Instrumental Variables Estimation for Infinite Order Panel Autoregressive Processes

We consider instrumental variables 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. Instrumental variables approaches are useful to obtain well-behaved estimators in panels with large cross-sections. We establish the consistency and asymptotic normality of the instrumental variables estimators, including the Anderson–Hsiao, generalized method of moments, and double filter instrumental variables estimators. The theoretical results are obtained using double asymptotics under which both the cross-sectional sample size and length of time series tend to infinity. The finite-sample performance of the estimators is examined using Monte Carlo simulation