The goal of this paper is to develop techniques to simplify semiparametric inference. We do this by deriving a number of numerical equivalence results. These illustrate that in many cases, one can obtain estimates of semiparametric variances using standard formulas derived in the well-known parametric literature. This means that for computational purposes, an empirical researcher can ignore the semiparametric nature of the problem and do all calculations as if it were a parametric situation. We hope that this simplicity will promote the use of semiparametric procedures.

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. [C12, C36].