Asymptotically Uniform Tests After Consistent Model Selection in the Linear Regression Model

This article specializes the critical value (CV) methods that are based upon (refinements of) Bonferroni bounds, introduced by McCloskey to a problem of inference after consistent model selection in a general linear regression model. The post-selection problem is formulated to mimic common empirical practice and is applicable to both cross-sectional and time series contexts. We provide algorithms for constructing the CVs in this setting and establish uniform asymptotic size results for the resulting tests. The practical implementation of the CVs is illustrated in an empirical application to the effect of classroom size on test scores.