New evidence on nominal exchange rate predictability

Abstract

The Meese–Rogoff puzzle, one of the well-known puzzles in international economics, concerns the weak relationship between nominal exchange rates and market fundamentals. The purpose of this paper is to show that market fundamentals do in fact matter in forecasting nominal exchange rates. In particular, we emphasize the importance of the Harrod–Balassa–Samuelson effect in modeling deviations from purchasing power parity. Based on the post-Bretton Woods period, we provide solid out-of-sample evidence that rejects the random walk forecast model at medium-term and long-term forecast horizons. We also find mild evidence for out-of-sample predictability of nominal exchange rates over the short term.

Introduction

Since the publication of the seminal paper by Meese and Rogoff (1983), the predictability of exchange rates has been the subject of an ongoing scholarly debate in empirical international finance and has inspired a large volume of papers over the past two decades. Meese and Rogoff (1983) compare the predictive ability of a variety of exchange rate models and conclude that no existing structural exchange rate models can reliably beat random walks at short- or medium-term forecast horizons in out-of-sample forecast contests. Their finding is robust to assumptions of different fundamentals such as purchasing power parity (PPP) and uncovered interest rate parity, as well as to the use of the realized value of fundamentals in the forecast period and is now known as the Meese–Rogoff Puzzle. This puzzle is also sometimes referred to as the exchange rate disconnect puzzle (Obstfeld and Rogoff, 2000). Meese and Rogoff's findings are quite striking since a random walk model is not embedded within any economic wisdom or theory. The goals of research on exchange rate predictability over the past two decades have been to uncover the reasons which explain the Meese–Rogoff puzzle and to provide evidence which rejects the random walk forecast model.

A number of authors have found evidence which beats random walk forecasts in out-of-sample contests (e.g. Chinn and Meese, 1995, Mark, 1995, MacDonald and Marsh, 1997). The empirical procedure and the robustness of results in the previously mentioned literature have been challenged by a number of authors (e.g. Cheung et al., 2005, Kilian, 1999, Berkowitz and Giorgianni, 2001, Berben and van Dijik, 1998, Rossi, 2005). Recently several authors have applied the panel approach to show evidence of co-integration between exchange rates and fundamentals and then have provided evidence which beats random walk forecasts (e.g. Mark and Sul, 2001, Groen, 2000). However, these articles fail to examine the significance of deviations between two forecast errors.

One possible explanation for the Meese–Rogoff puzzle is that the linear forecasting model fails to capture important non-linearities in the data. However, a number of authors have found that allowing for regime switching in exchange rate models does not improve the out-of-sample predictability of the models (e.g. Engel and Hamilton, 1990, Engel, 1994). Other forms of non-linearity have also been found to be largely unimportant for exchange rates (e.g. Diebold and Nason, 1990, Meese and Rose, 1991). Recent empirical work has supported non-linear, mean-reverting adjustment of real exchange rates and has shown that the exponential smooth transition autoregressive (ESTAR) model provides a parsimonious fit to the data (e.g. Michael et al., 1997, Taylor et al., 2001, Taylor and Peel, 2000). Given the fact that real exchange rates follow an ESTAR process, Kilian and Taylor (2003) provide in-sample evidence to beat the random walk forecast at horizons of 2–3 years, but their out-of-sample evidence is fairly weak. Based on simulation results, Kilian and Taylor (2003) argue that the reason for the poor out-of-sample predictability of their model may be due to the short sample period available for empirical analysis.

Most existing literature which applies the ESTAR model to describe real exchange rate dynamics assumes that the long-run equilibrium of real exchange rates is time invariant and hence ignores the effects of real factors on the equilibrium of real exchange rates. Several articles argue that productivity differentials between countries affect real exchange rates (e.g. Harrod, 1939, Balassa, 1964, Samuelson, 1964). The Harrod–Balassa–Samuelson (HBS) effect suggests that, under some assumptions, fast growing economies will experience a rising relative price of non-tradables and hence a real appreciation over time. In this case, deviations from PPP will revert to an equilibrium trend instead of a constant mean implying that the real exchange rate would exhibit a trend behavior if one takes the Harrod–Balassa–Samuelson (HBS) effects into account.¹ Based on the idea of differential productivity growth in tradables and non-tradables, Obstfeld (1993) develops a simple stochastic model in which real exchange rates contain a pronounced deterministic trend. Kilian and Taylor (2003) argue that the HBS effect is significant when long historical data are used, but may not be significant in the shorter post-Bretton Woods period. Their arguments are also underscored by recent empirical findings with long historical data (e.g. Lothian, 1990, Cuddington and Liang, 2000, Lothian and Taylor, 2000, Lothian and Taylor, 2008, Taylor, 2002, Peel and Venetis, 2003, Taylor and Taylor, 2004). However, Bergin et al. (2006) point out that “the HBS effect has not always been a fact of economic life, and appears to be a phenomenon of only the postwar period.” Their empirical evidence reveals that the effect virtually vanishes from the data if one looks back fifty years or more. Several recent studies also point out the significance of the HBS effect on equilibrium real exchange rates over the post-Bretton Woods period, which indicates the significance of the HBS effect even in relatively short spans of data (Paya et al., 2003, Paya and Peel, 2003, Sollis, 2005).²

If the HBS effect is significant and is neglected in an empirical exchange rate model, then the estimation would suffer from omitted-variable bias, which could in turn result in the failure of the model in its out-of-sample predictability. The purpose of this paper is two-fold. First, we combine the non-linear adjustment of real exchange rates and the HBS effect in a model and then apply it to address the issue of nominal exchange rate predictability. Second, we investigate the significance of the HBS effect in enhancing exchange rate forecasts by examining whether the failure to reject the random walk forecast as observed in most existing literature can be explained solely by the restriction of short sample period.

Using the data over the post-Bretton Woods period for several industrialized countries, we obtained the following significant findings. First, our model fits the data reasonably well and shows that real effects (such as the HBS effect) on the equilibrium real exchange rate are important even in relatively short spans of data. Second, we provide strong out-of-sample evidence which rejects the random walk forecast of nominal exchange rates at horizons of 2–4 years. We also find mild evidence for out-of-sample predictability of nominal exchange rates when forecast horizons are less than one year. These results are robust to several newly developed statistical tests, to different sample periods and to different initial windows of estimation. Our findings are illuminating since they indicate that taking the HBS effect into account in an ESTAR model can help to strengthen the recursive out-of-sample predictability of the long-horizon regression equation.³ Using a less parsimonious model we obtain evidence of out-of-sample predictability. To the best of our knowledge, our paper is the first paper that provides solid out-of-sample evidence to reject random walk forecasts at short-term, medium-term and long forecast horizons.⁴

Third, simulation results point out that our bootstrap tests have correct size and good power given the modified ESTAR dynamics of real exchange rates. There is no indication that the power of bootstrap tests increases with forecast horizons. The contribution of the paper is to complement the existing literature by providing new out-of-sample evidence on the predictability of nominal exchange rates, which enriches our understanding of the Messe–Rogoff puzzle.

The article proceeds as follows. Section 2 provides a brief discussion of the HBS effect and several issues in its empirical application. Section 3 describes the estimation results of our model. Section 4 offers the bootstrap tests provided by Kilian (1999) and Kilian and Taylor (2003) given the modified ESTAR dynamics of real exchange rates. The size and power analysis of the bootstrap tests are given in Section 5. Section 6 concludes our discussion.