9409707 Newey This project develops improved inference procedures for some frequently used econometric methods. The goal is to find approximations that improve on the usual large sample approach, and that are easy to implement. The proposal includes two specific projects and extensions. The projects are: bootstrapping for generalized methods of moments estimation and selecting the number of instrumental variables. Generalized method of moments estimation is widely applied in econometrics, so that reliable inference methods are needed. It is known that the usual large sample inferences do not work well in some cases. This project develops an improvement using bootstrap methods. The improvement will require a modification of well known bootstrap methods. It is based on sampling from a distribution that imposes the same moment restrictions as the estimator, which is different than the usual bootstrap. The usefulness of the proposed methods will be illustrated by empirical and simulation examples. The proposed research will also consider extensions of the approach to other models such as those where conditional moment restrictions are imposed. The project also considers inference with instrumental variables. Instrumental variables estimators are one of the most widely applied types of generalized method of moments estimators. An important practical problem is the choice of the number of instrumental variables to use in particular applications. The problem is of particular interest in the recent literature on estimation of "program evaluation" models, where instrumental variables are used to approximate the conditional probability of being treated. This research will use an asymptotic mean-square error criteria to derive some simple rules for choosing the number of instrumental variables. The efficacy of the selection rule will be considered in empirical and simulation examples. Also this research will be extended to consider rules for choosing the number of variables in other models, such as the sample selection model that has been widely used in econometrics.