Purchasing power parity over two centuries: trends and nonlinearity

In two recent contributions Lothian and Taylor, and Cuddington and Liang, produced empirical evidence that annual data for the dollar-sterling real exchange rate spanning two centuries exhibited a non-linear deterministic trend. This trend could be proxying Harrod-Balassa-Samuelson effects. Lothian and Taylor showed that a linear stationary autoregressive mode, which embodied a cubic trend, implied much faster mean reversion of the real exchange rate to shocks than a model that excluded the trend. This article shows that both non-linearity and a deterministic trend can be allowed for in a theoretically appealing manner and that the fitted models provide a parsimonious explanation of both the dollar-sterling and franc-sterling real exchange rates over the two centuries of data. Generalized impulse response function analysis of the models demonstrates that the speed of adjustment to shocks can be even faster when trends are considered.