This chapter examines the relationship between exchange rates and the business cycle. A principal goal is to assess the extent to which exchange rate movements reflect countries’ relative positions over the business cycle. Are the influences similar across countries and at different points in time? The importance of this question is highlighted by the late 1990s conjuncture of low inflation, sustained economic growth, and appreciated currencies in the United States and United Kingdom compared to relatively slack conditions in continental Europe and a weak euro. The conclusion of the research summarized in this paper is that cyclical movements in activity have substantial effects on exchange rates, though these are of course not the only or at all times the most important influence on currencies.

There are a number of potential reasons why the United Kingdom and United States may be enjoying such a fortuitous inflation/growth combination, including productivity improvements associated with information technology and the relatively slow growth in competing countries that has kept a lid on prices of raw materials. Additionally, the exchange rate may play an important role, with the appreciating currencies in the United States and United Kingdom helping to attenuate inflation in each country, both because of the direct effect on the cost of primary inputs and importables, and from the feedthrough to the nontraded goods sector via the wage bargaining process. In recent years, the exchange rate-business cycle link appears to have worked to the advantage of policymakers in the United Kingdom and United States, while the corresponding depreciation of the yen may also be viewed as beneficial to the Japanese economy given that country’s relatively weak growth performance.

The study first reviews the literature on the determinants of exchange rates and the relationship with business cycles, and then presents direct empirical evidence on the connection. Somewhat surprisingly, there is little work that looks directly at the exchange rate-business cycle relationship. Because of this, a principal focus in this survey is on the role of asset yields and the corresponding interest rate differentials between countries and maturities; these are then used to examine the relationship between exchange rate movements and the business cycle. This mechanism and related analytical frameworks are discussed in the second section, after which the existing empirical evidence is reviewed. The next section provides new empirical evidence, first on the link between real exchange rates and real interest rate differentials for a number of key bilateral and effective exchange rates over the post-1973 period of floating exchange rates, and then on the decomposition of exchange rate movements into a permanent component and business-cycle movements. The chapter ends by drawing conclusions.

## Exchange Rate Models: Some Scaffolding and an Overview

In thinking about the relationship between the economic cycle and the exchange rate, it is instructive to start with a discussion of models of nominal and real exchange rates. Since these are comprehensively surveyed elsewhere—see, for example, MacDonald (1988), MacDonald and Taylor (1992), and Frankel and Rose (1995)—the discussion here is not intended to be exhaustive or rigorous but, rather, to focus on implications for the relationship between the business cycle and exchange rates and then to motivate the empirical work that follows.

Perhaps the simplest nominal exchange rate model is purchasing power parity (PPP), in which the equilibrium level of an exchange rate is determined by relative prices—absolute PPP—or relative PPP, where the exchange rate changes in response to inflation differentials. Although PPP in itself has limited applicability for the central focus of this study, it is helpful in motivating the decomposition of real exchange rates into the permanent and transitory components that are taken to correspond to long-run and cyclical movements, respectively. Absolute PPP, which relies on arbitrage in the trade account, may be stated as:

where *s _{t}* denotes the nominal exchange rate (domestic price of a unit of foreign exchange) at time

*t*,

*p*is the domestic price level,

_{t}*q*the reversions back to trend. Efficient markets PPP, which relies on capital account arbitrage, posits that the real exchange rate follows a random walk and therefore all of the exchange rate movements are driven purely by permanent components. Problems and pitfalls in constructing data to examine equation (1) and the empirical evidence are discussed in MacDonald (1995a).

^{T}_{t}Since price and inflation movements are linked to the business cycle—although there has been widespread discussion of whether in the current phase of the cycle in the United Kingdom and United States there has been a decoupling of this relationship—PPP could be used in a limited sense to address the central issue of this paper. However, since it excludes the variables central to the business cycle—namely, output and interest yields—PPP alone has only limited applicability to the task at hand and is therefore not a direct focus in this survey.

Perhaps the most useful general model in the current context is the two-country open economy IS-LM model with rational expectations, in which capital is assumed to be perfectly mobile and prices are sticky in the short run, with the central feature that the exchange rate moves to clear *both* goods and asset markets. This model is usually referred to as the extended, or eclectic, Mundell-Fleming model.^{1} This model has been set forth by various authors, including *inter alia*, Dornbusch (1976), Frankel (1979), Flood (1981), and Mussa (1982). Obstfeld (1985) provides a synthesis in a deterministic setting, while Clarida and Gali (1994) present a version with stochastic shocks.

From the perspective of this paper, the key component of the model is the condition of uncovered interest rate parity which governs relative nominal interest rates between countries:

where *E _{t}Δs_{t+k}* denotes the expected change in the exchange rate between periods

*t*and

*t*+

*k*,

*i*denotes a nominal interest rate with maturity

_{t}*k*, an asterisk denotes a foreign magnitude, a “prime” (′) indicates that a variable is defined as home relative to country (e.g.,

*x*′ =

*x*−

*x*

^{*}), and all variables apart from interest rates are in logs. Using the standard Fisher decomposition to define the real interest rate,

where

Equation (2) can also be rewritten in terms of the real exchange rate as:

This shows that a relatively lower domestic real interest rate must be compensated by the expectation of a real appreciation.

The demand for home output relative to foreign output,

A price setting equation captures short-run price inertia:

Equation (5) states that the price level in period *t* is an average of the market-clearing price expected at time *t*-1 to prevail at time *t*, *t*,

The relative money market equilibrium condition between the home and foreign country is given by:

where *m*^{′} denotes the relative money supply, *α* is the income elasticity of demand for money, and *β* is the interest rate semi-elasticity (the equation is defined so that *α* and *β* are positive).

In the presence of less than fully flexible prices, an exogenous fall in aggregate demand that pushes output below its trend will lead, other things being equal, to a relatively lower interest rate, a capital outflow, and an exchange rate depreciation (both real and nominal). For the lower interest rate to be consistent with interest parity, the currency must be expected to appreciate in both real and nominal terms; this appreciation takes place as demand returns to trend. The dynamic path of the exchange rate is the path that coincides with an increasing relative interest rate—the traditional capital flow relationship between the exchange rate and relative interest rates. Indeed, this is likely to be compounded if monetary authorities have an explicit reaction function in which interest rates are raised to attenuate inflationary pressure. If the recession is instead caused by an adverse supply shock, this would lead to an initial rise in the interest rate (real and nominal) and a currency appreciation (both real and nominal), with the consequent expectation of a currency depreciation being translated into an actual depreciation as supply returns to trend, with relative interest rates similarly falling. If a monetary tightening is the source of the recession (either through a fall in the supply of money or increased demand for money), interest rates would initially rise and the real exchange rate would appreciate on impact, eventually depreciating back to trend as output adjusted. The similarity of the effects of these two shocks means that it is in practice difficult to distinguish between their relative importance without imposing restrictions on the causal relationships between the variables, such as in Clarida and Gali (1994).

Although the Mundell-Fleming model stresses the importance of both goods and asset markets in determining exchange rates, it does not take into account stock-flow implications of asset accumulation or allow for time-varying exchange risk premia.

The “flexible price monetary model of exchange rates” (FPMM) can be derived from the above framework by assuming that prices are continuously flexible, purchasing power parity holds at all times, output is fixed at the full employment level, and there are no demand shocks:^{2}

Equation (7) asserts that in a flexible price equilibrium, an exchange rate is driven purely by conditions of asset market equilibrium (relative excess money supplies), with goods market conditions having no independent influence. In the flexible price variant of the monetary model, equation (7) is assumed to hold continuously in both the short and long run—see, among others, Bilson (1978), Frenkel (1978) and Hodrick (1987), while in the sticky price variant (SPMM) it holds only in the long run (see Dornbusch (1976) and Frankel (1979).

How useful is equation (7) from the perspective of thinking about business cycle issues? A stylized fact is that a currency typically appreciates in the upswing of an economic cycle and depreciates in the downswing. Equation (7) neatly captures this effect: higher income increases money demand and thus leads to an appreciation of the nominal exchange rate (and vice versa in a slump). This is consistent with a demand shock in the generalized model but not a supply shock. Since in the FPMM, output changes are driven only by supply side effects, the difference in the sign here relates to the fact that output affects the exchange rate only through the demand for assets, with relative prices moving to satisfy asset market equilibrium, and not through interest rates, which simply equal expected inflation. The FPMM must thus be regarded as having limited applicability for the task at hand since it ignores the relationship between asset yields and output.

Of course, equation (7) is usually estimated as a reduced form that could also be consistent with the more general eclectic model—for example, if interest rates are given a capital flow interpretation. That is, the domestic and foreign interest rates would, respectively, have negative and positive signs, and income a positive sign in the forecasting equation for the nominal exchange rate. This is brought out clearly by Frankel (1979) in a real interest differential (RID) variant of the monetary model. This assumes a form of regressive expectations in which the exchange rate is expected to change in proportion to the gap between the equilibrium and actual exchange rate and the expected inflation differential:

Equation (8) indicates that in long-run equilibrium, when

This indicates that whether *s _{t}* is above or below

The RID model may be thought of as relaxing the assumption of the FPMM that the expectations model of the term structure holds, replacing it instead with an assumption of market segmentation, so that a monetary impulse can have different effects on short and long interest rates. In particular, a monetary tightening can increase the short rate through the liquidity effect, while at the same time decreasing the long rate through an expected inflation effect. To the extent that the output expansion emanates from the supply side and thereby has a moderating influence on inflation (price movements), the business cycle could have an effect on exchange rates that is separate from that of interest yields. This effect relies on price flexibility, and would thus not be present in the case of sticky prices. Assuming

where the *s* and *l* superscripts denote short- and long-term interest rates, respectively. Although the RID reduced form is in the spirit of the eclectic Mundell-Fleming model, in terms of the relative interest rate effects, it nevertheless constrains output to have a purely asset market role in the exchange rate equilibrium process; as in the FPMM, increased output has a negative influence on the exchange rate. Indeed, this model has a long-run solution that is equivalent to that of the FPMM.

The above models all assume that non-money assets are perfect substitutes. However, proponents of the portfolio balance approach—Allen and Kenen (1980), Branson (1977), and Dornbusch and Fischer (1980)—argue that nonmoney assets are likely to be imperfect substitutes across countries, so that equation (8) holds only on a risk-adjusted basis. Dooley and Isard (1982) demonstrate that in a model in which there are two types of money (home and foreign) and two bonds (home and foreign), the risk premium, *θ _{t}*, may be defined by the following expression (see also Frankel (1983)):

where *B* denotes domestic non-money assets and *B** foreign non-money assets.

In the context of the above framework, Frankel (1983) and Hooper and Morton (1982) demonstrate that a reduced form in the spirit of the portfolio balance approach is:

Equation (12) is usually referred to as a hybrid model monetary-portfolio balance reduced form.^{3} The relationship between the net supply of non-money assets (effectively net foreign assets) and the risk premium is assumed to be positive in the portfolio model: an increased risk premium requires a currency depreciation to equilibrate asset markets. It is not entirely clear if the addition of a risk premium to equation (7) or (10) gives much insight with respect to the impact of the business cycle on the exchange rate. One way in which risk premia could be related to business cycles is through effects of the economic cycle on countries’ fiscal positions and thereby relative debt stocks. For example, governments often use the upswing of a cycle, and associated buoyant tax revenues, to repatriate government debt and, conversely, downswings often have implications for increased government debt as increased fiscal deficits drive up the outstanding stock of debt.

## A Review of the Empirical Evidence

This section reviews empirical evidence on the exchange rate-business cycle relationship. Evidence on the factors that influence nominal exchange rates is examined first, followed by several strands of the literature on the influences of real exchange rates.

### Nominal Exchange Rates and the Business Cycle

The most general monetary approach equation may be expressed as a reduced form:

where the φ’s are parameters to be estimated and ε_{t} is a disturbance term. The strict form of the monetary model implies φ_{1} = −φ_{2} = 1, while φ_{3} and φ_{4} should take on values that are close to estimated income elasticities from money demand functions, and φ_{5} and φ_{6} should take on values close to interest rate semi-elasticities also from money demand functions. The hypothesised values of unity for φ_{1} and φ_{2} are those expected, in equilibrium at least, from either the flex-price and fix-price monetary models. However, it is important to note that even within the monetary tradition there is a view that these coefficients may be less than one in absolute value; see, for example, Mussa (1979). There is a large body of empirical work on equation (13) and variants thereof; MacDonald and Taylor (1993) provide a survey.^{4} The focus here is on recent empirical work, the preponderance of which uses cointegration-based methods.

Table 4.1 presents a selection of estimates of equation (13); as is typical with cointegrated systems, the results indicate that the estimation procedure used makes a difference. For example, using the less efficient Engle-Granger method, there is no evidence of the expected long-run relationships, whereas there is clear evidence of cointegration when the more efficient Johansen (1995) method is used. The signs and magnitudes of coefficients are often far from those expected from a pure FPMM interpretation. However, the majority of cases show the negative association between the exchange rate and income consistent with the standard business cycle story that a country with relatively rapid income growth should have an appreciating exchange rate. The interest rate coefficients in Table 4.1 do not support a standard business cycle interpretation, but are, in general, supportive of the FPMM. For example, all but one of the coefficients on the short term interest rate differential are positive, thereby favoring the FPMM association between the exchange rate and the interest differential. There is, however, somewhat more support for the business cycle relationship when long interest rates are used (four out of six coefficients are correctly signed here).

**Cointegration Results for the Monetary Model**

*s _{t}* =

*m*+

_{t}*m*

^{*}

_{t}+

*y*+

_{t}*y*

^{*}

_{t}+

*i*+

_{t}*i*

^{*}

_{t}

**Cointegration Results for the Monetary Model**

*s _{t}* =

*m*+

_{t}*m*

^{*}

_{t}+

*y*+

_{t}*y*

^{*}

_{t}+

*i*+

_{t}*i*

^{*}

_{t}

Source, Currencies, Period | m | m^{*} | y | y^{*} | i^{s} | i^{s}^{*} | i^{l} | i^{l}^{*} | Cointegrated? Method? |
---|---|---|---|---|---|---|---|---|---|

Baillie-Selover (1987); ¥-$ | No | ||||||||

1973:3 to 1983:12 | 0.065 | … | 0.458 | … | 0.005 | … | 0.035 | … | Engle-Granger |

Baillie-Selover (1987); CS-$ | No | ||||||||

1973:3 to 1983:12 | −0.466 | … | −0.047 | … | 0.010 | … | −0.003 | … | Engle-Granger |

Kearney-MacDonald (1990): A$-$ | Yes | ||||||||

1984:1 to 1988:12 | 0.186 | … | 0.946 | … | 0.022 | … | −0.012 | … | Engle-Granger |

MacDonald-Taylor (1993); DM-$ | Yes | ||||||||

1976:1 to 1990:12 | 1 | … | −1 | … | 0.049 | −0.050 | … | … | Johansen |

MacDonald-Taylor (1994); £-$ | No | ||||||||

1976:1 to 1990:12 | −0.471 | 1.06 | −0.733 | −0.284 | … | … | −0.052 | 0.004 | Engle-Granger |

MacDonald-Taylor (1994); £-4 | Yes | ||||||||

1976:1 to 1990:12 | 0.209 | −0.49 | −0.098 | 0.646 | … | … | 0.035 | 0.086 | Johansen |

Cushman and others (1997); Turkish lira-$ | Yes | ||||||||

1981Q3−92Q4 | 0.21 | … | −1.13 | … | 1.14 | … | … | … | Johansen |

Kouretas (1997); C$-$ | Yes | ||||||||

1970:6−1994:5 | −0.12 | −0.79 | −0.32 | 032 | 0.08 | −0.02 | … | … | Dynamic OLS |

**Cointegration Results for the Monetary Model**

*s _{t}* =

*m*+

_{t}*m*

^{*}

_{t}+

*y*+

_{t}*y*

^{*}

_{t}+

*i*+

_{t}*i*

^{*}

_{t}

Source, Currencies, Period | m | m^{*} | y | y^{*} | i^{s} | i^{s}^{*} | i^{l} | i^{l}^{*} | Cointegrated? Method? |
---|---|---|---|---|---|---|---|---|---|

Baillie-Selover (1987); ¥-$ | No | ||||||||

1973:3 to 1983:12 | 0.065 | … | 0.458 | … | 0.005 | … | 0.035 | … | Engle-Granger |

Baillie-Selover (1987); CS-$ | No | ||||||||

1973:3 to 1983:12 | −0.466 | … | −0.047 | … | 0.010 | … | −0.003 | … | Engle-Granger |

Kearney-MacDonald (1990): A$-$ | Yes | ||||||||

1984:1 to 1988:12 | 0.186 | … | 0.946 | … | 0.022 | … | −0.012 | … | Engle-Granger |

MacDonald-Taylor (1993); DM-$ | Yes | ||||||||

1976:1 to 1990:12 | 1 | … | −1 | … | 0.049 | −0.050 | … | … | Johansen |

MacDonald-Taylor (1994); £-$ | No | ||||||||

1976:1 to 1990:12 | −0.471 | 1.06 | −0.733 | −0.284 | … | … | −0.052 | 0.004 | Engle-Granger |

MacDonald-Taylor (1994); £-4 | Yes | ||||||||

1976:1 to 1990:12 | 0.209 | −0.49 | −0.098 | 0.646 | … | … | 0.035 | 0.086 | Johansen |

Cushman and others (1997); Turkish lira-$ | Yes | ||||||||

1981Q3−92Q4 | 0.21 | … | −1.13 | … | 1.14 | … | … | … | Johansen |

Kouretas (1997); C$-$ | Yes | ||||||||

1970:6−1994:5 | −0.12 | −0.79 | −0.32 | 032 | 0.08 | −0.02 | … | … | Dynamic OLS |

Other particularly relevant cointegration-based studies analyze the joint interaction of UIP and PPP; these include Johansen and Juselius (1992), Juselius (1991, 1995), MacDonald and Marsh (1997, 1999), Juselius and MacDonald (1999), and La Cour and MacDonald (2000). This framework leads to a reduced form relationship similar to equation (9), with the empirical component involving estimation of a vector of the following form:

where the first term may be interpreted as the deviation from PPP, which in terms of equation (9) is

The first equation is a relationship for the deutsche mark-dollar exchange rate, while the second is for the yen-dollar rate. Both relationships are estimated over the period January 1983 to December 1997 using the Johansen methodology. In addition to showing the negative association between the exchange rate (both real and nominal) and the interest differential, these results indicate that the relationship is much stronger—by a factor of about 2½—for Japan than for Germany.

### Real Exchange Rates and the Business Cycle

This section examines direct empirical evidence on the real exchange rate—business cycle relationship, with particular emphasis on the relationship between the real exchange rate and real interest rate differentials. This is best explored by rearranging equation (3), the real UIP condition as:

Because the empirical work in the next section focuses on effective (multilateral) exchange rates rather than bilateral rates, the real exchange rate is henceforth written as foreign currency per home currency, so that an increase in *q* corresponds to an appreciation of the domestic currency. Equation (14) describes the current equilibrium exchange rate as determined by two components, the expectation of the real exchange rate in period *t* + *k* and the (negative of) the real interest differential with maturity *t* + *k*. It is commonplace in this literature—for example, Meese and Rogoff (1988)—to assume that the unobservable expectation of the exchange rate, *E _{t}(q_{t+k})*, is the “fundamental equilibrium exchange rate,” which is denoted by

One strand of this literature assumes that equation (15) is the sticky-price representation of the monetary model. With the further assumption that ex ante PPP holds, then

Regression-based estimates of the relationship between the real exchange rate and the real interest differential can conveniently be split into two groups: one that assumes the equilibrium real exchange rate equals a constant and therefore does not model its determinants, and a second that explicitly focuses on modeling these determinants. Papers that assume a constant equilibrium real rate typically focus on the following regression equation:

Equation (16) may be derived from (15) by assuming that the equilibrium rate, *β*_{0}. Edison and Melick (1999) demonstrate that the expected signs of β_{1} and β_{2} are positively proportional to the maturity of the long-term bonds underpinning the interest rates. However, in the derivation of equation (16) proposed by MacDonald and Nagasuya (1999), the only requirement is that β_{1} and β_{2} are positive and negative, respectively.

A number of single equation tests of the real exchange rate—real interest rate specification in equation (16) fail to uncover a statistically significant link between real exchange rates and real interest differentials, although the coefficients typically have the correct sign and are therefore consistent with the predictions of the Mundell-Fleming model. Papers in this category include Campbell and Clarida (1987), Meese and Rogoff (1988), Edison and Pauls (1993), Throop (1993), and Coughlin and Koedijk (1990).^{5} However, as in the PPP literature, the failure to find a statistically significant result seems to be a consequence of the particular estimator used. For example, MacDonald (1997), Clark and MacDonald (1998), and Edison and Melick (1999) utilize the econometric methods of Johansen and find clear evidence of both significant cointegration and correctly signed coefficients. Perhaps the most convincing evidence in favor of the real exchange rate-real interest rate relationship is contained in MacDonald and Nagasuya (1999), who use the panel cointegration estimator of Pedroni to examine a panel data set containing data for 14 industrial countries. Clear evidence is found of statistically significant cointegrating relationships and coefficient estimates that are supportive of the real interest rate-business cycle link. Table 4.2 summarizes results from these papers that clearly indicate that the traditional business cycle relationship is in the data for the major currencies.

**Estimates of the Real Exchange Rate-Real Interest Rate Relationship**

*q _{t}* =

*β*

_{0}+

*β*

_{1}

*r*+

*β*

_{2}

*r*

^{*}

*+*

_{t}*v*

_{t}**Estimates of the Real Exchange Rate-Real Interest Rate Relationship**

*q _{t}* =

*β*

_{0}+

*β*

_{1}

*r*+

*β*

_{2}

*r*

^{*}

*+*

_{t}*v*

_{t}Source, Currencies | β_{1} | β_{2} | |
---|---|---|---|

MacDonald (1998) | |||

Sample: 1975–1993, Quarterly | |||

Deutsche mark, effective | 0.116 | −0.189 | |

Yen, effective | 0.286 | −0.185 | |

U.S. dollar, effective | 0.406 | −0.328 | |

Clark and MacDonald (2000) | |||

Sample: 1960–1997, Annual | |||

Canadian $, effective | 0.578 (0.24) | … | |

U.K. pound, effective | 0.817 (0.11) | … | |

U.S. dollar, effective | 0.809 (0.51) | … | |

MacDonald and Nagasuya (1999) | |||

Sample 1974–1994, Quarterly | |||

Panel of 14 bilateral exchange rates | 0.834 (0.38) | … |

**Estimates of the Real Exchange Rate-Real Interest Rate Relationship**

*q _{t}* =

*β*

_{0}+

*β*

_{1}

*r*+

*β*

_{2}

*r*

^{*}

*+*

_{t}*v*

_{t}Source, Currencies | β_{1} | β_{2} | |
---|---|---|---|

MacDonald (1998) | |||

Sample: 1975–1993, Quarterly | |||

Deutsche mark, effective | 0.116 | −0.189 | |

Yen, effective | 0.286 | −0.185 | |

U.S. dollar, effective | 0.406 | −0.328 | |

Clark and MacDonald (2000) | |||

Sample: 1960–1997, Annual | |||

Canadian $, effective | 0.578 (0.24) | … | |

U.K. pound, effective | 0.817 (0.11) | … | |

U.S. dollar, effective | 0.809 (0.51) | … | |

MacDonald and Nagasuya (1999) | |||

Sample 1974–1994, Quarterly | |||

Panel of 14 bilateral exchange rates | 0.834 (0.38) | … |

Using the methods of Beveridge and Nelson to decompose real exchange rates into permanent and transitory components, Baxter (1994) also finds a statistically significant relationship between real exchange rates and real interest rates. Baxter argues that the previous failure to capture the real interest rate-real exchange rate relationship stems from the use of a first difference transformation (for example, Meese and Rogoff (1988) use this transformation). Although the difference operator ensures that *I*(1) variables are transformed into stationary counterparts, it also removes the medium and low frequency information from the data, thereby removing any implicit business cycle relationship. Moreover, first differencing the data presupposes that the effect of real interest rates on the real exchange rate is permanent, while to the extent that equation (16) represents a reduced form representation of the sticky price monetary model, the relationship between the two variables would be expected to be transitory.

Baxter (1994) regresses the transitory component of the real exchange rate to the real interest differential:

The dependent variable is obtained from a decomposition of the real exchange rate into transitory and permanent components; the specification assumes that the permanent component follows a random walk. Equation (17) is estimated for a number of bilateral country pairings, using both univariate and multivariate Beveridge-Nelson decompositions to derive *q ^{T}_{t}*, and both ex post and ex ante measures of the real interest differential. The majority of the estimates turn out to be positive and statistically significant, the exception being those for the United Kingdom, and her findings indicate that the favorable results reported above are not estimation-specific. This approach highlights the importance of examining the components of the variables that provide the relationship rather than discarding them by first differencing. The next section presents some new estimates of the real interest-rate real business cycle relationship using the methods of Baxter. However, before presenting these results, other methods by which to decompose real exchange rates into permanent and transitory components are first discussed.

### Distinguishing Permanent and Transitory Components of Real Exchange Rates

The decomposition of the real exchange rate into transitory and permanent components can be represented as:

q=_{t}q+^{P}_{t}q,^{T}_{t}

where *q ^{T}_{t}* is the transitory real exchange rate that corresponds to the cyclical component, and

*q*represents the permanent component. Assuming that the permanent component follows a random walk gives:

^{p}_{t}

q=^{P}_{t}μ+q+ ε^{P}_{t-1},^{P}_{t}

where μ is a trend representing differential productivity growth, and ε is a white-noise error. Since the transitory component simply equals a random stochastic term, there is clearly no business cycle-exchange rate relationship. However, if *q ^{T}_{t}* is assumed to be mean-reverting, this gives:

q= ρ^{T}_{t}q+ ε^{T}_{t-1}, 0<ρ<1^{T}_{t}

In this case, the real exchange rate has a transitory, mean-reverting component that may be interpreted as the part of the exchange rate related to the business cycle. The next section discusses methods used to carry out this decomposition, followed by a review of empirical results.

### Methods to Separate Permanent and Transitory Exchange Rate Movements

Perhaps the most popular method of decomposing real exchange rates (and indeed a range of other macro series) into permanent and transitory components is the ARIMA based (time-domain) procedure of Beveridge and Nelson (1981; henceforth BN). An ARIMA model of the first difference of the relevant series is estimated, and then the coefficients used to calculate the long-run multiplier, C(1). This facilitates construction of the permanent component which is in turn used to derive the cyclical component from the actual data.

Baxter and King (1995) discuss an alternative to the BN decomposition into permanent and transitory components, which is to use band-pass (BP) filters to decompose a series into components of movements within specific bands of frequencies. For example, Baxter (1994) decomposes the real exchange rate into three components: the *trend*, or long-term, component corresponding to movements with frequencies of greater than 32 quarters; the *business cycle* component of movements with frequencies between 6 and 32 quarters; and the *irregular* component of high frequency fluctuations (from 2 to 5 quarters). Statistical analysis can then be performed using only the business cycle components or only the trend/permanent components or some mix of these, with the aim of allowing a direct comparison of the business cycle elements of the various series. A further advantage of the BP filter over the BN decomposition is that it does not rely on the first difference operator, which as discussed by Baxter removes the frequencies in the data that are typically interpreted as corresponding to the cycle—in quarterly data, for example, movements with frequencies of 6 quarters or more.

While the BP filter and BN decomposition are both univariate in nature, there are a number of multivariate methods of extracting the business cycle component. The first is the multivariate version of the BN decomposition, which involves estimating a VAR model for two or more series and using matrix of long-run multipliers to extract the permanent and transitory components in a manner analogous to the univariate BN approach. An interesting conclusion to emerge from the widespread use of this method—see Evans (1989), Cochrane (1990), and King and others (1991)—is that if the information set includes variables that Granger-cause subsequent changes in the variable of interest, then the variance of the transitory component derived from such a system must exceed the ratio of the transitory component to the permanent component derived from a univariate BN decomposition. Both the multivariate and univariate BN models start by first differencing the data. In the presence of cointegrated variables, however, a VAR system constructed using only differences of variables will be misspecified since it fails to incorporate the stationary interactions of the levels of the variables. Such misspecifications can have important and significant implications for impulse response analysis. Gonzalo and Granger (1995) demonstrate how a vector of variables that exhibit cointegration may be decomposed into permanent and temporary components.

### Empirical Results

A useful starting point in testing for the importance of permanent components in real exchange rates are the tests of the time-series properties of real exchange rates using unit root testing methods. MacDonald (1999) surveys this literature, finding that real exchange rates typically do contain a unit root, implying that there is no significant transitory component in real exchange rates. However, it is well known that such tests have low power to reject the null of a unit run when it is in fact false. Using the variance ratio test, Huizinga (1987) argues that, on average, over 10 (industrial) currencies and 11 years of adjustment, around 60 percent of the variance of real exchange rates is permanent and 40 percent transitory (interestingly, after five years, the average value suggests that real exchange rates are driven solely by the permanent component). Huizinga then uses univariate BN decompositions to construct the long-run components of his chosen currencies and draw inferences about the extent of over or undervaluation of particular currencies. For example, the dollar is estimated to have been overvalued for the two-year period 1976-78, undervalued for the four-year period from late 1978 to late 1982, and overvalued for the three year period from early 1983 to early 1986. The post-1985 depreciation of the dollar is estimated to have been just right in terms of returning it to the long-run exchange value against the pound.

Cumby and Huizinga (1991) use a multivariate BN decomposition based on a bivariate VAR of the real exchange rate and the inflation differential to compare the permanent component of the real exchange rate with the actual rate for the dollar against the deutsche mark, yen, sterling, and Canadian dollar. The permanent components generally vary considerably over time but are somewhat more stable than the actual exchange rate, often leaving large and sustained deviations of real exchange rates from the predicted “equilibrium” values. These transitory deviations may be related to the business cycle, though the decomposition does not include a measure of real activity.

Clarida and Gali (1994) present both univariate and multivariate BN decompositions of the real exchange rates of Germany, Japan, Britain, and Canada vis-à-vis the U.S. dollar (the latter are generated from a trivariate VAR consisting of the change in the real exchange rate, output growth, and the inflation rate). The top half of Table 4.3 reports the results for the ratio of the variance of the BN transitory component to the variance of the total real exchange rate change. On average for the four exchange rates, the univariate results show that around 80 percent of the variance of the real exchange rate is permanent and only 20 percent transitory. This suggests that only a small part of real exchange rate movements are possibly related to business cycle fluctuations. For Germany and Japan, however, the picture changes quite dramatically with the multivariate decompositions, with 70 and 60 percent of the variance of movements in the respective real exchange rates attributed to transitory components. Clarida and Gali ascribe the difference in the results to the fact that in the dollar–deutsche mark and dollar-yen systems, inflation has significant explanatory power for real exchange rates even after taking into account past movements in real exchange rates and output.

**Permanent and Transitory Variance Ratios for the Real Exchange Rate**

^{1}Source: Clarida and Gali (1994).

^{2}Source: Baxter (1994).

**Permanent and Transitory Variance Ratios for the Real Exchange Rate**

Currencies | Trivariate System | Univariate System | |
---|---|---|---|

Ratio of transitory variance to actual variance^{1} | |||

DM-$ | 0.705 | 0.235 | |

Yen-$ | 0.591 | 0.233 | |

£-$ | 0.385 | 0.146 | |

C$-$ | 0.210 | 0.143 | |

Ratio of permanent variance to transitory variance^{2} | |||

DM-$ | 1.72 | 1.94 | |

Yen-$ | 0.67 | 1.68 | |

£-$ | 0.75 | 1.43 | |

C$-S | 0.72 | 1.45 | |

FF-$ | 2.43 | 2.30 |

^{1}Source: Clarida and Gali (1994).

^{2}Source: Baxter (1994).

**Permanent and Transitory Variance Ratios for the Real Exchange Rate**

Currencies | Trivariate System | Univariate System | |
---|---|---|---|

Ratio of transitory variance to actual variance^{1} | |||

DM-$ | 0.705 | 0.235 | |

Yen-$ | 0.591 | 0.233 | |

£-$ | 0.385 | 0.146 | |

C$-$ | 0.210 | 0.143 | |

Ratio of permanent variance to transitory variance^{2} | |||

DM-$ | 1.72 | 1.94 | |

Yen-$ | 0.67 | 1.68 | |

£-$ | 0.75 | 1.43 | |

C$-S | 0.72 | 1.45 | |

FF-$ | 2.43 | 2.30 |

^{1}Source: Clarida and Gali (1994).

^{2}Source: Baxter (1994).

Baxter (1994) also reports univariate and multivariate BN decompositions for a number of currencies; these are summarized in the bottom half of Table 4.3. The results for the univariate tests are similar to those of Clarida and Gali in that the permanent component of the real exchange rate always exceeds the transitory component, with the sharpest results for the pound. As with Clarida and Gali, however, the multivariate decompositions reveal that the transitory component dominates in several of the currency pairings, although the variance ratio for the sterling-dollar rate actually increases in the multivariate setting. Baxter also presents correlations of the permanent and transitory components across countries. For the univariate models, the permanent components are all strongly correlated across countries with correlation coefficients in excess of 0.5, but the transitory components show no such clear-cut pattern, with positive correlations for the deutsche mark-Swiss franc and French franc-Swiss franc rates (both vis-à-vis the dollar), but zero or negative correlations for most other currencies. The multivariate correlations, however, reveal much stronger evidence of positive correlations across countries; interestingly, the only currency pairings to produce negative correlations are those involving sterling. In summary, multivariate analysis appears to be necessary to provide substantial evidence of a business cycle component in real exchange rates.

### “Direct” Empirical Evidence

The identification scheme proposed by Clarida and Gali (1994) introduces structural shocks of supply, demand, and nominal (“monetary”) into the Mundell-Fleming framework. In the long run, the real equilibrium exchange rate is a function of demand and supply shocks, while in the short run, the existence of price stickiness means that the real exchange rate responds to nominal shocks as well as to demand and supply shocks. A positive supply side shock that boosts U.S. output relative to foreign output is predicted to produce a real depreciation of the dollar, a fall in U.S. prices, and higher U.S. output. A positive permanent demand shock leads to a permanent real appreciation of the dollar, a higher price level, and increased output to the extent that prices are sticky. A negative U.S. money supply shock results in a nominal dollar depreciation, higher U.S. price level, and increased U.S. output with sticky prices. If the nominal shock is permanent, it leads to a permanent dollar depreciation as well, but by construction not a permanent real depreciation. Clarida and Gali (1994) estimate the model using a structural VAR along the lines of Blanchard and Quah in which restrictions are placed on the permanent effects of shocks on certain variables while leaving the transitory, or short-term, effects unconstrained. The focus is on the sources of real exchange rate fluctuations since the inception of floating exchange rates for the bilateral exchange rates between the dollar and the deutsche mark, yen, pound, and Canadian dollar over the period 1974:Q1 to 1992:Q1. The imposed restrictions are that nominal shocks affect the price level in the long run but have only transitory effects on the real exchange rate and output; supply and demand shocks have permanent effects on the real exchange rate, but only supply shocks affect the long-run level of (relative) output. This approach has become increasingly popular, with additional exchange rates and variations on the included variables being estimated by (among many others) Chadha and Prasad (1997) for Japan, Astley and Garrett (1996) for the United Kingdom, and Thomas (1997) for Sweden.

Clarida and Gali find that at a horizon of 4 quarters, nominal shocks account for about 50 and 30 percent of the variance of the mark and yen rates, respectively, with the effect eventually diminishing to zero at longer horizons. However, nominal shocks have only a small influence on exchange rates for Canada and the United Kingdom, accounting for only around 1 percent of the movements in these currencies against the U.S. dollar. For all four real exchange rates, demand shocks account for virtually all of the remaining variance, leaving little role for supply shocks.

The impulse response analysis for the dollar-deutsche mark exchange rate suggests that the real exchange rate depreciates by 3.8 percent (the nominal rate overshoots by 4 percent) in response to a one standard deviation nominal shock, while U.S. output rises relative to German output by 0.5 percent and U.S. inflation rises relative to German inflation by 0.3 percent. The output and real exchange rate effects of a nominal shock last for 16 to 20 quarters. In response to a one standard deviation shock to relative demand, the dollar appreciates in real terms by 4 percent vis-à-vis the deutsche mark, U.S. relative output rises by 0.36 percent, and there is a 0.44 percent rise in U.S. inflation relative to Germany. The effect of the demand shock on the exchange rate is permanent, with a 6 percent real appreciation after 20 quarters. A one standard deviation relative supply shock produces a (wrongly signed) 1 percent dollar appreciation in quarter 2, but this quickly goes to zero, with the appreciation after 20 quarters only 0.2 percent above the initial exchange rate.

Chadha and Prasad (1997) apply the Clarida-Gali approach to the yen-dollar real exchange rate over the period 1975-96. Supply shocks are found to account for two-thirds of the variance in Japanese output growth relative to the United States, with demand shocks explaining one-third, and nominal shocks playing only a very small role (this is the case for forecast horizons through 40 quarters). After around 8 quarters, supply and demand shocks each account for roughly one quarter of the forecast error variance of the real exchange rate, leaving the remaining 50 percent explained by nominal shocks. Chadha and Prasad interpret this as suggesting that monetary and fiscal policy have a substantial effect on the dollar-yen real exchange rate over the business cycle (the transitory fluctuations), with only a small role for supply shocks such as innovations in productivity shocks. Although this result suggests that supply shocks have not been pervasive, it is also found that these shocks are important when they do occur, as a “typical” supply shock (that is, a shock of one standard deviation in magnitude) leads to a permanent real exchange rate depreciation of around 8 percent, while a demand shock leads to a permanent appreciation, also of around 8 percent. A nominal shock leads to an initial real depreciation, but this is eventually offset with the real rate exchange rate returning to the initial level by the end of two years.

Although the approach of Clarida and Gali and others is insightful and certainly in the spirit of the relationship between exchange rates and the business cycle, as discussed by Stockman (1994), it nonetheless suffers from a number of important problems. First, the identification procedure forces all temporary shocks that are common to the three variables of output, inflation, and exchange rates to have a nominal origin, so that the transitory effects of events such as oil price shocks and changes in fiscal policy are subsumed under nominal shocks. A similar argument holds for temporary demand shocks. Second, in setting up the identifying assumptions, it is assumed that the innovations to demand and supply are uncorrelated, which, for a variety of reasons, seems implausible (i.e., a positive shock to aggregate demand spurs investment, which increases the capital stock and thus aggregate supply). Third, the finding that nominal shocks generally account for only a small part of movements in relative output raises the question of whether this is due to the way nominal shocks are specified.^{6}

The empirical work on real exchange rate relationships can be summarized in the following way. The real exchange rates of leading industrial countries have important transitory components, the magnitude of which depends on the particular currency and the methods used to decompose permanent and transitory fluctuations. In the applications so far, the richer the information set in terms of the number of variables used, the larger is the transitory component relative to the permanent component.

Irrespective of the methods used, empirical evidence based on the real exchange rate-real interest rate model points to the importance of transitory components such as business cycle fluctuations in explaining movements in real exchange rates. This is particularly the case for the deutsche mark and yen, but less so for the pound. However, these findings are based in a sense on averages constructed from data for the post-1973 period of floating rates, which could possibly disguise important regime shifts such as financial deregulation that occurred in the 1980s. This deregulation potentially increased the mobility of capital and thus affected the relationship between interest rates and exchange rates.

## New Empirical Evidence

In this section, new evidence on the exchange rate-business cycle relationship is provided using data for the major four pre-EMU currencies—the deutsche mark, yen, pound sterling, and dollar. The analysis includes both the bilateral values against the dollar and a real effective exchange rate for all four currencies.

### Data Description and Some Stylized Facts

Since most empirical work on exchange rate modeling utilizes monthly data, this tradition is followed here. To be consistent with the effective exchange rates, all real exchange rates are constructed as the foreign currency per unit of domestic currency, so that an increase in the real exchange rate represents a domestic appreciation. The data span the period from January 1975 to October 1997. Real bilateral exchange rates are constructed for the deutsche mark, yen, and pound vis-à-vis the U.S. dollar by subtracting relative CPI growth—monthly inflation—from the (log) nominal exchange rate. The effective real exchange rates are constructed by taking a weighted average of the real bilateral rates of the other 6 industrial countries, with bilateral trade volumes as the weights. This permits construction of an effective real exchange rate for the U.S. dollar vis-à-vis the rest of the world. Foreign prices and interest rates are constructed in an analogous fashion, with real interest rates constructed using a 12-period backward-looking moving average of inflation. Annual interest rates are divided by 1,200 to provide monthly rates, while the inflation rate is the one month change in the log of the price level. Other measures of the real interest rate such as the one period ex post and the one period ex ante rates give quantitatively similar results.

Figures 4.1 to 4.3 show the bilateral real exchange rates and real interest rates between the U.S. dollar and the three other currencies. These charts essentially confirm the point made in the last section that although many econometric studies have failed to unearth a statistically significant relationship between real exchange rates and real interest rates, simple observation—an “ocular regression”—suggests that there is in many instances the expected positive relationship (positive, given the way the real exchange rate is defined).

For Germany, Figures 4.1 shows that movements in real long-term interest rates coincide with the appreciation of the deutsche mark in the late 1970s and the subsequent depreciation through 1982, as well as the appreciation from 1985-91. However, there are also periods such as 1981-84 and 1992-94 during which there is little apparent association between the real exchange rate and the real interest differential. A positive relationship also emerges when short-term interest rates are used, with the positive relationship working better for the periods from 1981-84 and 1992. This suggests that both short- and long-term interest rates are needed to pin down the real exchange rate-real interest rate relationship, possibly because long rates capture the determinants of capital mobility, while short rates capture monetary-side liquidity effects arising from price stickiness.

For the dollar-yen bilateral rate in Figure 4.2, the positive real exchange rate-real interest rate relationship seems to work best when long rates are used, with the real differential tracking the exchange rate fairly well through 1986. In contrast to the deutsche mark, short rates do not seem to add explanatory power to long rates. Figure 4.3 provides similar results for the U.K. pound, with long- and short-term interest rates again having differential periods of explanatory power. Short rates do best in explaining the dramatic appreciation of sterling in the late 1970s, although neither interest rate explains much of the subsequent depreciation (not surprisingly, since this is thought to have been largely driven by the dollar). It has become something of a stylized fact that the dollar appreciation from 1980-85 is difficult to explain solely in terms of fundamentals (see, for example, MacDonald (1988). The sterling long-term interest rate differential does, however, pick up the positive association at other times, such as 1989-91 and 1995-96.

**Japan: Real Bilateral Exchange Rate and Interest Rate**

(1975 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**Japan: Real Bilateral Exchange Rate and Interest Rate**

(1975 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**Japan: Real Bilateral Exchange Rate and Interest Rate**

(1975 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Real Dollar Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Real Dollar Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Real Dollar Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

In summary, Figures 4.1 to 4.3 suggest two important stylized facts. First, the positive real exchange rate-real interest rate relationship, synonymous with the business cycle in many exchange rate models, is clearly “in the data” for the leading currencies. Second, in general terms, short and long interest rates have different effects over the business cycle, so that econometric work that excludes one or the other in trying to tie down the real exchange rate-real interest rate link is likely to produce a misspecified relationship. This is important, since most of the work surveyed in the previous section focuses on one pair of interest rates at a time.

Figures 4.4–4.7 show the effective exchange rate counterparts to the bilateral relationships. These largely confirm the discussion above. A clear positive association is seen between real exchange rates and the real interest rate differential in all charts, though this is perhaps not as striking as in the bilateral data, and there are again some important differences between short and long rates. Figure 4.7 for the United States is worth highlighting. There is a close relationship between the real effective exchange rate and the real long-term interest rate differential; this is particularly evident for the steep rise of the dollar in the early 1980s and the depreciation starting in 1985. Indeed, interest rate effects seem to account for much of this episode.

**Germany: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**Germany: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**Germany: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**Japan: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**Japan: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**Japan: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**United States: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**United States: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

**United States: Real Effective Exchange Rate and Interest Rate Differential**

(1990 = 100 for exchange rate; in percentage points for interest rate)

Sources: IMF,*International Financial Statistics*; and authors’ calculations.

### Using Band-Pass Filters to Focus on the Business Cycle Relationships

A second set of stylized facts is derived from the decomposition of the real exchange rate-real interest rate relationship into irregular, business cycle, and trend components using band-pass filters. As discussed above and following Baxter (1994), the irregular components are movements with frequencies of 6 to 15 months (corresponding to 2 to 5 quarters); the business cycle component is composed of movements with frequencies from 18 to 96 months (corresponding to 6 to 32 quarters); and the trend component is movements with frequencies greater than 96 months (corresponding to 8 years or more). The filtered data are constructed using 36 monthly leads and lags, again corresponding to Baxter’s use of 12 quarters. This means that 36 observations are lost at each end of the sample period. The bilateral band-pass results are shown in Figures 4.8–4.10, while Figures 4.11–4.14 provide the results using effective (multilateral) data.

**Germany: Band-Pass Filter of Real Bilateral Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Germany: Band-Pass Filter of Real Bilateral Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Germany: Band-Pass Filter of Real Bilateral Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Japan: Band-Pass Filter of Real Bilateral Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Japan: Band-Pass Filter of Real Bilateral Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Japan: Band-Pass Filter of Real Bilateral Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Band-Pass Filter of Real Bilateral Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Band-Pass Filter of Real Bilateral Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Band-Pass Filter of Real Bilateral Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Germany: Band-Pass Filter of Real Effective Exchange Rate and Real Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Germany: Band-Pass Filter of Real Effective Exchange Rate and Real Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Germany: Band-Pass Filter of Real Effective Exchange Rate and Real Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Japan: Band-Pass Filter of Real Effective Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Japan: Band-Pass Filter of Real Effective Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**Japan: Band-Pass Filter of Real Effective Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Band-Pass Filter of Real Effective Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Band-Pass Filter of Real Effective Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**United Kingdom: Band-Pass Filter of Real Effective Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**United States: Band-Pass Filter of Real Effective Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**United States: Band-Pass Filter of Real Effective Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

**United States: Band-Pass Filter of Real Effective Exchange Rate and Interest Rate Differential**

*International Financial Statistics*; and authors’ calculations.

Figures 4.8–4.10 show that there is a clear business cycle component to the real exchange rates and real interest differentials, with in many instances the expected positive association suggested by most models. In some cases, however, the correlation between exchange rates and interest rates is actually not as apparent with the bandpass filters as in the raw data of Figures 4.1–4.7. A possible reason for this is that although the data have been decomposed into three separate components, the charts focus on only one at a time, and the remaining components also contain information on the relationship between exchange rates and business cycles. For the deutsche mark and the yen, the positive association seems clearest at the business cycle and irregular frequencies, while for the pound, all three frequencies exhibit the positive association, especially for short-term interest rates.

Figures 4.11–4.14 show the decompositions for effective (multilateral) exchange rates and interest rate differentials. These are similar to their bilateral counterparts, with many instances of the expected positive relationship between interest rates and exchange rates at both business cycle and other frequencies. In contrast to the bilateral data, however, the decompositions for the pound sterling in Figure 4.13 suggest a negative association between the exchange rate and the real interest differential; this is particularly clear at the business cycle frequency. It is noteworthy that as in the raw data, differences arise between the results with short- and long-term interest rates; this is most notable in the case of the pound. An interesting result with both bilateral and effective exchange rates is that at the irregular frequency, the filtered interest rate differentials often anticipate exchange rate movements with the correct sign. This is evident, for example, in Figure 4.12 for the yen, where the two turning points in the yen series in 1988 and 1991 are predicted by prior turns in the high-frequency interest rate differential.

Table 4.4 presents the results of regressions of the business cycle component of the real bilateral and effective exchange rates on the business cycle components of the real interest rate differentials (both short- and long-term interest rates in the same regression). The results using bilateral exchange rates confirm the expected positive relationship between the real exchange rate and the interest differential for all exchange rates and both interest rates. For all three currencies against the dollar, the coefficients are of the same order of magnitude for each interest rate maturity, with larger effects of interest rates on exchange rates for long rates than for short rates. The U.K. pound is different from the other two currencies in that the coefficient on the short rate, although smaller in magnitude than that on the long rate, is estimated far more precisely and accounts for most of the explanatory power of the regression. This is consistent with the findings of Baxter (1994) and Clarida and Gali (1994) that the bilateral relationship between the pound sterling and the dollar is different from the dollar-yen and dollar—deutsche mark relationships. The regression results for the multilateral exchange rates are less consistent, with a negative relationship between the exchange rate and short-term interest rate differentials for the yen, pound, and dollar, and a negative coefficient for the long-term interest rate for the deutsche mark and pound sterling.

**Business Cycle Components of Real Exchange Rates and Real Interest Rate Differentials**

*q _{t}* =

*α*+

*β*(

_{s}*r*−

_{t}*r*)

^{*}_{t}*+*

_{short}*β*

_{1}(

*r*−

_{t}*r*)

^{*}_{t}*+*

_{long}*U*

_{t}*t*-statistics in parentheses.

**Business Cycle Components of Real Exchange Rates and Real Interest Rate Differentials**

*q _{t}* =

*α*+

*β*(

_{s}*r*−

_{t}*r*)

^{*}_{t}*+*

_{short}*β*

_{1}(

*r*−

_{t}*r*)

^{*}_{t}*+*

_{long}*U*

_{t}Currency | Interest Rate Maturity | Bilateral | Multilateral |
---|---|---|---|

Deutsche mark | Short | 0.331 | 0.453 |

(0.98) | (2.28) | ||

Long | 1.377 | −0.129 | |

(5.20) | (−047) | ||

Yen | Short | 1.033 | −1.596 |

(1.18) | (−3.24) | ||

Long | 1.135 | 4.181 | |

(1.69) | (5.83) | ||

Pound sterling | Short | 0.741 | −0.364 |

(21.41) | (−1.38) | ||

Long | 1.255 | −1.775 | |

(4.12) | (−3.49) | ||

U.S. dollar | Short | … | −4.468 |

(−4.90) | |||

Long | … | 7.616 | |

(6.24) |

*t*-statistics in parentheses.

**Business Cycle Components of Real Exchange Rates and Real Interest Rate Differentials**

*q _{t}* =

*α*+

*β*(

_{s}*r*−

_{t}*r*)

^{*}_{t}*+*

_{short}*β*

_{1}(

*r*−

_{t}*r*)

^{*}_{t}*+*

_{long}*U*

_{t}Currency | Interest Rate Maturity | Bilateral | Multilateral |
---|---|---|---|

Deutsche mark | Short | 0.331 | 0.453 |

(0.98) | (2.28) | ||

Long | 1.377 | −0.129 | |

(5.20) | (−047) | ||

Yen | Short | 1.033 | −1.596 |

(1.18) | (−3.24) | ||

Long | 1.135 | 4.181 | |

(1.69) | (5.83) | ||

Pound sterling | Short | 0.741 | −0.364 |

(21.41) | (−1.38) | ||

Long | 1.255 | −1.775 | |

(4.12) | (−3.49) | ||

U.S. dollar | Short | … | −4.468 |

(−4.90) | |||

Long | … | 7.616 | |

(6.24) |

*t*-statistics in parentheses.

### Clarida and Gali Revisited: A Bilateral and Multilateral Perspective

This section estimates the structural VAR of Clarida and Gali to examine the influences of supply, demand, and nominal shocks on exchange rates. As noted above, this involves placing long-run restrictions on a three-variable VAR with relative output growth, real exchange rate growth, and relative inflation. The restrictions are that nominal shocks are restricted to affect only prices in the long run with no permanent effect on output or the real exchange rate; demand shocks affect both inflation and the real exchange rate in the long run but have no permanent effect on output; and supply shocks have permanent effects on all three variables. No constraints are imposed on the short-run effects of any of the shocks on any of the three variables. Two important differences between the implementation here and that of Clarida and Gali are that the sample period used is longer, spanning the period 1978-97, and the use of both bilateral and effective exchange rates rather than solely bilateral rates. Quarterly data are used to maintain comparability with the results of Clarida and Gali, with eight lags in each equation.

Table 4.5 presents the variance decompositions for the (growth rate of) the quarterly bilateral real exchange rates at the forecast horizons of 1, 4, 12, 20, and 40 quarters. Since 36 quarters is usually taken as the limit of the business cycle, these horizons illustrate the extent to which different shocks drive the real exchange rate over the business cycle. Since the demand and nominal shocks have no permanent effects on output, these can be interpreted as pertaining to the business cycle, whereas the supply shock reflects the long-run forces of productivity and thrift that lead to permanent changes in the output. Note that demand shocks have permanent effects on real exchange rates—an assumption that is in itself controversial—however, they are labeled as a “cyclical” factor because they have only transitory effects on output.

**Variance Decompositions for the Real Exchange Rate from the Structural VAR**

**Variance Decompositions for the Real Exchange Rate from the Structural VAR**

Bilateral Exchange Rate | Multilateral Exchange Rate | |||||
---|---|---|---|---|---|---|

Quarter | Supply | Demand | Nominal | Supply | Demand | Nominal |

Germany | ||||||

1 | 12.0 | 76.4 | 11.6 | 14.7 | 73.1 | 12.2 |

4 | 12.8 | 67.8 | 19.4 | 16.9 | 70.0 | 13.1 |

12 | 19.7 | 61.5 | 18.7 | 19.1 | 67.6 | 13.3 |

20 | 20.6 | 61.0 | 18.4 | 19.3 | 67.3 | 13.4 |

40 | 20.7 | 60.9 | 18.4 | 19.3 | 67.2 | 13.5 |

Japan | ||||||

1 | 2.0 | 60.1 | 37.9 | 8.5 | 13.4 | 78.1 |

4 | 6.2 | 58.7 | 35.1 | 7.8 | 16.4 | 75.8 |

12 | 3.4 | 51.3 | 40.3 | 8.7 | 17.8 | 73.5 |

20 | 8.8 | 50.8 | 40.4 | 12.8 | 17.2 | 70.0 |

40 | 8.8 | 50.8 | 40.4 | 13.3 | 17.1 | 69.6 |

United Kingdom | ||||||

1 | 23.9 | 75.9 | 0.2 | 4.5 | 72.8 | 22.7 |

4 | 23.1 | 69.8 | 7.1 | 9.2 | 66.8 | 24.0 |

12 | 25.8 | 63.3 | 10.9 | 10.6 | 66.7 | 22.7 |

20 | 25.6 | 62.2 | 12.2 | 10.9 | 66.4 | 22.7 |

40 | 25.5 | 61.9 | 12.6 | 11.0 | 66.4 | 22.6 |

United States | ||||||

1 | … | … | … | 41.7 | 58.3 | 0.0 |

4 | … | … | … | 49.2 | 49.3 | 1.5 |

12 | … | … | … | 46.9 | 45.1 | 8.0 |

20 | … | … | … | 46.2 | 44.9 | 8.9 |

40 | … | … | … | 46.0 | 45.0 | 9.0 |

**Variance Decompositions for the Real Exchange Rate from the Structural VAR**

Bilateral Exchange Rate | Multilateral Exchange Rate | |||||
---|---|---|---|---|---|---|

Quarter | Supply | Demand | Nominal | Supply | Demand | Nominal |

Germany | ||||||

1 | 12.0 | 76.4 | 11.6 | 14.7 | 73.1 | 12.2 |

4 | 12.8 | 67.8 | 19.4 | 16.9 | 70.0 | 13.1 |

12 | 19.7 | 61.5 | 18.7 | 19.1 | 67.6 | 13.3 |

20 | 20.6 | 61.0 | 18.4 | 19.3 | 67.3 | 13.4 |

40 | 20.7 | 60.9 | 18.4 | 19.3 | 67.2 | 13.5 |

Japan | ||||||

1 | 2.0 | 60.1 | 37.9 | 8.5 | 13.4 | 78.1 |

4 | 6.2 | 58.7 | 35.1 | 7.8 | 16.4 | 75.8 |

12 | 3.4 | 51.3 | 40.3 | 8.7 | 17.8 | 73.5 |

20 | 8.8 | 50.8 | 40.4 | 12.8 | 17.2 | 70.0 |

40 | 8.8 | 50.8 | 40.4 | 13.3 | 17.1 | 69.6 |

United Kingdom | ||||||

1 | 23.9 | 75.9 | 0.2 | 4.5 | 72.8 | 22.7 |

4 | 23.1 | 69.8 | 7.1 | 9.2 | 66.8 | 24.0 |

12 | 25.8 | 63.3 | 10.9 | 10.6 | 66.7 | 22.7 |

20 | 25.6 | 62.2 | 12.2 | 10.9 | 66.4 | 22.7 |

40 | 25.5 | 61.9 | 12.6 | 11.0 | 66.4 | 22.6 |

United States | ||||||

1 | … | … | … | 41.7 | 58.3 | 0.0 |

4 | … | … | … | 49.2 | 49.3 | 1.5 |

12 | … | … | … | 46.9 | 45.1 | 8.0 |

20 | … | … | … | 46.2 | 44.9 | 8.9 |

40 | … | … | … | 46.0 | 45.0 | 9.0 |

At all horizons, demand shocks are the most important influence on movements of the bilateral exchange value of all three currencies with the dollar, with these shocks being somewhat less important in Japan, where around 50 percent of the variance is attributable to demand shocks by quarter 40, compared to just over 60 percent for Germany and the United Kingdom. The remaining variance in Germany is split roughly evenly between the supply and nominal shocks, while for Japan the nominal shock is nearly as important as the real shock. Nominal shocks hardly matter in the United Kingdom, a result that matches the findings of Clarida and Gali. Following the interpretation that the sum of the demand and nominal shock represents the business cycle, the results using bilateral data vis-à-vis the dollar indicate that around 90 percent of the variance of the Japanese yen and German mark exchange rates are driven by business cycle influences, with the remaining 10 percent reflecting longer-run supply factors. These results are generally similar to those of Clarida and Gali, the main difference being that in their results the German demand shock explains a smaller proportion of the total variance than the Japanese shock.

Figure 4.15 shows the responses of the real exchange rate to one standard deviation shocks to supply, demand, and nominal shocks (each shock represents an increase in the home variable relative to the foreign variable). Demand and supply shocks have similar effects across the three currencies, producing an initial appreciation reaching about 4 to 6 percent in the case of the demand shock and 2 percent for the supply shock. Although the demand shock is correctly signed in terms of the underlying model, the supply shock is not, as the model predicts that the currency should depreciate in real terms. In Japan, the effect of the supply shock eventually goes to zero, in constrast to the permanent appreciations experienced in Germany and the United Kingdom. The nominal shock produces an initial depreciation for the mark and yen with overshoots of 2 and 4 percent, respectively, before the effect of the nominal shock goes to zero (by construction). In contrast, for sterling the nominal shock produces a wrongly signed real appreciation of 2 percent before dying out. These results are in general similar to Clarida and Gali, particularly the perversely signed result of supply shocks for Germany and the United Kingdom.

**Real Bilateral Exchange Rate: Response to Shocks**

**Real Bilateral Exchange Rate: Response to Shocks**

**Real Bilateral Exchange Rate: Response to Shocks**

The VAR results are next used to pick out the cyclical component of the real exchange rate. This is done by using the interpretation given above that demand and nominal shocks are cyclically related, in that these two shocks have only transitory effects on output in the Clarida-Gali framework. The level of the real exchange rate with no cyclical effects is calculated by subtracting the cumulated forecast errors attributed to demand and nominal shocks from the actual value of the real exchange rate. Figure 4.16 shows the actual real exchange rates for the deutsche mark, yen, and pound sterling against the dollar and the calculated real exchange rate without cyclical effects. In interpreting these results, it is important to bear in mind that the supply side shocks are wrongly signed for all three currencies and that a date must be chosen for each currency in which it is assumed that there are no cyclical effects on the exchange rate; the results are thus relative to this baseline, as changing the date would not change the pattern of the exchange rate calculated without cyclical effects but would move the whole series up or down. In the case of the mark, the results suggest that business cycle factors played little role in the depreciation of the mark from 1978-81, since the exchange rate with no cyclical effects is essentially identical to the actual exchange rate (that is, supply side factor largely caused the depreciation). However, cyclical factors had an important role in the further depreciation from 1982-85 and the subsequent appreciation through 1986—that is, the exchange rate would have been smoother without cyclical effects. Cyclical factors appear to have mainly contributed to the strength of the deutsche mark against the dollar in late 1994 and early 1995. For the bilateral yen-dollar rate, the post-1981 depreciation seems to have been driven by both supply and cyclical factors, although the sustained post-1985 appreciation is explained in large measure by cyclical influences (particularly demand rather than nominal shocks, though these are not distinguished in Figure 4.16). Cyclical factors appear to have driven the strength of the yen against the dollar in 1994. For sterling, it is interesting to note that supply shocks played an important role in the post-1986 appreciation of sterling, possibly reflecting the impact of the Thatcher reforms in labor markets.

**Structural VAR: Real Bilateral Exchange Rate**

**Structural VAR: Real Bilateral Exchange Rate**

**Structural VAR: Real Bilateral Exchange Rate**

Table 4.5 shows that the variance decompositions for the exchange rate using multilateral data contain some important differences with the bilateral counterparts. This is most striking for Japan, where the nominal shock now explains the predominant component of the variance of the real rate, nearly 70 percent after ten years, followed by demand and then supply shocks. For the United Kingdom, nominal shocks are more important and supply shocks less with the multilateral data than was the case against the dollar, while the reverse is the case in Germany.^{7} The total contribution of the business cycle shocks (demand and nominal) in explaining exchange rate movements is quite similar across the three currencies—85 to 90 percent—leaving about 10 to 15 percent of exchange rate movements explained by supply side factors. This is not the case for the United States, where nominal shocks account for less than 10 percent of exchange rate movements, with demand shocks explaining more than supply shocks initially but roughly equal shares after a few quarters.

The impulse responses using multilateral data are shown in Figure 4.17. As with the bilateral data, demand shocks eventually lead to permanent real appreciations of all currencies. A nominal shock again leads to initial real depreciations before an appreciation back to zero, though with substantially more persistence in the case of the yen. However, the key difference concerns the effect of the supply shock on the real rate. In the bilateral case this was wrongly signed for all three currencies. With the multilateral data, however, the initial effects of this shock are correctly signed for Germany and Japan, though the long-term effects on the exchange rate in these countries and the United Kingdom are fairly small. However, the effect of a supply shock remains perverse for the dollar.

**Response of Real Effective Exchange Rate to Shocks**

**Response of Real Effective Exchange Rate to Shocks**

**Response of Real Effective Exchange Rate to Shocks**

Figure 4.18 shows the four real effective exchange rates and the values calculated by taking out business cycle influences. For Germany, the results are fairly similar to those from the bilateral exchange rate with the dollar: supply factors explain the movements in the effective exchange value of the deutsche mark through 1984, cyclical factors account for the subsequent weakness and then appreciation and depreciation through 1989, and then supply factors again explain the appreciation of the deutsche mark from 1991 to 1994. As with the bilateral exchange, the appreciation from 1994–95 is explained by Germany’s relatively strong cyclical position (relative being an important word in this instance, since German output returned essentially to trend in 1994 after several years above potential). For Japan, the 1986-90 appreciation of the yen is again explained by cyclical factors, but the appreciation through 1995 is largely driven by positive supply shocks. The 1996 collapse of the yen, however, is driven entirely by cylical factors. In the multilateral data, the sustained downward trend in sterling through the late 1980s is largely explained by the cyclical nominal and demand shocks. Indeed, the positive supply side effects of the Thatcher era would have implied an appreciation of the real effective rate (given the perverse result of the impulse response), but this was offset by demand effects, possibly associated with financial deregulation. Finally, the results using the effective exchange value of the dollar suggest that cyclical factors account for an important part of the dollar appreciation in the first part of the 1980s.

**Real Effective Exchange Rate**

**Real Effective Exchange Rate**

**Real Effective Exchange Rate**

## Conclusions

This study has explored the relationship between the business cycle and the exchange rate, both through a selective survey of the exchange rate literature and by generating some new empirical results. That this is the first attempt at providing a comprehensive overview of this relationship may in part reflect the fact that the exchange rate-business cycle link is at best only implicit in most exchange rate models.

Perhaps the clearest theoretical link between the economic cycle and the exchange rate is contained in the extended Mundell-Fleming model: a cyclical expansion of output, for example, squeezes liquidity which, in turn, puts upward pressure on the home interest rate and leads to an appreciation of the exchange rate. It is this relationship which is most the focus of this chapter. However, there are other links. For example, the monetary model of the exchange rate also predicts that an output expansion leads to an exchange rate appreciation, although the channel is more direct: prices must fall to maintain money market equilibrium and, through PPP, this leads to an exchange rate appreciation. In the portfolio balance model, a risk premium is also an important influence on the exchange rate, and risk premia could be related to business cycles through the effect of the cycle on countries’ fiscal positions and thereby relative debt stocks. However, evidence of a foreign exchange risk premium is weak at best, so that this avenue is not explored in this chapter.

Empirical evidence generally supports the theoretical connection between business cycles and exchange rates. This is true both for the direct connection between output and exchange rates as in the monetary approach, and for the more general link between exchange rates and interest rates. This is particularly the case when interest rates and exchange rates are decomposed into transitory and permanent components, as is done in this paper with band-pass filters. Finally, evidence from structural VARs shows that business cycle factors are the dominant factor in accounting for recent exchange rate movements in the United States, Germany, Japan, and United Kingdom.

The existence of a relationship between business cycles and exchange rates has important implications for policy and multilateral surveillance. When business cycles are not synchronized across countries, variations in exchange rates can play a useful stabilizating role, especially when economies are open and internationally integrated. The link between exchange rates and business cycles means that the existence of desynchronized expansions across countries in effect provides a “safety valve” for inflationary pressures, as changes in exchange rates can lead to a redistribution of demand from countries near the top of their business cycles to those where demand is weak and there is spare capacity. A challenge for policy evaluation is to distinguish exchange rate movements warranted by international cyclical divergences from movements due to changes in medium-term fundamentals or episodes of overshooting or gross misalignments.

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^{}1

Extended because of the inclusion of forward-looking expectations and an explicit supply side relationship, both of which are features missing from the original Mundell-Fleming model.

^{}2

This framework can also be derived from the generalized asset pricing model of Lucas (1982).

^{}3

Strictly speaking, this relationship relies for its derivation on a short-long distinction that is not made in this paper.

^{}4

Hoffman and Schlagenhauf (1983), Finn (1986), Woo (1985) and MacDonald and Taylor (1993) test the rational expectations or forward looking version of this expression; see De Jong and Husted (1995) for a critique of this approach.

^{}5

Throop (1993) reports some evidence for cointegration between real exchange rates and the real interest rate differential, but this is not robust to a small sample correction.