Exchange Rates and the Term Structure of Interest Rates

James M. Boughton

doi:10.5089/9781451956771.024.A002

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Exchange Rates and the Term Structure of Interest Rates

Author: Mr. James M. Boughton

Publication Date:: 01 Jan 1988

eISBN:: 9781451956771

Language:: English

Keywords:: SP; primary-commodity-exporting country; commodity price; Kähkönen hold; liberalization program; Laursen-Metzler effect; Exchange rates; Real exchange rates; Consumption; Dollarization; Income tax systems; Middle East; Sub-Saharan Africa; Central America; North Africa; Southern Europe; Global; interest rate differential; rate of depreciation; interest differential; cross-equation restriction; term-structure equation; Yield curve; Long term interest rates; Short term interest rates; Europe

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Empirical tests of exchange rate models in recent years have established that the exchange rates of major currencies follow a pattern that approximates a random walk but that may also be explained in some part by financial market theory. Although standard monetary models have not succeeded in capturing exchange rate movements, some portfolio-balance models have shown more promise. This paper extends one such model by incorporating information about the term structure of interest rates to determine whether exchange rate movements have been linked more closely to short- or long-term interest rates and to see whether the performance of the model can be improved by the inclusion of this more detailed information.

Abstract

The issue of whether it is principally short- or long-term rates that matter for exchange rate determination is important because differentials among interest rates in the large industrial countries have behaved quite differently across the maturity spectrum. Figure 1 shows differentials between nominal U.S. interest rates and a weighted average of nominal rates in the next four largest countries (Japan, the Federal Republic of Germany, France, and the United Kingdom), along with an index of the effective exchange rate between the United Stales and those countries. The first, rather obvious, point illustrated by this figure is that there is no simple causal relationship between exchange rates and interest rate differentials, whether the differentials are short or long run. Whatever relationships exist can be uncovered only by allowing for the joint endogeneity of these variables. But it is also clear that the surface impression of the interactions must depend on the maturity to which the interest rates apply.^¹

Broadly speaking, the U.S. dollar appreciated slightly from 1973 through 1976, then depreciated through 1980, appreciated through 1984, and then turned downward once again. Meanwhile, nominal short-term interest differentials moved favorably, in general, for dollar-denominated assets through 1981 before trending downward, whereas the favorable trend on long-term differentials persisted through 1984. Figure 2, which shows the same data in real rather than nominal terms, also shows marked differences in patterns between short- and long-term differentials. Note especially that there was no discernible trend in short-term real differentials from 1979 through 1984, whereas long-term differentials moved sharply in favor of dollar-denominated assets.

These differences are difficult to interpret. That long-term differentials appear to be more closely related to exchange rate swings, at least during the early 1980s, lends itself to several interpretations. The correlation could imply that long-term real differentials are what mattered most in contributing to the dollar’s strength in that period; that the negative effect on U.S. economic activity from the currency appreciation had a stronger negative pull on short-term U.S. interest rates than on long-term rates; or that greater arbitrage (that is, smaller risk premiums) in short-term markets tended to pull those differentials toward zero; and so forth. All that can be inferred from Figures 1 and 2 is that the choice of maturity is not trivial.

The question of whether short- or long-term interest rates should be more important in explaining exchange rate movements is theoretically ambiguous except under fairly strict assumptions. At one extreme, as-sume that all interest-bearing assets are perfect substitutes and that purchasing power parity (PPP) holds continuously.^² In this case, nominal interest rate differentials between countries will purely reflect differ-entials in expected inflation rates or—equivalently—expected movements in the nominal exchange rate. In the absence of anticipated shifts in the inflation rate, nominal interest differentials should be identical at all maturities, and one could equally well choose any maturity. It is easily established that these conditions have not held in practice, even to a weak approximation. The observation that nominal differentials have varied widely across the maturity spectrum implies that market participants have a complex expectation about the time path of the future inflation rate, that assets at different maturities have differing degrees of substitutability, that PPP does not hold in the short run, or some combination of the above.

One popular way of relaxing this strict combination of assumptions is to assume that the real exchange rate may depart from its PPP level for a substantial period of time, but that it is always expected to return home at a fixed speed.^³ With this assumption added to the others above, the real exchange rate will appreciate in response to a positive real interest differential. In this case, the choice of maturity is still immaterial be-cause the real interest differential is expected to decline geometrically as the maturity lengthens. To illustrate, let

\begin{matrix} ɛ = \hat{π} - λ (ρ - \bar{ρ}) & (1) \end{matrix}

\begin{matrix} \hat{i} - ɛ = 0, & (2) \end{matrix}

where

ε = the expected rate of depreciation

π = the expected inflation rate

ρ= the logarithm of the real exchange rate

i = the instantaneous rate of return.

A circumflex (̂) indicates a differential between the home country and abroad, and the bar indicates a long-run equilibrium value.

Because λ in this type of model is assumed to be a constant, ε - $\hat{π}$ (and, therefore, the real interest differential) must be expected to decline over time as ρ approaches p. That is, next period’s short-term real interest rate differential must be smaller than this period’s because the real exchange rate for the next period must be expected to be closer to its equilibrium value than it is today. If one assumes that long-term interest rates reflect the expected path of short-term rates and that the expected inflation rate is the same in the short run and long run, the term structure of the interest rate differential will be fully determined by equations (1) and (2). Furthermore, the interest rate differential will approach the expected inflation differential as the maturity approaches infinity. Again, it appears that this stylized scenario is far from descriptive of the data for major countries: real long-term differentials, at least ex post, are frequently larger than those for short-term assets.

Another way of viewing the term-structure relationship is to abandon the assumption that the exchange rate is expected to return to equilibrium at a fixed rate, and to assume instead that it will return to equilibrium by a certain date. As long as no restrictions are imposed on the adjustment path, there is no necessary relationship between long-and short-term interest differentials. Furthermore, short-term differentials will be irrelevant because they will bear no necessary relationship with the size of the current disequilibrium in the exchange rate. A very simple version of this type of model (see Shafer and Loopesko (1983)) may be written as follows:

\begin{matrix} ρ = e - \hat{p} & (3) \end{matrix}

\begin{matrix} ρ - \bar{ρ} = (e - \bar{e}) - (\hat{p} - \hat{\bar{p}}) & (4) \end{matrix}

\begin{matrix} e - \bar{e} = N {\hat{i}}_{n} & (5) \end{matrix}

\begin{matrix} \hat{p} - \hat{\bar{p}} = N \hat{π}, & (6) \end{matrix}

where

e = the logarithm of the nominal exchange rate

p = the logarithm of the price level

i_n = the interest rate for an asset of maturity of N years.

Equation (3) defines the real exchange rate, and equation (4) de-scribes the departure of the real exchange rate from its long-run equi-librium value. Equation (5) is the integral version of equation (2); it states that—under the assumption of uncovered interest parity—the gap between the current exchange rate and its equilibrium value must be equal to the cumulative difference in returns on assets denominated in the two currencies. The value of N must be at least as great as the length of time that the exchange rate is expected to take to return to equi-librium.^⁴ Finally, equation (6) notes that the total expected change in relative price levels is equal to the cumulated differential in expected inflation rates.

The solution to this model is

\begin{matrix} ρ = \bar{ρ} + N {\hat{r}}_{n}, & (7) \end{matrix}

where ${\hat{r}}_{n}$ is the real interest rate differential for a maturity of N years. Clearly, this model implies that one should look at long-term rather than short-term interest rates, unless one wishes to argue that PPP can in general be expected to be restored over short periods. In addition, the model leads to another very strong conclusion: the slope coefficient in a regression linking interest differentials and exchange rates should rise proportionally with the length to maturity. An equation such as (7) that is estimated using ten-year bonds should yield a coefficient of 10, and one with twenty-year bonds should yield a coefficient of 20. Empirical tests of this model by Shafer and Loopesko (1983) and by Boughton (1987) rejected this strong version.^⁵

Further relaxation of restrictions—for example, to allow for shifts in the long-run equilibrium real exchange rate, more flexible expectations processes for either exchange rates or interest rates, or limited substi-tutability among securities denominated in different currencies—would in general imply that both short- and long-term interest rates would matter in the determination of the exchange rate. Given the poor per-formance of the more restricted models, such generalizations would appear to be warranted. The difficulty is to know just how to specify a less restricted model while retaining tractability.

Section I sets out a portfolio-balance model in which both short- and long-term interest rate differentials affect exchange rate movements. Section II presents empirical estimates of the model, and Section III discusses some simulation exercises. Conclusions are offered in Section IV.

I. Theoretical Considerations

Development of a model that incorporates both short- and long-term interest rate differentials must begin by considering the nature of the rigidities or imperfections that are hypothesized to break down the simpler relationship. As noted above, the simplest models are invalidated by the direct observation of nominal differentials that vary across the term structure. In general, two types of hypothesis may be advanced to gener-ate a less restricted model. First, the degree of substitutability—that is, the magnitude of the “risk premium”—may not be uniform across the maturity spectrum. Second, the expected rate of depreciation might not be uniform.^⁶

Several papers in recent years have tested the first of these null hy-potheses—invariance of the risk premium across the maturity spec-trum—jointly with a specific expectations hypothesis, usually that of perfect foresight. That is, market participants are assumed to have had unbiased expectations of the time path of the exchange rate that actually occurred. The nonlinearity of observed exchange rate paths implies that considerable variance could have occurred in the term structure of nom-inal interest rate differentials without violating the joint null hypothesis.

Evidence on models of this type (maturity-independent risk premium and perfect foresight) has been mixed. A few studies—notably Clarida and Campbell (1987) and Park (1985) —have found that short- and longer-term “expected” differentials tend to move together, but several others—including Hakkio and Leiderman (1986), Longworth (1985), and Giovannini (1980)—have presented tests that lead to rejection of the null hypothesis. Without going into the details of these various tests, it seems safe to assert that there is a sufficient empirical basis for concluding that it is worth considering models that allow for a maturity-dependent elasticity of substitution (risk premium), a maturity-dependent (and non-perfect-foresight) expected rate of depreciation, or both.

Another recent line of research has focused on the possibility that investors view the determination of the exchange rate differently in the short run and long run, on the grounds that “fundamental” factors have less of an effect on short-run movements The rationale for such an assumption might be that groups of investors have preferred maturity habitats and have expectations that are not necessarily consistent with those of other groups. To take the simplest case, one group (say, arbi-traging firms) might invest only in assets with maturities of no more than thirty days and might act on the basis of static expectations with respect to the nominal exchange rate: portfolio decisions in this market would be made on the basis of nominal short-term interest differentials. Another group (say, pension funds) might invest only in securities with maturities of ten years or more and might have expectations based on the return of the real exchange rate to a perceived PPP level; portfolio decisions in this market would be based on expected real long-term interest rate differentials.

Estimates of the importance of different expectations processes have been generated by Frankel and Froot (1987). Their tests were based on surveys of market expectations over horizons ranging from one week to one year with respect to the exchange rate between the U.S. dollar and the Japanese yen. Frankel and Froot concluded that short-term expec-tations were characterized in large part by “bandwagon” effects, where-as longer-term expectations took account of the possibility of a return toward an equilibrium rate. They also argued that such behavior may be irrational because it seems to imply that investors on average expect to be able to ride a short-run bandwagon but get off ahead of the market. If the markets for widely spaced maturities are effectively segregated, however, each investor could be behaving rationally within the confines of a particular maturity habitat.

These general considerations can be developed into a portfolio-balance model of exchange rate determination characterized by pre-ferred habitats in terms of both currency denomination and maturity. The basic structure for the analysis that follows is adapted from Boughton (1983, 1984).

The first structural relationship in this two-country model is a demand function for securities denominated in the foreign currency (f, expressed as a percentage of total net financial assets); this demand is hypothesized to be determined by expected returns relative to returns available on similar securities that are denominated in the home currency. For sim-plicity, it is assumed that there are two available maturities (short, s; and long,l). Aggregating the demands for the two maturities gives the following equation:

\begin{matrix} f^{d} = f_{0} - f_{1} ({\hat{i}}_{l} - ɛ_{l}) - f_{2} ({\hat{i}}_{s} - ɛ_{s}) . & (8) \end{matrix}

Next, it is hypothesized that short- and long-term exchange rate ex-pectations are formed by independent processes. Long-term expecta-tions are founded on PPP: the nominal exchange rate is expected to depreciate at the rate of the expected inflation differential between the two countries. That is, investors do not attempt to take account of any difference between the current level of the real exchange rate and its unknown PPP (or fundamental equilibrium) level, and they therefore expect the real exchange rate to follow a random walk.^⁷ This hypothesis is expressed by

\begin{matrix} ɛ_{l} = \hat{π} . & (9) \end{matrix}

In contrast, short-term expectations are hypothesized to be founded on one of two concepts: either that the nominal exchange rate will follow a random walk (ε_s = 0) or that it will depreciate at a rate equal to the nominal interest differential ( $ɛ_{s} = {\hat{i}}_{s}$ ). The latter condition will hold if short-term securities are perfect substitutes, since arbitrage will then ensure that the nominal interest rate differential equals the expected rate of depreciation. A more general hypothesis, incorporating these two notions as special cases, is that the short-run expected rate of depreci-ation is a weighted average of the rate determined by arbitrageurs and by speculators with static expectations:

\begin{matrix} ɛ_{s} = θ {\hat{i}}_{s}, & (10) \end{matrix}

where θ = 1 under perfect arbitrage and θ = 0 under static expectations.

The supply of foreign-currency assets is assumed to be determined in the long run by the cumulated balance on private capital flows between the two countries (-k). In the short run, however, this equality will not necessarily hold because capital flows can be financed in either currency. The real exchange rate is hypothesized to equate continuously the de-mand for foreign-currency assets with the existing stock; that stock, however, may adjust gradually over time. Hence there will be an adjust-ment process in response to gaps between f_d and — k:

\begin{matrix} Δ ρ = λ_{1} (f^{d} + k) . & (11) \end{matrix}

Equation (11) does not fully capture the adjustment process in the model because the current account (hence the capital account) balance will itself respond gradually to changes in the real exchange rate. Equa-tion (12) is a highly simplified version of this real-sector adjustment, which assumes that the Marshall-Lerner condition is satisfied with a one-period lag:

\begin{matrix} Δ k = k_{0} - k ρ_{- 1} . & (12) \end{matrix}

Equation (12) obviously does not adequately capture the dynamics of the adjustment process, but it should at least reflect the medium-term role of the real exchange rate as an influence on the current account balance.^⁸ A more complete representation would include a lengthy distributed lag on the real exchange rate.

Equations (8)—(12) constitute a partial equilibrium block explaining changes in the exchange rate. Assuming for simplicity that domestic prices are determined exogenously, one may write the block solution conveniently in terms of the real exchange rate:

\begin{matrix} ρ = λ_{1} (f_{0} + k_{0}) - λ_{1} f_{1} {\hat{r}}_{1} - [λ_{1} f_{2} (1 - θ)] {\hat{i}}_{s} + (1 - λ_{1} k) ρ_{- 1} + λ_{1} k_{- 1} . & (13) \end{matrix}

Most of the structural parameters of the block may be identified by estimating equation (13), the major exception being that 8 and/; cannot be disentangled.^¹

An interesting feature of equation (13) is that the exchange rate is affected by nominal short-term interest differentials and by real long-term differentials. This property is a consequence of the different na-tures of the two hypothesized expectations functions, since inflation matters only in the longer run. Given this hypothesis, there is an econo-metric advantage to the formulation because these two differentials are less collinear than would be the case for two nominal or two real differentials at different maturities.^¹⁰

The model may be closed by the specification of an interest rate block comprising a money market (determining the short-term interest rate) and either a term-structure equation or some other representation of the determination of the long-term interest rate. Equation (14) is a straight-forward money demand equation, in which the demand for real money balances is related to real income and the nominal short-term interest rate:

\begin{matrix} M^{d} / p = l_{0} + l_{1} y - l_{2} i_{s} . & (14) \end{matrix}

As a general proposition, the money demand function could also include long-term interest rates and other rates of return, such as the inflation rate and Tobin’s q. Long-term rates, however, may be eliminated on the assumption that the selection among interest-bearing securities is sepa-rable from the choice between money and bonds in asset holders’ utility functions.^¹¹ For simplicity, rates of return on physical assets are ignored.

The supply of money is expressed as a reaction function in which the arguments are the targeted money stock (μ) and the short-term real interest rates both at home and abroad. For a given monetary target, money growth will be allowed to rise in response to a rise in the domestic real interest rate, although it is also assumed that some effort will be made to keep domestic real rates in line with those prevailing abroad. These considerations lead to:

\begin{matrix} M^{s} = m_{0} + m_{1} μ + m_{2} r_{s} - m_{3} r_{s}^{*} . & (15) \end{matrix}

Changes in the nominal short-term interest rate are assumed to be determined by the state of excess demand in the money market:^¹²

\begin{matrix} Δ i_{s} = λ_{2} (M^{d} - M^{s}) . & (16) \end{matrix}

This dynamic condition, together with the two market-equilibrium func-tions, determines the level of the short-term rate. The reduced-form solution to this sub-block is:^¹³

\begin{matrix} i_{s} = β_{0} + β_{1} Y - β_{2} μ + β_{3} π + β_{4} r_{s}^{*} + β_{5} i_{s . - 1} & (17) \end{matrix}

The final requirement for the model is an equation that determines the long-term interest rate. There are at least two approaches to consider: a term-structure equation or a reduced-form equation summarizing the “fundamental” macroeconomic factors related to long-term rates. Un-fortunately, neither approach has been applied with notable success in the empirical literature.

Many attempts have been made to estimate term-structure equations on the basis of expectations theory, and in general the results have not supported the theory. Mankiw (1986, p. 63), for example, summarized the evidence on the term structure in four major countries and concluded that “fluctuations in the slope of the yield curve... largely reflect changes in the term premium”; however, “neither [of the leading the-ories of the term premium] seems able to explain observed interest rate fluctuations.” Mankiw therefore explains the data through a simple conditional forecasting equation that is not founded on a specific theory of market behavior:

\begin{matrix} i_{l} - i_{s} = s_{0} - s_{1} (i_{s} - i_{s, - 1}) - s_{2} (i_{s, - 1} - i_{s, - 2}) + s_{3} (i_{l, - 1} - i_{s, - 1}) . & (18) \end{matrix}

Note that equation (18) is included in the model not to “explain” the term structure but to take into account the observed empirical regu-larities between short- and long-term interest rates.

An alternative approach would be to derive a reduced-form equation summarizing the relationships between long-term interest rates and other macroeconomic variables. This approach has been used in many studies, going back to the portfolio-balance analysis of Feldstein and Eckstein (1970). These authors estimated an equation in which the yield on U.S. corporate bonds was related to private gross national product (GNP), the stock of government debt, the monetary base (all in real per capita terms), and the expected inflation rate. More recent studies have re-estimated this type of equation over a longer data base and have found results quite different from, and in general with a poorer fit than, the original. (See, for example, Barth, Iden, and Russek (1984-85), who found that several variations on this theme that had appeared to be successful are actually rather unstable.) An apparent exception, how-ever, was the study by De Leeuw and Holloway (1985), in which the yield on three-year U.S. government bonds was related to the monetary base, the cyclically adjusted federal debt, and the expected inflation rate.

The “structural” approach would, in principle, be more consistent with the specification of the above model: unlike the term-structure approach, it does not require the assumption of effective arbitrage be-tween short- and long-term asset markets. In view of the limited empir-ical success for both approaches, however, the best way to describe the determination of long-term interest rates remains an open question. For the present study, tests have been made both with equation (18) and with structural equations similar to those just described; the results reported below use equation (18). Similar results were obtained with the alterna-tive structures because in all cases the behavior of long-term rates is primarily autoregressive; neither short-term rates nor the various struc-tural variables contribute much explanatory power.

II. Empirical Estimates

The semi-reduced-form model represented by equations (13). (17), and (18) was estimated for the three largest industrial countries—the United States, Japan, and the Federal Republic of Germany—using monthly data for the period from May 1973 through December 1985. For the United States, the “rest of the world”—that is, the region that is relevant for measuring foreign variables and the exchange rate—was taken to be a weighted average of the next four largest industrial coun-tries: Japan, Germany, France, and the United Kingdom, with the weights being approximately those used in measuring the SDR. For the other countries, the rest of the world is the United States. (For discussion of the rationale for this weighting pattern, see Boughton (1984).) A detailed description of the data is given in the Appendix.

Estimation of the three-equation model was based on the assumption that real private domestic demand (y) and national price levels (mea-sured by the deflator for y) are exogenous; although not strictly credible, this assumption certainly should be much more applicable to these large countries than it would be to others, and more applicable to the domestic demand deflator than to consumer prices. In addition, the short-term interest rate in the United States has been taken as a control variable, eliminating equation (17) for that country. Estimation of equation (17) was not helpful for the United States, perhaps because monetary tar-geting may have been applied less consistently there than in Japan or Germany.

Even with these variables given, there remain several simultaneities and cross-equation restrictions in the model. Notably, the foreign inter-est rates in the U.S. equations are weighted averages of variables that are determined endogenously elsewhere. Consequently, the model was esti-mated as a simultaneous system of eight behavioral relations (equations (13), (17), and (18) for Japan and Germany, and equations (13) and (18) for the United States) and three identities defining the endogenous foreign interest rates.^¹⁴ This system was estimated by an iterative full-information, maximum-likelihood (FIML) routine with linear cross-equation constraints, using a modified Newton-Raphson procedure to maximize the likelihood function.^¹⁵

^{Table 1.}

Estimated Reduced-Form Equations

Note: Numbers in parentheses are asymptotic t-ratios.

^{^a/}The t-ratios are for difference from unity, not zero.

^{^b/}For long-term interest rate.

^{Table 1.}

Estimated Reduced-Form Equations

					Fed. Rep. of
		Description of Term	United States	Japan	Germany
		Equation (13): Real exchange rate
Long-term real			-0.112	-0.015	-0.102
		interest differential	(2.17)	(0.25)	(1.78)
Short-term nominal			-0.160	-0.117	-0.214
		interest differential	(2.94)	(2.01)	(2.89)
Lagged real exchange rate^{^a}/			0.978	0.975	0.950
			(1.85)	(1.26)	(3.04)
Cumulated external balance			0.057	-0.009	0.032
			(2.62)	(0.15)	(2.33)
	Root mean-square error		0.071	0.102	0.111
		Equation (17): Short-term interest rate
Real income			—	2.428	2.322
				(1.64)	(2.20)
“Targeted” money growth			—	-0.647	-0.891
				(1.04)	(2.31)
Expected inflation rate			—	0.045	0.134
				(4.65)	(3.61)
Real short-term			—	0.012	0.069
		foreign interest rate		(0.89)	(3.94)
Lagged interest rate^{^a}/			—	0.949	0.909
				(3.19)	(4.29)
	Root mean-square error		—	0.178	0.217
		Equation (18): Term structure
Change in short rate			-0.801	-0.649	-0.372
			(34.55)	(6.41)	(3.23)
Lagged change in short rate			-0.059	-0.055	-0.034
			(2.50)	(1.19)	(1.14)
Lagged term structure”			0.968	0.990	0.967
			(2.96)	(0.84)	(3.04)
	Root mean-square error^_b/		0.094	0.086	0.054

Note: Numbers in parentheses are asymptotic t-ratios.

^{^a/}The t-ratios are for difference from unity, not zero.

^{^b/}For long-term interest rate.

^{Table 1.}

Estimated Reduced-Form Equations

					Fed. Rep. of
		Description of Term	United States	Japan	Germany
		Equation (13): Real exchange rate
Long-term real			-0.112	-0.015	-0.102
		interest differential	(2.17)	(0.25)	(1.78)
Short-term nominal			-0.160	-0.117	-0.214
		interest differential	(2.94)	(2.01)	(2.89)
Lagged real exchange rate^{^a}/			0.978	0.975	0.950
			(1.85)	(1.26)	(3.04)
Cumulated external balance			0.057	-0.009	0.032
			(2.62)	(0.15)	(2.33)
	Root mean-square error		0.071	0.102	0.111
		Equation (17): Short-term interest rate
Real income			—	2.428	2.322
				(1.64)	(2.20)
“Targeted” money growth			—	-0.647	-0.891
				(1.04)	(2.31)
Expected inflation rate			—	0.045	0.134
				(4.65)	(3.61)
Real short-term			—	0.012	0.069
		foreign interest rate		(0.89)	(3.94)
Lagged interest rate^{^a}/			—	0.949	0.909
				(3.19)	(4.29)
	Root mean-square error		—	0.178	0.217
		Equation (18): Term structure
Change in short rate			-0.801	-0.649	-0.372
			(34.55)	(6.41)	(3.23)
Lagged change in short rate			-0.059	-0.055	-0.034
			(2.50)	(1.19)	(1.14)
Lagged term structure”			0.968	0.990	0.967
			(2.96)	(0.84)	(3.04)
	Root mean-square error^_b/		0.094	0.086	0.054

Note: Numbers in parentheses are asymptotic t-ratios.

^{^a/}The t-ratios are for difference from unity, not zero.

^{^b/}For long-term interest rate.

The estimation results for the system are summarized in Table 1. It is difficult to assess adequately the goodness of fit for a system of interdependent equations such as this. The coefficient of determination(R²) for the system is .9667, but this high value reflects in part the presence of lagged endogenous variables in several equations. An alternative, which is especially useful for reduced-form exchange rate equations, is to calculate F”-statistics in relation to the variance of changes in the dependent variable. An equation that explains a significant portion of the variance of changes in real exchange rates may be judged to fit the data about as well as other estimates; this point is discussed in Boughton (1987). The fits for all of the exchange rate equations listed in Table 1 are significant at the 99 percent confidence level.^¹⁶

Also of interest is the evaluation of serial correlation in the error processes of the individual equations, which could signal a mis-specification or the omission of important influences. For the model shown in Table 1. some first-order serial correlation—measured by Durbin’s h-statistic—appears to be present in the term-structure equations for the United States and Germany, and for the interest rate equations for Germany and Japan, In addition, the Japanese term-structure equation appears to have some higher-order serial correlation, as measured by the Box-Pierce X²-statistic. Software limitations make it quite cumbersome to try to correct for serial correlation in this model, so the affected equations are presented as is. Nonetheless, the equations that are of key interest—the exchange rate equations—seem to have well-behaved and uncorrelated error processes.

The exchange rate equations for the United States and Germany are broadly satisfactory in terms of sign and significance levels of the coefficients. Both short-term and long-term interest differentials are significantly related to exchange rate movements (except for Japan, where the long-term differential is insignificant). The portfolio effect is significant for both the United States and Germany but is essentially zero for Japan. As for the interest rate and term-structure equations, the signs are all as hypothesized, and most appear to be significant. Again, the equations for Japan are less satisfactory than those for the other two countries.

Table 2 presents estimates of the structural coefficients derived from the reduced-form regressions. To obtain these coefficients, it was necessary to assume values for θ (the short-term expectations parameter) and l₁ (the income elasticity of the demand for money). For simplicity, 0 has been set to zero (so that the nominal exchange rate is expected to follow a random walk in the short run), and l₁ has been set to unity; the effects of different assumptions could, of course, be readily calculated.

With these assumptions, a rise of 1 percentage point in the short-term interest differential is shown to induce a shift in desired portfolios toward home-currency assets amounting to 2 percent of total portfolios in the United States and 3¼ percent of total portfolios in Germany. (The effect in Japan cannot be estimated because of the reversed sign on λ₁ in equation (13),) The effects of shifts in long-term differentials are some-what larger: 2¾ percent in the United States and 6¾ percent in Germany.

The estimates of λ₁ suggest that a 1 percent increase in the demand for foreign-currency assets, or a 1 percent decrease in the stock of such assets outstanding, will lead to a 5¾ percent depreciation in the real effective exchange rate for the U.S. dollar. For Germany the depreciation amounts to 3¼ percent, whereas for Japan there is a statistically insignificant perverse effect. To complete the circle, the estimated values for K suggest that a 1 percent depreciation in the real exchange rate will generate a strengthening of the current account balance amounting to less than ½ of 1 percent of portfolios for the United States and just over 1½ percent for Germany. A perhaps more familiar way of expressing this estimate is that a 10 percent real depreciation would strengthen the U.S. current account balance by 1¼ percent of GNP; for Germany the strengthening is estimated at a very strong 3½ percent of GNP.

^{Table 2.}

Structural Coefficients

Source: Derived from Table 1, under the assumptions that θ = 0 and l₁ = 1.

^{Table 2.}

Structural Coefficients

	Coefficient	United States	Japan	Fed. Rep. of Germany
Equation (8)
	f₁	1,951	—	3.231
	f₂	2.788	—	6.779
Equation (11)
	λ₁	0.057	-0.009	0.032
Equation (12)
	K	0.388	—	1.572
Equation (14)
	1₂	—	0.002	-0.019
Equation (15)
	m₁	—	0.266	0.384
	m₂	—	0.019	0.058
	m₃	—	0.005	0.030
Equation (16)
	λ₂	—	2.557	2.553

Source: Derived from Table 1, under the assumptions that θ = 0 and l₁ = 1.

^{Table 2.}

Structural Coefficients

	Coefficient	United States	Japan	Fed. Rep. of Germany
Equation (8)
	f₁	1,951	—	3.231
	f₂	2.788	—	6.779
Equation (11)
	λ₁	0.057	-0.009	0.032
Equation (12)
	K	0.388	—	1.572
Equation (14)
	1₂	—	0.002	-0.019
Equation (15)
	m₁	—	0.266	0.384
	m₂	—	0.019	0.058
	m₃	—	0.005	0.030
Equation (16)
	λ₂	—	2.557	2.553

Source: Derived from Table 1, under the assumptions that θ = 0 and l₁ = 1.

The money demand equations display semi-elasticities with respect to short-term interest rates (l₂) that are close to zero. On the supply side, however, there is a significant influence from domestic interest rates, in real terms. Therefore, in this model the observed negative correlation between nominal interest rates and the stock of money that is usually attributed primarily to the shape of the demand function is instead attributed to the authorities’ reaction functions. A rise in the inflation rate in this system raises the nominal interest rate but (in the short run) lowers the real rate; through the reaction function, money growth is then reduced.

The reaction functions for Germany and Japan also suggest that foreign interest rates have an influence that is perhaps a fourth to a half as large as that of domestic interest rates. Finally, the adjustment function (equation (16)) for the money markets in both countries is such that a 1 percent rise in the demand for money, or reduction in supply, will induce a rise in the level of domestic short-term interest rates of about 2½ percentage points.

III. Simulations

To test the performance of the model and to evaluate its implications regarding the importance of various determinants of exchange rates, several simulation experiments were run. These included dynamic simulations over the full sample period and counterfactual simulations that control for changes in selected variables.

In contrast to the single-equation estimation errors or the results of static full-model simulations, the dynamic simulations allow the prediction errors to cumulate over time. For a highly autoregressive process such as those generating changes in exchange rates, the errors are likely to cumulate rather than to be offsetting. As Hendry has emphasized, this cumulation of errors should not be regarded as evidence against the validity of the model, but only as an evaluation of the joint influence of the variables that have been treated as exogenous in the specification of the model.^¹⁷ In the present case, these nonmodeled variables include inflation rates, lagged monetary growth, real domestic demand, and lagged external balances.

The results of this exercise are shown in Figure 3. It is readily seen that the amplitudes of exchange rate swings are greatly understated. This finding is typical of all asset-market exchange rate models. The nonmodeled variables are themselves highly autoregressive, and so the simulated time path for the exchange rate tends to be quite smooth and not to reflect the actual, more erratic behavior of the exchange rate. What is sought is a measure of the extent to which the model picks up the direction and the timing of the broad swings.

For the effective rate of the U.S. dollar, the model predicts the depreciation that occurred from 1973 through 1977, the appreciation from 1981 through 1984, and the depreciation in 1985. It does not indicate the bouyancy of the currency in 1976, its weakness in 1974 and the first half of 1980, or the final surge in its value in 1984 and the first two months of 1985. These omissions may reflect the presence of strong speculative pressures during these periods; in addition, dynamic simulations over a long period such as this should not be expected to track short-run move-ments very well. On the whole, of course, the predictions for the bilateral exchange rates mirror those of the effective dollar rate. Nonetheless, during the 1980s, when the real value of the deutsche mark declined against the dollar by much more than did the Japanese yen, the simu-lations do pick up the difference in behavior between these two rates. Overall, the model seems to capture the broad trends in major exchange rates reasonably well.

The more specific question approached through simulations in this exercise concerns the role of each determining variable in generating the predicted movements shown in Figure 3. To have a convenient basis for comparison, count erf actual simulations were performed over the period of the U.S. dollar’s appreciation—from June 1980 through February 1985. That is, the model was run dynamically with actual values for all exogenous variables through June 1980; then, in turn, each major determining variable was forced to follow an artificially smoother path to illustrate its importance in generating observed changes in exchange rates.

For this purpose, four counterfactual simulations were undertaken. First, short-term interest rates were exogenized; that is, it was assumed for this simulation that the monetary authorities of each country would allow monetary growth to vary by enough to stabilize nominal short-term interest rate differentials in relation to the United States. As in the basic model, short-term interest rates in the United States were assumed to be determined exogenously. For the second simulation, shifts in the term structure of interest rates were eliminated by setting long-term rates in each country equal to observed or predicted values of short-term rates, plus the June 1980 difference between long and short rates.

In the third simulation, each country was assumed to use fiscal and other policies to keep both real domestic demand and the domestic demand deflator in line with the values in the United States. Specifically, real domestic demand in each country would grow at the same rate as that in the United States, with inflation differentials maintained at their June 1980 levels. Finally, for the fourth simulation, the cumulated external balance (k) in each country was held at its June 1980 level; the implication of this assumption is that the external balances are such as to keep net external assets or liabilities growing at the same rate as total private financial portfolios. Net-deficit countries would remain in deficit, but only by enough to stabilize portfolio allocations; the converse would apply for surplus countries.

The results of the counterfactual simulations, summarized in Table 3, show the overriding importance of monetary policy in the context of this model. For all three exchange rate indices, movements in short-term interest rate differentials have been the single most important identified factor contributing to the observed swings. The effect of this first simu-lation is that short-term rates outside the United States rise very sharply in tandem with U.S. rates in 1980 and 1981 and in general remain above control levels throughout the period. Notably, to maintain a constant differential in relation to the United States, German short-term interest rates would have had to reach more than 19 percent by end-1980, compared with an actual level of 10 percent; throughout the simulation period they average about 4 percentage points above the control path. The weighted-average rate for the four countries outside the United States was 11.2 percent in June 1980, or 2.7 percentage points above the U.S. rate. By December 1980, this rate was still 11,2 percent, whereas it would have had to go to 21.3 percent to maintain the initial differential. Overall, each of these countries would have had to tighten monetary policy substantially to prevent the widening of differentials that was observed in the early 1980s. Had this happened, the simulation suggests that a major portion of the observed exchange rate swings would not have occurred.

^{Table 3.}

Counterfactual Dynamic Simulations of Real Exchange Rates, June 1980 through February 1985

(In percent)

Note: For the United States, the effective rate was used: for the two other countries, the bilateral rate against the U.S. dollar was used. Percentage changes are first differences in logarithms; a positive change is an appreciation.

^{^a/}These simulated changes do not add to the total simulated change, owing to interactions and omitted disturbances

^{Table 3.}

Counterfactual Dynamic Simulations of Real Exchange Rates, June 1980 through February 1985

(In percent)

			Change	United States	Fed. Rep. of Germany	Japan
Actual				60.5	-68.4	-31.1
Simulated				15.1	-17.9	5.9
	Change attributable to:^a
		Short-term interest
			differentials	27.1	-27.0	-9.6
		Shifts in term structure		-6.8	3.6	0.4
		Differences in growth
			and inflation	1.2	-2.1	0.3
		External balances		6.7	-7.0	-0.3

^{^a/}These simulated changes do not add to the total simulated change, owing to interactions and omitted disturbances

^{Table 3.}

Counterfactual Dynamic Simulations of Real Exchange Rates, June 1980 through February 1985

(In percent)

			Change	United States	Fed. Rep. of Germany	Japan
Actual				60.5	-68.4	-31.1
Simulated				15.1	-17.9	5.9
	Change attributable to:^a
		Short-term interest
			differentials	27.1	-27.0	-9.6
		Shifts in term structure		-6.8	3.6	0.4
		Differences in growth
			and inflation	1.2	-2.1	0.3
		External balances		6.7	-7.0	-0.3

^{^a/}These simulated changes do not add to the total simulated change, owing to interactions and omitted disturbances

The other simulations show smaller but—in most cases—noi negligible effects. In the second simulation, for which long-term interest rates were adjusted to prevents shifts in the term structure, the effects work opposite to the prevailing trends over the simulation period. Notably, the term structure shifted toward an upward tilt by less in the United States than in the other major countries during this period.^¹⁸ Consequently, the observed shifts in the term structure worked to lessen the appreciation of the U.S. dollar compared with what would otherwise have occurred.

Holding differentials in income growth and inflation constant, as in the third simulation, has the general effect of raising income and lowering inflation in both Germany and Japan through most of the simulation period. The largest effect is on the growth rate of real private domestic demand in Germany, which was observed to average close to zero during the period concerned; in this simulation, growth averages more than 4 percent a year. Growth in Japan is raised by about 1¼ percent a year. With higher growth and lower inflation, the demand for money is higher in Europe and Japan. Consequently, interest rate differentials are squeezed, and the exchange rate swings are dampened. Nonetheless, despite the magnitude of the exogenous changes, the induced effects on exchange rates are quite small.

The final simulation involves holding k constant after June 1980 in each country. For the United States, this assumption prevents the cumulated private capital balance from declining from 1.1 percent of total portfolios in June 1980 to -4.8 percent in September 1982 (reflecting a strong current account position) and then from rising to 14.5 percent by end-1985. Similar cycles in the opposite direction are eliminated for Germany and Japan. In essence, then, this simulation asks how exchange rates would have behaved if the U.S. current account position had not strengthened in 1981-82 and then weakened sharply, and conversely tor the other two major countries. The effect is seen to be negligible for Japan; for the United States and Germany the exchange rate swings are dampened by some 7 percentage points.

IV. Conclusions

This paper has argued that understanding of the determination of major-currency exchange rates can be enhanced by reference to infor-mation about the term structure of interest rates. In theory, the relationships among the effects of interest rates at different maturities are ambiguous except under restrictive and unrealistic assumptions. These relationships have been untangled here by specifying a portfolio-balance model in which short- and long-term securities markets are segregated into preferred maturity habitats and in which the processes determining exchange rate expectations are different in each habitat. An implication of these assumptions is that exchange rates are affected by nominal short-term interest differentials and by real long-term differentials.

Empirical estimates of the model—using monthly data (1973-85) for the United States, the Federal Republic of Germany, and Japan— suggest that both short and long interest rate differentials do matter, except that long rates do not seem to have a significant effect on the yen-dollar exchange rate. In the equation for the effective exchange rate of the U.S. dollar, a rise of 1 percentage point in the short-term differ-ential is estimated to induce a 2 percent appreciation; a commensurate rise in the real long-term differential induces an appreciation of about 2¾ percent.

Counterfactual dynamic simulations of the model indicate, among other things, that the factors that caused the observed shifts in shortterm differentials between June 1980 and February 1985 (the period of the dollar’s major appreciation) were responsible for an appreciation of the dollar amounting to some 27 percent, compared with an observed real effective appreciation of about 60 percent. In contrast, term-structure shifts worked in the opposite direction and are estimated to have limited the dollar’s appreciation by about 7 percent. Other determining factors, while significant, accounted for smaller currency movements during the early 1980s.

APPENDIX Data Used in the Model

The following variables were used for estimating the model:

i^s Short-term interest rates: rates on money-market instruments with maturities of about three months—United States, certificates of deposit; Japan, discount rate on two-month private bills: Federal Republic of Germany and United Kingdom, interbank deposits; France, money rate against private paper
i_t Long-term interest rates: yields on government bonds with maturities of ten to twenty years—United States, twenty-year constant maturities; Japan, over-the-counter sales of interest-bearing government bonds with maturities of ten years or more; Germany, public authority bonds; France, national equipment bonds of 1965, 1966, and 1967: United Kingdom, twenty-year maturities
i* Foreign interest rates: for the countries other than the United States, the U.S. rate serves as the foreign rate; for the United States, the foreign rate is a weighted average of the rate for the four other countries listed above, with the weights based on the relative weights used in the SDR basket of currencies as of end-1980—0.3276 for Germany and 0.2241 each for Japan, France, and the United Kingdom
K The cumulated balance on private capital, as a percentage of total private portfolios: first, each country’s balance of payments is separated into ten to twelve components (merchandise exports and imports, service transactions, transfers, direct and portfolio capital transactions, official transactions); second, wherever monthly data are not available for one or more components, each series is benchmarked on a closely related series or interpolated; third, the balance on private capital is derived as the negative of the sum of the current account and official transactions; fourth, this balance is cumulated from the beginning of 1965 to obtain the numerator of k; fifth, the denominator is the stock of government debt held by domestic nonbank sectors, minus the numerator (that is. plus the cumulated balance on the current account and official capital); for further description of the role of k in the model, and the basis for this measure of k, see Boughton (1984)
μ The targeted rate of monetary growth: on the assumption that the authorities seek, other things being equal, to maintain steady downward pressure on the rate of monetary growth, this variable is defined here as c [2 ln (M_t-1 - ln (M_t-2)], where c (0 < c < 1) is an arbitrary constant that becomes embedded in the regression coefficients; the money stock (M) is broadly defined—United States. M2; Japan. M2 plus certificates of deposit; Germany, M3; France, resident M2; United Kingdom, sterling M3
π The expected inflation rate: for calculating long-term real interest rates, a nine-month centered average of actual inflation rates; for short-term real rates, a three-month average; prices are measured by the deflator for private domestic demand in each country
ρ Real exchange rates: relative price levels (p, domestic demand deflators) adjusted for exchange rate changes; exchange rates are end-period; for the U.S. effective rate, weights are the same as those used for foreign interest rates(i*)
y Real income: natural logarithm of the deflated level of private domestic demand.

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Mr. Boughton, an Advisor in the Research Department, holds advanced degrees from the University of Michigan and Duke University and was formerly Professor of Economics at Indiana University. He has published two books on monetary economics and numerous articles in economic journals.

The author thanks Joshua Aizenman, Assaf Razin. and his colleagues in the Research Department for comments on earlier drafts.

The interest rate data used in this paper are yields to maturity in domestic markets; real interest rates are calculated with reference to inflation in domestic goods-price indices. The conditions for constant yield-curve differences with these data are presumably stronger than would be the case for Euro-currency markets or for holding-period yields. The analysis could be extended usefully in that direction, but empirical estimation would be problematic for long-term assets

These assumptions underlie the models developed by Frenkel (1976), Mussa (197), Bilson (1978), and others. Note that the hypothesis of perfect substitut-ability requires uncovered as well as covered interest rate parity.

These assumptions characterize the Dornbusch-Frankel extension of Frenkel’s model; for an exposition, see Frankel (1983) and Boughton (1988). The implied term-structure relationship is also discussed briefly in Frankel (1979).

*Once $ρ = \bar{ρ},$ real returns on short-term assets will be equalized. Hence it should not matter whether N is equal to or greater than that maturity. Note that if $\hat{π} \neq 0, \bar{e} a n d \hat{\bar{p}}$ will be time dependent, but the conclusions will be unaffected.

See footnote 51 in Shafer and Loopesko (1983, p. 57) for a list of reasons that the strict version might not hold.

A third possibility is that market participants might have maturity-dependent expectations of the inflation rate while simultaneously having a single expected path for the exchange rate. This possibility does not seem as realistic as the two mentioned here and so is ignored in the following discussion.

This hypothesis is consistent with the long-run equilibrium of the model, as long as the equilibrium real exchange rate is constant over time.

In the steady state, when Δk = 0 and ρ is at its long-run equilibrium value $\bar{ρ}$ equation (12) then reduces to $k_{0} = k \bar{ρ} .$ That is, if k represents the adjustment process, then k₀ expresses the effects of the fundamental determinants of the real exchange rate.

In versions of this model discussed in earlier papers (Boughton (1983,1984)), the supply function for foreign-currency assets was explicitly introduced as a function of relative returns as well as of the cumulated capital balance. In that more general formulation, the structural parameters were less well-identified, but the form of the block solution was similar to equation (13).

The simple correlation coefficients between short- and long-term nominal interest differentials are 0.69, 0.70, and 0,78 for the United States, the Federal Republic of Germany, and Japan, respectively. The correlations between nom-inal short-term differentials and real long-term differentials are -0.06,0.46, and -0.09 for these same countries.

The conditions for, and the implications of. this assumption are discussed in Tobin (1969). Without this assumption, the reduced-form equation for i, (equa-tion (17)) would include a term in i, with an expected negative coefficient.

This formulation assumes slow adjustment of a financial-market price; alter-native hypotheses would be that goods prices adjust gradually in response to excess money demand or that the money stock adjusts gradually. The former would require a more general equilibrium framework than has been developed here, whereas the latter would seem to be inconsistent with the view expressed in equation (15)—-that the monetary authorities control the money stock through a reaction function. Tests of these alternatives would constitute a useful extension of the estimates presented below.

The structural parameters of equations (14)—(16) may be recovered from the reduced-form estimates of equation (17) as long as one parameter is determined independently. A convenient choice is which may be estimated from other studies of the income elasticity of the demand for money. Equation (17) also imposes the same elasticity on real output and the price level by using nominal income (V); note that money, income, and prices are all expressed as natural logarithms.

Identities are required for the nominal and real short-term foreign interest rates and for the real long-term foreign interest rate.

The program is SIMUL, developed by Clifford R. Wymer of the Fund.

The F-statisties for these three equations are 5.17 (the U.S. dollar effective rate), 4.39 (the dollar-deutsche-mark rate), and 3.50 (the dollar-yen rate). These statistics may be compared with those reported in Table 1 of Boughton (1987, pp. 46-47), where the model was similar to the present one except that short-term interest differentials were omitted; the sample period was the same, al-though the current data set has been updated. The corresponding statistics in the earlier paper were 6.63, 3.25, and 2.70, respectively; the last two were significant only at the 95 percent confidence level.

Dynamic simulation “cannot discriminate between models in terms of the validity of their estimated parameters, nor their congruity with the sample evi-dence.... In fact, what dynamic simulation tracking accuracy mainly reflects is the extent to which the explanation of the data is attributed to non-modelled variables” (Chong and Hendry (1986, p. 673)).

During the first two years of the simulation period, U.S. short-term interest rates were quite high. Consequently, the co unterf actual experiment results in correspondingly high long-term rates; during the later years, the effect is to reduce long-term rates, but by relatively smaller amounts. For the other coun-tries, the experiment reduces long-term rates over most or all of the simulation period.

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IMF Staff papers: Volume 35 No. 1

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1988: Issue 001

Publisher:: International Monetary Fund

ISBN:: 9781451956771

ISSN:: 1020-7635

Pages:: 228

DOI:: https://doi.org/10.5089/9781451956771.024

Keywords
APPENDIX Data Used in the Model
References

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U.S. Nominal Interest Rate Differentials and Effective Exchange Rate, 1973-85

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U.S. Real Interest Rate Differentials and Real Effective Exchange Rate, 1973-85

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Full-Sample Dynamic Simulations of Real Exchange Rates

(Index: 1975-84 = 100)

^{Table 3.}

Counterfactual Dynamic Simulations of Real Exchange Rates, June 1980 through February 1985

(In percent)

			Change	United States	Fed. Rep. of Germany	Japan
Actual				60.5	-68.4	-31.1
Simulated				15.1	-17.9	5.9
	Change attributable to:^a
		Short-term interest
			differentials	27.1	-27.0	-9.6
		Shifts in term structure		-6.8	3.6	0.4
		Differences in growth
			and inflation	1.2	-2.1	0.3
		External balances		6.7	-7.0	-0.3

^{^a/}These simulated changes do not add to the total simulated change, owing to interactions and omitted disturbances

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I. Theoretical Considerations

II. Empirical Estimates

III. Simulations

IV. Conclusions

APPENDIX Data Used in the Model

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