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98 CHAPTER 3. THE MONETARY MODELthey have a tendency to fall apart out of sample. There are many possibleexplanations for the instability, but ultimately, the reason boilsdown to the failure to Þnd a time-invariant relationship between the exchangerate and the fundamentals. Although their conclusions regardingthe importance of macroeconomic fundamentals for the exchangerate were nihilistic, Meese and Rogoff established a rigorous tradition ininternational macroeconomics of using out-of-sample Þt or forecastingperformance as model evaluation criteria.Panel Long-Horizon RegressionLet’s return to Mark and Sul’s analysis. They evaluate the predictivecontent of the monetary model fundamentals by initially estimating theregression on observations through 1983.1. Note that the regressand in(3.26) are past (not contemporaneous) deviations of the exchange ratefrom the fundamentals. It is a predictive regression that generates actualout-of-sample forecasts. The k = 1 regression is used to forecast 1-quarter ahead, and the k = 16 regression is used to forecast 16 quartersahead. The sample is then updated by one observation and a new setof forecasts are generated. This recursive updating of the sample andforecast generation is repeated until the end of the data set is reached.β = 0 if the monetary fundamentals contain no predictive content or iftheexchangerateandthefundamentalsdonotcointegrate.Let observations T − T 0 to T be sample reserved for forecast evaluation.If ŝ it+k − s it is the k−step ahead regression forecast formed at t,the root-mean-square prediction error (RMSPE) of the regression isvuT XR 1 = t 1 (ŝ it − s it−k )T 2 .0 t=T 0The monetary fundamentals regression is compared to the random walkiidwith drift, s it+1 = µ i + s it + ² it where ² it ∼ (0, σi 2 ). The k−step aheadforecasted change from the random walk is ŝ it+k − s it = kµ i .LetR 2 bethe random walk model’s RMSPE. Theil’s [134] statistic U = R 1 /R 2 isthe ratio of the RMSPE of the two models. The regression outperformsthe random walk in prediction accuracy when U