A Non-Linear Multivariate Model of the U.K. Real Exchange Rate

This paper discusses linearity testing for the UK real exchange rate within a multivariate framework. First we estimate a long-run real exchange rate relationship within a system involving real wages, the unemployment rate and the real price of oil. Then we adopt a logistic transition function for the estimated relationship and show that non-linearities in the discrepancy between the real exchange rate and its implied long-run level affect the short-run real exchange rate equation. We also find that when the real exchange rate is undervalued, unemployment falls as firms respond to an improvement in domestic competitiveness by increasing their demand for labour. At the same time, workers respond to the improvement in domestic competitiveness by demanding and getting higher wages. Further, the effect on unemployment and wages is nonlinear