Jive for Panel Dynamic Simultaneous Equations Models

We consider the method of moments estimation of a structural equation in a panel dynamic simultaneous equations model under different sample size combinations of cross-sectional dimension, N, and time series dimension, T. Two types of linear transformation to remove the individual-specific effects from the model, first difference and forward orthogonal demeaning, are considered. We show that the Alvarez and Arellano (2003) type GMM estimator under both transformations is consistent only if T/N → 0 as (N, T) → ∞. However, it is asymptotically biased if T^3/N → κ ≠ 0 < ∞. Since the validity of statistical inference depends critically on whether an estimator is asymptotically unbiased, we suggest a jackknife bias reduction method and derive its limiting distribution. Monte Carlo studies are conducted to demonstrate the importance of using an asymptotically unbiased estimator to obtain valid statistical inference