A Minimum Mean Squared Error Semiparametric Combining Estimator

In the context of competing theoretical economic–econometric models and corresponding estimators, we demonstrate a semiparametric combining estimator that, under quadratic loss, has superior risk performance. The method eliminates the need for pretesting to decide between members of the relevant family of econometric models and demonstrates, under quadratic loss, the nonoptimality of the conventional pretest estimator. First-order asymptotic properties of the combined estimator are demonstrated. A sampling study is used to illustrate finite sample performance over a range of econometric model sampling designs that includes performance relative to a Hausman-type model selection pretest estimator. An important empirical problem from the causal effects literature is analyzed to indicate the applicability and econometric implications of the methodology. This combining estimation and inference framework can be extended to a range of models and corresponding estimators. The combining estimator is novel in that it provides directly minimum quadratic loss solutions.