Statistical inference for panel dynamic simultaneous equations models

We study the identification and estimation of panel dynamic simultaneous equations models. We show that the presence of time-persistent individual-specific effects does not lead to changes in the identification conditions of traditional Cowles Commission dynamic simultaneous equations models. However, the limiting properties of the estimators depend on the way the cross-section dimension, N, or the time series dimension, T, goes to infinity. We propose three limited information estimator: panel simple instrumental variables (PIV), panel generalized two stage least squares (PG2SLS), and panel limited information maximum likelihood estimation (PLIML). We show that they are all asymptotically unbiased independent of the way of how N or T tends to infinity. Monte Carlo studies are conducted to compare the performance of the PLIML, PIV, PG2SLS, the Arellano-Bond type generalized method of moments and the Akashi-Kunitomo least variance ratio estimator. We demonstrate that the reliability of statistical inference depends critically on whether an estimator is asymptotically unbiased or not.