We consider instrumental variables (IV) estimation of a possibly infinite order dynamic panel autoregressive (AR) process with individual effects. The estimation is based on the sieve AR approximation, with its lag order increasing with sample size. Transforming the variable to eliminate individual effects generates an endogeneity problem, particularly when the time series is only moderately long. IV approaches are useful to obtain well-behaved estimators in panels with large cross sections. We establish the consistency and asymptotic normality of the IV estimators, including the Anderson-Hsiao, generalized method of moments, and double filter IV (DFIV) estimators. The theoretical results are obtained under homoskedasticity using double asymptotics under which both the cross-sectional sample size and the length of the time series tend to infinity. The finite-sample performance of the estimators is examined using Monte Carlo simulation. Our preferred estimator is the DFIV estimator, as it exhibits excellent performance in terms of bias and coverage probability, despite its finite-sample distribution being relatively dispersed.
Lee et al. (Mon,) studied this question.