IV, GMM or likelihood approach to estimate dynamic panel models when either N or T or both are large

Abstract

We examine the asymptotic properties of IV, GMM or MLE to estimate dynamic panel data models when either NorT or both are large. We show that the Anderson and Hsiao (1981, 1982) simple instrumental variable estimator (IV) or maximizing the likelihood function with initial value distribution properly treated (quasi-maximum likelihood estimator) is asymptotically unbiased when either N or T or both tend to infinity. On the other hand, the QMLE mistreating the initial value as fixed is asymptotically unbiased only if N is fixed and T is large. If both N and T are large and NT→c (c≠0,c<∞) as T→∞, it is asymptotically biased of order NT. We also explore the source of the bias of the Arellano and Bond (1991) type GMM estimator. We show that it is asymptotically biased of order TN if TN→c (c≠0,c<∞) as N→∞ even if we restrict the number of instruments used. Monte Carlo studies show that whether an estimator is asymptotically biased or not has important implications on the actual size of the conventional t-test.