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

Jia Li; Zhipeng Liao; Wenyu Zhou

doi:10.1162/rest.a.1696

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

Jia Li¹; Zhipeng Liao²; Wenyu Zhou³

¹ School of Economics, Singapore Management University, Singapore [email protected] · ² Department of Economics, UCLA, Los Angeles, CA 90095 [email protected] · ³ School of Economics and Academy of Financial Research, Zhejiang University, Hangzhou, Zhejiang 310058, China

The Review of Economics and Statistics 2026

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.

DOI: 10.1162/rest.a.1696
Pages: 1-46
Language: en
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Sources: crossref openalex