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The predictive power of equilibrium exchange rate models

Prepared by Michele Ca’ Zorzi, Pablo Anaya Longaric and Michał Rubaszek

Published as part of the ECB Economic Bulletin, Issue 7/2021.

1 Introduction

Central banks carefully monitor the evolution of exchange rates. In the case of the European Central Bank (ECB) and other major central banks, the exchange rate is not a policy target. But the “market value” of the euro is highly relevant for understanding the medium-term inflation outlook via its impact – through import prices and through general equilibrium effects – on the real economy.

It would therefore be very useful to be able to anticipate future exchange rate movements, but this has proven rather elusive, especially at short horizons. The view that exchange rates are largely disconnected from economic fundamentals at short horizons has mainly predominated since the seminal paper by Meese and Rogoff (1983), which showed that exchange rate models were unable to deliver more accurate nominal exchange rate forecasts than the simple prediction of “no change” associated with the random walk (RW) model.

The difficulty of predicting exchange rates with systematically better results than by using the RW model, especially at short-horizons, was reiterated by Rogoff (2008) and, more recently, in the influential articles by Rossi (2013) and Cheung et al. (2019).

Exchange rates have an important role beyond their key contribution to understanding the inflation outlook. While, in line with their monetary policy strategies, the ECB, the US Federal Reserve System and other major central banks do not treat the exchange rate as a target variable,

they are mindful that if large and persistent nominal exchange rate fluctuations occur, real exchange rate misalignments may develop over time that could have significant implications for the economic outlook. This is because over- and undervalued currencies, in an environment of price rigidity, could lead to competitiveness imbalances, excessive real exchange rate volatility and, potentially, sharp economic adjustments with adverse effects on consumption and production. This is the context in which currencies’ “fair value” is often discussed. In exceptional instances, major central banks have intervened directly or only verbally in foreign exchange markets in a concerted manner to influence exchange rate dynamics. It is hence not surprising that academics and policymakers have continued to strive in recent decades to improve their methodological frameworks for assessing equilibrium exchange rates (e.g. Bussière et al., 2010; Phillips et al., 2013; Fidora et al., 2017; Couharde et al., 2018; and Cubeddu et al., 2019).

Recent papers have argued that concepts of equilibrium exchange rates, besides their intrinsic interest, could be helpful for understanding and predicting exchange rate movements. These papers suggest that, even if the dynamic adjustment of exchange rates cannot be fully anticipated, it is known that they should eventually adjust to their equilibrium, i.e. a terminal condition defined by economic theory. For example, Ca’ Zorzi et al. (2016) and Ca’ Zorzi and Rubaszek (2020)

show that it is sufficient to assume that the real exchange rate gradually converges to the simplest definition of the equilibrium exchange rate, i.e. relative purchasing power parity (PPP), to produce surprisingly accurate real and nominal exchange rate forecasts. In theory, this approach is best suited to predicting real exchange rates, as the concept of the equilibrium exchange rate is defined in real terms. But empirical evidence shows that real exchange rate adjustments occur primarily through currency movements rather than via relative price changes. Thus, at least for countries with moderate inflation rates, measures of real equilibrium exchange rates can also be employed to forecast nominal exchange rates. From a different starting point, Ca’ Zorzi et al. (2017) and Eichenbaum et al. (2020) suggest that more advanced macroeconomic models, known as dynamic stochastic general equilibrium (DSGE) models – which assume that real and nominal exchange rate fluctuations are driven by differences in the monetary policy stance adjusted for risk premia – also offer a fairly good description of exchange rate dynamics and perform well overall in forecasting real and, to a lesser extent, nominal exchange rates. The explanation for this is that, like simpler approaches, such models imply a gradual return of the real exchange rate toward its equilibrium PPP value, but they tend to underestimate the empirical regularity of a strong co-movement between real and nominal exchange rates.

The key question addressed in this article is whether concepts of equilibrium exchange rates other than PPP might strengthen the predictability of exchange rates. To the extent that long-term drivers of exchange rates can be understood, and hence the equilibrium exchange rate can be estimated more precisely, it should in theory be possible to better forecast the future trajectory of the real and nominal exchange rate. For that purpose, this article evaluates the predictive power of three popular equilibrium exchange rate models. Besides the PPP model, we also investigate simplified versions of the behavioural equilibrium exchange rate (BEER) and the macroeconomic balance (MB) approaches along the lines of Ca’ Zorzi et al. (2022).

2 Three methods for assessing equilibrium exchange rates

Equilibrium exchange rate models are employed to decompose the real exchange rate (rerrer) into its equilibrium (rereqrereq) and misalignment (rermisrermis) components:

The split between the two components depends in part on the time horizon that is used. As discussed by Driver and Westaway (2005), exchange rate movements are driven by long, medium and short-term economic fundamentals and by an unexplained component.

The approach taken in this article is to distinguish between movements of the equilibrium exchange rates, and movements of the exchange rate around the equilibrium. The former are driven by long and medium-term economic fundamentals, while the latter are driven by short-term fundamentals and an unexplained component. This is consistent with theoretical general equilibrium models, in which over the business cycle fluctuations in exchange rates around their equilibria are partly driven by central banks’ relative monetary policy stance, adjusted for risk premia. The definition of equilibrium exchange rates is hence important from a monetary policy perspective.

The first equilibrium exchange rate model considered here is the PPP model, i.e. the oldest theory of real exchange rate determination, which was restored to prominence in modern times by Gustav Cassel and is…

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