Essays on Uniformly Valid Inference ProceduresPublic Deposited
The first chapter of this dissertation develops a two-stage inference method for structural parameters in the linear instrumental variables model. In the first stage, a new statistic is used to detect whether the correlation between the structural error and the reduced form error is small. In the second stage, a hypothesis about a component of the structural parameter vector is tested using a t-test based on either the ordinary least squares or on the two-stage least squares, depending on the first-stage result. Conditional on the value of this new statistic, the probability of accepting the null hypothesis can be calculated based on the normality of asymptotic distributions, and explicit formulas for the asymptotic size and power of this test can be derived. The asymptotic size will depend on nuisance parameters, and the power will depend on nuisance parameters and a local parameter. Based on direct calculations, this test is consistent in size and has attractive power properties. The second chapter of this dissertation studies inference in generalized method of moments models when the data set is obtained by combining data from different sources. In the case where we have different numbers of observations for different variables in our data set, and where some of the moments depend only on the data we have more observations on, we find that one estimator for the moment conditions, defined to be the Adjusted estimator, has smaller asymptotic variance than commonly used estimators. Moreover, the Adjusted estimator achieves the smallest asymptotic variance in a particular set of linear estimators. We then show that this property on asymptotic variance translates to better power in inference. The third chapter of this dissertation extends the results of the second chapter to inference in moment inequality models, when the data set is obtained from combined data sources. A necessary step for doing inference in moment inequality models is to estimate the moment conditions. We show that, following a general method of moments procedure, inference based on the Adjusted estimator is uniformly consistent in size, and has better power against certain types of alternatives than the same procedure based on commonly used estimators.