Combining Estimators to Improve Structural Model Estimation Under Quadratic Loss

Abstract

Asymptotically, semi parametric estimators of the parameters in linear structural models have the same sampling properties. In finite samples the sampling properties of these estimators vary and large biases may result for sample sizes often found in practice. With a goal of improving asymptotic risk performance and finite sample efficiency properties, we investigate the idea of combining correlated structural equation estimators with different finite and asymptotic sampling characteristics. Based on a quadratic loss measure, we provide a risk domination result and present evidence that the finite sample performance of the resulting combination estimator is superior to that of a leading traditional moment based estimator. A basis for interval estimation and inference for the combination estimator is demonstrated.

Keywords: Combined estimators, quadratic loss, ill-conditioned design, semiparametric estimation, data dependent shrinkage, instrumental variables

JEL Classification: C10, C24