The contribution of economic fundamentals to movements in exchange rates

Abstract

Starting from the asset pricing approach of Engel and West, we examine the degree to which fundamentals can explain exchange rate fluctuations. We show that it is not possible to obtain sharp inferences about the relative contribution of fundamentals using only data on observed monetary fundamentals—money minus output differentials across countries—and exchange rates. We use additional data on interest rate and price differentials along with the implications of the monetary model of exchange rates to decompose exchange rate fluctuations. In general, we find that money demand shifts, along with observed monetary fundamentals, are an important contributor to exchange rate fluctuations.

Introduction

The well-known paper by Meese and Rogoff (1983) showed that a simple random walk model for exchange rates can beat various time series and structural models in terms of out-of-sample forecasting performance. Although some of the subsequent literature on exchange rate predictability find evidence in favor of beating the random walk benchmark, most of those results do not hold up to scrutiny. The extant literature has found the linkage between the nominal exchange rate and fundamentals to be weak (Cheung et al., 2005, Sarno, 2005). This weak linkage has become known as the “exchange rate disconnect puzzle”.

Engel and West (2005) took a new line of attack in this analysis and demonstrate that this so-called disconnect between fundamentals and nominal exchange rates can be reconciled within a rational expectations model. The Engel and West (2005) model implies that the exchange rate is the present discounted value of expected economic fundamentals. Specifically,

$$s_t=f_t+E_t\left[{\displaystyle \sum _{j=1}^{\infty }{\psi }^j\cdot \Delta f_{t+j}}\right]+R_t\text{,}$$

where s_t is the spot exchange rate, f_t is the current value of observed fundamentals (for example money growth and output growth differentials), and ψ is the discount factor. The term R_t includes current and expected future values of unobserved fundamentals (risk premia, money demand shocks, etc.) as well as perhaps “nonfundamental” determinants of exchange rate movements.

The “exchange rate disconnect puzzle” reflects the fact that fluctuations in s_t − f_t can be “large” and persistent, while the promise of the present value approach is that this disconnect can be explained by the expectations of future fundamentals. The potential empirical success of the Engel and West model hinges on two major assumptions. First, fundamentals are non-stationary. Second, the factor used to discount future fundamentals is “large” (between 0.9 and unity). Nonstationary fundamentals impart nonstationarity to exchange rates while a large discount factor gives greater weight to expectations of future fundamentals relative to current fundamentals. As a result, current fundamentals are only weakly related to exchange rates as exchange rates appear to follow an approximate random walk. The first assumption of nonstationary fundamentals has been supported by empirical work (Engel and West, 2005, Engel et al., 2007), however, only recently has there been direct evidence in support for the second assumption of a large discount factor (Sarno and Sojli, 2009).

The key research question that still remains is to what extent can expectations of future fundamentals explain exchange rate movements? The challenge in evaluating the present value model is that not only the expected future fundamentals are not observed but other economic fundamentals, i.e. the R_t in Eq. (1.1), are also not observed. Indeed, Engel and West (2005) acknowledge that the kind of decompositions based on forecasting observed fundamentals such as those applied to stock prices (see Campbell and Shiller, 1988) is made difficult by the presence of unobserved fundamentals.³

In this paper, we use a simple monetary model of exchange rates to specify explicitly the relationship between economic fundamentals and exchange rates. To sharpen our focus on expectations about future fundamentals, we use a state-space model to conveniently model the relationship between observed fundamentals and the unobserved predictable components of fundamentals. We integrate the state-space model into the present value model of the exchange rate to show the links between the predictable component of fundamentals and exchange rate fluctuations. We use annual data on the pound to the dollar exchange rate, money, output, prices, and interest rates for the UK and US from 1880 to 2010. The directly observed fundamental in our model is money supply differentials between the UK and US minus output differentials between the UK and the US. This variable has been the primary focus of the literature's examination of fundamentals' contribution to exchange rate movements. For example, Mark (1995) evaluates the ability of this variable to forecast the future exchange rate movements for a set of countries including the United States, Canada, Germany, Japan, and Switzerland since the end of the Bretton Woods regime. Rapach and Wohar (2002) construct this variable for 14 industrial countries covering a period of more than a century and study the cointegration relationship between the exchange rates and the fundamentals. Mark and Sul (2001) further demonstrate that the panel data techniques are able to find more evidence of predictability of this variable to the future exchange rate movements. More recently, Cerra and Saxena (2010) conduct a comprehensive study of a very large dataset consisting of 98 countries and find more evidence that this fundamental variable helps to forecast the future exchange rate movements.

We show that a state-space model using only two observables—money supply minus output differential and the exchange rate—has difficulty inferring the relative importance of expected future fundamentals. Using Bayesian model averaging across different specifications of the state-space model, we show that the posterior distribution of the contribution of observed fundamentals to the variance of exchange rates is bimodal, with roughly equal weight placed on close to a zero contribution and on close to a 100% contribution. The reason for this great uncertainty about the relative contributions of observed fundamentals is that in the data the predictable component of changes in observed fundamentals is relatively small compared to the unpredictable component—most of the information about future fundamentals is contained in exchange rates rather than observable fundamentals. This makes identification of the separate contribution of expectations of future observed fundamentals problematic.

To solve this identification problem, we bring additional information to bear on the analysis which helps to move us away from the polar cases of 0% and 100% variance decomposition. First we incorporate data on interest rate and price differentials by including two additional observation equations in our state-space model—one corresponding to a relative money demand equation and the other to deviations from covered interest parity. These additional observation equations provide information about previously unobserved fundamentals—money demand shifters and uncovered interest parity risk premium. Another source of information is prior information about key parameters in the state-space model. Specifically, prior information about the half-life of deviations from purchasing power parity help to identify expected future deviations from purchasing power parity while prior information about the interest semi-elasticity of money demand helps determines the value of the discount factor. These additional sources of information can result in sharper inference about the relative contribution of the various fundamentals. Specifically, we find that monetary fundamentals, especially money demand shifters, explain the bulk of exchange rate movements. Fluctuations in the risk premium play a lesser role.

Our findings have important implications for exchange rate models that relate the exchange rate fluctuations to the economic fundamentals such as the output and monetary factors. Our results indicate that these economic fundamentals, either directly observed or indirectly inferred, contribute to exchange rate movements in a substantial way. The large literature that finds it difficult for economic models to produce a better out-of-sample forecast for the exchange rate than a random walk may simply be due to the predictable component of fundamentals being small relative to the unpredictable component. That is, a simple regression cannot detect the small signals buried under the volatile noise.

The rest of the paper is organized as follows. In Section 2, we outline the simple monetary model of exchange rates used by Engel and West (2005) to show how the spot exchange rate can be written as a function of expectations of future fundamentals, some of which are observed and some of which are unobserved. In Section 3, we develop a state-space model to describe the dynamics of the predictable component of observed fundamentals and embed it in the simple rational expectations monetary model of exchange rates. In Section 4, we demonstrate using Bayesian model averaging that there is substantial uncertainty about the quantitative contribution of observed fundamentals to exchange rate movements. In Section 5, we use additional information to obtain tighter inferences about relative contributions of observed and unobserved fundamentals. Section 6 conducts a sensitivity analysis to alternative model specifications and choice of priors. In Section 7, we provide additional evidence that the factor that is a major contributor to exchange rate movements is truly associated with money demand shifters. Section 8 concludes.