ is based on the data sample from
1961:IQ through 1979:IVQ. Hence, this regression generates a true forecast because it uses
available data to predict future (out-of-sample)
real GDP growth.16
The predicted GDP series from the in-sample
and out-of-sample regressions are broadly similar and generally follow the actual GDP data.
The root mean square error (RMSE) of the predictions is 2.04 for the in-sample and 2.10 for
the out-of-sample forecasts. It is not surprising
that the in-sample regression performs slightly
better. If we calculate the RMSE over the last
10 years of our data set (1985:IIIQ to 1995:IIIQ),
the in-sample regression (RMSE 1.07) again
does better than the out-of-sample regression
(RMSE 2.09).
■ 15 The t statistics are Newey–West corrected with five lags. This
offsets the bias created by overlapping prediction intervals (a serious problem in this case, as indicated by the Durbin–Watson statistic).
■ 16 We also corrected the regression for a more subtle problem.
Because first-quarter GDP numbers become available only after the first
quarter ends, we should not use those numbers in a regression. (That is,
as of the first quarter, we still don’t know the four-quarter growth rate over
last year’s first quarter.)
32
F I G U R E
4
Real GDP Predictions:
In-Sample
NOTE: Shaded areas indicate recessions.
SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis; and
authors’ calculations.
F I G U R E
5
Real GDP Predictions:
Out-of-Sample
NOTE: Shaded areas indicate recessions.
SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis; and
authors’ calculations.
T A B L E
1
RMSE of Forecasts
1965:IVQ–
1995:IIIQ
1985:IIIQ–
1995:IIIQ
2.04
2.10
3.15
2.37
2.49
2.19
n.a.
n.a.
1.07
2.09
1.66
1.36
1.46
2.06
0.63
1.13
Yield spread: in-sample
Yield spread: out-of-sample
Naive
Leading indicators
Lagged GDP
Lagged GDP plus yield spread
DRIa
Blue Chip
a. DRI forecasts are missing two quarters.
SOURCE: Authors’ calculations.
We use this RMSE criterion to compare the
yield spread forecasts with those derived from
other techniques. The results are reported in
table 1.
For the entire sample, the yield curve
emerges as the most accurate predictor of real
economic growth. Furthermore, adding the
yield spread to a lagged GDP regression
improves the forecast, while adding lagged
GDP to the yield spread worsens the forecast.
For in-sample regressions, adding variables
never hurts, but it quite commonly reduces the
performance of the out-of-sample regressions.
Curiously, the 1985–95 subsample completely reverses the results. The yield spread
becomes the least accurate forecast, and adding
it to lagged GDP actually worsens the fit. The
leading indicators emerge as the best of the
“low-cost” forecasts, and the two professional
services do markedly better than the rest. In
part, this may reflect the simple specifications
used in the regression forecasts: With more
lags, a simple regression forecast is often better
than a sophisticated model (see Chatfield
[1984], chapter 5). But the change is even more
significant than that. Using unpublished data,
Harvey (1989) finds that over the 1976–85
period, the yield spread performs as well as or
better than seven professional forecasting services (including DRI but not Blue Chip).
The dramatic drop in forecasting ability may
result from several factors. It certainly reflects a
changing relationship between the yield curve
and the economy. The coefficients in the termspread regression demonstrate this. At the
beginning of the sample, using only 20 data
points (five years of quarterly data), the coefficient on the term spread is –0.14 (statistically
insignificant). Midway through the sample,
after 70 data points, the coefficient is 1.48, and
for the whole sample, 0.98. While one advantage of an out-of-sample procedure is that it
allows the coefficients to change, the influence
of the first 20 years may force the “wrong”
coefficient on the last 10. It is also quite reasonable that the relationship between the yield
curve and the real economy might have
changed over 30 years. Advances in technology, new production processes, changes in
market organization or in the way the market
reacts to new information, or even shifts in
Federal Reserve policy (the famous “Lucas critique”) might have altered the relationship
between the yield curve and real activity.
Evidence suggests that both the timing and
the size of the relationship between the yield
curve and real activity has in fact changed. If
33
T A B L E
2
Correlations between Lagged Yield
Spread and Real GDP Growth
Lag
0
1
2
3
4
5
6
7
8
1960:IQ–
1995:IIIQ
1960:IQ–
1985:IIQ
1985:IIIQ–
1995:IIIQ
0.041
0.206
0.366
0.481
0.540
0.505
0.423
0.331
0.218
0.075
0.252
0.439
0.585
0.666
0.624
0.523
0.398
0.251
0.143
0.358
0.538
0.641
0.684
0.708
0.736
0.721
0.660
SOURCE: Authors’ calculations.
F I G U R E
6
Real GDP Predictions: Blue Chip
NOTE: Shaded area indicates recession.
SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis;
and Blue Chip Economic Indicators, various issues.
F I G U R E
we look at the correlations between the yield
spread and real GDP growth at different lags
(table 2), we see that the recent period has
higher correlations between lags of yield
spreads and real GDP growth. We also see that
the largest correlation for the early (and total)
period, 0.666, occurs at a lag of four quarters,
exactly the lag used in our regressions. In the
recent period, however, despite a higher correlation at four lags, the highest correlation
(0.736) is reached at six quarters. The correlations drop off more slowly in the latter period
as well. This accounts for our somewhat paradoxical conclusion: Despite better correlations
between the yield curve and real GDP—with
an in-sample RMSE that beats even the Blue
Chip forecast—regressions using past data are
less reliable predictors.
It is somewhat instructive to make a more
detailed comparison with the sophisticated forecasts. The Blue Chip predictions can be considered out-of-sample because each one is based
on data available at the time of the prediction.
Figure 6 plots the Blue Chip consensus forecasts
against actual real GDP growth. The Blue Chip
forecasts appear much smoother than GDP, as
they consistently underpredict real GDP when
economic growth is high and overpredict real
GDP when economic growth is negative.
The DRI forecasts are plotted in figure 7.
These appear broadly similar to the Blue Chip
forecasts, although the DRI series is more
volatile. Like the Blue Chip forecasts, the DRI
forecasts generally underpredict GDP when
economic growth is high and overpredict GDP
when economic growth is low. Our out-ofsample forecasts based on the yield spread
overpredict GDP growth for all but one quarter
during the 1985:IIIQ–1995:IIIQ period (corresponding to the Blue Chip and DRI data sets).
7
Real GDP Predictions: DRI
IV. Conclusion
Does the yield curve accurately predict real
a. 1985:IIIQ and 1987:IIQ data are missing.
NOTE: Shaded area indicates recession.
SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis;
and DRI/McGraw–Hill.
economic growth? Answering this seemingly
simple question requires a surprising amount
of preliminary work. Much of this paper is devoted to refining the initial question to confront
the realities of the financial marketplace.
Fortunately, the answer is less complex, if
somewhat nuanced. The 10-year, three-month
spread has substantial predictive power, and in
this we confirm a variety of earlier studies.
Over the past 30 years, it provides one of the
best (in our sample, the best) forecasts of real
growth four quarters into the future. Over the
past decade, it has been less successful: Indeed,
34
the yield curve was the worst forecast we examined. This shift seemingly results from a
change in the relationship between the yield
curve and real economic activity—one that has
become closer, but nonetheless has made
regressions based on past data less useful.
An interesting topic for future research
would be to examine whether simple fixes,
such as a rolling regression model or more
lags, could improve the recent performance of
the yield curve. Certainly the simple yield
curve growth forecast should not serve as a
replacement for the consensus predictions of
the Blue Chip panel or the DRI econometric
model. It does, however, provide enough
information to serve as a useful check on the
more sophisticated forecasts and to encourage
future research into the reasons behind the
yield curve’s worsening performance.
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@FedFRASER