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

We develop an inference method for parameters identified by conditional moment restrictions, which are implied by economic models such as rational behavior and Euler equations. Building on Bierens (1990), we propose penalized maximum statistics and combine bootstrap inference with model selection. Our method is optimized to have nontrivial asymptotic power against a set of $n^{-1/2}$-local alternatives of interest by solving a data-dependent max-min problem for tuning parameter selection. Extensive Monte Carlo experiments show that our inference procedure becomes superior to those available in the literature when the number of irrelevant conditioning variables increases. We demonstrate the efficacy of our method by a proof of concept using two empirical examples: rational unbiased reporting of ability status and the elasticity of intertemporal substitution.