Purchasing power parity and the long memory properties of real exchange rates: Does one size fit all?

a r t i c l e i n f o JEL classification: C12 C22 C32 F30 F31 Keywords: Fractional Integration Nonlinear modelling Mean reverting process Long-memory process This paper examines the time series behavior of monthly bilateral real exchange rates (RER) on a comprehensive sample of 78 industrialized and developing countries, using the US Dollar, the UK Pound and the German Deutsche Mark as numeraires. We suggest a three step testing procedure based on recently introduced econometric techniques, in order to assess the mean-reverting properties of the RER and to address the question of whether real exchange rates follow a non linear process or a long memory process. The main results are as follows. Firstly, most of the bilateral real exchange rates under study are not mean-reverting. Secondly, the nonlinear ESTAR type adjustment is far from being prominent. Finally, only few bilateral RER exhibit true long memory mean-reverting properties. Most models of international trade and open economy rest on the hypothesis of purchasing power parity (PPP). At the aggregated level, this hypothesis implies that the nominal exchange rate should converge to the ratio of price levels between two countries, i.e. the real exchange rate (RER) should be a mean-reverting process. The empirical validity of this PPP assumption remains one of the most active and controversial issues in international economics (Taylor, 2006; Taylor and Taylor, 2004). Empirical methodologies and results are mixed. Generally, the usual unit-root tests conclude that PPP does not hold during the post-Bretton Woods period (see Section 2 for a brief survey). Some potential reasons to explain this puzzle are first that countries under study have very heterogeneous exposure to foreign markets, different commercial links with the leading countries (such as the United States, the United Kingdom, or Germany) and have experienced a variety of exchange rate regimes during the last thirty years. Secondly, it may also be that usual testing techniques are inadequate in presence of non-standard dynamics, such as nonlinearity, structural instability, or long memory processes. This article addresses these empirical difficulties to check PPP during the post-Bretton Woods period in two ways. First, we use a broader set of countries than the set considered in the literature: we thus consider monthly data on 78 CPI-based bilateral real exchange rates of industrialized and developing economies, over the period 1970–2006. For each currency, we consider three bilateral nominal exchange rates, the numeraire being alternatively US Dollar, …