To Aggregate, Pool, or Neither: Testing the Rational-Expectations Hypothesis Using Survey Data
Bonham, Carl S., Cohen, Richard H., Journal of Business & Economic Statistics
It is well known that, even if all forecasters are rational, unbiasedness tests using consensus forecasts are inconsistent because forecasters have private information. However, if all forecasters face a common realization, pooled estimators are also inconsistent. In contrast, we show that when predictions and realizations are integrated and cointegrated, microhomogeneity ensures that consensus and pooled estimators are consistent. Therefore, contrary to claims in the literature, in the absence of microhomogeneity, pooling is not a solution to the aggregation problem. We reject microhomogeneity for a number of forecasts from the Survey of Professional Forecasters. Therefore, for these variables unbiasedness can only be tested at the individual level.
KEY WORDS: Aggregation bias; Heterogeneity bias; Microhomogeneity; Survey forecast.
Survey data have been used extensively in direct tests of the rational-expectations hypothesis (REH). [See Holden, Peel, and Thompson (1985), Lovell (1986), or Pesaran (1987) for recent surveys of the literature on testing the REH.] These data are most commonly used in "consensus" form; that is, the cross-section of survey responses is averaged to form a single time series prediction. (Some authors have used other measures of central tendency, such as the median, geometric, or harmonic mean.) Testing the REH using consensus forecasts has, however, been criticized because aggregation may introduce at least two kinds of bias. Figlewski and Wachtel (1981, 1983) showed that, since each forecaster's information set contains some private information (known only to that forecaster), least squares (LS) coefficient estimates in consensus unbiasedness regressions are inconsistent. In addition, Keane and Runkle (1990) argued that consensus parameters may lead to false acceptance of the unbiasedness hypothesis because averaged data may conceal individual deviations from rationality. Thus, rationality tests need to be conducted using disaggregated data.
Rather than estimating individual regressions, Figlewski and Wachtel (1981, 1983) and Keane and Runkle (1990) advocated pooling all observations to increase degrees of freedom. However, Zarnowitz (1985) pointed out that, when the target variable is constant for all forecasters in a given time period, correlation between regressor and error results in downward bias of the pooled estimator.
It is important to note that most researchers have implicitly assumed stationary targets and predictions. However, many macroeconomic series are integrated. For cointegrated targets and predictions, we show that, when individual unbiasedness regressions share the same coefficients across forecasters--that is, microhomogeneity exists--both consensus and pooled parameters can be consistently estimated. Furthermore, if microhomogeneity does not hold, false acceptance of the unbiasedness hypothesis may occur in consensus tests, even in the unlikely event that offsetting individual biases allow parameters to be consistently estimated. Therefore, this article shows that microhomogeneity is crucial for both consensus and pooled tests of the unbiasedness hypothesis.
Section 1.1 describes the two types of bias that arise from improper use of consensus forecasts, and Section 1.2 describes the heterogeneity bias that arises from improper pooling. In Section 2, we test microhomogeneity in unbiasedness regressions using five forecast series from the Survey of Professional Forecasters (SPF). We extend Zellner's (1962a) microhomogeneity test to the case of generalized method of moments (GMM) estimation and adapt a weighting matrix suggested by Keane and Runkle (1990), which accounts for the possibility that forecast errors follow moving average processes both for individuals and across survey respondents. We show that for nearly all forecast series microhomogeneity does not hold. At least for these heterogeneous forecasts, unbiasedness should only be tested at the individual level. …