In this paper the recent literature on long-run exchange rate modeling is surveyed. In particular, we review the voluminous literature that tests for a unit root in real exchange rates and the closely related work on testing for a unit root in the residual from a regression of the nominal exchange rate on relative prices. We argue that the balance of evidence is supportive of the existence of some form of long-run exchange rate relationship. The form of this relationship, however, does not accord exactly with a traditional representation of the long-run exchange rate, and we offer some potential explanations.
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Macdonald, R. Long-Run Exchange Rate Modeling: A Survey of the Recent Evidence. IMF Econ Rev 42, 437–489 (1995). https://doi.org/10.2307/3867529