CAN CONSUMER ATTITUDES FORECAST TILE MACROECONOMY?
Chopin, Marc C. ; Darrat, Ali F.
Marc C. Chopin [*]
Ali F. Darrat [**]
I. Introduction
Researchers and policy-makers have often used surveys of consumer
attitudes to forecast economic performance. The perceived importance of
consumer attitudes is evidenced by the attention paid to announcements
made by the Conference Board and the inclusion of the Index of Consumer
Confidence (ICC) in the Commerce Department's Index of Leading
Economic Indicators. However, as Katona (1978) notes, the use of
consumer attitudes for forecasting is based on the assumption that
"attitudes and expectations intervene between stimuli and response
and they change before behavior changes." If changes in the
attitudes precede changes in consumer behavior, then knowledge of these
attitudes could help explain consumer spending and saving patterns
[Liken and Kotler (1983), Kinsey and Collins (1994)]. However, if
attitudes change after or concurrently with other movements in the
economy, then measures of consumer attitudes will add little to models
designed to forecast the economy. Therefore, the temporal ordering
between co nsumer attitudes and their behavior should determine the
value of attitudes measures in forecasting models.
Studies examining the value of consumer attitudes for forecasting
economic performance have thus far failed to produce a consensus. For
example, Juster and Watcher (1972), Kelly (1990), Throop (1991), and
Carrol, Fubrer and Wilcox (1994) all report evidence suggesting that the
ICC contains useful information for predicting consumer spending. In
contrast, Hymans (1970), Lovell (1975), and Burch and Gordon (1984)
contend that such measures are poor predictors of consumer spending. In
spite of the controversy surrounding the predictive value of consumer
attitudes, Gaski and Etzel (1986) conclude that "these surveys
(measuring consumer attitudes) are still used in business
planning."
We should point out that most of previous studies in this area
focus on the contemporaneous correlation between some measures of
consumer attitudes and economic conditions. However, in forecasting
models, contemporaneous correlations are of limited usefulness. Indeed,
it is now widely recognized that strong correlations between any two
variables are insufficient to identify the cause and effect
relationships between them. More valuable information may be found by
examining movements in variables that precede changes in others. For
example, if changes in consumer attitudes precede changes in consumer
spending, then measures of consumer attitudes will be useful for
economic and business forecasting. However, if changes in consumer
spending precede changes in consumer attitudes, then measures of
consumer attitudes will have no forecasting value.
Empirical work on the above issue of causality remains extremely
sparse. Recently, two papers have investigated the causal relationship
between indices of consumer attitudes and other economic variables, and
they too report conflicting results. After testing for
Granger-causality, Garner (1991) concludes that the ICC (and a similar
measure published by the University of Michigan) are largely unreliable
predictors of consumer spending. On the other hand, Huth, Eppright, and
Taube (1994) also examine the Granger-causal relationships between four
measures of consumer attitudes and various business and economic
variables. In contrast to the conclusions reached by Garner, Huth et al.
claim that the four measures of consumer attitudes provide useful
information for forecasting changes in several measures of consumer
spending, business and economic activity.
While these two studies represent an important step forward in the
examination of the information content of measures of consumer
attitudes, both studies appear seriously flawed. In particular, they
examine the causal linkage in the context of bivariate models whose
inferences are known to be potentially biased due to the
"omission-of-variables" phenomenon [Lutkepohl (1982, 1993)].
Furthermore, although Granger-causality tests are sensitive to changes
in the lag structure [Thornton and Batten (1985)], both studies are
tainted by the fact that they impose a common lag for all variables.
More disturbing, perhaps, is that neither study incorporates possible
cointegratedness among the variables. If cointegration does in fact
exist, then both studies become seriously misspecified, as we will
discuss below.
In this paper, we use a flexible lag structure and a multivariate
model to investigate the Grangercausal relationships among consumer
attitudes and several macro variables, namely, retail sales, personal
disposable income, inflation, stock prices, money supply, and interest
rates. We also test for the stationarity of the series and check for
possible cointegration underlying them. We derive our Granger-causality
inferences from a multivariate vector-error-correction-model (VECM).
The remainder of the paper is organized as follows. Section II
provides a brief description of the data along with the results from
stationarity and cointegration tests. Section III reports the causality
results. Section IV offers some concluding remarks.
II. Data, Stationarity and Cointegration Results
The Conference Board's Index of Consumer Confidence (ICC) is
widely used as a measure of consumer attitudes and has received
considerable attention in both the academic and popular press.
Furthermore, Huth, et. al. (1994) find that the Conference Board's
ICC is preferred to the University of Michigan's ICS when
predicting changes in economic activity. These factors have piqued our
interest in the ICC as the measure of consumer attitudes. Our objective
is to estimate the marginal value of measures of consumer confidence in
models designed to predict macroeconomic activity and changes in retail
sales.
Garner (1991), Leeper (1992) and Throop (1991) suggest that,
particularly during normal economic times, consumer attitudes merely
reflect the state of the economy. For example, according to these
researchers, increases in consumer's income and decreases in
inflation or interest rates, ceteris paribus, will result in improved
consumer wellbeing and attitudes. If consumer attitudes do nothing more
than reflect past or prevailing economic conditions, then measures of
consumer confidence will add little or nothing to models including
measures of economic performance upon which consumer attitudes are
based. In contrast, Katona and Mueller (1953) argue that consumer
attitudes are not merely a reflection of current economic conditions and
that measures of macroeconomic performance are not viable substitutes
for measures of consumer attitudes. This question of whether consumer
attitudes simply reflect changes in the economy or contain information
not captured by measures of economic performance lies at the heart of
the debate about the value of consumer attitudes in models used to
predict changes in consumer spending.
To identify the Granger-causal ordering and estimate the marginal
impact of measures of consumer confidence on estimates of consumer
spending, our model includes several measures of economic performance
and policy variables. To incorporate possible effects of consumers'
income and wealth on consumer confidence, we include personal disposable
income (PI) and the Dow Jones Industrial Average (DOW) in the model. As
we note above, we expect to find a positive relationship between income
and consumer confidence. Furthermore, increases in the DOW are expected
to reflect market participants forecasts of firm profitability, interest
rates and the economy. We expect increases in the DOW to reflect
improvements in the economic well being of consumers. To capture the
impact of changes in the cost of living and the cost of borrowing on
consumer attitudes, we add the CPI annualized inflation rate (INF) and
the three-month Treasury bill rate (SR). To reflect the impact of
monetary policy on the economy and consumer attitu des, we include
changes in the monetary base (MB). Changes in retail sales proxy for
changes in consumer spending (RT). Since most economic decisions occur
at the microeconomic level, it may be advisable to scale the variables
by the size of population when analyzing macroeconomic issues.
Therefore, we express all aggregate variables in their per capita figures. [1] The tests are implemented at the monthly frequency over
June 1977 to November 1996, and the data came from the DRI/Citibase data
tape.
As noted above, we examine the causal relationship between consumer
attitudes and several macroeconomic variables by testing for
Granger-causality using a multivariate VECM. Prior to estimations, we
inspect our variables for any possible nonstationarity. [2] Granger and
Newbold (1974) demonstrate that nonstationary time series yield spurious
results. Further, Phillips (1986) and Stock and Watson (1989, 1993) find
that nonstationary data may produce incorrect inferences since t-, F-and
[[chi].sup.2] statistics do not converge to their limiting distributions
even asymptotically. After converting our variables to stationary
series, we then test for cointegration (long-run relationship) among the
variables. Models that ignore possible cointegratedness underlying the
variables, when it exists, are biased for they filter out important
low-frequency information [See Harris (1995)]. Finally, we allow for a
flexible lag structure for each variable, with the order of entry and
the number of lags of each variable inclu ded in the model determined
using the Akaike FPE procedure in conjunction with the well-known
specific-gravity criterion.
Table 1 reports the results from the Augmented Dickey-Fuller (ADF)
test of nonstationarity. As we can see from the table, all series appear
nonstationary in levels, but become stationary in first-differences.
These results are robust to the inclusion or exclusion of a time trend.
[3]
Having determined that each of the seven series is stationary in
first-differences, we test next for the existence of cointegration
(long-run equilibrium) relationships among the variables included in the
model. In light of recent econometric literature [e.g., Cheung and Lai
(1993), and Gonzalo (1994)], we employ the Johansen (1988) efficient
procedure to test for cointegration, and also to identify the number of
cointegrating vectors, should cointegration be found. When testing for
cointegration, we use the Akaike Information Criterion (AIC) to
determine the proper lag length in the Johansen model. Results show that
six lags minimize the AIC and also whiten the residuals. We note that
all seven variables were initially included in the cointegrating space
under investigation. However, a likelihood ratio (LR) test suggested
that one of the variables (the DOW) should be excluded to yield a
parsimonious cointegrating vector [[[chi].sup.2] = 2.39,
[[chi].sup.2](0.05) = 7.8l]. [4] The Johansen test results for the
parsimonious vector are assembled in Table 2.
The Johansen test statistics are adjusted for the finite-sample
bias using the correction factor proposed by Reimers (1992), and Cheung
and Lai (1993). Both the trace and the maximal eigenvalue tests of the
Johansen approach suggest that there are three non-zero (stationary)
cointegrating vectors linking the variables. Thus, estimating a standard
VAR without due allowance for the underlying cointegrating relationship
will yield biased results. Granger's (1991) Representation Theorem further implies that we should specify a Vector Error Correction Model,
VECM, (instead of a VAR) in which causality is detected among the
variables in at least one direction. To ensure statistical efficiency,
we estimate error-correction terms from the parsimonious six-variable
cointegrating vector using the Johansen maximum-likelihood method. These
error correction terms then enter each of the equations prior to
estimating the order of entry and the lag structure for the remaining
variables in each equation. Our next task is to identify the
Granger-causal inter-relationships in the context of the VECM.
III. Causality Linkages Between Consumer Attitudes and the
Macroeconomy
As Ahking and Miller (1985) and Thornton and Batten (1985)
demonstrate, the use of a common lag for all variables in a given model
is overly restrictive and theoretically baseless. In addition,
Granger-causality tests and policy inferences from VARs or VECMs are
known to be very sensitive to lag specifications [Hafer and Sheehan
(1991)]. Therefore, unlike Garner (1991) and Huth et al. (1994), an
objective data-based technique should be used to specify the
model's lag structure. According to the Monte Carlo evidence
reported by Thornton and Batten (1985), we employ Akaike's final
prediction error (FPE) criterion to select the appropriate lag structure
for each variable included in our VECM. [5] Once again, it is important
to note that we avoid possible biases resulting from the omission of the
underlying long-run relationships among the variables by including the
associated error correction terms. [6]
We use the FPE procedure to estimate seven equations, one for each
endogenous variable. We then pool the seven resultant equations and
estimate them as a system using Zellner's Seemingly Unrelated
Regression (SUR) technique. Zellner's SUR yields consistent and
asymptotically efficient estimates on the assumption that the errors in
each equation are themselves uncorrelated. With the final VECM as the
maintained hypothesis, we conduct a series of over- and under-fitting
tests using SUR system estimations to further refine the model
specification. That is, we add and then remove two lags of each variable
in each equation, one at a time, and use the likelihood ratio test to
determine the significance of the added or deleted lags. Over- and
under-fitting tests amount to testing the robustness of the maintained
model to alternative lag specifications. We also test for
autocorrelation of the residuals and the temporal stability of the
coefficient estimates. [7] Finally, we perform likelihood ratio tests
within the system estimations to test for the joint significance of the
lagged coefficient estimates for each variable in each equation. [8]
These system likelihood ratio tests form the basis of our
Granger-causality inferences. The final VECM results take the form of
model (1). The variables DICC, DRT, DSR, DMB, DINF, DPI, and DDOW
represent, respectively, the logarithmic [9] first-differences of the
following variables, the index of consumer attitudes, per capita retail
sales, the three-month Treasury bill rate, the per capita money base,
the annualized CPI inflation rate, per capita disposable personal
income, and the Dow Jones Industrial Average. The coefficients,
[[[Beta].sub.ij].sup.k](L) denotes the number of lags (k) of variable j
included in equation i, [alpha]'s are the constants, [xi]'s
are the three error-correction terms, the [gamma]'s are their
associated coefficients, and the [e.sub.i]'s are Gaussian
disturbance terms.
Table 3 displays the Granger-causality test results on the basis of
system likelihood ratio statistics estimated by the SUR procedure. As we
mentioned earlier, a large number of over- and under-fitting tests were
performed on the maintained model to ascertain the robustness of the
specification to various alterations. The results from likelihood ratio
tests (relegated to an Appendix available from the authors upon request)
generally indicate that the maintained model as given above is an
adequate representation of the data during the estimation period.
We now discuss the Granger-causality results. Following Jones and
Joulfaian (1991) and Perman (1991), the joint significance of lagged
independent variables in any equation reflects short-run
Granger-causality, while the significance of the error-correction terms
in the equation is indicative of long-run Granger-causality. Since our
main concern in this paper is on the predictive content of the
variables, we focus below on our findings for short-run linkages that
are more relevant to the forecastability issue.
Our results from the VECM reported in Table 3 suggest that only
changes in inflation and in the DOW cause significant movements in the
measure of consumer attitudes. Of course, this finding is intuitive and
can be easily vindicated. Changes in inflation impact the cost of living
and the real values of financial assets, both of which are important
concerns for consumers. Similarly, changes in the DOW reflect the
economy's overall performance and are linked to consumers'
wealth. Not surprisingly, therefore, these two variables (inflation and
the DOW) appear to have significantly shaped consumer attitudes. The
results further suggest that the impact of inflation and the DOW on
consumer attitudes is relatively swift and completed within two to three
months. Perhaps equally important, none of the remaining variables
appears to have impacted consumer attitudes. In other words, our
empirical results suggest that consumers, once they incorporate
information on inflation and the stock market, do not attach much impor
tance to changes in other macro variables like interest rates or
monetary policy moves when forming their sentiment about the future of
the economy.
For forecasting retail sales, we have obtained decidedly strong
evidence that only the behavior of the stock market (as proxied by
changes in the DOW) causes significant changes in retail sales. In
particular, changes in the ICC (and other macro variables) seem to add
little to forecast retail sales. We should note that this inference for
the ICC is supported by the fact that the FPE criterion suggests the
removal of the ICC variables from the retail sales equation. Moreover,
to check whether we have been misled by the FPE procedure, we relax this
FPE zero restriction by over-fitting the model with two non-zero lags on
the ICC variable. The resultant likelihood ratio statistic still fails
to indicate significance [[chi].sup.2] = 1.70, [[chi].sup.2](0.05) =
5.99].
In contrast to retail sales, our empirical results indicate that
the ICC contains valuable information for predicting personal disposable
income [[[chi].sup.2] = 12.86, [[chi].sup.2](0.05) = 7.811. Thus,
changes in consumer attitudes appear to anticipate movements in personal
income, rather than reflect them. Besides personal disposable income,
changes in the ICC also cause significant movements in short-term
interest rates [[chi].sup.2] = 9.74, [[chi].sup.2](0.05) = 7.81] and in
the DOW [[[chi].sup.2] = 7.06, [[chi].sup.2](0.05) = 5.99]. However, the
ICC does not exert any causal impact upon inflation or base money. On
balance, then, the ICC appears to be a reliable predictor of certain
macro variables, but not of others. To repeat, changes in the measure of
consumer attitudes contain useful information for predicting personal
disposable income, interest rates and movements in stock prices. On the
other hand, the ICC is of little value in models used to forecast retail
sales, inflation, or monetary policy. Therefore, unlike Garner (1991)
and Huth et. al (1994), the evidence we obtain suggests that measures of
consumer attitudes do have predictive contents, though not uniformly
across the economic spectrum.
Before concluding, observe that our VECM results can also be useful
to distill indirect causality linkages. For example, the ICC does not
directly cause changes in retail sales. Yet, it can still influence
retail sales indirectly through interactions with the DOW. As the
results from the DOW equation indicate, the ICC causes significant
changes in the DOW, which in turn impacts retail sales. Thus far, we
have focused on short-run causality. However, we should note that each
of the seven estimated equations contains three error-correction terms
to approximate long-run Granger-causality. With the exception of the DOW
equation, at least one of the error-correction terms proves
statistically significant in each of the remaining six equations. These
results accord well with the presence of a long-run equilibrium
relationship among the variables in the parsimonious cointegrating
vector. This finding also implies that overlooking cointegratedness
would have resulted in biased inferences.
IV. Concluding Remarks
This paper examines empirically the cause-and-effect relationships
between consumer attitudes and several key macroeconomic variables. To
that end, we use the recent cointegration and error-correction modeling
technique in a multivariate setting.
The empirical results we obtain from monthly data over 1977-1996
suggest the presence of significant long-run (equilibrium) relationships
among the variables. By virtue of the Granger Representation Theorem,
there must be Granger-causality among the variables in the model in at
least one direction. Results from our VECM confirm the presence of these
causal linkages among several variables in the model.
The evidence which consistently emerges is that the ICC does
contain valuable information for predicting some macroeconomic variables
but not others. In particular, changes in the ICC can predict movements
in personal disposable income, interest rates, and to some extent, also
the DOW.
However, the ICC proves an unreliable predictor for retail sales,
inflation or monetary policy moves. As for the factors responsible for
changes in consumer attitudes, the evidence suggests two possible
culprits; namely, changes in inflation and in the DOW. These results
lend support to the view that consumers closely watch the inflation
outlook and the behavior of the stock market when formulating their own
sentiment. Our results partly, although not completely, support the
conclusions of Huth et al. (1994). Like them, we find that measures of
consumer attitudes are useful for economic forecasting. Unlike them, we
do not find evidence that such measures are useful uniformly or even
generally across the economic and business spectrum.
(*.) Associate Professor of Economics, Louisiana Tech University
(**.) Professor of Economics, Louisiana Tech University
The authors wish to acknowledge capable research assistance of
Thanomsak Suwanoi and Maosen Zhong. Suggestions from an anonymous
referee also helped to improve the paper. Any remaining errors are the
sole responsibility of the authors.
Notes
(1.) Recent research has also recommended the use of per capita
variables in order to avoid measurement errors. See Heston (1994).
(2.) Any variable is said to be stationary if its stochastic
properties (mean, variance, and covariance) are time invariant.
(3.) Note that PI proves stationary in first-differences only when
a time trend is included in the testing equation.
(4.) The exclusion hypothesis is easily rejected for each of the
remaining six variables. The LR statistics (with d.f. = 3) are 24.79 for
ICC; 21.05 for retail sales; 219.47 for interest rates; 17.74 for base
money; 15.72 for inflation; and 19.61 for personal disposable income.
(5.) The FPE procedure amounts to minimizing a function of the
one-step-ahead prediction error. It is a compromise between the
predictive power of a model and its complexity, the latter measured by
the model order. See Darrat (1988) for a detailed account of the FPE
procedure.
(6.) Similar to the bias from omitting one relevant long-run
cointegrating relationship from the model, when it exits, the omission
of additional relevant cointegrating relationships will also result in
an omitted variable bias.
(7.) The results, available from the authors upon request, evince no severe problems of autocorrelations or unstable parameters. Testing
for possible pitfalls in our model is important in order to achieve, in
the words of Hendry and Ericsson (1991, p. 19), "a congruent model,
that is, one which captures the salient features of existing data and is
interpretable in the light of available economic theory."
(8.) Note that the VECM model is specified so that only lagged
values of the endogenous variables appear as explanatory variables.
Contemporaneous relationships among the variables are reflected in the
innovations. [See Hsiao (1981), and Sephton (1988)].
(9.) We apply the natural logarithmic transformation in order to
stabilize the variance of the series over time (i.e., induce
homoscedasticity). This transformation also appears reasonable since the
logarithmic first-differences of a given variable approximate its
percentage changes.
References
Ahking, F. W., and S. M. Miller, "The Relationship Between
Government Deficits, Money Growth, and Inflation." Journal of
Macroeconomics 7 (Fall 1985): 447-467.
Burch, S. W., and S. Gordon, "The Michigan Surveys and the
Demand for Consumers Durables." Business Economics 19 (October
1984): 40-44.
Carrol, D. C., J. C. Fuhrer, and D. W. Wilcox, "Does Consumer
Sentiment Forecast Household Spending? If So, Why?" American
Economic Review 84 (December 1994): 1397-1408.
Cheung, Y. W., and K. S. Lai, "Finite-Sample Sizes of
Johansen's Likelihood Ratio Tests for Cointegration," Oxford
Bulletin of Economics and Finance 55 (August 1993): 313-328.
Darrat, A. F., "Have Large Budget Deficits Caused Rising Trade
Deficits?" Southern Economic Journal 54 (April 1988): 879-887.
Garner, A., "Forecasting Consumer Spending: Should Economists
Pay Attention to Consumer Confidence Surveys?" Federal Reserve Bank
of Kansas City, Economic Review 76 (May/June 1991): 57-71.
Gaski, J. F., and M. J. Etzel, "The Index of Consumer
Sentiment Toward Marketing." Journal of Marketing 50 (July 1986):
71-81.
Gonzalo, J., "Five Alternative Methods of Estimating Long-Run
Equilibrium Relationships." Journal of Econometrics 60 (January
1994): 203-233.
Granger, C. W. J., "Developments in the Study of Cointegrated
Economic Variables," Long-Run Economic Relationships: Readings in
Cointegration, edited by R. F. Engle and C. W. J. Granger (Oxford:
Oxford University Press, 1991): 65-80.
_____, and P. Newbold, "Spurious Regressions in
Econometrics." Journal of Econometrics 2 (July 1974): 111-120.
Hafer, R. W., and R. G. Sheehan, "Policy Influence Using VAR
Models." Economic Inquiry 29 (January 1991): 44-52.
Harris, Richard, I. D., Using Cointegration Analysis in Econometric
Modeling (Hertfordshire: Prentice Hall/Harvester Wheatsheaf, 1995)
Hendry, D. F. and N. R. Ericsson, "An Econometric Analysis of
U.K. Money Demand in Monetary Trends in the United States and the United
Kingdom by Milton Friedman and Anna J. Schwrtz." American Economic
Review 81 (March 1991): 8-38.
Heston, A., "A Brief Review of Some Problems in Using National
Accounts Data in Level of Output Comparison and Growth Studies."
Journal of Development Economics 44 (1994): 29-52.
Hsiao, C., "Autoregressive Modeling and Money-Income Causality
Detection." Journal of Monetary Economics 7 (January 1981): 85-106.
Huth, W. L., D. R. Eppright, and P. M. Taube, "The Indices of
Consumer Sentiment and Confidence: Leading or Misleading Guides to
Future Buyer Behavior." Journal of Business Research 29 (1994):
199-206.
Hymans, S., "Consumer Durable Spending: Explanation and
Prediction." Brookings Papers on Economic Activity 2 (1970):
173-199.
Johansen, S. "Statistical Analysis of Cointegrating
Vectors." Journal of Economic Dynamics and Control 12
(June-September 1988): 241-254.
Jones, J. D. and D. Joulfain, "Federal Government Expenditures
and Revenues in the Early Years of the American Republic: Evidence from
1792 to 1860." Journal of Macroeconomics 14 (Winter 1991): 133-155.
Juster, F. T., and P. Watchel, "Anticipatory and Objective
Models of Durable Goods Demand." American Economic Review 62
(September 1972): 564-579.
Katona, G., "Behavioral Economics." Challenge
(September/October 1978): 14-18.
_____, and E. Mueller, Consumer Attitudes and Demand, 1950-1952,
Ann Arbor, MI: Survey Research Center, University of Michigan.
Kelly, D., "The Plunge in Confidence Will Hit Spending--But
How Hard?" DRI/McGraw Hill U.S. Review (September 1990).
Kinsey, J., and M. I. Collins, "Index of Consumer
Expectations: Food Price Effects and Durable Goods Expenditures."
The Journal of Consumer Affairs 28 (Winter 1994): 255-277.
Leeper, E. M., "Consumer Attitudes: King for a Day,"
Economic Review, Federal Reserve Bank of Atlanta, July/August 1992:
1-15.
Lilien, G., and P. Kotler, Marketing Decision Making. A Model
Building Approach (New York: Harper and Row, 1983).
Lovell, M., "Why Was the Consumer Feeling So Sad?"
Brookings Papers on Economic Activity 2 (1975): 473-479.
Lutkepohl, H., "Non-Causality Due to Omitted Variables."
Journal of Econometrics 19 (1982): 367-378.
_____. Introduction to Multiple Time Series Analysis, Second
Edition (Berlin, Germany: Springer-Verlag, 1993).
Perman, R., "Cointegration: An Introduction to the
Literature." Journal of Economic Studies 18 (1991): 3-30.
Phillips, P. C. B., "Understanding Spurious Regressions."
in Journal of Econometrics 33 (December 1986): 311-340.
Reimers, H. E., "Comparisons of Tests for Multivariate
Cointegration." Statistical Papers 33 (1992): 335-359.
Sephton, P. S., "On Interest Rate Innovations and Anticipated
Monetary Policy," Economics Letters 28 (1988): 177-180.
Stock, J., and M. Watson, "Interpreting the Evidence on
Money-Income Causality." Journal of Econometrics 40 (January 1989):
161-182.
______, "A Simple MLE of Cointegrating Vectors in Higher Order
Integrated System." Econometrica 61 (July 1993): 783-820.
Thornton, D. L., and D. S. Batten, "Lag-Length Selection and
Tests of Granger-Causality Between Money and Income." Journal of
Money, Credit and Banking 17 (May 1985): 164-178.
Throop, A., "Consumer Sentiment and the Economic
Downturn." Federal Reserve Bank of San Francisco, Weekly Letter
(March 1, 1991).