Calibration as Testing, Type I Error in the Equity Premium Puzzle

A test of a dynamic, macroeconomic model with free parameters is provided by comparing its features, such as moments, with those of historical data. We provide a method for studying the distribution of the sample moment under the null hypothesis that the model is true. We calculate the size of tests of the recursive, exchange economy studied by Mehra and Prescott (1985) which compare model-generated and actual equity premia. With the parameter setting of Mehra and Prescott, the approximate size of their test is zero, while alternate, empirical representations of this economy or alternate moment-matching tests yield large probabilities of type I error.