Instrumental variables estimation of a nearly nonstationary, heterogeneous error component model

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This paper studies instrumental variables (IV) estimation for an error component model with stationary and nearly nonstationary regressors. It is assumed that the numbers of cross section and time series observations are infinite. Furthermore, autoregressive disturbances are assumed for the error component model, the structure of which may vary with individuals. The estimators considered are the Within-IV-OLS, Within-IV-GLS and IV-GLS estimators. The GLS estimators use Gohberg's formula, which is particularly useful when autoregressive structures are imposed on the disturbance terms. Sequential limit theories for the estimators are derived, and it is shown that all of the estimators have normal distributions in the limit. Additionally, Wald tests for coefficient vectors are shown to have chi-square distributions in the limit. Simulation results regarding the estimator efficiency and the size of the Wald tests are also reported. The results show that the Within-IV-GLS and IV-GLS estimators are more efficient than the Within-IV-OLS estimator in most cases and that the Wald tests keep nominal size reasonably well. The relation between the trade and budget deficits of 23 OECD nations is examined using the panel IV estimators. The empirical results support the view that the budget and trade deficits move in the same direction.