Abstract
Nominal exchange rate regressions, in which the h-period change in the nominal exchange rate (NER) is regressed on the h-th lag of the real exchange rate (RER), are used to assess whether the RER predicts future NER adjustment. We show that these regressions are generally mis-specified relative to a VAR-type data generating
process, and that the reliability of inference about the RER’s predictive power depends critically on the horizon, on whether the RER is stationary, and on the sample size. Monte Carlo simulations show that, when the RER is stationary, the regressions estimate horizon-dependent projection coefficients rather than the adjustment coefficient, and cannot reveal shifts in the adjustment mechanism. When the RER is non-stationary, conventional tests reject the null of no predictive power far too often. At long horizons the regression also becomes spurious in the sense of Granger and Newbold, and non-standard critical values do not solve the problem. Empirically, we revisit the finding of Eichenbaum, Johannsen and Rebelo (2021) that, under inflation targeting, the RER predicts NER changes at horizons of three years and longer. NER-regressions for Norway and the UK reproduce this finding on the original sample period. However, the estimates shrink as the sample is extended. For the UK, for example, the lagged RER becomes insignificant once the regression is re-specified to have near white-noise residuals. The empirical regularity is therefore less robust than it appears, which matters for the assessment of monetary policy models that have been calibrated to match it.