Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the Ppp Hypothesis

This paper studies asymptotic and finite sample properties of statistics devised to test for the null of no cointegration in nonstationary pooled time series panels as both the cross section and time series dimensions grow large. The paper finds that for panels with homogenous long run parameters, the spurious regression coefficient estimates become consistent even under the null of no cointegration, and this generates a superconsistency result for panels whereby it becomes irrelevant for the asymptotic distributions whether the residuals are known or are estimated. For heterogenous panels, on the other hand, this asymptotic equivalency does not hold, and the use of stationarity tests that are convergent for raw data can even become divergent when applied to estimated residuals. Furthermore, the direct use of unit root tests for estimated residuals can generate data dependencies that are not present in unit root statistics that are applied to raw panel data. The paper therefore derives asymptotic distributions for panel cointegration statistics that circumvent these problems, and also reports on finite sample properties of these statistics based on Monte Carlo simulations for a varying number of time periods and cross sections. These statistics allow for complete heterogeneity of the dynamics and potential cointegrating relationships across members of the panel. Finally, an empirical application of these panel cointegration statistics is demonstrated for the purchasing power parity hypothesis, which has been difficult to evidence on the basis of conventional single series cointegration tests. 1 PANEL COINTEGRATION; ASYMPTOTIC AND FINITE SAMPLE PROPERTIES OF POOLED TIME SERIES TESTS WITH AN APPLICATION TO THE PPP HYPOTHESIS