Potentia pitfalls in determining multiple structural changes with an application to purchasing power parity

We investigate the empirical performance of the Bai and Perron multiple structural change tests and show that the use of their critical values may cause severe size distortions in persistent series. To correct these size distortions while maintaining a good power, we implement the Bai structural change test and extend it in two directions, developing a new procedure to choose the number of breaks and a restricted version that specifically models breaks that imply mean or trend reversion. Using our new methodologies, we reconcile the results of unit root tests with those of tests for structural change when testing for long-run purchasing power parity.