Regression Analysis with Many Specifications: A Bootstrap Method for Robust Inference

We consider a set of linear regression models that differ in their choice of regressors, and derive a method for inference that controls for the set of models under investigation. The method is based around an estimate of the distribution for a class of statistics, which can depend on two or more models. An example is the largest R2 over a set of regression models. The distribution will typically depend on all models in a complex way and does not have a known analytical form. This problem is solved by a bootstrap implementation that incorporates the relevant dependence across models. We illustrate the method with an application where monthly stock returns are regressed on different subsets of lagged variables. The method is applied to estimate the distribution of the maximal R2 under the null hypothesis of no explanatory power. In spite of the large number of models, the maximal R2 is significant. JEL Classification: C12, C2, C52, C53.