Exchange rate prediction redux: New models, new data, new currencies

Abstract

Previous assessments of nominal exchange rate determination, following Meese and Rogoff (1983) have focused upon a narrow set of models. Cheung et al. (2005) augmented the usual suspects with productivity based models, and “behavioral equilibrium exchange rate” models, and assessed performance at horizons of up to 5 years. In this paper, we further expand the set of models to include Taylor rule fundamentals, yield curve factors, and incorporate shadow rates and risk and liquidity factors. The performance of these models is compared against the random walk benchmark. The models are estimated in error correction and first-difference specifications. We examine model performance at various forecast horizons (1 quarter, 4 quarters, 20 quarters) using differing metrics (mean squared error, direction of change), as well as the “consistency” test of Cheung and Chinn (1998). The purchasing power parity estimated in the error correction form delivers the best performance at long horizons by a mean squared error measure. Moreover, along a direction-of-change dimension, certain structural models do outperform a random walk with statistical significance. While one finds that these forecasts are cointegrated with the actual values of exchange rates, in most cases, the elasticity of the forecasts with respect to the actual values is different from unity. Overall, model/specification/currency combinations that work well in one period and one performance metric will not necessarily work well in another period and alternative performance metric.

Introduction

Nearly fifteen years ago, three of the authors embarked upon an assessment of the then dominant empirical exchange rate models of the time.⁵ Over the past decade, the consensus – such as it was – regarding the determinants of exchange rate movements has further disintegrated. The sources of this phenomenon can in part be traced to the realities of the new world economy, and in part to the development of new theories of exchange rate determination. Now seems a good time to re-visit in a comprehensive fashion the question posed in our title.

To motivate this exercise, first consider how different the world was then. The “New Economy” was an established phenomenon, with accelerated productivity growth in the US. Inflation and output growth, across the advanced economies, appeared to have entered a prolonged and durable period of relative stability, a development dubbed “The Great Moderation”. If one were to ask a typical international finance authority what the most robust determinant of the dollar-based exchange rate (shown in Fig. 1, Fig. 2, Fig. 3) was, the likely answer would be “real interest differentials”. Compare to the present situation of short term policy rates bound at zero (Fig. 4) and possibly unrepresentative of the actual stance of monetary policy (shadow rates in Fig. 5), slowing productivity growth, and repeated bouts of financial risk intolerance and illiquidity (VIX and TED spreads in Fig. 6). Observed real interest differentials at the short horizon are likely to be close to zero, given the zero lower bound, and low inflation worldwide.

It is against this backdrop that several new models have been forwarded in the past decade. Some explanations are motivated by new findings in the empirical literature, such the correlation between net foreign asset positions and real exchange rates. Others, such as those based on central bank reaction functions have now become well established in the literature. Or models that relate the exchange rate to interest rate differentials at several horizons simultaneously. But several of these models have not been subjected to comprehensive examination of the sort that Meese and Rogoff conducted in their original 1983 work. While older models have been ably reviewed (Engel, 2014, Rossi, 2013), we believe that a systematic examination of these newer empirical models is due, for a number of reasons.

First, while some of these models have become prominent in policy and financial circles, they have not been subjected to the sort of rigorous out-of-sample testing conducted in academic studies.

Second, the same criteria are often used, neglecting many alternative dimensions of model forecast performance. That is, the first and second moment metrics such as mean error and mean squared error are considered, while other aspects that might be of greater importance are often neglected. We have in mind the direction of change – perhaps more important from a market timing perspective – and other indicators of forecast attributes.

In this study, we extend the forecast comparison of exchange rate models in several dimensions.

• Eight models are compared against the random walk. Of these, four were examined in our previous study (Cheung et al., 2005). The new models include a real interest differential model incorporating shadow interest rates, Taylor rule fundamentals, a sticky price monetary model augmented with risk proxies, and an interest rate model incorporating yield curve factors. In addition, we implement a different specification for purchasing power parity.

• The behavior of US dollar-based exchange rates of the Canadian dollar, British pound, Japanese yen, Swiss franc, and the euro are examined. The German mark has dropped out, while the last two exchange rates are added.

• The models are estimated in two ways: in first-difference and error correction specifications.

• Forecasting performance is evaluated at several horizons (1-, 4- and 20-quarter horizons) and three sample periods: post-1982, post-dot.com boom and post-Crisis onset. We have thus evaluated out of sample periods, spanning the times that have witnessed notable changes in the global environment.

• We augment the conventional metrics with a direction of change statistic and the “consistency” criterion of Cheung and Chinn (1998).

It is worthwhile to stress that our study is not aimed at determining which model best forecasts, but rather aimed at determining which model appears to have the greatest empirical content, by which we mean the ability to reliably predict exchange rate movements. Were our objective the former, we would not conduct ex post historical simulations where we assume knowledge of the realized values of the right hand side variables.

Consistent with previous studies, we find that no model consistently outperforms a random walk according to the mean squared error criterion at short horizons. Somewhat at variance with some previous findings, we find that the proportion of times the structural models (as a group) outperform a random walk at long horizons is slightly greater than would be expected if the outcomes were merely random, 16%, using a 10% significance level. The aggregate average outperformance rate, however, does not convey the superior performance of individual specifications. The error correction specification of purchasing power parity, in particular, performs especially well at longer horizons of one year and 5 years; it beats the random walk benchmark 80% (21 out of 26 cases) of the time.

The direction-of-change statistics indicate more forcefully that the structural models do outperform a random walk characterization by a statistically significant amount. The structural models (as a group) outperform a random walk 29% of the time. Under this performance criterion, the first-difference specification of BEER model outperforms the random walk benchmark 70% (23 out of 33 cases) of the time, while the error correction specification of purchasing power parity outperforms 54% (21 out of 39 cases) of the time.

In terms of the “consistency” test of Cheung and Chinn (1998), some positive results are obtained. The actual and forecasted rates are cointegrated 60% of the time, and is much more often than would occur by chance for all the models. However, in most of these cases of cointegration, the condition of unitary elasticity of expectations is rejected, so very few instances of consistency are found.

We conclude that the question of exchange rate predictability (still) remains unresolved. In particular, while the oft-used mean squared error and the direction of change criteria provide an encouraging perspective, more so than in our previous study, and the direction of change results are, relatively speaking, even more positive. As in our previous study, the best model and specification tend to be specific to the currency and out-of-sample forecasting period.