Non-linear adjustment to purchasing power parity: an analysis using Fourier approximations

Abstract

This paper estimates the dynamics of adjustment to long run purchasing power parity (PPP) using data for 18 mayor bilateral US dollar exchange rates, over the post-Bretton Woods period, in a non-linear framework. We use new unit root and cointegration tests that do not assume a specific non-linear adjustment process. Using a first-order Fourier approximation, we find evidence of non-linear mean reversion in deviations from both absolute and relative PPP. This first-order Fourier approximation allows us to capture many features of the nonlinear decay detected in the data. Our results are consistent with theoretical arguments on
international goods markets arbitrage under transaction costs as well as with an emerging strand of empirical literature. In this sense, this paper contributes towards forming a consensus on the presence of nonzero transaction costs across a broad range of countries.