Learning before testing: A selective nonparametric test for conditional moment restrictions

• Main Authors: LI, Jia, LIAO, Zhipeng, ZHOU, Wenyu
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2022
• Subjects: Conditional moments; Lasso; Machine learning; Series estimation; Uniform inference; Variable selection.; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2566; https://ink.library.smu.edu.sg/context/soe_research/article/3565/viewcontent/Learning_Before_Testing.pdf
• Institution: Singapore Management University

This paper develops a new test for conditional moment restrictions via nonparametric series regression, with approximating series terms selected by Lasso. Machine-learning the main features of the unknown conditional expectation function beforehand enables the test to seek power in a targeted fashion. The data-driven selection, however, also tends to distort the test’s size nontrivially, because it restricts the (growing-dimensional) score vector in the series regression on a random polytope, and hence, effectively alters the score’s asymptotic normality. A novel critical value is proposed to account for this truncation effect. We establish the size and local power properties of the proposed selective test under a general setting for heterogeneous serially dependent data. The local power analysis reveals a desirable adaptive feature of the test in the sense that it may detect smaller deviations from the null when the unknown function is less complex. Monte Carlo evidence demonstrates the superior finite-sample size and power properties of the proposed test relative to some benchmarks.