5 - Finite Sample Properties of GMM estimators and Tests

Summary

Although GMM estimators are consistent and asymptotically normally distributed under general regularity conditions, it has long been recognized that this first–order asymptotic distribution may provide a poor approximation to the finite sample distribution. In particular, GMM estimators may be badly biased, and asymptotic tests based on these estimators may have true sizes substantially different from presumed nominal sizes.

This chapter reviews these finite sample properties, from both the theoretical perspective, and from simulation evidence of Monte Carlo studies. The theoretical literature on the finite sample behavior of instrumental variables estimators and tests is seen to provide valuable insights into the finite sample behavior of GMM estimators and tests.

The chapter then considers Monte Carlo simulation evidence of the finite sample performance of GMM techniques. Such studies have often focussed on applications of GMM to estimating particular models in economics and finance, e.g., business cycle models, inventory models, asset pricing models, and stochastic volatility models. This survey reviews and summarizes the lessons from this simulation evidence.

The final section examines how this knowledge of the finite sample behavior might be used to conduct improved inference. For example, bias corrected estimators may be obtained. Also, properly implemented bootstrap techniques can deliver modified critical values or improved test statistics with rather better finite sample behavior. Alternatively, analytical techniques might be used to obtain corrected test statistics.