Nonlinear purchasing power parity under the Gold Standard.

• Author: Paya, Ivan

1. Introduction

   Recent theoretical analysis of purchasing power deviations (see, e.g., Dumas 1992; Sercu, Uppal, and Van Hull 1995; and O'Connell and Wei 1997) demonstrates how transactions costs or the sunk costs of international arbitrage induce nonlinear adjustment of the real exchange rate to purchasing power parity (PPP). Globally mean-reverting this nonlinear process has the important property of exhibiting near unit root behavior for small deviations from PPP since small deviations from PPP are left uncorrected if they are not large enough to cover the transactions costs or the sunk costs of international arbitrage.

   A parametric nonlinear model, suggested by the theoretical literature, that captures the nonlinear adjustment process in aggregate data is the exponential smooth transition autoregression model (ESTAR) of Ozaki (1985). A smooth, rather than discrete, adjustment mechanism is motivated by the theoretical analysis of Dumas (1992). Also, as postulated by Terasvirta (1994) and demonstrated theoretically by Berka (2002), in aggregate data regime changes may he smooth, rather than discrete, given that heterogeneous agents do not act simultaneously even if they make dichotomous decisions. (1) Recent empirical work (e.g., Michael, Nobay, and Peel 1997; Taylor, Peel, and Sarno 2001, Peel and Venetis 2002) has reported empirical results that suggest that the ESTAR model provides a parsimonious fit into a variety of data sets, particular for monthly data for the interwar and postwar floating period as well as for annual data spanning 200 years, as reported in Lothian and Taylor (1996). In addition, nonlinear impulse response functions derived from the ESTAR models show that although the speed of adjustment for small shocks around equilibrium will be highly persistent, larger shocks mean-revert much faster than the glacial rates previously reported for linear models (Rogoff 1996). In this respect, the ESTAR models provide some solution to the PPP puzzle outlined in Rogoff (1996). (2)

   The ESTAR model can also provide an explanation of why PPP deviations analyzed from a linear perspective appear to be described by either a nonstationary integrated I(1) process, or alternatively, described by fractional processes (see, e.g., Diebold, Husted, and Rush 1991). Taylor, Peel, and Sarno (2001), and Pippenger and Goering (1993) show that the Dickey-Fuller tests have low power against data simulated from an ESTAR model. Michael, Nobay, and Peel (1997) and Byers and Peel (2003) show that data that is generated from an ESTAR process can appear to exhibit the fractional property. That this would be the case was an early conjecture by Acosta and Granger (1995). Given that the ESTAR model has a theoretical rationale, whereas the fractional process is a relatively nonintuitive one, the fractional property might reasonably be interpreted as a misleading linear property of PPP deviations (Granger and Terasvirta 1999).

   Whereas the empirical work employing ESTAR models provides some explanation of the glacially slow adjustment speeds obtained in linear models, there is one aspect of the empirical work that is worthy of further attention. A second way of explaining the Rogoff puzzle, raised by Rogoff himself, (3) is to relax the assumption that the equilibrium real exchange rate is a constant (see, e.g., Canzoneri, Cumby, and Diba 1996; and Chinn and Johnston 1996). Theoretical models, such as that of Balassa (1964) and Samuelson (1964), imply a nonconstant equilibrium in the real exchange rate if real productivity growth rates differ between countries. (4) Nonlinear models that incorporate proxies fur these effects are found to parsimoniously fit post-Bretton Woods data for the main real exchange rates (see Venetis, Paya, and Peel 2002; and Paya, Venetis, and Peel 2003). Naturally, models that ignore this effect may generate misleading speeds of PPP adjustment to shocks. In this regard, the empirical results of Hegwood and Papell (2002) for the Gold Standard period are particularly interesting. Balassa-Samuelson effects are one of the major arguments for the numerous equilibrium mean shifts found in Hegwood and Papell (2002) for the real exchange rates in the 16 real exchange rate series analyzed in Diebold, Husted, and Rush (1991) for the period 1792-1913 under the Gold Standard. Hegwood and Papell (2002) assume linear adjustment around an occasionally changing equilibrium determined on the basis of the Bai-Perron (1998) test for multiple structural breaks. They report that quick mean reversion around an occasionally changing mean provides a more reasonable representation of the data than does fractional integration, which was originally reported by Diebold, Husted, and Rush (1991) for their data set. They conclude that long-ran PPP (LRPPP) does not hold but instead it is quasi-PPP (QPPP) theory-the one supported by their analysis of the data. They also state that the slow convergence of LRPPP is due to the unaccounted mean shifts in the equilibrium rate and that a reduction of more than 50% is achieved in the half-lives of shocks when those shifts are included in the model.

   These results are potentially important and provide motivation for our study. Hegwood and Papell (2002) only consider the impacts of structural breaks in the context of linear adjustment. In this article, we further examine the real exchange rate adjustment mechanism in the 19th and early 20th centuries under the Gold Standard by employing an ESTAR framework that allows for both a constant and structural breaks in the equilibrium real rate. Because the gold standard era was a high point of international cooperation (Diebold, Husted, and Rush 1991, p. 1254) and it was a symmetric arrangement (both parts were committed to maintain parities), the symmetric nonlinear ESTAR model is an appropriate model of real exchange rate behavior at that time. We find that ESTAR models incorporating the structural breaks employed by Hegwood and Papell (2002) provide a parsimonious explanation of the data. We determine the significance of the structural breaks via bootstrap and Monte Carlo analysis. We then investigate the speeds of adjustment obtained from nonlinear impulse response functions in these models and compare them to the estimated models that exclude structural breaks. Our results provide further support, on a new data set, for the hypothesis that real exchange rates are stationary, symmetric, nonlinear processes that reverted in this time period to a changing equilibrium real rate. The half-life of shocks implied by the nonlinear impulse response functions were found to be dramatically faster than those obtained in models that do not include the breaks. Clearly, our results support those of Hegwood and Papell (2002).

   The rest of the article is organized as follows. In section 2, we discuss the ESTAR model considered in our empirical applications and report empirical estimates of ESTAR models where the real exchange rate long run path is modeled both as a variable or a constant. Section 3 presents the Monte Carlo simulation exercise for the confidence interval of the statistics. Section 4 presents the results of the estimated impulse response functions for the nonlinear models. Finally, section 5 summarizes our main conclusions.

2. Nonlinear PPP

   We analyze properties of a set of currencies (dollar, pound, Deutsche mark. French franc, Belgian franc, and Swedish krona) spanning the period 1792-1913. We use the same data set as in Diebold, Husted, and Rush (1991) and Hegwood and Papell (2002). (5) This data set includes 10 real exchange rates using wholesale price index (WPI) as the deflator of the nominal exchange rate, and six real exchange rates that use the consumer price index (CPI) as the deflator. We normalize all of the real rates so that the first observation is set equal to zero. Hegwood and Papell (2002) could not reject the null of a unit root on the basis...