On the unstable relationship between exchange rates and macroeconomic fundamentals

Highlights

• We analyze the unstable relationship between exchange rates and macro fundamentals.

• We argue that this results from unknown structural parameters.

• The relationship is then driven by parameters expectations.

• These expectations can vary significantly as a result of "scapegoat" effects.

Abstract

Survey evidence shows that the relationship between the exchange rate and macro fundamentals is perceived to be highly unstable. We argue that this unstable relationship naturally develops when structural parameters in the economy are unknown. We show that the reduced form relationship between exchange rates and fundamentals is then driven not by the structural parameters themselves, but rather by expectations of these parameters. These expectations can vary significantly over time as a result of perfectly rational “scapegoat” effects. These effects can be expected to hold more broadly in macro and finance beyond the application to exchange rates in this paper.

Introduction

The weight that foreign exchange traders attach to different macro fundamentals as drivers of exchange rates fluctuates considerably over time. This was first documented by Cheung and Chinn (2001) through a survey of U.S. foreign exchange traders. More extensive evidence of these time-varying weights of macro fundamentals was recently reported by Fratzscher et al. (2012) based on data from Consensus Economics for 12 currencies over a period of 9 years. Forty six foreign exchange market participants from large countries are asked on a monthly basis to “rank the current importance of a range of different factors in determining exchange rate movements.” The rankings, on a scale from 0 to 10 for six key macroeconomic indicators, vary significantly over time for all six indicators. The survey evidence suggests a time-varying relationship between exchange rates and macro fundamentals. Fratzscher et al. (2012) confirm this by regressing changes in exchange rates on the macro fundamentals as well as the fundamentals interacted with the survey weights. The latter are statistically significant, implying that the derivative of the exchange rate with respect to a fundamental depends on its survey weight. The time-varying ranking of the macro fundamentals therefore implies a time-varying relationship between exchange rates and fundamentals.

The main goal of this paper is to show that large and frequent variations in the relationship between the exchange rate and macro fundamentals occur naturally when there is uncertainty about the structural parameters in the economy. We show that with parameter uncertainty, the relationship between a forward looking variable like the exchange rate and macro fundamentals is determined not by the structural parameters themselves, but rather by the expectations of structural parameters. Moreover, we show that these expectations can vary significantly over time, giving rise to a highly unstable reduced form relationship between exchange rates and fundamentals. This happens even though agents are perfectly rational Bayesian learners.

In addition to the usual learning process, whereby parameter expectations converge to their actual values, expectations can exhibit large short-term fluctuations. These are due to a mechanism that we refer to as a “scapegoat” effect. Some information about the nature of structural parameters can be derived by analyzing macroeconomic data and exchange rates. But these data are also driven by shocks to unobserved fundamentals. Such unobserved fundamentals can generate considerable confusion in the short to medium run. When the exchange rate fluctuates as a result of an unobserved macroeconomic shock, it can be optimal for agents to give more weight to an observed macro fundamental and therefore making it a “scapegoat”.¹ For example, if the dollar depreciates it may be natural to attribute it to a large current account deficit, even when the depreciation is unrelated to this deficit.

When we refer to a variable as becoming a scapegoat, we mean that the expectation of the structural parameter associated with that variable becomes much larger than the structural parameter itself, so that the variable temporarily has a large weight in the reduced form exchange rate equation. As in the example above, this may be caused by an unrelated change to an unobserved fundamental. More generally, we will show that even when the true structural parameters are constant the expectation of structural parameters is affected by changes in both observed and unobserved fundamentals. In that context we also think of the term scapegoat more broadly as referring to a situation where macroeconomic news that is unrelated to changes in structural parameters nonetheless leads to rational changes in beliefs about structural parameters. We show that this leads to a time-varying relationship between the exchange rate and fundamentals.

In illustrating the importance of such scapegoat effects, and their role in the unstable reduced form relationship between exchange rates and fundamentals, we slightly generalize the “canonical” exchange rate model. There is a broad class of exchange rate models that can be reduced to a single stochastic difference equation, derived from an interest rate parity equation and an equation that relates the interest differential to observed fundamentals. The latter can be obtained either from monetary policy specifications or money market equilibrium in a standard monetary model. We assume that the underlying parameters in this second equation, such as monetary policy or money demand parameters, or the relationship between policy targets and observed fundamentals, are not perfectly known. Moreover, we assume that some macro fundamental is not observable.

Our paper is not the first to introduce parameter uncertainty and Bayesian learning in a standard exchange rate model. Lewis (1989) assumes the existence of a one-time change in the constant term of the money demand equation. Kaminsky (1993) assumes that money growth is equal to a drift term that can switch between two values based on a Markov process. In both cases agents learn about the unknown parameters through Bayesian updating. Tabellini (1988) emphasized that such a framework can lead to increased exchange rate volatility relative to the case where parameters are known.² However, these papers do not consider uncertainty about parameters multiplying fundamentals and the role of unobserved fundamentals. Consequently, the scapegoat effect is not present in this prior literature.

To examine the quantitative relevance of the effects we describe, we calibrate the model to data for 5 industrialized countries, matching moments related to interest rates and exchange rates and the explanatory power of observed fundamentals. We find that the derivative of the exchange rate with respect to fundamentals can be very volatile when structural parameters are unknown. However, we show that this instability in the reduced form relationship between exchange rates and macro fundamentals is not detected by standard parameter instability tests based on regressions of exchange rates on fundamentals.

We show that knowing the time-varying weights improves the explanatory power of fundamentals for exchange rates. While this improvement is not large in a statistical sense, it may be important in an economic sense since small increases in predictive power can generate substantial economic gains. This point is illustrated by the existence of a large carry trade industry that is based on the statistically small predictive power of interest differentials (in terms of R²s).

The next section presents the model. It shows that the relationship between the exchange rate and fundamentals depends on expectations of structural parameters. We then go on to derive how these expectations are updated with a Kalman filter. Section 3 calibrates the model based on data on interest rates and exchange rates and presents numerical results for the relationship between exchange rates and fundamentals based on simulations. Section 4 discusses the empirical relevance of the scapegoat effect, time-varying structural parameters and the broader role of the mechanism in macroeconomics and finance. Section 5 concludes.