Because of the importance of inflation expectations, Lloyd B. Thomas Jr. (Fall 1999, p. 125-44) reexamines "the evidence on the nature and performance of various measures of expected inflation, with special attention given to the issue of rationality" (p. 126). Thomas tests the unbiasedness hypothesis using the Livingston and Michigan survey forecasts for the 1960 to 1997 time period and is unable to reject the null hypothesis of unbiasedness. Unfortunately, two types of problems due to aggregation plague such tests: private information bias and micro-heterogeneity bias. Therefore, for these survey forecasts, consensus regressions should generally not be used to test rationality; rationality can only be tested at the individual level.

Carl S Bonham

Richard H Cohen

English

Research Papers in Economics

 
 
 
 
 
 
 
 
 
 
 
 
 
 
TESTING THE RATIONAL EXPECTATIONS 
 HYPOTHESIS USING SURVEY DATA 
 
 By 
 
Carl S. Bonham and Richard H. Cohen 
 
 
  Working Paper No. 00-7 
April 2000 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Testing the Rational Expectations Hypothesis using Survey Data
Carl S. Bonham and Richard H. Cohen
*
April 22, 2000
  Because of the importance of inflation expectations, Lloyd B. Thomas Jr. (Fall
1999, p. 125-44) reexamines  "the evidence on the nature and performance of various
measures of expected inflation, with special attention given to the issue of rationality"
(p. 126). Thomas studies the accuracy and rationality of one-year-ahead mean survey
forecasts of CPI inflation. He examines data from three different surveys: the
Livingston Survey of professional economists, the Institute of Social Research
(Michigan) Survey of Households, and the Federal Reserve Bank of Philadelphia’s
Survey of Professional Forecasters.   Thomas tests the unbiasedness hypothesis using
the Livingston and Michigan survey forecasts for the 1960 to 1997 time period and is
unable to reject the null hypothesis of unbiasedness.
Thomas warns of potential pitfalls in drawing inferences about rationality from
tests based on survey data.  For example, agents may have insufficient incentive to
make optimal use of their resources when responding to the survey.  A related issue is
that some forecasters may behave strategically and fail to reveal their true forecasts
(Thomas, 1999, p. 137).  In addition, it may be rational for agents to assign a
probability of less than one to an announced regime change that is eventually
implemented.  Similarly, it may be rational for agents to assign a probability of greater
                                                
* Carl S. Bonham is Associate Professor of Economics, University of Hawaii at Manoa (e-mail:
bonham@hawaii.edu). Richard H. Cohen is Assistant Professor of Economics, Business & Economics
Division, Lyon College (email: rcohen@lyon.edu).2
than zero to a potential regime change that does not occur.  The resulting systematic
forecast errors characterize the well-known peso problem.
Each of Thomas’ warnings describes a potential source of statistical bias in
individual forecasts.  Indeed, the rational expectations literature has interpreted
Muthian rationality to mean that the "subjective expectations of individuals are exactly
the true mathematical conditional expectations implied by the model itself"  (Begg
1982, p. 30, emphasis added).  However, rather than examining the rationality of
individual forecasts, Thomas tests the rationality of "consensus" forecasts, that is, the
mean forecast across respondents.  In particular, his unbiasedness tests regress the
actual inflation rate on the consensus forecast and a constant.  Unfortunately, two types
of problems due to aggregation plague such tests: private information bias and micro-
heterogeneity bias.
First, Figlewski and Wachtel (1983) demonstrated that aggregation leads to
inconsistent coefficient estimates in consensus regressions. Their conclusions hold
when forecasters use private information, even if a consensus exists in the sense that all
forecasters produce rational forecasts.  The inconsistency occurs because both the
consensus regression error and the consensus forecast contain an average of individual
forecasters' private information.
  Second, as pointed out by Keane and Runkle (1990), aggregation may mask
systematic individual differences.  In fact, given the complex, potentially changing
nature of the data generating process for inflation, it is likely that agents will differ in
their choice of both public and private information set variables and in how efficiently
they process the information in these variables.  Consequently, some agents are likely3
to produce forecasts that do not satisfy the optimality conditions of the REH.
Therefore, the coefficients in individual unbiasedness regressions may differ across
forecasters, i.e. micro-heterogeneity exists. Bonham and Cohen (2000) show that, in
such cases, parameter estimates in consensus regressions are either inconsistent or lead
to false acceptance of the unbiasedness hypothesis due to the averaging of individual
biases.  Figure 1 demonstrates this possibility for a sample of two forecasters: each
produces biased forecasts, yet the consensus forecasts are unbiased.
Figure 1:  Misleading Consensus Regression
Theil (1954) studied the properties of aggregated regressions in general.
Because he was not concerned with private information bias, which is unique to testing
the rational expectations hypothesis, he simply assumed that both consensus and
individual parameters could be estimated consistently.  He defined aggregation bias as
the difference between the mathematical expectation of the macro (consensus)
coefficient and the average of the corresponding micro (individual) coefficients.  He
0
2
4
6
8
10
12
0 2 4 6 8 10 12
A
c
t
u
a
l
Forecast
Individual 1's
Regression Line
Individual 2's
Regression Line
Consensus
Regression
Line4
showed that coefficients in macro relationships generally depend upon complicated
combinations of corresponding and noncorresponding micro coefficients.  For instance,
the intercept in a consensus unbiasedness equation will be a function not only of the
individual intercepts, but also individual slope coefficients.  Therefore, what Theil
meant by aggregation bias was that individual behavioral parameters generally could
not be mapped to a single corresponding macro parameter.  Theil showed that a
sufficient condition for perfect linear aggregation is the equality of all individual
coefficient vectors, i.e., micro-homogeneity.  The restrictiveness of this sufficient
condition led Theil to conclude that macro parameters are not useful in studying micro
behavior.  Thus, Theil assumed consistency of consensus and individual parameter
estimates and used micro-homogeneity as a condition for economic interpretation.
Bonham and Cohen (2000) use micro-homogeneity as a pretest both for consistent
estimation of consensus unbiasedness regressions and valid interpretation of tests of the
unbiasedness hypothesis.
Both cross-sectional forecast dispersion and micro-heterogeneity appear to be
very common in panels of survey forecasts.  For example, in their retrospective on the
Survey of Professional Forecasters, Zarnowitz and Braun (1992, pp. 45-46) conclude:
“The distribution of the [forecast] error statistics show that there is much dispersion
across the forecasts…. Forecasters differ in many respects and so do their products.
The idea that a close consensus persists, i.e., that current matched forecasts are
generally alike, is a popular fiction.  The differentiation of the forecasts usually
involves much more than the existence of just a few outliers.”  Thus, the very use of the
term consensus forecast is generally a misnomer.5
The view that individual forecasts differ widely is also prominent in the
literature on forecast combination.  In fact, for combinations of forecasts to dominate
individual predictions, it must be true that individual survey respondents make use of
private information, so that individual forecasts are heterogeneous.  Unfortunately, the
same heterogeneity of individual forecasts that makes the consensus forecast generally
superior to individual forecasts also renders the consensus forecast uninformative about
the rationality of those individual forecasts.
Bonham and Cohen (2000) test for micro-homogeneity in a Seemingly
Unrelated Regression system, adapting a variance covariance structure suggested by
Keane and Runkle (1990).  Bonham and Cohen (2000) find evidence of micro-
heterogeneity for the GNP deflator, as well as several other variables in the SPF.  We
know of two other papers that have tested for micro-homogeneity in unbiasedness
regressions using survey forecasts.  Pearce (1984) used a SUR system and rejected
micro-homogeneity for unbiasedness tests on S&P stock price index forecasts from the
Livingston Survey.  More recently, Batchelor and Dua (1991) rejected micro-
homogeneity for unbiasedness regressions on real GNP and GNP deflator forecasts
(among others) from the Blue Chip Economic Indicators forecasting service. Thus, for
these survey forecasts, consensus regressions should not be used to test rationality;
rationality can only be tested at the individual level.6
References
Batchelor, Roy, and Pami Dua.  1991. “Blue Chip Rationality Tests.” Journal of
Money, Credit, and Banking, 23, pp. 692-705.
Begg, David K. H. 1982.  The Rational Expectations Revolution in
Macroeconomics.  Baltimore, Md.: Johns Hopkins University Press.
Bonham, Carl S. and Richard H. Cohen.  2000. “To Aggregate, Pool or Neither:
Testing the Rational Expectations Hypothesis Using Survey Data.” University of
Hawaii at Manoa Economics Department Working Paper, February, 2000-03R.
http://www2.soc.hawaii.edu/econ/workingpapers/003abstract.html
Figlewski, Stephen and Paul Wachtel.  1983. “Rational Expectations,
Informational Efficiency, and Tests Using Survey Data: A Reply.” Review of
Economics and Statistics, 65, pp. 529-531.
Keane, Michael P. and David E. Runkle 1990.  “Testing the Rationality of Price
Forecasts: New Evidence from Panel Data.” American Economic Review, September,
80, pp. 714-735.
Thomas, Lloyd B. Jr. 1999.  “Survey Measures of Expected U.S. Inflation.”
Journal of Economic Perspectives.  Fall, 13, pp. 125-44.
Theil, Henri 1954.  Linear Aggregation of Economic Relations.  Amsterdam:
North-Holland Publishing Company.
Zarnowitz, Victor and Phillip Braun.  1993. “Twenty-Two Years Of The NBER
ASA Quarterly Economic Outlook Surveys: Aspects and Comparisons of Forecasting
Performance,'' in Business Cycles, Indicators, and Forecasting. Stock, James H. and
Mark W. Watson, eds.  Chicago, IL.:  University of Chicago Press.

The Rational Expectations Revolution in Macroeconomics.

To Aggregate, Pool or Neither: Testing the Rational Expectations Hypothesis Using Survey Data.”

Testing the Rational Expectations Hypothesis using Survey Data

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Testing the Rational Expectations Hypothesis using Survey Data

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