Inference for parameters identified by conditional moment restrictions using a generalized Bierens maximum statistic

TL;DR

This paper introduces a new inference method for parameters identified by conditional moment restrictions, using penalized maximum statistics and bootstrap-based model selection to improve power without prior instrument relevance knowledge.

Contribution

It develops a novel, data-driven inference approach based on a generalized Bierens maximum statistic, enhancing power and robustness in models with conditional moment restrictions.

Findings

Demonstrates superior performance over existing methods in Monte Carlo simulations.

Effectively handles weak or irrelevant instruments without prior information.

Provides a practical inference procedure for economic models with conditional moment restrictions.

Abstract

Many economic panel and dynamic models, such as rational behavior and Euler equations, imply that the parameters of interest are identified by conditional moment restrictions. We introduce a novel inference method without any prior information about which conditioning instruments are weak or irrelevant. Building on Bierens (1990), we propose penalized maximum statistics and combine bootstrap inference with model selection. Our method optimizes asymptotic power by solving a data-dependent max-min problem for tuning parameter selection. Extensive Monte Carlo experiments, based on an empirical example, demonstrate the extent to which our inference procedure is superior to those available in the literature.