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 past forecast accuracy.

翻译：经济调查中的理性受访者可能将任何中心趋势度量（其（潜在隐藏的）预测分布的中心趋势度量，例如均值、中位数、众数或这些度量的任意凸组合）报告为点预测。当受访者使用的中心趋势度量未知时，我们提出了预测理性检验。我们克服了一个识别问题，该问题在中心趋势度量彼此相等或处于局部邻域时出现，例如（精确或近似）对称分布的情况。作为基础构件，我们还提出了众数预测理性的新颖检验。我们将检验应用于纽约联邦储备银行消费者预期调查中的收入预测。我们发现这些预测可合理化作为众数预测，但不能作为均值或中位数预测。我们还发现，当按过去收入、年龄、工作稳定性和过去预测准确性对样本分层时，受访者使用的中心趋势度量存在异质性。