Small Sample Properties of Panel Time-Series Estimators with I(1) Errors

Monte Carlo simulations are used to explore the small sample properties of a mean group and two pooled panel estimators of a regression coefficient when the regressor is I(1). We compare and contrast the effect of I(0) and I(1) errors and homogeneous and heterogeneous coefficients in a design based on two typical PPP panels. The results confirm that the asymptotic theory is relevant to practical applications. With I(0) errors and homogeneous coefficients, the estimators are unbiased, dispersion depends on the signal-noise ratio and falls at rate T(root-N) as expected. With I(1) errors and no cointegration, the estimators are unbiased and dispersion falls at rate root-N. When heterogeneity with I(0) errors is introduced, the dispersion of the pooled estimators falls at rate root-N but that of the mean group continues to fall at rate T(root-N). Finally, the pooled estimators are likely to lead to distorted inference both in the case of I(1) errors and of I(0) errors with heterogeneous coefficients. The mean group estimators, however, are generally correctly sized. An application to a panel of OECD economies suggests that the PPP hypothesis-nominal exchange rates and price differentials move one-for-one in the long run-seems to hold even if real exchange rates are subject to permanent shocks