What do we know about real exchange rate nonlinearities?

Nonlinear modeling of adjustments to purchasing power parity has recently gained much attention. However, a huge body of the empirical literature applies ESTAR models and neglects the existence of other competing nonlinear models. Among these, the Markov Switching AR model has a strong substantiation in international finance. Our contribution to the literature is fivefold: First, ESTAR and MSAR models from a unit root perspective are compared. To this end, a new unit root test against MSAR is proposed as the second contribution. Thirdly, the case of misspecified alternatives in a Monte Carlo setup with real world parameter constellations is studied. The ESTAR unit root test is not indicative, while the MSAR unit test is robust. Fourthly, the case of correctly specified alternatives is considered and low power of the ESTAR but not for the MSAR unit root test is observed. Fifthly, an empirical application to real exchange rates suggests that they may indeed be explained by Markov Switching dynamics rather than ESTAR.

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