Halbert White SBR-9511253 The P.I. proposes to use the bootstrap to determine the sampling distribution of model specification error tests. The bootstrap has been increasing rapidly in statistics and specification tests, where critical values based on asymptotic distributions appear to often lead to over-rejection of correct specifications, are a natural place to apply this powerful method. Examples of tests that will be studied are: information matrix tests, tests based on nonparametric estimators and neural net estimators, and test of whether a particular subset of variables belong in a regression. The P.I. also proposes to develop high breakdown estimators that are insensitive to significant amounts of data contamination. The P.I. also intends to apply the methods developed to a number of empirical applications.