Empirical exchange rate models of the seventies: Do they fit out of sample?

This study compares the out-of-sample forecasting accuracy of the structural exchange rate models that had come to dominate the 1970s literature against simple time series alternatives, and finds that a random walk does at least as well as any of them. The competitors are three “asset” models – the flexible-price monetary (Frenkel-Bilson) model, the sticky-price monetary (Dornbusch-Frankel) model, and the Hooper-Morton model, which extends the latter to let the long-run real exchange rate move with unanticipated trade balance shocks – all nested in a single quasi-reduced form in relative money supplies, relative real income, the short-term interest differential, the expected long-run inflation differential and cumulated home and foreign trade balances. Against them stand six univariate time series techniques applied to raw and prefiltered data, a random walk with an estimated drift, an unconstrained vector autoregression in the same variables, the forward rate, and the spot rate itself. Estimation uses monthly, seasonally unadjusted data from March 1973, the start of the floating-rate period, through June 1981; forecasting begins in November 1976, and every model’s parameters – including its seasonal parameters – are re-estimated each period by rolling regression so that only information available at the time of each forecast is used. Horizons are one, three, six and twelve months, chosen to match the available forward rate maturities. The critical design choice is that the structural models are given the benefit of the doubt: their forecasts are built from the actual realized future values of their own explanatory variables, which “directly addresses one possible defense of these models: structural exchange rate models have explanatory power, but predict badly because their explanatory variables are themselves difficult to predict.” Even so, “none of the models achieves lower, much less significantly lower, RMSE than the random walk model at any horizon” for the dollar/mark, dollar/pound, dollar/yen or trade-weighted dollar. The result survives estimating the structural models by ordinary least squares, generalized least squares and Fair’s instrumental variables method, allowing lagged adjustment, freeing the domestic and foreign coefficients, swapping M1-B for M2 or the reserve-adjusted base, trying alternative inflation-expectations proxies, substituting price levels for monetary variables, running the models on cross-rates to sidestep unstable US money demand, starting the forecast period in November 1978, and ending it in November 1980. The authors are careful about what they can and cannot claim statistically: because formal tests of forecast-accuracy differences require restrictive assumptions, they assert only that “the other models do not perform significantly better than the random walk model,” not that the random walk is significantly better. They are equally careful that their result is not good news: “while the random walk model may be as good a predictor as any of major-country exchange rates, it does not predict well,” with root mean square errors of 1.99 percent at one month and 8.65 percent at twelve months even for the more predictable trade-weighted dollar, and 3.70 and 18.3 percent for the dollar/yen rate. Companion constrained-coefficient experiments lead them to conclude that “neither sampling error nor simultaneous equations bias can fully explain the results,” and they canvass – without settling among – structural instability from the oil shocks and policy-regime changes, inadequate modelling of expectations, failure to capture real disturbances, and misspecified money demand, describing the ranking of these explanations as “at this point speculative.”

Richard A. Meese | Macro Paper Warehouse

Empirical exchange rate models of the seventies: Do they fit out of sample?