Adaptive estimation of regression models via moment restrictions

Abstract

This paper considers adaptive estimation of regression models by means of generalized method of moments estimators. Two models are considered, one with an i.i.d. disturbance that is independent of the regressors and one with a conditionally symmetric but (possibly) heteroskedastic disturbance. For both cases the paper develops linearized estimators that are asymptotically efficient if the number and variety of moment conditions are allowed to grow at an appropriate rate with the sample size. In the general symmetric case no other adaptive estimator has yet been proposed. Also, results of a small Monte Carlo study indicate that in the independence case the small sample performance of the generalized method of moments estimator can be quite good vis-a-vis other estimators previously proposed.