Purchasing Power Parity: Model Specification and Related Econometric Issues

In formulating PPP as a testable hypothesis a model needs to be specified. PPP models can be classified, according to the degree of restriction, into three types: the univariate model, the bivariate model and the multivariate model. The univariate model is arrived at by imposing the restrictions representing the properties of symmetry and proportionality to derive an expression for the real exchange rate. This model is given by (9.1) q t = s t − p t + p t * $$ {q_t} = {s_t} - {p_t} + p_t^* $$ Testing for PPP would, in this case, boil down to testing the behaviour of the real exchange rate, q t . This specification implies that cointegration between the nominal exchange rate and relative prices is a necessary but not a sufficient condition for long-run PPP to hold, the sufficient condition being that there is one-to-one correspondence between the nominal exchange rate and relative prices. In this case, empirical testing is concerned with the property of mean reversion in the real exchange rate. In the jargon of cointegration analysis, this specification implies the imposition of the restriction of (1,−1,1) on the cointegrating vector. Hence it is the real exchange rate, not the residuals of the unrestricted cointegrating vector, that is tested for unit root.