Job market paper
I propose an inference procedure for a test of many zero restrictions in models for which parameter identification failure may be present. Existing tests cannot simultaneously accommodate identification failure and a parameter vector with large dimension. The test is based upon estimating a sequence of smaller dimension models and examining the maximum of the resulting estimators, and the maximum estimator reduces size distortion when the dimension of the parameter vector is large. The procedure is based on the bootstrap and does not require that we analytically calculate the limiting distribution of the maximum statistic. Several empirical examples are discussed and an empirical exercise examines a test of omitted nonlinearity in exchange rate dynamics.