Modelling optimal instrumental variables for dynamic panel data models

This paper considers a new two-stage instrumental variable estimator of panel data models with predetermined or endogenous explanatory variables. The instruments are fitted values from period-specific first-stage equations based on all available lags, which are similar to those in standard GMM estimation. The difference is that first-stage fitted values are not unrestricted but are chosen to satisfy the constraints implied by a VAR process with random effects. As a result the number of free first-stage parameters is dramatically reduced, while retaining predictive power from all lags. The estimators are asymptotically efficient when the VAR restrictions hold, but remain consistent if they do not. Since the instruments are parameterized using a fixed number of coefficients for any value of T, the properties of the resulting estimators are not fundamentally affected by the relative dimensions of T and N, contrary to standard panel GMM. Empirical illustrations are reported using firm- and country-level panel data.