Learning Before Testing: A Selective Nonparametric Test for Conditional Moment Restrictions

Abstract We develop a new test for conditional moment restrictions via nonparametric series regression, with approximating functions selected by Lasso. A key novelty of our approach is to account for the effect of the data-driven selection, yielding a new critical value constructed on the basis of a nonstandard truncated-Gaussian asymptotic approximation. We show that the test is correctly sized and attains a well-defined sense of adaptiveness that may result in better power than existing methods. The improvement afforded by the new test is demonstrated in a Monte Carlo study and an empirical application on the conditional evaluation of inflation forecasts.