Testing for parameter constancy in the time series direction in panel data models

We propose tests for parameter constancy in the time series direction in panel data models.We construct a locally best invariant test based on Tanaka [Time series analysis: nonstationary and noninvertible distribution theory. NewYork:Wiley; 1996] and an asymptotically point optimal test based on Elliott and Müller [Efficient tests for general persistent time variation in regression coefficients. Rev Econ Stud. 2006;73:907-940]. We derive the limiting distributions of the test statistics as T →∞while N is fixed, and calculate the critical values by applying numerical integration and response surface regression. Simulation results show that the proposed tests perform well if we apply them appropriately.