Purchasing Power Parity for Traded and Non-traded Goods: A Structural Error Correction Model Approach

When univariate methods are applied to real exchange rates, point estimates of autoregressive coefficients typically imply very slow rates of mean reversion. Rogoff (1996) discusses that the remarkable consensus of 3-5 year half-lives of purchasing power parity (PPP) deviations is found among studies using long-horizon data. However, a recent study by Murray and Papell (2002) calculates confidence intervals for estimates of half-lives for long-horizon and post-1973 data, and concludes that univariate methods provide virtually no information regarding the size of the half-lives. This paper estimates half-lives of real exchange rates for traded and non-traded goods with a system method based on Kim, Ogaki, and Yang’s (2001) structural Error Correction Model (ECM). This system method employs a modified version of Mussa’s (1982) model with traded and non-traded goods in which the exchange rate exhibits overshooting as in Dornbush’s (1976) model. The model includes a gradual adjustment equation, in which the domestic price of the traded good adjusts to the long-run equilibrium level determined by PPP. Kim, Ogaki, and Yang’s (2001) system method combines the single equation IV method with Hansen and Sargent’s (1982) method, which applies Hansen’s (1982) Generalized Method of Moments (GMM) to linear rational expectations models. In this paper, we estimate half-lives of real exchange rates based on traded good price indices, those based on non-traded good price indices, and those based on general price indices. The half-lives of the real exchange rates based on traded good price indices are expected to be shorter than those based on non-traded good or general price indices. We use the producer price indices (PPI), the consumer price indices (CPI), and GDP deflators from 1973 Q1 to 2001 Q1 to construct the real exchange rates for traded, non-traded, and general prices, respectively. The seven countries included in our study are Canada, France, Germany, Italy, Japan, the United Kingdom and the United States. When the system method is applied, our point estimates indicate shorter half-lives for traded good price indices than for non-traded and general good price indices.