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
