Purchasing power parity under high and low volatility regimes

Abstract

This article adopts Markov switching models to establish and examine several types of nonlinear dynamics in exchange rate returns and provide a new test to analyse presence of purchasing power parity (PPP) after controlling for various market states. In contrast with Engle and Hamilton (1990) focusing on discussing the dual state setting on the first moment of quarterly data for major industrial countries’ currencies, we concentrate more on the second moment for monthly data and add an analysis of developing countries’ currencies. Our empirical findings are consistent with the following notions. First, volatility-switching behaviours are more (less) remarkable for developing (industrialized) countries’ currencies. Second, we denote the high volatility state of exchange markets of developing (industrialized) countries as a crisis (an unusual) condition. Moreover, PPP would be valid at the low (high) volatility state for developing (industrialized) countries.

Notes

¹ A number of prior studies analysed the nonlinear dynamics of exchange rate returns via MS models. Those studies include Bekaert and Hodrick (1993), Engel and Hakkio (1993) and Nicolas et al . (2000).

² Since when p ₁₁ (p ₂₂) = 1, once the process enters state 1 (2), it would never return to state 2 (1).

³ We randomly generate 50 sets of initial values, and then derive the ML function value for each of the 100 sets of initial value, respectively. The mapped converged measure of the greatest ML function value then serves to estimate the parameter.

⁴ For three kinds of currencies of developing countries in this article, the Schwarz value estimates of the setting with switching in variances (no switching) are −476.823, −272.420 and −326.468 (−620.684, −332.427 and −379.111) for the case of South Korea, Thailand and Mexico, respectively. In contrast, for the case of industrial countries, the Schwarz value estimates of the setting with switching in variances (no switching) are −629.611, −663.733 and −649.100 * (−642.288, −657.961 and −642.842) for the case of the UK, Germany and France, respectively.

⁵ The MS model recognizes the 1997 Asian financial crisis period as a high volatility regime for South Korea and Thailand.