  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 income forecasts from
the Federal Reserve Bank of New York's Survey of Consumer Expectations. We find
these forecasts are rationalizable as mode forecasts, but not as mean or median
forecasts. We also find heterogeneity in the measure of centrality used by
respondents when stratifying the sample by past income, age, job stability, and
survey experience.
