Academic journal article Journal of Money, Credit & Banking

Purchasing Power Parity and Markov Regime Switching

Academic journal article Journal of Money, Credit & Banking

Purchasing Power Parity and Markov Regime Switching

Article excerpt

RECENT IMPORTANT CONTRIBUTIONS on the question of whether purchasing power parity (PPP) holds in the twentieth century yielded mixed results. Taylor (2002) constructed a real exchange rate data set for over 100 years (from 1850 to 1996) for 20 countries, a larger uniform annual data set than had ever been studied before. Using the augmented Dickey-Fuller (ADF) test and the DF-GLS test of Elliott et al. (1996), Taylor found evidence of PPP over the twentieth century. Lopez et al. (2005) extended Taylor's data through 1998, and focused on 16 developed countries, out of the 20 countries included in Taylor's data set. Using different lag selection criteria for the ADF and the DF-GLS tests, Lopez et al. concluded that PPP held for only 9 out of the 16 countries.

The present paper revisits this discussion on the validity of PPP in the twentieth century by incorporating in the unit root tests an important feature of real exchange rates, namely, regime switching. The paper utilizes the recently developed literature on stochastic unit root processes introduced in Granger and Swanson (1997) and Leybourne et al. (1996), and further elaborated in Rahbek and Shephard (2002). In the stochastic unit root approach, there are periods (or epochs) of stationarity, referring to the stationarity regime, and periods of non-stationarity, referring to the non-stationarity regime. Applied to PPP, this approach corresponds to the idea that there are periods in which the real exchange rate is moving away from parity and thus behaving as a non-stationary process, namely, a regime during which PPP does not hold, and periods in which the real exchange rate is mean reverting and thus behaving as a stationary process, namely a regime during which PPP holds. Neither regime lasts forever. For instance, the non-stationary behavior of the real exchange rate may switch to a stationary behavior, and thus the non-stationarity regime may switch to the stationarity regime, due to the equilibrating effect of the real interest rate differential (Dumas 1992). This indicates a stochastic nature in the switching from one regime to the other. An interesting empirical issue that arises from this, pursued by the paper, is to test for regime switching in the stationarity property, i.e., to test for regime-dependent stationarity. Importantly, the paper provides a probabilistic answer as to whether PPP holds at any year and in each year in the twentieth century, by calculating the probability that the real exchange rate is in the stationarity regime at any year and in each year within the sample period.

The structure of the paper is as follows. Section 1 discusses the background justifying the introduction of regime switching in unit root tests and outlines the econometric approach adopted. Section 2 discusses the empirical findings, and Section 3 concludes.


As Taylor's original data set and Lopez et al.'s extended data set span a long period with various important economic events taking place, accounting for different regimes and thus regime switching in the real exchange rate behavior becomes crucial. A priori justification of regime switching in real exchange rates is based on several grounds.

Firstly, on theoretical grounds, Dumas (1992) has shown that the logarithmic real exchange rate switches from a regime of parity deviations to a regime of mean reversion. The real interest rate differential between the countries involved plays a vital role in triggering this switch: a large differential indicates a strong expected mean reversion in the real exchange rate; switching is triggered when the rate differential reaches its largest value, which occurs also when the deviation from PPP reaches its largest value. Secondly, Engel and Hamilton (1990) documented evidence of long swings in various exchange rates. Long swings refer to switching from an appreciation regime to a depreciation regime, with each regime lasting for years. …

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