Penalized-R2 Criteria for Model Selection

Abstract:     
It is beneficial to observe that popular model selection criteria for the linear model are equivalent to penalized versions of R2. Let PR2 refer to any one of these model selection criteria. Then PR2 serves the dual purpose of selecting the model and summarizing the resulting fit subject to the penalty function. Furthermore, it is straightforward to extend the logic of PR2 to instrumental variables estimation and the non-parametric selection of regressors. For two-stage least squares estimation, a simulation study investigates the finite-sample performance of PR2 to select the correct model in cases of either strong or weak instruments.

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