The Meese–Rogoff results stimulated significant research in the area, and numerous attempts have been made to overturn the results using a variety of data, sample periods, methodologies and model specifications. Most of these attempts have been ‘unsuccessful’ in the sense that they could not overturn the Meese–Rogoff results by producing lower forecasting errors than the random walk. Some economists, however, have claimed victory over the random walk (by producing numerically smaller forecasting errors), thus overturning the Meese–Rogoff results, but they failed to conduct formal testing and opted instead to derive inference from the numerical values of measures of forecasting accuracy. Otherwise, they (the ‘victors’) used dodgy procedures that boil down to beating the random walk with a random walk augmented with explanatory variables. Although a minority of economists attempted and succeeded in resolving the puzzle by using alternative measures of forecasting accuracy, they undermined the significance of their work by not claiming that their results overturned the Meese–Rogoff conclusion. This is a manifestation of confirmation bias at its best and the reason why a trivial issue has become a ‘puzzle’.

As a result of fear of the tyranny of the status quo, the conclusion that is widely held by the profession is that the random walk cannot be outperformed in forecasting exchange rates: this is the Meese–Rogoff puzzle. It is a puzzle because it makes no sense for profit-maximising firms to spend money on forecasts when the random walk provides free and more accurate forecasts (the so-called market-based forecasting). And it (the puzzle) is allegedly a disgrace to the profession because the enormous amount of work that has been done in the field of exchange rate economics has not led to the formulation of a model that is better than the (naive) random walk. This is why the Meese–Rogoff paper has become so frequently cited and even described as ‘seminal’ or (at worst) ‘influential’. The paper was celebrated on its 25th anniversary by a series of papers commemorating the occasion, when it was revealed that the paper had been rejected by the American Economic Review because the editor felt that the results would offend and embarrass any potential referee! The fact of the matter is that there is nothing seminal or influential about the Meese and Rogoff paper. If anything, the paper is flawed, and what looks like a puzzle is not a puzzle at all. It is bewildering why this observation has not been recognised when it is crystal clear. And it is flabbergasting that brilliant economists feel ashamed for not being able to beat the random walk (in the Meese and Rogoff sense) when this is a natural outcome, as we shall demonstrate later. Those brilliant economists have instead fallen into the murky water of the alleged puzzle.

Believing that there is a puzzle, economists have put forward several explanations for the Meese–Rogoff finding. Meese and Rogoff themselves explained the puzzle in terms of some econometric problems, including simultaneous equations bias, sampling errors, stochastic movements in the true underlying parameters, model misspecification, the failure to account for non-linearities, and the proxies used for inflationary expectations. Many economists support the model inadequacy proposition that exchange rate models do not provide a valid representation of exchange rate behaviour in practice (for example, Cheung and Chinn, 1998). Many more explanations have been suggested to resolve the puzzle, as we are going to find out later.

The main reason underpinning, and the root cause of, the Meese–Rogoff puzzle has been overlooked in the literature. Assessing forecasting accuracy exclusively by the magnitude of the forecasting error (which is what Meese and Rogoff did) may explain why the random walk cannot be outperformed. In fact, we should expect nothing other than the failure of exchange rate models to produce smaller forecasting errors than the random walk. Actually, this observation is equally valid for other financial prices and for macroeconomic variables. When forecasting accuracy is assessed by a broader range of metrics, the Meese and Rogoff results can be overturned with considerable ease.

The purpose of this study is to reconsider the Meese–Rogoff puzzle by utilising a wider range of forecasting accuracy measures that do not rely exclusively on the magnitude of the forecasting error. The main proposition that we put forward is that exchange rate models can outperform the random walk in out-of-sample forecasting when forecasting accuracy is assessed by measures that take into account more than just the magnitude of the forecasting error. We will also demonstrate that other explanations, such as those suggested by Meese and Rogoff themselves, cannot explain the puzzle.

Meese and Rogoff compared the forecasts generated by the models with those generated by the random walk (with and without drift). On the basis of a numerical comparison of the forecasting errors, they concluded that the random walk could not be outperformed in forecasting exchange rates. This was the case despite the fact that the forecasts were generated by using the actual future values of the explanatory variables (rather than forecasting them) to provide the model with the maximum forecasting ability (this, however, is a common practice in ex post forecasting). They did not conduct formal testing to determine the statistical significance of the difference between the forecasting errors of a model and the random walk. In their follow up study, Meese and Rogoff (1983b) undermined the strength of their original conclusion by stating that the random walk performs ‘as well as’ the structural models, but this still means that the random walk cannot be outperformed.

The Meese–Rogoff finding has been discussed widely by the profession since 1983. Several explanations are put forward for the failure of exchange rate models to outperform the random walk in out-of-sample forecasting. The empirical failure of the models is attributed to either theoretical or econometric problems (Neely and Sarno, 2002). Cheung and Chinn (1998) attribute the puzzle to theoretical problems (that is, exchange rate models provide an inadequate explanation of exchange rate behaviour). More puzzling are the related claims that the Meese–Rogoff finding is yet to be ‘comprehensively’ overturned, that it constitutes a puzzle and that it represents a serious weakness in the field of international monetary economics. For example, Abhyankar et al. (2005) describe the Meese–Rogoff findings as a ‘major puzzle in international finance’. Evans and Lyons (2005) comment that the Meese–Rogoff finding ‘has proven robust over the decades’ despite its being ‘the most researched puzzle in international macroeconomics’. Fair (2008) describes exchange rate models as ‘not the pride of open economy macroeconomics’ and contends that the ‘general view still seems pessimistic’. Engel et al. (2007) summarise the current state of affairs by stating that the ‘explanatory power of these models is essentially zero’. Frankel and Rose (1995) argue that the puzzle has a ‘pessimistic effect’ on the field of exchange rate modelling in particular and international finance in general. Bacchetta and van Wincoop (2006) describe the ‘puzzle’ as most likely the major weakness of international macroeconomics. Neely and Sarno (2002) consider the Meese and Rogoff conclusion to be a ‘devastating critique’ of the monetary approach to exchange rate determination and to have ‘marked a watershed in exchange rate economics’.

Flood and Rose (2008) emphasise the point that the Meese–Rogoff results are ‘devastating for the field of international finance’, going as far as claiming that ‘the area [international finance] has fell into disrepute’ and that ‘the area is not even represented on many first-rate academic faculties’!! Thus there is an apparent bewilderment as to why exchange rate models cannot outperform the random walk, leading to dramatic claims about the miserable state of international finance and international monetary economics, which allegedly have fallen into disrepute. These claims are gross overstatements, to say the least. Even economists who actually overturned the Meese–Rogoff results by using alternative measures of forecasting accuracy portrayed their results so modestly as to perpetuate the myth of the puzzle and the historical significance of the Meese–Rogoff work. It is no exaggeration to say that those economists who have ridden the bandwagon make the Meese and Rogoff work look as if it were in the same league as the work of Grigori Perelman, the Russian mathematician who in the early 21st century solved the Poincaré conjecture, which had been one of the most important and difficult open problems in topology since 1904. One of the few papers that challenge the Meese–Rogoff methodology and conclusions without making any apology is that of Moosa and Burns (2014a) – this paper provided the motivation for writing this book, and this book is an extension of the paper.

Most subsequent studies made the same mistake, but some of them correctly used the Diebold–Mariano (1995) test without emphasising the point that Meese and Rogoff failed to do that; hence, their (Meese and Rogoff’s) results could not be taken seriously. Should we excuse Meese and Rogoff because this test was not available in the early 1980s when they carried out their work? No, because the AGS test of Ashley et al. (1980) was available then, but most likely they were not aware of its existence. Even if no test is available, deriving inference from the numerical values of statistics estimated with standard errors is not exactly right, particularly in a paper that has received so much attention. Ironically, Rogoff himself is a co-author of a paper suggesting that claims of outperforming the random walk result from a failure to check robustness with respect to alternative out-of-sample tests (Rogoff and Stavrakeva, 2008). This statement stands in stark contrast to the original Meese and Rogoff study in which they failed to check the robustness of their findings.

If the underlying exchange rate (or any financial price) is relatively stable, the forecasting error of the random walk will be small. As the price becomes more volatile, the forecasting error of the random walk grows bigger. At the same time, however, the forecasting error produced by any model will grow bigger as well. Thus, if we start from a situation of a stable price, in which the forecasting error of the random walk is smaller than that of the model, then as long as the error of the random walk does not grow faster than that of the model, the model will always produce a higher root mean square error. This observation is equally valid for other financial prices such as stock prices.

By using simulated data to account for a wide range of volatility, Moosa (2013) demonstrates that as volatility rises, the forecasting error of any model rises more rapidly than that of the random walk. Likewise, Moosa and Vaz (2014) demonstrate, by using two stock price models, that as price volatility rises, the RMSE of the random walk rises but the RMSE of the model rises more rapidly. It follows that the Meese–Rogoff finding is a natural outcome, not a puzzle, and that nothing is remarkable about their results. As the period-to-period change in the exchange rate is typically small (which is by definition the magnitude of the error of the random walk), the random walk will always produce a very small magnitude of error, making it almost impossible for the exchange rate model to generate a numerically smaller and statistically different RMSE. But this should not mean that the random walk is good and models are bad.