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orKing raper series
Consumer Confidence and
Economic Fluctuations
John G. Matsusaka and Argia M. Sbordone
Working Papers Series
Macroeconomic Issues
Research Department
Federal Reserve Bank of Chicago
November 1993 (WP-93- 13)
FEDERAL RESERVE BANK
OF CHICAGO
CONSUMER CONFIDENCE AND ECONOMIC FLUCTUATIONS
JOHN G. MATSUSAKA
D e p a r tm e n t o f F in a n ce a n d B u sin e ss E c o n o m ic s
S ch o o l o f B u sin e ss A d m in is tr a tio n
U n iv e r s ity o f S o u th e rn C a lifo rn ia
L o s A n g e le s, C a lifo rn ia 9 0 0 8 9 -1 4 2 1
ARGIA M. SBORDONE
E c o n o m ic R esea rch D e p a r tm e n t
F ed era l R e se rv e B a n k o f C h ica g o
C h icago, Illin ois 6 0 6 0 4 -1 4 1 3
I f co n su m e rs b e c o m e p e s s im is tic a b o u t th e s t a t e o f th e eco n o m y, can th e r e b e a
s lo w d o w n in o u tp u t, even i f th e ir p e s s im is m is n o t b a se d on e c o n o m ic fu n d a m e n ta ls ?
A r e c e n t class o f m a c ro e c o n o m ic m o d e ls sh o w s th e a n sw e r is y e s , i f th e r e a re “s t r a t e
g ic c o m p le m e n ta r itie s ” a n d m u ltip le eq u ilib ria . In th is p a p e r w e in v e s tig a te th e lin k
b e tw e e n c o n su m e r co n fid en ce a n d e c o n o m ic flu c tu a tio n s fo r th e p e r io d 1 9 5 3 -1 9 8 8
u sin g v e c to r a u to re g re ssio n s. In all m o d e ls, a fte r c o n tro llin g fo r va ria b le s th a t p r o x y
fo r e c o n o m ic fu n d a m e n ta ls, th e h y p o th e s is th a t c o n su m e r s e n tim e n t d o e s n o t cau se
G N P (in th e G ra n g e r se n se ) can b e r e je c te d . V arian ce d e c o m p o s itio n s s u g g e st th a t
c o n s u m e r s e n tim e n t a c c o u n ts fo r b e tw e e n 13 p e r c e n t a n d 2 6 p e r c e n t o f th e in n o v a tio n
v a r ia n c e o f G N P .
*We thank Joonmo Cho, Giorgio De Santis, Robert Erikson, Selahattin Imrohoroglu,
Douglas Joines, Narayana Kocherlakota, Robert Kollman, Fulvio Ortu, Ian Parry, Christo
pher Phelan, Pedro Teles, Mark Watson, Michael Woodford, anonymous referees, and work
shop participants at The University of Chicago for many helpful comments.
September 1993
I. INTRODUCTION
The idea that consumer sentiment might cause output fluctuations is popular in the
business press.1 It is easy to see where this belief comes from: in Figure 1 we plot an index
of consumer sentiment against recessions for the postwar period.2 The pattern is striking; all
recessions were preceded by a fall in confidence, and all major falls in consumer sentiment
were followed by a recession (except in 1965 which, while not a recession, was the so-called
“growth recession.”) Apparently either consumers were correctly forecasting output falls, or
declines in consumer sentiment were inducing declines in output.
It has been recognized for some time that business cycle and growth models can exhibit
multiple (Nash) equilibria if they contain strategic complementarities.3 In a conventional
single equilibrium model, output fluctuates only in response to changes in economic funda
mentals, where the list of fundamentals includes technology, government purchases, money
supply, the price of oil, and so on. In a multiple equilibria model output responds to funda
mentals, but in addition there can be fluctuations as the economy shifts between equilibria.
Perhaps the most intriguing feature of these models is that output can fluctuate simply
because everyone expects it to. Put differently, expectations can be self-fulfilling in that
if people expect bad times they get them. Thus, this class of models offers a theoretical
rationalization of how consumer sentiment can affect GNP. Although these models intro
duce dramatically different policy considerations than single equilibrium models, many of
their observable implications are the same. As a result, their empirical relevance is largely
unknown.
In this paper, we study the behavior of the U.S. economy for the period 1953-1988.
Our central purpose is to evaluate empirically how much truth there is, if any, to the idea
that consumer sentiment causes fluctuations in GNP. Following Granger and others we take
causality to imply temporal precedence, that is, if one series causes another, then movements
in the forcing series precede movements in the forced series. We verify that the temporal
ordering suggested in Figure 1, consumer sentiment leads GNP, is statistically significant.
1 Examples from the last recession are “Economy in the U.S. Isn’t Nearly as Sour As the Country’s Mood.
But Pessimism Could Become A Self-Fulfilling Prophecy Further Stalling Recovery. Can Attitude Be Ev
erything?” on the front page of The Wall Street Journal, November 4, 1991, and “Recession: Case of Bad
Attitude? President Bush says people should be more confident—and that would restore economic vigor.
But consumers cite layoffs and lost wages,” from the front page of the Los Angeles Times, November 9, 1991.
2 A recession as defined by the NBER is indicated with a vertical bar.
3 Roughly speaking, a model contains strategic complementarities if each agent’s optimal action is positively
correlated with the action of other agents. A representative but incomplete list of the literature would include
Ball and Romer [1991], Bryant [1983, 1987], Cass and Shell [1983], Kiyotaki [1985], Milgrom and Roberts
[1990], Murphy, Shleifer, and Vishny [1989], Roberts [1987], Shleifer [1986], and Weil [1989]. Cooper and
John [1988] provide a good overview. On theoretical objections see Woodford [1987].
1
Temporal precedence is not enough for our purposes, however, because the evidence that
movements in consumer confidence precede movements in output can be interpreted in two
ways. Either consumer sentiment causes GNP or it simply a n tic ip a te s GNP.
We attem pt to disentangle the two possibilities by estimating a series of vector au
toregressions including GNP, consumer sentiment, and various other series that capture
fundamentals or are good predictors of GNP. The working assumption is that if consumer
sentiment can forecast GNP movements even after controlling for fundamentals and other
publicly-available predictors of output, some support is provided for the idea that consumer
sentiment causes output fluctuations. In our baseline regressions, the control variable is an
index of leading indicators, composed of fundamentals and purely predictive variables. To
check for robustness we consider a number of other controls, a “textbook” set of funda
mentals that includes government spending, money supply, and sensitive materials prices;
components of the leading indicators; and a default risk variable that has been identified as
an excellent predictor of output movements. For each set of vector autoregressions we test
whether consumer sentiment Granger causes GNP.
Our main finding is that even after controlling for economic fundamentals and other
good predictors of GNP, changes in consumer sentiment have a statistically significant effect
on output fluctuations. In other words, we find evidence of Granger causality running
from consumer sentiment to GNP. We also attempt to assess the economic significance of
consumer sentiment by decomposing the variance of GNP innovations. Our second finding
is that while sentiment is not the most important factor in GNP fluctuations it plays a
quantitatively significant role: between 13 percent and 26 percent of GNP innovation variance
can be attributed to variations in consumer sentiment. The evidence suggests that consumer
confidence is an important independent factor in economic fluctuations, and more tentatively,
it appears to provide some support for the class of macroeconomic models with strategic
complementarities.
The paper proceeds as follows. The next section provides a simple illustrative model
that exhibits multiple equilibria for some parameter values. Its main features are consistent
with the bulk of the macroeconomics literature on strategic complementarities, but we hope
it is more transparent. The model also calls attention to some interesting features of actual
economies that have been underexplored in this context. Section III discusses the related
literature. In Section IV we present the evidence. Granger causality tests are reported that
assess how important, if at all, consumer sentiment is in determining the level of aggregate
production. Section V draws a few conclusions.
2
II. AN ILLUSTRATIVE MODEL
It is easier to discuss the empirical procedures with a concrete example in mind. In this
section we sketch a stylized model of output fluctuations that exhibits the basic features of
multiple equilibria models. The model is amenable to generalization in a number of directions
that we do not pursue; our goal is to illustrate the central issues in as simple a manner as
possible.
The model is motivated by two features of actual economies that have not received much
attention in the recent macroeconomics literature, (i) many goods are produced to buyer
specifications, and (ii) once goods are customized they become less valuable to other buyers.
In fact, production to order is important in such industries as construction, machine tools,
steel, women’s apparel, and durables manufactures in general [Zarnowitz, 1973]. What makes
this interesting is that these are the industries where the business cycle primarily occurs.
We model customization by assuming there is one consumption good, call it a house,
that a person can have made to her specifications—she can choose the color of its paint. She
can also buy a house on the resale market or from developers who build without having a
buyer lined up. Because a resold house and a developer’s house are not specialized to her
tastes—the paint is the wrong color—they give her lower utility. In our one period model
consumers submit orders for custom-made goods at the start of the period, keeping their
expected income in mind. If they order more than they can afford, they must resell part of
their order, which is costly because other buyers place a relaitvely low value on the custom
features. If they order too little, they must enter the resale market as buyers, which means
they must buy goods whose custom features they dislike. Because consumers strive to match
their orders with their income, expectations can be self-fulfilling: if, for some reason, people
expect low incomes they submit low orders, leading the build-to-order firms to have low
employment, and consumers to have low incomes.
We assume there is a continuum of identical agents over the interval [0,1]. Agent i has a
utility function of u ( i ) —
—
where l(i) is her labor and c(i ) is her consumption value.
To capture the idea of specialized goods, her consumption value is written c(i) = co{i) + r c \ { i )
where co(i) is goods she has custom-made and ci(i) is goods that are not custom-made. She
prefers goods that are customized: r < 1.
There is a competitive production sector that produces Y goods where Y = A / q l ( i ) di.
All integrals that follow are over [0,1]. Firms are jointly and equally owned and all profits are
immediately returned as dividends (although in equilibrium profits are zero). The aggregate
production function (we sometimes call it “the firm”) is completely described by A which
represents economic fundamentals. The production technology is the same for custom goods
3
and generic goods so /co(z)di + /cx(z)di = Y . One way to think of this is that the cost
of painting a house is the same for every color. If labor demand exceeds labor supply we
assume that employment is rationed equally among workers.4
The sequence of actions in a period is as follows. First, each agent i submits orders
for a quantity q ( i ) of custom-made goods taking as given the price of custom-made and
generic goods. This is the upper bound on person i’s consumption of custom goods, that
is, co(i ) < q( i ) . After orders are placed the firms produce and pay wages. Then workers
are obligated to take delivery of their orders and a secondary market for consumption goods
opens, which we call a resale market. Workers who do not have sufficient funds to pay for
their orders must enter the resale market and sell part of their goods to pay off their debts.
In addition, firms can sell whatever non-customized goods they produced. When trading is
concluded consumption occurs.
Let p o be the price of custom-made goods, p, be the price of goods in the resale market,
and w be the wage rate. We normalize po = 1 and think of the wages paid by the firm as
claims to a unit of the consumption good. These claims can be redeemed for one unit of the
good which puts a ceiling on the equilibrium price in the resale market: p, < 1.
In the resale period, if there are consumers who ordered more than they can afFord, they
attem pt to raise money by selling some of their orders. They will be met by people who
ordered less than they can afford, and are trying to spend their extra income (claims). The
interactions of these buyers and sellers determines pt . It turns out that there is rational
expectations equilibrium for any p, 6 [0, l].5 The rest of this example is confined to the case
where px = r. This is an appealing case because goods in the resale market are discounted
just enough to compensate for the lower utility they deliver.
The next two propositions show that the behavior of the economy depends in an impor
tant way on the value of r. In particular, when r = 1 there is a unique equilibrium where
output is determined only by fundamentals. When r < 1 there is a continuum of equilibria
and expectations have self-fulfilling effects on the level of output. Here and below an aster
isk is used to denote equilibrium quantities, for example, equilibrium utility for agent i is
«*(<) = *■(•■) - !*-(*?•
PROPOSITION 1. If r = 1 there is a unique equilibrium with Y = A 2.
One way this can be rationalized is by assuming that each worker produces a separate component of the
consumption good. A more formal way to model this behavior would be to write the production technology
as y=>lminj l(i). In keeping with the spirit of our model as an example, we eschew this additional formality
because it makes the same point while introducing a heavier burden of notation.
0 We shall not prove this here, but note that it follows from the fact that no equilibrium has an active
market in both customized and non-customized goods. In practice, exactly where the resale price settles will
depend on the structure of the resale market and the nature of the bargaining that takes place.
4
4
If r = p i = 1 the firm finds it equally profitable to sell in the custom market and the
resale market. Then the firm’s profit is A f l(i) di —w J l( i) di. Equilibrium requires w m = A
and the firm hires as many as will work at that wage. From the consumer’s maximization
problem, l m(i) = w ’ — A . Then Y m = A f /*(i) di = A 2. Q .E .D .
P ro o f.
The intuition behind the proposition is that when p x = r = 1 the price in the ordered
goods market is the same as the price in the resale market so from the firm’s point of view
a good produced to order is as valuable as a good produced to stock. Then it pays a wage
equal to A and hires as much labor as is supplied at that wage. Given the utility function,
each person supplies A units of labor. The equilibrium is Pareto optimal.
In the situation described by Proposition 1 there is a unique equilibrium. There is no
sense in which consumer expectations affect production. Output fluctuates only in response
to changes in economic fundamentals, A . In these situations, when there are no customizing
effects, the model behaves in what might be called the conventional way.
The next proposition states that when r < 1 there is a continuum of equilibria. The
argument has two parts. First, the firm produces only to order, that is, it produces only as
many goods as are ordered in the customized market. The reason is that if the firm produces
for the resale market the wage rate is p \ A , and after working enough to supply the custommade demand, agents will not supply additional labor at the wage p \ A . Second, given their
income, which they take as exogenous, consumers order exactly as many customized goods
as they can pay for. They lose if they enter the resale market either as buyers or sellers. In
these cases a coordination failure occurs; if everyone could get together and jointly submit
high orders efficiency would be attained.
PROPOSITION 2. If r < 1 there is an equilibrium with
Y
=
SA2
for any
S
€ (r, 1).
Consider an arbitrary 5 € (r, 1 ). The proof demonstrates that there is an equilibrium
for S where q m(i) = S A , l* (i) = S'A, and w m — A . In the proposed equilibrium person i
is willing to supply labor of l( i) = A but the demand is only l* (i) = S A , according to the
rationing rule. At the margin if the firm adds a unit of labor it generates revenue p xA . But
the marginal disutility of labor at l* {i) is S A > p xA .
Agents are atomistic so they take /*(i) and w ‘ as given. If person i orders q ( i ) > q * (i)
then she has to raise q (i) — q’ (i) in the resale market to cover her debts. This costs her
P ro o f.
{q (i)
—9*(0)/Pi in consumption. Her utility is then
“(0 = 9(0 “ (?(0 “ 9'(0)/Pi ~ ^"(O2 = 9“(0 “ ^ * (0 2 + (1 - l/? i)(9 (0 “ 9‘ (0) < «*(0»
where the inequality follows because
w * l‘ ( i) — q (i) = q ’ ( i) — q (i)
px
= r < 1 . If she orders
q (i)
<
q~{i)
to spend in the resale market. This buys Cx(z) =
5
then she has
(q m(i) — q { i ) ) / p i -
Her utility is then u(t) = q(i) + r ( q M(i) - q ( i ) ) / p i -
= q*(i) - \ l ‘ ( i )2 = u*(i). Thus,
person i has no incentive to place higher or lower orders. Q. E. D.
The proposition implies that the level of output is determined not only by economic
fundamentals, A , but also by an arbitrary parameter, 5, which can be thought of as consumer
sentiment. In an important sense it can be said that consumer expectations c a u se output.
If consumers believe the equilibrium will be S then it is individually rational for them
to take actions that bring about the S equilibrium. The interesting conclusion is that
aggregate production can fluctuate in response to waves of optimism and pessimism, even if
the underlying technology does not change. Perhaps more intriguing, in view of the recent
behavior of the U.S. economy, is that the model suggests GNP can become stalled at low
levels even when there is nothing wrong with the fundamentals of the economy.
III. RELATED LITERATURE
How can we tell if strategic complementarities are a real concern, as the business press
believes, or are merely of theoretical interest? One approach would be to try to measure r or
p 0 — p i . Intuition suggests it is easy for parameter values to lie in the necessary range. For
example, suppose a person orders a house built. She has many options, what color paint,
what fixtures, how many rooms, what kind of carpeting or floors, and so on. If she has to
sell the house, probably she will need to give the buyer a price break because her custom
features are not the buyer’s first choice. It is plausible, then, that p i < p 0 for durable goods;
if r < 1 there are multiple equilibria. An obvious problem with this way of examining the
theory is that it is intimately linked to our model, which is quite stylized.
Still, this example suggests that one way to test for multiple equilibria is to estimate
directly the parameters of the model. Dagsvik and Jovanovic [1991] is a nice example of
this approach. They estimate a fairly general Phillips curve capable of exhibiting multiple
equilibria; then the parameters are examined to see if they lie in the multiple equilibria
region of the parameter space. Their evidence indicates unique equilibria in all three time
periods they investigate: 1901-1940, 1921-1940, and 1951-1986. The authors note that their
approach is limited in that they are forced to posit an exogenous and constant equilibrium
selection mechanism .6
Oh and Waldman [1991, 1993] take a completely different approach, one which is closer
in spirit to ours. Rather than try to estimate a particular model, they identify a general
6 im r o h o r o g lu [1993] u se s a sim ila r a p p ro a ch to lo o k for n o n -fu n d a m e n ta ls in th e 1 923 G e r m a n h y p erin fla
tio n , w ith la r g e ly n e g a tiv e r e su lts.
6
characteristic of coordination failure models and look for behavior consistent with that fea
ture. Cooper and John [1988] show that what drives the multiple equilibria property of all
these models is “strategic complementarities”: if everyone but person i takes the “high”
action (in our model, submits high orders) then it is in person i ’s interest to take the high
action as well.
Oh and Waldman observe that when there are strategic complementarities people have
an incentive to try to catch the waves: they want to invest when output is high and cut
back when it is low. Therefore, in a world with strategic complementarities investment and
output should respond to what people expect output to be. Their key insight is that if there
is an announcement that the economy is about to boom and everyone believes it then future
output should be high, even if the announcement is based on false information. In effect,
people use the announcements to coordinate.
As a measure of false forecasts, Oh and Waldman use revisions of the government’s
Index of Leading Indicators (ILI). They look to see if these revisions had an effect on fu
ture economic activity. Their evidence is mixed but more often than not it supports the
idea that ILI revisions predict movements in industrial production, consistent with strategic
complementarities. However, as they note, if the ILI provides new information to firms and
consumers (that is, information other than what equilibrium is selected), then revisions can
have effects even when there are no strategic complementarities
In this paper we focus on another implication of multiple equilibria models: expecta
tions are self-fulfilling. Specifically, we estimate a number of vector autoregressions and ask
whether consumer sentiment about the future Granger causes GNP.' The basic intuition
behind the test comes from Proposition 2, which shows that the level of output is Y = SA2.
In contrast to models with a unique equilibrium, in a multiple equilibrium model consumer
sentiment (5) has an effect on output (F) even after controlling for fundamentals (A). All
coordination failure models generate an output relation analogous to Proposition 2 because
consumers must expect to be in a particular equilibrium in order for the economy to move
there.
IV. EVIDENCE
A.
D e s c r ip tio n o f th e D a ta a n d V a riables
To measure consumer sentiment, we use the Index of Consumer Sentiment (ICS) con
structed by the Survey Research Center at the University of Michigan. The ICS captures7
7 O u r ap p ro a ch is r e la te d to an o ld er lite r a tu r e th a t in v e stig a te d th e a b ility o f co n su m er a tt itu d e s to p r e d ic t
p u rch a ses o f d u ra b le g o o d s, for e x a m p le , F riend an d A d a m s [1964].
7
consumer confidence about the economic present and future from survey responses to the
five questions listed in Panel A of Table I .8 The output series is GNP. We also performed
the tests substituting the value of goods output for GNP, and arrived at similar conclusions.
The main control variable is the Index of Leading Indicators (ILI), compiled by the Bureau
of Economic Analysis at the U.S. Department of Commerce. We use the version of the
ILI that expired in 1989—after 1989, the ILI includes the Index of Consumer Expectations,
which is based on the same questions as the ICS [Hertzberg and Beckman, 1989]. The series
comprising the ILI are indicated in Panel B of Table I. In various regressions we also include
as controls government expenditure, the components of the ILI, and the difference between
the rate of interest on six-month commercial paper and the rate of interest on six-month
Treasury bills, which we call “default risk.”
The data run quarterly from 1953:1 to 1988:4, except for the default risk variable which
runs from 1959:1. GNP and the ILI are seasonally adjusted at the source; the ICS does not
appear to have a seasonal component. GNP and the ILI are expressed in log differences.
This transformation makes the series approximately mean and variance stationary. The
questions comprising the ICS ask about changes as well as about levels, suggesting that the
ICS is a measure of change in sentiment. Given this and the fact that the ICS is trendless,
the estimates use the ICS in levels. Default risk is also expressed in levels. Rather than
take a strong stand on a particular number of lags, in most cases we report estimates from
models with lags of 1, 2, 3, and 4 quarters, although we find that the 4 lags model tends to
provide the best fit. The effects under consideration are weak with more than 4 lags. Ten
observations are missing from the ICS for the 1950s and one for the 1960s. This makes for
133 observations. The data are published by the U.S. Department of Commerce in S u r v e y
o f C u rre n t B u sin e ss.
B.
O u t p u t a n d C o n s u m e r S e n tim e n t
Causality is a difficult concept in science and particularly so in economics where we
seldom have the luxury of controlled experiments. The most common empirical approaches
in economics to causality inference are based on the idea of “Granger causality.” Roughly
speaking, series
ments in
y.
x
is said to Granger cause series
y
if movements in
x
help to predict move
Granger causality has the look of “true” causality so we believe it provides a
8 T h e S u r v e y R e se a r c h C e n ter p u b lish e s a se c o n d in d e x c a lled th e In d e x o f C o n su m e r E x p e c ta tio n s (I C E ),
b a s e d o n th e a n sw e r s to q u e stio n s 2, 3 , a n d 4 . W e u se th e IC S in s te a d o f th e IC E for tw o r e a so n s. F ir st,
w e b e lie v e th e r e sp o n s e s to q u e stio n s 1 an d 5 g iv e a fu ller p ic tu r e o f c o n su m e r s e n tim e n t. S e c o n d , w e fo u n d
t h a t th e IC E g a v e u n s ta b le r e su lts a cro ss su b sa m p le s. S ee C u r tin [1982] for a m o r e e x te n s iv e d isc u ssio n o f
th e IC S .
8
natural stepping off point for empirical investigation. However, it should be kept in mind
that Granger causality is neither a necessary or sufficient condition for true causality to
exist.9
Our empirical strategy is to demonstrate first that Granger causality exists from the ICS
to GNP, and second, that this relation is robust to inclusion of a large number of alternative
specifications. We begin with a simple two variable system including only GNP and the ICS.
Two types of evidence are reported to test if changes in consumer sentiment predict changes
in output. The first test is the so-called “Granger test.” Bivariate vector autoregressions are
estimated of the form
'Yt
.St.
'«(£)
b(iy
AL)
<*(£).
'Yt
.St.
+
'ey/
.est.
where Yt is GNP growth in quarter t , S t is the ICS, x ( L ) is a polynomial in the lag operator
L, and t is an error.10 If the block of coefficients represented by b (L ) are not jointly equal
to zero then we can reject the hypothesis that there is not Granger causality from consumer
sentiment to GNP. The system also provides a statistical summary of the link apparent in
Figure 1 .
Table II presents the results for 1 , 2, 3, and 4 lags.11 In the table, each column is a
regression. The number of lags and the dependent variable are indicated at the top of each
column. The main entry for each variable is the p-value for the F-statistic testing whether
the block of coefficients are jointly equal to zero. In all four models, the hypothesis that the
ICS coefficients in the GNP equation are jointly equal to zero can be rejected at better than
the 1 percent level. In other words, ICS innovations help to predict GNP movements.
Table II also reports the sum of each block of coefficients and the standard error of
the sum. The sum of ICS coefficients is positive in all GNP equations and significantly
different from zero at better than the 1 percent level. There is a subtle difference between
this information and that provided by the F-statistic. The F-statistic looks at the role of
the ICS in explaining quarterly GNP fluctuations while the sum of coefficients represents
the “long run” effect of the ICS on the level of GNP.
The sum and block of GNP coefficients in the GNP equations are never significantly
different from zero. The GNP coefficients in the ICS equations are always negative and
marginally significant in the 3 and 4 lags models. This curious effect recurs throughout the
estimates below. Finally, the ICS does an excellent job predicting its own movements.
9 O n ca u sa lity in e c o n o m e tr ic s se e G ew ek e, M eese a n d D e n t [1983] an d th e S e p te m b e r /O c to b e r 1988 sp e c ia l
is su e o f th e Journal of Econometrics.
10 A ll r e p o r te d r esu lts are d raw n from e q u a tio n s th a t also in c lu d e a c o n s ta n t term .
11 H ere a n d b e lo w , th e IC S is sc a le d b y a fa cto r o f 1,000 for c la r ity o f p r e se n ta tio n .
9
A variant of the Granger test, described by Geweke, Meese, and Dent [1983], evaluates
whether possible forcing variable x decreases the forecast variance of variable y . Let the
residual variance of y in an autoregression be a2 . Let the residual variance when x is
included as an explanatory variable be <t>2. Let the number of observations be N and the
number of lags k. Geweke, Meese, and Dent show that
m
=
~
n
xi
asymptotically under the null hypothesis of no Granger causality. They argue that this type
of test has better small sample properties than the Granger test above. The results for 77 are
presented in Table III. In all four models the ICS decreases the forecast variance of GNP at
better than the 1 percent level of significance. Because p ( k ) > T](k) in small samples, the
ICS significantly decreases forecast variance using p as well.
C.
O u tp u t, C o n su m e r S e n tim e n t, a n d L e a d in g In d ic a to r s
Tables II and III show that the ICS helps to predict GNP, and thus by definition that
GNP is Granger caused by ICS. However, bivariate estimates do not make a compelling
case for true causality between the ICS and GNP because they fail to address the obvious
possibility that the correlation is driven by a third variable acting on both the ICS and
GNP. Suppose that in reality GNP is caused entirely by a production shifter, say the price
of oil, but with a lag of six months. How do we know that consumer sentiment is not simply
a forecast of GNP based on observation of the price of oil? Because there are an infinite
number of potential third variables, in general it is impossible to prove that a correlation
is not caused by some omitted third variable. However, it is possible to evaluate if it is
caused by specific variables. Our approach is to introduce into the vector autoregressions
a succession of plausible variables that consumers might be using to forecast output and
examine if they can eliminate the ICS-GNP correlation. To the extent that these third
variables are unable to account for the correlation, the more confident we can be that the
ICS-GNP relation is not spurious.
The next step is then to estimate vector autoregressions including control variables that
are correlated with economic fundamentals, that is,
'v r
At
.s t .
=
a (L )
m
C(£)■
d (L )
e (i)
m
A L )
M i)
i(i).
10
'Y t At
.S t.
’ «y,'
+ €.4,
. est .
where A t represents the control variables. Series that are exogenous and have a good ability
to forecast GNP are desirable. Inclusion of a large number of series in a vector autoregression
consumes degrees of freedom and complicates statistical inference, so we choose a single series
incorporating the effects of a number of different predictors, the ILI, which is explicitly
constructed to forecast GNP movements. The ILI is a composite index that includes a
number of series that might be considered forcing variables (money supply, sensitive materials
prices). It also contains endogenous variables (inventories, unemployment claims). Because
the ILI contains both exogenous and endogenous variables, one expects the relationship
between the ILI and ICS to exhibit bidirectional causality if sentiment is causal. That is, the
hypothesis that consumer sentiment causes output is not inconsistent with the possibility
that it also reflects current information.
The results are reported in Table IV. The table is formatted in the same way as Table II.
There are three pieces of evidence on the ICS-GNP relation. First, p-values are presented
corresponding to the F-statistic on the block of ICS coefficients in the GNP equations, that
is, the test of c ( L ) = 0. The hypothesis that the ICS coefficients are jointly zero can be
rejected at better than the 5 percent level in all models. The sum of ICS coefficients is
positive and significantly different from zero at the 1 percent level in all models. The third
relevant statistic, reported at the bottom of the table, tests for the block exogeneity of GNP
and the ILI with respect to the ICS. A x2 is constructed by scaling the difference between
the log determinant of the residual covariance matrix of the estimated system and that of a
bivariate GNP-ILI system. This statistic allows for the possibility that the ICS affects GNP
in d ir e c tly through the ILI. The hypothesis that GNP and the ILI are block exogenous can
be strongly rejected in the 1, 2, and 4 lags models. The x2 from the 3 lags model does not
attain statistical significance at conventional levels, but it is the sole exception to otherwise
uniform evidence that the ICS predicts GNP, and as we discuss below, the 3 lags model can
be statistically rejected in favor of the 4 lags model.
Turning to other coefficients, it can be seen that GNP does a poor job predicting its
own innovations, as above. Not surprisingly, the ILI predicts GNP. In the ILI equations,
GNP appears to have a negative effect while the ICS has a positive effect after three or four
quarters. The ICS equation indicates that consumer sentiment has a substantial autore
gressive component. The leading indicators have a positive effect, suggesting that consumer
sentiment is in part a forecast based on fundamentals. However, a comparison with Table II
reveals that inclusion of ILI does not add much to the ICS R . GNP has a negative effect,
suggesting a kind of regression to the mean in expectations; when times have been good for
a while people believe all good things must end and when times have been bad they believe
there is nowhere to go but up.
11
Consumer sentiment appears to have a statistically significant effect on GNP. We would
like to know if it has a q u a n tita tiv e ly significant effect. Comparing the estimates in Table IV
with those for bivariate vector autoregressions of GNP and the ILI (not included) shows
that addition of the ICS adds only 2 percent to 4 percent to the R . The ILI and ICS move
together so this crude estimate is probably a lower bound on the marginal contribution of
sentiment to explaining GNP fluctuations.
A better way to assess the quantitative importance of consumer confidence in GNP
fluctuations is to use the vector autoregression residuals to decompose the forecast variance
of GNP into contributions by each of the variables. The technique is briefly outlined below; a
comprehensive discussion can be found in Sims [1980a] (see also Sims [1980b] and Litterman
and Weiss [1985]). As a caveat to this sort of exercise we should repeat Schiller’s [1987]
observation that variables which have very small effects in explaining long run variance
nevertheless may be highly important in certain situations.
Let u be a three element vector of forecast errors for a trivariate vector autoregression
and E the covariance matrix associated with the u process. A corresponding orthonormal
vector v and a lower triangular matrix G can be found such that G G ' = E and G v — u.
Because v is orthonormal and G is lower triangular the variance of the forecast error of each
of the endogenous variables can be decomposed into percentage contributions by innovations
in each of the three equations. This procedure can be used to decompose variances of any
arbitrary length forecast.
The percentage contributions are sensitive to the decomposition method, specifically to
the ordering of variables in the equation. For example, by construction the first variable listed
contributes 100 percent of its own one-period-ahead forecast variance. Because G is lower
triangular it is conventional to place forcing variables early in the order and endogenous
variables later. For this reason the hypothesized driving variables, the ICS and ILI, are
placed first in the first two decompositions. Consumer sentiment is placed last, somewhat
atheoretically, in the third decomposition to describe the worst case.
Decompositions of GNP and the ICS from one to eight quarters ahead are presented
in Table V.12 The estimates are for the 4 lags model in Table IV. Here and below, when
choosing which model to decompose we were guided by the following selection rule. First we
computed the distance between the residual covariance matrixes of the 3 and 4 lags models.
If they were significantly different, we chose the 4 lags model. If not, we compared the 2 and
3 lags models. If they were significantly different, we chose the 3 lags model, and so on. The
variables are listed in the order they appear in the u vector.
12 R A T S v er sio n 4 .0 2 w a s u se d to p erfo rm th e v a ria n ce d e c o m p o s itio n s. T h e r o u tin e ig n o r e s th e sa m p lin g
error c o m p o n e n t o f th e p ro c e ss an d co n sid ers o n ly th e e q u a tio n error.
12
In the top GNP decomposition, the variance of ICS explains 14.4 percent of the onequarter ahead forecast variance of GNP, rising to 25.8 percent eight quarters ahead. In the
bottom decomposition, which is the worst case for finding an effect of consumer sentiment,
the ICS explains 12.9 percent of the eight-quarter-ahead variance. Recall that the zero
percent estimate of the one-quarter-ahead contribution in the last equation is entirely an
artifact of the decomposition technique. Rough bounds on the mean effect of the ICS on
GNP then would be between 13 percent and 26 percent. It seems reasonable to conclude
that movements in consumer confidence are quantitatively important in explaining GNP
fluctuations.
The ICS decompositions provide evidence on the exogeneity of consumer sentiment. In
the top panel, the ICS explains 83.6 percent of its own innovation variance eight quarters
ahead. In the worst case for the ICS, the bottom panel, consumer sentiment still explains
72.1 percent of its eight-quarter-ahead innovation variance. Although consumer sentiment
appears to be affected by GNP and ILI movements, neither of these variables can explain the
majority of sentiment variation. This suggests that the ICS is to a large degree exogenous
with respect to these variables, and tends to undermine the notion that sentiment is nothing
more than a forecast of output.
D.
R o b u s tn e s s
The results in the previous section support the hypothesis that consumer sentiment con
tributes to fluctuations in aggregate output. However, like the test of Oh and Waldman
[1990], the estimates can be interpreted in more than one way. In particular, there remains
the possibility that we have omitted an economic fundamental which is forcing both the con
sumer sentiment and GNP series. This section explores a number of different specifications
and variables in pursuit of such a fundamental.
First, we estimate a set of vector autoregressions with GNP, the ICS, and three “text
book” control variables, money supply, government spending, and sensitive materials prices.
We call these textbook controls because they are staples of almost every macroeconomics
textbook. If one were to ask economists to name exogenous factors that cause GNP fluctu
ations, these variables would probably appear on most lists.
Table VI reports evidence from these vector autoregressions. To conserve space, only
the GNP and ICS equations are reported, and only the coefficients on GNP and the ICS.
The ICS coefficients in the GNP equation are of primary interest. The F-statistic on the
block of ICS coefficients is significant at the 10 percent level in the 1 lag model and just
beyond conventional significance levels in the 2, 3, and 4 lags models. Some fall in precision
of estimates is to be expected, especially in the model with 4 lags, because of the loss of
13
degrees of freedom. The sum of ICS coefficients is positive and statistically significant in all
models. The magnitude of the sum in the 1 lag and 2 lags models is quite a bit lower than
in Table IV, but about the same for the 3 and 4 lags model, indicating that the controls rob
consumer sentiment of some power in the first two quarters.
The most important statistic is the x2 that tests for the block exogeneity of GNP and
the controls with respect to the ICS. Recall that this indicates whether ICS has any effect
on the system, direct or indirect. Block exogeneity can be rejected at approximately the 1
percent level in all models. Taken together, the estimates suggest that the textbook set of
controls cannot account for the ICS-GNP relation.
The bottom panel of Table VI reports variance decompositions. To maintain compara
bility with other tables we choose to present the decomposition of the 4 lags model, although
in this case our selection criteria suggested that the 2 and 3 lags models would be fine as
well. In any case, the 2 and 3 lags decompositions are substantially the same. As in Table V
we decompose GNP and the ICS. The sum of the percentage contribution of controls is indi
cated in the column headed “X.” Again, to conserve space, only two orderings are reported.
In the GNP equation, when the ICS is ordered before the controls, consumer sentiment can
account for over 20 percent of the innovation variance of output, with its explanatory power
peaking 3 and 4 quarters ahead at 23.7 percent. When the ICS is listed after the controls,
it experiences only a minor decline—4 quarters ahead it still explains 18.6 percent of GNP
innovation variance. In the ICS equation, the ICS accounts for no less than 65 percent of its
own innovation variance when listed first, and no less than 56 percent when listed after all
the controls. The decompositions from the textbook system do not differ in substance from
the ILI system: the ICS has a quantitatively large effect on GNP, and the ICS appears to
have an important exogenous component, suggesting it is not simply a forecast of GNP.
The next set of vector autoregressions include as controls both the ILI and default risk,
the spread between the interest rate on corporate debt and treasury bills. The default risk
variable has attracted recent attention for its ability to predict GNP movements [Stock and
Watson, 1989]. It is not clear whether this variable reflects an economic fundamental or is
itself a non-fundamental, perhaps the animal spirits of investors.
Table VII reports vector autoregressions with GNP, the ICS, the ILI, and default risk,
indicated “DR” in the table. For space reasons, only the 4 lags model is reported. Again, our
test for number of lags suggests that models with fewer than 4 lags can be rejected at about
the 1 percent level. The key statistics, as usual, concern the ICS in the GNP equation. First,
the hypothesis that the block of ICS coefficients are jointly zero can be rejected at almost
the 5 percent level. Second, the sum of coefficients is positive and statistically different from
zero at better than the 5 percent level. Addition of the default risk variable leads to a modest
14
decrease in the magnitude of the sum. The x 2 statistic indicates that block exogeneity of
GNP, the ILI, and default risk with respect to the ICS can be rejected at roughly the 1
percent level. The evidence continues to point to a role for consumer confidence in economic
fluctuations.13
For this model, we report all of the equations and coefficients because the default risk
variable is of some interest in itself. This variable has a significant effect on the movement of
all variables in the system according to the F-statistic. The sum of default risk coefficients
is significant in the GNP, ILI, and default risk equations. Thus, default risk matters.
This is interesting because default risk is not obviously an economic fundamental. It
may be simply a good mirror of underlying fundamentals, but the failure of the ILI and
GNP to achieve statistical significance in the default risk equation does not square well with
this interpretation. The results were no better in the models with fewer lags. In fact, the
only variable identified as driving default risk in this system is the ICS. Taken together, the
evidence is not inconsistent with the idea that default risk represents investor sentiment, or
captures some other aspect of consumer confidence.
Table VIII reports the GNP and ICS variance decompositions for the model in Table VII.
The evidence follows the pattern established above. The ICS accounts for a healthy fraction
of the innovation variance of GNP, up to 21.8 percent eight quarters ahead in the worst
case decomposition ordering. Default risk serves primarily to rob the ILI of its explanatory
power. Furthermore, the ICS continues to appear largely exogenous. Even in the worst case
decomposition, consumer sentiment accounts for no less than 70 percent of its own innovation
variance. If anything, inclusion of default risk in the vector autoregressions suggests an even
more important role for consumer confidence as a causal factor.
In the final set of vector autoregressions, both default risk and the individual compo
nents of the ILI are included as controls.14 The benefit of this is that it avoids the ad hoc
parameter restrictions implied by construction of the ILI. The cost is that the large number
of component series rapidly consumes the available degrees of freedom.
The GNP and ICS coefficients for the GNP and ICS equations are reported in the upper
panel of Table IX. Variance decompositions are reported in the bottom panel. Beginning
as usual with the F-statistic on the block of ICS coefficients in the GNP equation, the
hypothesis that consumer sentiment does not Granger cause GNP can be rejected at about
13 T h e x 2 s t a t is t ic an d su m o f c o efficien ts are a lso s ta tis tic a lly sig n ific a n t in th e u n rep o r te d 1, 2, an d 3 la g s
m o d e ls, w h ile th e F s t a tis tic s lie ju s t o u ts id e s ta tis tic a l sig n ific a n c e .
14 T o b e p r e c ise , we use th e c o m p o n e n ts o f th e cu rren t ILI less th e IC E . T h e current ILI differs from
th e v e rsio n liste d in T a b le I in th a t it in clu d es th e IC E an d u n filled ord ers an d ex c lu d e s th e c h a n g e in
m a n u fa c tu r in g a n d tra d e in v en to ries.
15
the 5 percent level in the 1 lag and 3 lags models, but does not quite achieve statistical
significance in the 2 and 4 lags models. Here again, this test loses a fair amount of power
due to the large number of control variables, especially in the model with 4 lags. The sum
of the ICS coefficients is positive and significantly different from zero in all models. Most
important, the block exogeneity of GNP and the controls with respect to the ICS can be
rejected at better than the 1 percent level in all four models.
The bottom panel of Table IX reports variance decompositions for the 4 lags model. Here
again the models with fewer than 4 lags can be rejected when comparing the log determinants
of the residual covariance matrixes. Two decomposition orderings are reported, one that lists
the ICS before the controls (indicated as “X”) and one that lists it after the controls; GNP
is ordered last in both cases. In the first GNP decomposition, the ICS explains 21.6 percent
of the one-quarter-ahead variance; the effect falls gradually to 16.3 percent eight quarters
ahead. In the second GNP decomposition, the estimated ICS efFect is lower, peaking at
8.8 percent five quarters ahead. These effects are smaller than in previous tables, but not
trivial. In the ICS decompositions, the evidence continues to support the idea that the ICS
has a substanital exogenous component, that is, consumer sentiment is more than a forecast
based on available information. In the first decomposition, the ICS explains no less than 52
percent of its own innovation variance, while in the second no less than 31 percent.
The results in this section can be simply summarized. Even after controlling for a
number of good predictors of GNP, the ICS continues to add predictive power to the model.
These results cannot rule out the possibility that consumer sentiment is nothing more than
a forecast of output. However, under this interpretation it appears that consumers are
basing their forecasts on information that is unavailable to professional econometricians who
specialize in forecasting GNP movements. The alternative interpretation that consumer
confidence causes ouput movements seems no less plausible.
V. CONCLUSION
This paper explores the possibility that the economy’s total output occasionally varies
not in response to a shift in fundamentals but in response to a shift in consumer sentiment.
Specifically, the paper asks whether and to what extent exogenous declines in consumer
confidence cause recessions and conversely whether and to what extent bullish consumers
drive economic growth.
There are two inspirations for this research. The first is the fact that something called
“consumer confidence” plays an important role in popular explanations of business cycles
and in the public statements of business and political leaders. There is a long tradition
of confidence explanations for recessions. Keynes emphasized the “mass psychology of the
16
market” and “animal spirits” among investors, concluding that “(i)n estimating the prospects
of investment, we must have regard, therefore, to the nerves and hysteria and even the
digestions and reactions to the weather of those upon whose spontaneous activity it largely
depends.” During the Great Depression President Franklin D. Roosevelt and General Motors
Chairman Alfred P. Sloan, Jr., who disagreed in many ways on the role of government in
helping the economy, seemed to be of the same mind on the nature of the problem and
the primary impediment to recovery. Roosevelt’s famous inaugural speech contained the
statement, “let me assert my firm belief that the only thing we have to fear is fear itself”
while Sloan commented, “the main obstacle to the general revival of American enterprise is
the fear the foundation of the economy is in jeopardy.”15
Our empirical estimates for the United States, 1953-1988, uniformly reject the hypothe
sis that consumer sentiment does not cause GNP (in the Granger sense). This gives support
to the idea that exogenous changes in consumer sentiment have real effects on output. Ac
cording to our central vector autoregressions, between 13 percent and 26 percent of the
variance of GNP innovations is the result of waves of consumer sentiment, which suggests a
non-trivial role for expectations. Thus, the main contribution of the paper is a demonstra
tion that consumer confidence is an important independent factor in economic fluctuations,
a fact that did not previously rest on solid empirical ground [Leeper, 1991].
The second purpose of the paper is to provide some evidence on the rich collection of
macroeconomic models with strategic complementarities that have been developed in recent
years. All these multiple equilibria models have in common that expectations are selffulfilling—because agents must expect to be in a particular equilibrium before the economy
can move to it, their expectations in a sense cause the movement to the equilibrium. An
implication of these models, then, is that after controlling for movements in economic fun
damentals, changes in consumer sentiment lead to changes in GNP. Our estimates appear
to provide support for this key implication.
However, we caution that our evidence does not prove that expectations cause output
fluctuations. There remains the possibility that a missing third variable is forcing both
series. Even so, the results have power because we could have found that expectations were
completely insignificant. If that had been the case, it would have been safe to conclude that
multiple equilibria are not empirically important. Like Oh and Waldman [1990], then, our
results are open to an alternative interpretation. The two studies taken together constitute
an initial case in favor of the class of macroeconomic models that view some recessions as
coordination failures, but certainly additional research is called for.
15 Q u o ta tio n s in th e p a ra g ra p h are from K e y n e s [1964, p a g es 154, 161, 162], R o o se v e lt [1946, p a g e 13] an d
C ray [1980, p a g e 311], r e sp e c tiv e ly .
17
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a n d S tr u c tu r a l A n a ly s is
19
TABLE I
Components of the Index of Consumer Sentiment and Index of Leading Indicators
A. Index of Consumer Sentiment
1. We are interested in how people are getting along financially these days. Would you say
that you (and your family living there) are better off or worse off financially than you
were a year ago? Why do you say so?
2. Now looking ahead—do you think that a year from now you (and your family living
there) will be better off financially, or worse off, or just about the same as now?
3. Now turning to business conditions in the country as a whole—do you think that during
the next 12 months we’ll have good times financially, or bad times, or what?
4. Looking ahead, which would you say is more likely—that in the country as a whole we’ll
have continuous good times during the next five years or so, or that we’ll have periods
of widespread unemployment or depression, or what?
5. About the big things people buy for their homes—such as furniture, a refrigerator, a
stove, television, and things like that. Generally speaking, so you think now is a good
or a bad time for people to buy major household items? Why do you say so?
B. Index of Leading Indicators (1988 Version)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Average weekly hours of production or nonsupervisory workers in manufacturing.
Average weekly initial claims for unemployment insurance in state programs.
Manufacturers’ new orders in consumer goods and materials industries.
Contracts and orders for plant and equipment.
Index of new private housing units authorized by local building permits.
Index of stock prices of 500 common stocks.
Money supply, M2.
Percent of companies receiving slower deliveries from vendors.
Change in sensitive materials prices.
Change in business and consumer credit outstanding.
Change in manufacturing and trade inventories on hand and on order.
T A B L E II
Vector Autoregressions with G N P and the Index of Consumer Sentiment
1 lag
2 lags
3 lags
4 lags
D e p e n d e n t v a ria b le
D e p e n d e n t va ria b le
D e p e n d e n t va ria b le
D e p e n d e n t va ria b le
GNP
ICS
GNP
ICS
GNP
ICS
GNP
ICS
0.118
0.206
0.563
0.314
0.761
0.086
0.808
0.063
Sum of coefficients
Standard error
0.148
(0.094)
-0.066
(0.052)
0.063
(0.124)
-0.031
(0.072)
-0.085
(0.158)
-0.165+
(0.093)
-0.066
(0.198)
-0.263*
(0.108)
ICS
F: p-value
Sum of coefficients
Standard error
0.002
0.265**
(0.082)
0.000
0.946**
(0.045)
0.003
0.272**
(0.087)
0.000
0.936**
(0.050)
0.000
0.314**
(0.096)
0.000
0.979**
(0.056)
0.001
0.327**
(0.107)
0.000
0.995**
(0.058)
0.162
0.825
0.157
0.831
0.215
0.838
0.202
0.845
GNP
F: p-value
R2
T h is ta b le rep o rts in fo rm a tio n from vector a u to reg ressio n s Z t = < b ( L ) Z t + e t w h ere Z t c o n ta in s G N P and th e IC S. T h e 1, 2, 3, and 4 lags m o d els con tain 121,
115, 110, and 109 o b serv a tio n s, resp ectiv ely . Each colu m n is a regression . T h e d e p en d en t variable is in d ica ted a t th e top o f each co lu m n . In th e m ain
en tries, th e first n u m b er is th e p -valu e a sso c ia te d w ith th e F -sta tis tic for th e h y p o th e sis th a t the block o f coefficien ts are jo in tly eq u al to zero. B elow th is
is th e su m o f th e block o f co efficien ts and its sta n d a rd error. S ig n ifica n ce lev els on th e su m o f coefficien ts are in d icated as follow s: “* * ” is sig n ifica n t
rejection at 1 p e r c e n t,
is sig n ifica n t rejection a t 5 p ercen t, and “- f ” is sig n ifica n t rejection at 10 p ercen t.
T A B L E III
Forecast Error Tests for G N P and the Index of Consumer Sentiment
<72
<f>2
T](k)
Observations
1
0.0000895
0.0000829
8.89
121
2
0.0000855
0.0000785
9.42
115
3
0.0000871
0.0000752
15.01
no
4
0.0000886
0.0000769
14.44
109
Lags (k)
T h is ta b le r e p o r ts e v id e n c e o n w h e th e r th e IC S red u ces th e fo r e c a st v a ria n ce o f G N P . H ere a2 is th e resid u a l
v a ria n ce o f G N P in a n a u to r e g r e ssio n , <
t>2 is th e resid u a l v a ria n ce w h en IC S is in c lu d e d a s an e x p la n a to r y
v a ria b le, a n d ri=N((<?2-<j>2)/<72). T h e n u ll h y p o th e s is is th a t e x p e c ta t io n s d o n o t h e lp to fo r e c a st G N P . T h e tj
s t a t is t ic s a ll in d ic a te sig n ific a n t rejectio n a t b e tte r th a n th e 1 p e r c e n t le v e l.
T A B L E IV
Vector Autoregressions with GNP, the Index of Leading Indicators, and the Index of Consumer Sentiment
1
lag
2
Dependent variable
lags
3
Dependent variable
4
lags
Dependent variable
lags
Dependent variable
GNP
ILI
ICS
GNP
I LI
ICS
GNP
ILI
ICS
GNP
I LI
IC S
0 .1 4 9
0 .0 0 6
0 .0 0 2
0 .0 6 9
0 .0 4 6
0.011
0 .2 3 3
0.175
0.006
0.228
0.126
0.009
S u m o f coefficien ts
- 0 .1 3 8
- 0 .5 9 2 *
- 0 .1 8 2 * *
-0 .2 5 7 +
- 0 .9 1 3 * *
- 0 .1 1 1
- 0 .3 2 7 +
- 1 .1 6 1 *
- 0 .2 5 9 *
- 0 .3 9 7
- 1 .1 2 6 *
- 0 .3 1 6 *
S ta n d a rd error
(0 .0 9 5 )
(0 .2 1 3 )
(0 .0 5 6 )
(0 .1 3 7 )
(0 .3 2 9 )
(0 .0 8 6 )
(0 .1 9 5 )
(0 .4 6 3 )
(0 .1 1 6 )
(0 .2 4 2 )
(0 .5 3 5 )
(0 .1 3 3 )
0.000
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0.000
0.000
0 .0 0 0
0.000
0.000
GNP
F: p -v a lu e
ILI
F: p -v a lu e
S u m o f coefficien ts
0.249**
0.656**
0.101**
0.298**
0.659**
0.101**
0.290**
0.700**
0.110*
0.318**
0 .3 6 9 +
0 .0 7 8
S ta n d a rd error
(0 .0 4 1 )
(0 .0 9 2 )
(0 .0 2 4 )
(0 .0 5 4 )
(0 .1 3 0 )
(0 .0 3 3 )
(0 .0 7 5 )
(0 .1 7 9 )
(0 .0 4 4 )
(0 .0 9 2 )
(0 .2 0 5 )
(0 .0 5 1 )
0 .0 0 4
0 .3 9 6
0 .0 0 0
0 .0 1 0
0 .3 8 7
0.000
0.042
0.544
0.000
0.045
0.052
0.000
IC S
F: p -v a lu e
S u m o f coefficien ts
0.214**
0 .1 3 8
0.925**
0.236**
0 .2 4 6
0.920**
0.260**
0.299
0.955**
0.280**
0.474*
0.980**
S ta n d a rd error
(0 .0 7 3 )
(0 .1 6 2 )
(0 .0 4 3 )
(0 .0 7 5 )
(0 .1 8 1 )
(0 .0 4 5 )
(0 .0 8 8 )
(0 .2 0 8 )
(0 .0 5 2 )
(0 .0 9 8 )
(0 .2 1 8 )
(0 .0 5 4 )
0 .3 5 5
0 .3 1 3
0 .8 4 6
0 .3 6 3
0 .2 7 9
0.861
0 .3 4 7
0.258
0 .8 6 4
0 .3 3 9
0 .3 3 6
0.869
T?
x 2 : p -v a lu e
0.003
0 .0 0 3
0 .2 7 3
0 .0 2 2
(B lo c k e x o g e n e ity )
T h is ta b le rep orts in fo rm a tio n from vector a u to reg ressio n s Zt=4>(L)Z(-He w here Zt c o n ta in s G N P , th e IC S, and th e ILI. T h e 1, 2, 3, and 4 lags m o d els
co n ta in 121, 115, 110, and 109 o b se r v a tio n s, resp ectiv ely . E ach colu m n is a regression . T h e d e p e n d en t variable is in d icated a t th e to p o f each colu m n .
In th e m ain en tr ie s, th e first num ber is th e p -value a sso c ia te d w ith th e F -sta tis tic for th e h y p o th e sis th a t th e block o f coefficien ts are jo in tly eq u al to
zero. B elow th is is th e su m o f th e block o f coefficien ts and its sta n d a rd error. S ign ifican ce levels on th e su m o f coefficients are in d ica ted as follow s: “* * ”
is sig n ifica n t rejection a t 1 p ercen t,
is sig n ifica n t rejection a t 5 p erc e n t, and “- f ” is sig n ifica n t rejection at 10 percent. T h e x 2 s t a tis tic is for th e
h y p o th e sis th a t G N P and th e ILI are block ex o g en o u s w ith resp ect to th e IC S.
TABLE V
Decomposition of the Innovation Variance of G N P and the Index of Consumer Sentiment
from Vector Autoregressions with GNP, the ICS, and the ILI
G N P d e c o m p o s itio n
Quarter
1
4
8
ICS
14.4
21.1
25.8
ILI
10.8
21.8
21.7
GNP
74.8
57.1
52.5
G N P d e c o m p o s itio n
Quarter
1
4
8
ILI
22.5
39.0
35.2
ICS
2.7
3.9
12.3
GNP
74.8
57.1
52.5
G N P d e c o m p o s itio n
Quarter
1
4
8
GNP
100.0
71.5
62.9
ILI
0.0
25.S
24.3
ICS
0.0
2.7
12.9
IC S d e c o m p o s itio n
ICS
100.0
90.1
83.6
ILI
0.0
2.8
3.2
GNP
0.0
7.1
13.2
IC S d e c o m p o s itio n
ILI
25.2
32.5
22.4
ICS
74.8
60.4
64.5
GNP
0.0
7.1
13.2
IC S d e c o m p o s itio n
GNP
14.4
5.9
4.1
ILI
13.3
29.7
23.8
ICS
72.2
64.4
72.1
T h is ta b le r e p o r ts th e p e r c e n ta g e o f G N P an d IC S in n o v a tio n v a ria n ce th a t c a n b e a ttr ib u te d to each
v a ria b le in th e 4 la g s v e c to r a u to r e g r e ssio n . For ea ch m o d e l, th e d e c o m p o s itio n is c o m p u te d for th ree
d ifferen t ord erin g s o f th e v a ria b les. T h e q u arter (a h e a d ) o f th e in n o v a tio n v a ria n ce b e in g d e c o m p o s e d is
in d ic a te d in th e le ftm o s t c o lu m n . T h e r e m a in in g e n tries in d ic a te th e p e r c e n ta g e o f in n o v a tio n v a rian ce
a ttr ib u ta b le to th e v a ria b le at th e to p o f th e co lu m n .
T A B L E VI
Vector Autoregressions and Variance Decompositions of GNP, the Index of Consumer Sentiment,
and Textbook Controls
1 la g
2 la g s
3 la g s
4 la g s
IC S
GNP
IC S
GNP
IC S
GNP
IC S
0 .7 2 2
0 .1 9 4
0 .7 9 2
0 .2 1 4
0 .7 5 1
0 .1 6 3
0 .8 7 0
0 .2 9 9
0 .0 3 5
-0 .0 7 0
-0 .0 6 8
0.051
- 0 .2 3 9
-0 .0 9 5
-0 .2 0 5
(0 .0 9 9 )
(0 .0 5 4 )
(0 .1 3 9 )
(0 .0 7 7 )
(0 .1 9 3 )
(0 .1 0 7 )
(0 .2 5 4 )
0 .0 5 5
0 .0 0 0
0 .1 4 0
0 .0 0 0
0 .1 0 9
0 .0 0 0
GNP
GNP
F: p -v a lu e
S u m o f co e ffic ie n ts
S ta n d a r d error
-0 .1 6 9
(0 .1 3 2 )
IC S
F: p -v a lu e
S u m o f co e ffic ie n ts
0 .1 6 1 +
0 .8 7 3 "
0.194*
0.850**
0 .2 6 7 *
0.876**
S ta n d a r d error
(0 .0 8 3 )
(0 .0 4 5 )
(0 .0 9 0 )
(0 .0 5 1 )
(0 .1 1 0 )
(0 .0 6 2 )
0 .2 6 6
0 .8 5 0
0 .2 8 3
0.871
0 .2 8 5
0 .8 7 4
R2
0 .0 0 0
0 .0 0 0
x 2: p -v a lu e
0.000
0 .2 3 6 +
0.888**
(0 .1 3 5 )
0 .2 7 1
0 .0 0 0
IC S
X
GNP
IC S
7 3 .6
X
GNP
1
19.3
100.0
0 .0
0 .0
4
2 3 .7
18.7
5 7 .6
8 6 .1
11.4
2 .5
8
2 1 .7
3 0 .8
4 7 .5
65.1
2 8 .1
6 .8
X
IC S
GNP
X
IC S
GNP
9.5
16.9
7 3 .6
6 .6
9 3 .4
0 .0
1
0.871
0 .0 1 5
7.1
Q u a rter
(0 .0 7 0 )
ICS decomposition
G N P decomposition
Q u a rter
0 .1 5 8
4
2 3 .8
18.6
57.6
2 4 .0
7 3 .5
2.5
8
3 5 .0
17.5
4 7 .5
37.1
5 6 .1
6 .8
T h is ta b le r e p o r ts in fo r m a tio n fro m v e c to r a u to reg ressio n s Zt=$(L)Zt+et w h ere Ztc o n ta in s G N P , th e IC S , and con trol
v a ria b les. T h e c o n tr o ls are g o v e r n m e n t sp e n d in g , m o n e y su p p ly M 2, an d se n s itiv e m a te r ia ls p rices. E ach colu m n
in th e to p p a n e l c o r r e sp o n d s to a reg ressio n . O n ly th e G N P an d ICS r e g r e ssio n s are r e p o r te d , a n d o n ly th e G N P
an d IC S co e ffic ie n ts. T h e 1, 2, 3, and 4 lags m o d els c o n ta in 121, 115, 110, a n d 109 o b se r v a tio n s, resp ectiv ely .
T h e d e p e n d e n t v a ria b le is in d ic a te d a t th e top o f each co lu m n . In th e m a in e n tr ie s th e first n u m b er is th e p -v a lu e
a ss o c ia te d w ith th e F -s t a tis tic for th e h y p o th e s is th a t th e b lo ck o f c o e ffic ie n ts are jo in tly e q u a l to zero. B elo w th is
is th e su m o f th e b lo c k o f co e ffic ie n ts an d its sta n d a r d error. T h e x 2 s t a tis tic is for th e h y p o th e s is th a t G N P and th e
co n tro ls are b lo c k e x o g e n o u s w ith r e sp e c t to th e IC S . S ig n ifica n ce le v e ls on th e su m o f co e ffic ie n ts are in d ic a te d as
follow s: “* * ” is sig n ific a n t r e je c tio n a t th e 1 p ercen t level;
is sig n ific a n t a t th e 5 p e r c e n t level;
is sig n ifica n t
a t 10 p er c e n t. T h e b o tt o m p a n e l rep o rts th e p e r c e n ta g e o f G N P an d IC S in n o v a tio n v a ria n ce th a t ca n b e a ttr ib u te d
to each v a ria b le in th e 4 la g s v e c to r a u to r eg r e ssio n . T h e su m o f va ria n ce e x p la in e d b y th e co n tr o ls is rep o rted under
th e h e a d in g “X .”
T A B L E V II
Vector Autoregressions with GNP, the Index of Leading Indicators,
the Index of Consumer Sentiment, and Default Risk
D e p e n d e n t v a r ia b le
GNP
ILI
ICS
DR
0.177
-0.441+
(0.242)
0.038
-1.316”
(0.483)
0.020
-0.296*
(0.130)
0.516
0.028
0.097)
Sum of coefficients
Standard error
0.118
0.205+
(0.111)
0.313
0.061
(0.221)
0.016
0.050
(0.060)
0.183
0.066
(0.044)
ICS
F: p-value
Sum of coefficients
Standard error
0.063
0.230(0.099)
0.369
0.272
(0.198)
0.000
0.971
(0.054)
0.001
0.039
(0.040)
0.060
-0.661+
(0.396)
0.000
-2.603”
(0.791)
0.010
-0.117
(0.213)
0.000
0.754”
(0.159)
0.374
0.489
0.881
0.578
GNP
F: p -value
Sum of coefficients
Standard error
ILI
F: p -value
DR
F: p-value
Sum of coefficients
Standard error
--9
R
X2: p-value
(Block exogeneity)
0.011
T h is ta b le r e p o r ts in fo r m a tio n from a v e c to r a u to r e g r e ssio n Z t = $ ( L ) Z t + u w h ere Z t c o n ta in s G N P , th e IC S , th e ILI,
a n d d e fa u lt risk ( D R ) . T h e m o d e l has 4 la g s an d 109 o b se r v a tio n s. T h e d e p e n d e n t v a ria b le is in d ic a te d at th e to p
o f e a c h c o lu m n . In th e m a in en tr ie s, th e F -s ta tis tic is for th e h y p o th e s is th a t th e b lo c k o f co e fficien ts are jo in tly
e q u a l to zero . B e n e a th th e F is th e su m o f c o efficien ts a n d it s sta n d a r d error. T h e x 2 s t a t is t ic is for th e h y p o th e s is
th a t G N P , th e IL I, a n d d e fa u lt risk are b lo ck e x o g e n o u s w ith r e sp e c t to th e IC S . S ig n ific a n c e le v e ls o n th e su m o f
c o e ffic ie n ts are in d ic a te d a s fo llo w s: “* * ’ is sig n ific a n t r e je c tio n a t 1%,
is sig n ific a n t r e je c tio n a t 5%, a n d * + ’ is
sig n ific a n t r e je c tio n a t 10%.
T A B L E VIII
Decomposition of the Innovation Variance of G N P and the Index of Consumer Sentiment
from Vector Autoregressions with GNP, the ICS, the ILI, and Default Risk
G N P d e c o m p o sitio n
Quarter
1
4
8
ICS
11.7
14.5
26.9
ILI
4.9
11.3
10.8
DR
0.0
18.1
15.0
GNP
83.3
56.1
47.2
IC S d e c o m p o sitio n
ICS
100.0
86.3
85.9
G N P d e c o m p o s itio n
Quarter
1
4
8
ILI
11.8
19.4
16.5
ICS
4.9
6.3
21.3
DR
0.0
18.1
15.0
GNP
83.3
56.1
47.2
DR
2.0
27.4
22.3
ILI
9.7
9.7
8.8
GNP
88.2
58.4
47.2
ICS
0.0
4.5
21.8
DR
0.0
7.3
4.5
GNP
0.0
4.9
8.3
IC S d e c o m p o sitio n
ILI
16.7
21.0
14.9
G N P d e c o m p o sitio n
Quarter
1
4
8
ILI
0.0
1.5
1.3
ICS
83.3
66.9
72.3
DR
0.0
7.3
4.5
GNP
0.0
4.9
8.3
IC S d e c o m p o sitio n
DR
2.1
15.1
9.5
ILI
14.7
12.0
9.1
GNP
4.7
2.0
1.8
ICS
78.5
70.9
79.6
T h is ta b le r e p o r ts th e p e r c e n ta g e o f G N P an d IC S in n o v a tio n v a ria n ce th a t ca n b e a ttr ib u te d to each
variab le in th e 4 lags v e c to r a u to r e g r e ssio n . T h e d e c o m p o s itio n is c o m p u te d for th ree differen t o rd erin g s o f
th e v a ria b les. T h e q u a rter (a h e a d ) o f th e in n o v a tio n v a ria n ce b e in g d e c o m p o s e d is in d ic a te d in th e le ftm o s t
co lu m n . T h e rem a in in g en tr ie s in d ic a te th e p e r c e n ta g e o f in n o v a tio n v a ria n ce a ttr ib u ta b le to th e v a riab le at
th e to p o f th e c o lu m n .
T A B L E IX
Vector Autoregressions and Variance Decompositions of GNP, the Index of Consumer Sentiment,
Default Risk, and Leading Indicators Components
1 la g
GNP
2 la g s
3 la g s
4 la g s
IC S
GNP
IC S
GNP
IC S
GNP
IC S
0 .0 1 4
0 .0 4 8
0 .0 3 1
0 .1 2 3
0 .0 3 6
0 .1 7 8
0 .3 2 4
0 .5 7 1
S u m o f co e ffic ie n ts
- 0 .3 0 8 *
- 0 .1 3 7 *
-0 .4 8 2 *
-0 .0 2 4
-0 .8 2 0 *
- 0 .2 9 2 +
- 0 .8 5 5 +
-0 .2 6 3
S ta n d a r d error
(0 .1 2 3 )
(0 .0 6 9 )
(0 .2 3 0 )
(0 .1 2 3 )
(0 .3 2 8 )
(0 .1 6 8 )
(0 .4 9 8 )
(0 .2 5 0 )
0 .0 5 3
0 .0 0 0
0 .1 4 9
0 .0 0 0
0 .0 4 7
0 .0 0 0
GNP
F: p -v a lu e
IC S
F: p -v a lu e
S u m o f co e ffic ie n ts
0 .2 3 7 +
0 .781**
0 .2 7 8 +
0 .8 2 2 * “
0.462**
0 .942**
S ta n d a r d error
(0 .1 2 1 )
(0 .0 6 7 )
(0 .1 6 0 )
(0 .0 8 9 )
(0 .2 0 5 )
(0 .1 1 0 )
0 .3 3 6
0 .8 6 7
0 .3 3 0
0 .8 7 4
0 .3 6 9
0 .8 8 9
R2
0 .0 0 1
x 2: p -v a lu e
0 .0 0 0
IC S
0 .5 4 5 *
(0 .2 7 2 )
0 .3 1 5
0 .0 0 0
G N P decomposition
Q u a r te r
0 .2 5 4
X
GNP
IC S
0.855**
(0 .1 3 7 )
0 .8 8 7
0 .0 0 0
ICS decomposition
X
GNP
1
2 1 .6
3 1 .1
4 7 .3
100.0
0 .0
0 .0
4
16.3
5 4 .9
2 8 .8
6 4 .8
3 4 .6
0 .6
8
16.3
6 1 .8
2 1 .9
5 2 .9
4 6 .6
0 .5
Q u a r te r
0 .0 0 0
X
IC S
GNP
X
IC S
GNP
1
4 8 .0
4 .6
4 7 .4
3 9 .7
6 0 .3
0 .0
4
6 4 .1
7.1
2 8 .8
5 9 .6
3 9 .8
0 .6
8
7 0 .3
7 .8
2 1 .9
6 7 .8
3 1 .7
0 .5
T h is ta b le r e p o r ts in fo r m a tio n fro m v e c to r a u to r e g r e ssio n s Zt=$(L)Zt+ec w h ere Zt c o n ta in s G N P , th e IC S , an d co n tro l
v a ria b les. T h e co n tr o ls are d e fa u lt risk a n d th e c o m p o n e n ts o f th e cu rren t IL I, e x c e p t for th e IC E . T h e 1, 2, 3, an d 4
la g s m o d e ls c o n ta in 114, 112, 110, a n d 109 o b se r v a tio n s, r e sp e c tiv e ly . E a ch c o lu m n in th e to p p a n e l co rresp o n d s to a
reg ressio n . O n ly th e G N P an d IC S r e g ressio n s are r e p o r te d , a n d o n ly th e G N P a n d IC S c o e ffic ie n ts. T h e d e p e n d e n t
va ria b le is in d ic a te d a t th e to p o f ea ch c o lu m n . In th e m a in en tries th e first n u m b e r is th e p -v a lu e a ss o c ia te d w ith
th e F -s t a tis tic for th e h y p o th e s is th a t th e b lo ck o f co effic ie n ts are jo in tly e q u a l t o zero . B e lo w th is is th e su m o f
th e b lo ck o f c o e ffic ie n ts an d its th e sta n d a r d error. T h e x 2 s t a tis tic is for th e h y p o th e s is th a t G N P an d th e con trols
are b lo ck e x o g e n o u s w ith r e sp e c t to th e IC S . S ig n ifica n ce le v e ls for th e su m o f c o e ffic ie n ts are in d ic a te d as follow s:
“* * ” is sig n ific a n t r e je c tio n a t th e 1 p e r c e n t level;
is sig n ific a n t a t th e 5 p e r c e n t lev el; “+ ” is sig n ific a n t at 10
p e r c e n t. T h e b o t t o m p a n e l r e p o r ts th e p e r c e n ta g e o f G N P a n d IC S in n o v a tio n v a ria n ce th a t ca n b e a ttr ib u te d to
e a c h v a riab le in th e v e c to r a u to r e g r e ssio n s. T h e su m o f v a ria n ce e x p la in e d b y th e c o n tr o ls is r e p o r te d u n d er th e
h e a d in g “X .”
Figure 1 - Index of Consumer Sentiment (1953-1988)
@FedFRASER