Indirect estimators

Abstract

This paper is concerned with the study of the asymptotic and finite sample properties of 3 Indirect Inference Estimators which can be found in the relevant bibliographic references and are called GMR1,GMR2 and GT. In particular, we show that all 3 estimators’ first order Taylor expansions converge to the same asymptotic distribution, that is they are first order asymptotically equivalent. Next, we explore some finite sample properties using the second order expansions and we prove that under certain conditions the GMR2 estimator is second order unbiased. Finally, we will provide some empirical justification to the theory of indirect inference by performing several Monte Carlo experiments, using simple EGARCH and Stochastic Volatility models.