Testing forecast rationality for measures of central tendency

Rational respondents to economic surveys may report as a point forecast any measure of the central tendency of their (possibly latent) predictive distribution, for example the mean, median, mode, or any convex combination thereof. We propose tests of forecast rationality when the measure of central tendency used by the respondent is unknown. We overcome an identification problem that arises when the measures of central tendency are equal or in a local neighborhood of each other, as is the case for (exactly or nearly) symmetric distributions. As a building block, we also present novel tests for the rationality of mode forecasts. We apply our tests to survey forecasts of individual income, Greenbook forecasts of U.S. GDP, and random walk forecasts for exchange rates. We find that the Greenbook and random walk forecasts are best rationalized as mean, or near-meanforecasts, while the income survey forecasts are best rationalized as mode forecasts.