The Portfolio-Balance Model of Exchange Rates and Some Structural Estimates of the Risk Premium
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

This paper focuses on the portfolio-balance model as a framework for addressing unresolved issues about the behavior of exchange rates. Section I begins by spelling out the portfolio-balance framework and stressing that in its streamlined form it does not determine both the level and the expected rate of appreciation of the exchange rate. The portfolio-balance framework is a model that relates excess demands for stocks of outside assets to the expected yields on these assets. The relative levels of current and expected future exchange rates are determined as elements of expected yields, but by itself the portfolio-balance model does not determine the nominal values of either.

Abstract

This paper focuses on the portfolio-balance model as a framework for addressing unresolved issues about the behavior of exchange rates. Section I begins by spelling out the portfolio-balance framework and stressing that in its streamlined form it does not determine both the level and the expected rate of appreciation of the exchange rate. The portfolio-balance framework is a model that relates excess demands for stocks of outside assets to the expected yields on these assets. The relative levels of current and expected future exchange rates are determined as elements of expected yields, but by itself the portfolio-balance model does not determine the nominal values of either.

This paper focuses on the portfolio-balance model as a framework for addressing unresolved issues about the behavior of exchange rates. Section I begins by spelling out the portfolio-balance framework and stressing that in its streamlined form it does not determine both the level and the expected rate of appreciation of the exchange rate. The portfolio-balance framework is a model that relates excess demands for stocks of outside assets to the expected yields on these assets. The relative levels of current and expected future exchange rates are determined as elements of expected yields, but by itself the portfolio-balance model does not determine the nominal values of either.

Section II views the expected rate of appreciation of the exchange rate as the sum of an observable forward premium plus an unobservable exchange risk premium. Under the traditional assumption that wealth holders distinguish their interest-bearing assets by currency of denomination but not by debtor country, there is no premium for bearing political risk or country risk. The premium for bearing exchange risk is related to asset stocks and wealth variables, and it is shown that changes in the risk premium depend on budget deficits, current account imbalances, and official foreign exchange interventions. Section III begins with the widely recognized fact that observed forward premiums have been small, relative to the changes in exchange rates that have occurred since March 1973. By itself, that fact does not necessarily imply that exchange rate changes have been predominantly unexpected, since risk premiums may be large. Accordingly, the authors have interpreted empirical evidence on the size of the risk premium, as derived from the portfolio-balance model, and have found that it appears to explain only a small portion of the discrepancies between forward premiums and observed changes in exchange rates. This suggests (i) that current account imbalances have had small wealth effects on exchange rates, (ii) that there are only small errors in using forward premiums to represent expected rates of change in exchange rates, and (iii) that observed exchange rate changes have been predominantly unexpected and cannot be explained by the portfolio-balance framework in isolation.

Section IV discusses alternative assumptions that can be appended to the portfolio-balance framework to explain unexpected jumps in observed exchange rates in terms of revisions in expectations about future exchange rates. If future exchange rates are expected to be consistent with any of a variety of notions about long-run current account equilibrium, unexpected imbalances in observed current accounts may be associated with unexpected jumps in observed exchange rates.1 This viewpoint suggests the importance, however, of distinguishing between transitory and permanent shifts in current account positions, and of using a model of long-run current account positions to evaluate the extent to which rational market participants will revise their expectations about future (real) exchange rates in response to unexpected information about current account positions or their underlying determinants.

Section V concludes the paper by discussing some directions for future research, emphasizing the need to renovate the portfolio-balance model in order to pursue an understanding of the interactions between exchange risk and country risk.

I. Portfolio-Balance Framework

In the spirit of the original portfolio-balance models of McKinnon and Oates (1966) and McKinnon (1969), and the two-country formulation by Girton and Henderson (1977), consider a two-country, two-currency world in which there are two composite private sectors with distinguishable portfolio preferences. The net portfolio holdings of the two private sectors combined consist of interest-bearing and noninterest-bearing claims on governments.

Let MB and MB* denote the monetary bases of the home country and the foreign country—that is, the stocks of noninterest-bearing outside assets denominated, respectively, in domestic and foreign currencies. Let B and F denote the stocks of interest-bearing outside assets denominated, respectively, in domestic and foreign currencies. These stocks are measured net of the claims of official agencies on each other. The net holdings of private residents of the home country (H) and the foreign country (F) are denoted, respectively, by MBH, BH, FH and MBF*, BF, FF, such that

MBH=MB(1)
BH+BF=B(2)
FH+FF=F(3)
MBF*=MB*(4)

WH and WF denote the “wealths” of private home-country residents and private foreign residents, respectively, valued in domestic and foreign currency units

WH=MBH+BH+sFH(5)
WF=MBF*+BF/s+FF(6)

where the exchange rate (s) is measured as domestic currency per unit of foreign currency.2

The stocks of base money and bonds are determined by the interactions of monetary policies, government budget deficits, and official exchange market interventions. B is equal to the cumulative government budget deficit of the home country (∫DEF) minus cumulative open market purchases of bonds in exchange for base money issued by the monetary authority of the home country (MB) minus cumulative purchases of domestic-currency bonds by official foreign exchange intervention authorities in the home and foreign countries combined (∫INT)

B=DEFMBINT(7)

Similarly,

F=DEF*MB*+INT*(8)

where DEF* is the foreign budget deficit and INT* is the quantity of foreign bonds that are sold to purchase INT units of domestic bonds

INT*=INT/s(9)

Capital gains and losses on bonds are limited to those associated with exchange rate movements by assuming that B and F are one-period bonds; stocks of government debt are viewed to be refinanced at the beginning of each period.

The following behavioral assumptions have been made about the stocks of assets that are held in private portfolios. No distinctions are drawn between actual and desired portfolio holdings. The division of home-country private wealth between domestic money, domestic bonds, and foreign bonds is assumed to depend on the own rate of interest on domestic bonds (r); the expected domestic-currency yield on foreign bonds (r* - π), where r* is the own rate of interest on foreign bonds and π is the expected rate of appreciation in domestic currency; and a vector of other variables (Q), which conventionally includes an index of transactions demand.

MBH=mH(r,r*π,Q)WH(10)
BH=bH(r,r*π,Q)WH(11)
sFH=sfH(r,r*π,Q)WH(12)

Similarly, the division of WF between foreign money, domestic bonds, and foreign bonds depends on the own rate of interest on foreign bonds, the expected foreign-currency yield on domestic bonds, and a vector of other variables (Q*).

MBF*=mF(r*,r+π,Q*)WF(13)
BF/s=(1/s)bF(r*,r+π,Q*)WF(14)
FF=fF(r*,r+π,Q*)WF(15)

By definitions (5) and (6), the portfolio shares must add to unity

mH+bH+sfH=1(5)
mF+bF/s+fF=1(6)

The residents of each country are assumed to be risk averse and, accordingly, to view domestic and foreign bonds as imperfect substitutes.3

Behavioral assumptions (10)–(15) can be substituted in the market clearing conditions (1)-(4) to solve for the variables that clear asset markets. The case is considered in which asset stocks are predetermined and interest rates and exchange rates are variable. By constraints (5ʹ) and (6ʹ), only three of the four market-clearing conditions are independent. Thus, one can solve the system for only three of the four variables s, π, r, and r*. For example, if interest rates are regarded as being determined in money markets, independently of exchange rates in this model, then both the current level of the exchange rate and its expected rate of appreciation cannot also be determined endogenously. The portfolio-balance framework can be solved for the relative levels of current and expected future exchange rates, but it cannot determine the nominal values of either.

II. Exchange Risk Premium

The interest here is in solving the portfolio-balance model for π, the rate of appreciation in domestic currency that must be expected for asset markets to clear. It is convenient to write the solution in the form

π=r*r+ɸ(16)

where ɸ is in general a function of all the variables (other than π) on which portfolio behavior depends. The interest differential (r* - r) can be viewed as the forward premium in favor of domestic currency.4 Here, ɸ is the exchange risk premium that must be expected, over and above the interest differential or forward premium, for asset holders to be indifferent at the margin between uncovered holdings of domestic bonds and foreign bonds. In a risk-neutral world, ɸ would be identically zero.

To gain insights into ɸ in a risk-averse world, one can begin with a utility-maximizing portfolio selection framework, imposing restrictions that generate well-behaved portfolio-demand functions.5 In the present context, however, the authors have relatively weak judgments about appropriate utility functions and relatively strong judgments about the important properties of a well-behaved system of portfolio-demand functions. Accordingly, these latter judgments have been imposed directly by considering the following simplified version of the portfolio-balance model.

MBH=mH(r,Q)WHwith0mH1(10)
BH=bH(ɸ)[WHMBH]withbHʹ=bH/ɸ>0(11)
sFH=(1bH)[WHMBH](12)
MBF*=mF(r*,Q*)WF*with0mF1(13)
BF/s=bF(ɸ)[WFMBF*]withbFʹ=bF/ɸ>0(14)
FF=(1bF)[WFMBF*](15)

Money holdings depend on domestic interest rates, transactions demand variables, and wealths, while the shares of wealth that are not held as money are divided between domestic and foreign bonds as functions of the differential expected yield (ɸ = rr* + π).

In solving for π one can choose conditions (1), (2), and (4) as the three independent market-clearing conditions. Conditions (1), (4), (10ʹ), and (13ʹ) determine interest rates as functions of asset stocks, wealths, and transactions demand variables. Conditions (11ʹ), (14ʹ), (1), and (4) can be substituted in condition (2) to yield

B=bH(ɸ)[WHMB]+bF(ɸ)[sWFsMB*](17)

Condition (17) can then be inverted to solve for ɸ, the amount by which the rate of appreciation of domestic currency must be expected to exceed the interest differential if existing stocks of outside assets are to be willingly held uncovered. This condition is pictured in Figure 1: the quantity of domestic bonds supplied by public sectors is fixed at level B, independently of the risk premium; the domestic and foreign private demand curves for domestic bonds are positively sloped, since bHʹ and bFʹ are positive. Accordingly, for given levels of private wealths, the market-clearing level of the risk premium rises with the share of public debt that is denominated in domestic-currency units—that is, an increase in the stock of domestic bonds (matched by a reduction in the stock of foreign bonds) shifts the vertical supply curve to the right and raises the risk premium that is necessary to induce domestic and foreign portfolio managers to increase their combined demand (i.e., to slide along the BH + BF curve) by the increment in supply. Similarly, given the stock of domestic bonds, an increase in either home wealth or foreign wealth (through new public debt issues of foreign-currency bonds) shifts either the BH or the BF curve to the right, and the associated rightward shift in the BH + BF curve leads to a fall in the risk premium. These effects can be expressed formally by taking the total differential of condition (17) and rearranging terms to arrive at

Figure 1.
Figure 1.

Market for Bonds Denominated in Domestic Currency

Citation: IMF Staff Papers 1983, 004; 10.5089/9781451930610.024.A001

dɸ=dBbHd(WHMB)bFd(sWFsMB*)(WHMB)bHʹ+s(WFMB*)bFʹ(18)

where bHʹ, bFʹ, and, hence, the denominator are positive.

If one looks behind the determinants of wealths, one can derive an equivalent expression for dɸ in terms of budget deficits, current account imbalances, and intervention flows. Conditions (1), (2), (5), and (7) imply that

WH=DEFINT+sFHBF(19)

while conditions (3), (4), (6), and (8) similarly imply that

sWF=sDEF*+sINT*sFH+BF(20)

Conditions (7), (19), and (20) can be differentiated and substituted in the numerator of condition (18). In addition, if CAS denotes the home country’s current account surplus, which must satisfy the balance of payments identity,

CAS=sdFHdBFINT(21)

condition (18) can be shown to be equivalent to6

dɸ=(1bH)(DEFdMB)bFS(DEF*dMB*)(bHbF)CASINT(bHFH+bFFF)ds(WHMB)bHʹ+S(WFMB*)bFʹ(22)

Ceteris paribus, the expected rate of appreciation of domestic currency must increase (relative to the interest differential) to induce private portfolio managers to increase their holdings of domestic bonds by DEFdMB, and must decrease to induce private portfolio managers to increase their holdings of foreign bonds by DEF* – dMB*. A home-country current account surplus that shifts the residence of private wealth toward the home country will reduce the risk premium on domestic currency, ceteris paribus, if and only if private residents of the home country have a relatively stronger preference for domestic bonds than do private residents of the foreign country—that is, if and only if bHbF > 0. An intervention purchase of one unit of domestic bonds reduces the expected yield differential necessary to induce wealth holders to hold the reduced supply of domestic bonds. In this case, there is no redistribution of wealth (assuming no change in s) so that only the changes in portfolio shares bHʹ and bFʹ are important in determining the change in ɸ. It is also interesting that an intervention purchase of one unit of domestic bonds has the same effect on the risk premium as simultaneously reducing DEFdMB and increasing both s(DEF* – dMB*) and CAS by one unit each. Thus, the instantaneous effect on the risk premium of any change in the structure of fiscal deficits or current accounts can be offset by some intervention transaction. Moreover, an appreciation of foreign currency (ds > 0) reduces the risk premium on domestic bonds because it raises the domestic-currency valuations of both home-country and foreign wealths relative to the stock of domestic bonds (recall condition (18)). Finally, the magnitudes of these effects on the risk premium are inversely proportional to the degree of asset substitutability, as reflected by the parameters bHʹ and bFʹ. For the limiting case in which domestic bonds and foreign bonds are perfect substitutes, bHʹ = bFʹ = ∞ and ɸ never changes.

III. Accuracy of Exchange Rate Expectations

Having characterized the risk premium, let us now focus on the extent to which portfolio managers could plausibly have expected the changes in exchange rates that have been observed since March 1973. It is widely recognized that observed changes in exchange rates have been predicted poorly by forward premiums,7 but as represented by condition (16), the interest differential or forward premium is only one component of the expected change in the exchange rate. It is conceivable that the expected rate of change in the exchange rate reflects predominantly the risk premium, rather than the forward premium, and that the risk premium is also a good predictor of the observed changes in exchange rates that are not predicted by forward premiums. This possibility can be tested empirically by regressing actual changes in the dollar-deutsche mark exchange rate (net of the forward premium) on a general expression that characterizes the unobservable behavior of the risk premium. In doing so, it is important to extend the market-clearing condition (17) to include the net holdings of dollar bonds in countries outside the United States and the Federal Republic of Germany:

B=bH(ɸ)[WHMB]+bF(ɸ)[sWFsMB*]+bR(ɸ)WROW(17)

The three terms on the right-hand side of condition (17ʹ) represent, respectively, the net dollar bond holdings of private U.S. residents, private residents of the Federal Republic of Germany, and private and official residents of the rest of the world. WROW is the dollar valuation of the net money and bond holdings of the rest of the world, and bR(ɸ) is the share of this wealth that is held in the form of dollar-denominated interest-bearing assets.

The regression analysis here is based on an approximate solution of this market-clearing condition for ɸ, which is obtained by replacing each of the portfolio-share functions by a first-order Taylor approximation around some point ɸ0

bH(ɸ)=b¯H+bHʹ[ɸɸ0]bF(ɸ)=b¯F+bFʹ[ɸɸ0]bR(ɸ)=b¯R+bRʹ[ɸɸ0](23)

Under this substitution, the solution to condition (17ʹ) is

ɸ=ɸ0+Bb¯H[WHMB]b¯F[sWFsMB*]b¯RWROWbHʹ[WHMB]+bFʹ[sWFsMB*]+bRʹWROW(24)

If all three portfolio-share functions are assumed to exhibit the same elasticity (ϵ) with respect to the risk premium at ɸ0

ɸ0bHʹ/b¯H=ɸ0bFʹ/b¯F=ɸ0bRʹ/b¯R=(25)

Condition (24) can then be expressed as

ɸ=ɸ0+(ɸ0/)(BB¯)/B¯(26)

where the notation

B¯=b¯H[WHMB]+b¯F[sWFsMB*]+b¯RWROW(27)

is defined to represent the aggregate world demand for dollar bonds when the risk premium equals ɸ0.

In specifying this regression hypothesis, it is convenient to view the observed rate of appreciation of the exchange rate (x) as the sum of the expected rate of appreciation (π) plus an unexpected rate of appreciation (u). Given the decomposition of π in condition (16), one can write

x+rr*=ɸ+u(28)

Adding the behavioral model (26) together with time arguments, the regression hypothesis can be expressed as

x(t)+r(t)r*(t)=ɸ0+(ɸ0/)[B(t)B¯(t)/B¯(t)]+u(t)(29)

where ɸ0 and ɸ0/∊ are the parameters to be estimated and the unexpected changes u(t) are treated as unexplained residuals or error terms. The dependent variable is measured ex post as the observed percentage change in the exchange rate between the end of quarter t and the end of quarter t+ 1 minus the three-month percentage forward premium (or Eurocurrency interest differential) at the end of quarter t. The regression analysis is approached from the perspective that forward premiums have been poor predictors (or very small components) of observed changes in spot rates (cf. footnote 7); the object of the regression is to assess the extent to which this model of the risk premium explains observed changes in exchange rates over and above forward premiums. For this purpose, the analysis focuses on a variety of goodness-of-fit statistics. Moreover, because data on the currency compositions of the wealth variables used here are not available, the regression hypothesis has been tested over a range of constructions of B¯ that correspond to a broad range of plausible assumptions about b¯H,b¯F,andb¯R. The observations of exchange rates, forward premiums, asset stocks, and wealth variables represent 24 end-of-quarter data points during the period 1973–78. Data sources are described in the Data Appendix.

The regression estimates scan the plausibility set of the triplet (b¯H,b¯F,b¯R) using a grid of the 200 combinations of b¯H = 0.95, 0.90, 0.85, 0.80, 0.75; b¯F = 0.05, 0.10, 0.15, 0.20, 0.25; and b¯R = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8. The Cochrane-Orcutt procedure is used in all cases to correct for first-order serial correlation. Table 1 shows how the goodness-of-fit statistics and coefficient estimates vary as the prespecified portfolio-share parameters are varied one at a time from the point (b¯H,b¯F,b¯R) = (0.85, 0.15, 0.4). Also tabulated are two cases that generated maximum or minimum values of each of the goodness-of-fit statistics over the entire set of grid points. Each of the goodness-of-fit statistics and the estimates of ɸ0 and ɸ0/β change gradually and smoothly as the three portfolio-share parameters are varied in any direction (either one at a time or in combination), leaving the authors confident that scanning a finer grid would not have generated cases with substantially better fits.

Table 1.

Goodness-of-Fit Statistics and Parameter Estimates

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Ratio of the root-mean-square prediction error to mean absolute value of the independent variable.

Coefficient of correlation between the estimated risk premium and the dependent variable.

Number of observed changes in the dependent variable (of 24 total observations) that are predicted correctly in sign.

Average absolute value of the estimated risk premium divided by the average absolute value of the dependent variable.

Mean of the estimated risk premium.

These are t-statistics associated with the regression estimates ɸ0 and ɸ0/ϵ.

Coefficient of first-order autocorrelation in the residuals from the regressions after the Cochrane-Orcutt correction.

The basic conclusion that has been drawn from the regression analysis is that the risk premiums associated with this particular representation of the portfolio-balance model explain only a small part of the discrepancies between observed percentage changes in exchange rates and forward premiums. For all the grid points examined, the root-mean-square prediction error exceeds the mean absolute value of the dependent variable; and the highest coefficient of correlation between the estimated risk premiums and subsequent percentage changes in the exchange rate (over and above forward premiums) is 0.393. The estimated risk premiums correctly predict the direction of, at most, 18 of the 24 observed changes in exchange rates (relative to forward premiums); their average absolute value is less than two fifths of the average absolute magnitude of observed percentage changes in exchange rates. Under the null hypothesis that the least-squares estimates of ɸ represent expected changes in the exchange rate, the mean estimated risk premium over the sample period is −0.62 percent a quarter in all cases,8 an average (over time) expectation that the dollar would depreciate against the deutsche mark at a rate roughly 2.5 percent a year in excess of the forward premium on the deutsche mark—that is, by about 0.1 cent a month. The estimated elasticity of portfolio shares with respect to the risk premium is remarkably low in all cases; to the extent that this elasticity may be underestimated, however, the magnitudes of the estimated market-clearing risk premiums may correspondingly be overestimated and thus may explain an even smaller portion of observed changes in exchange rates.9

The failure of the analysis to explain more than a small part of observed changes in exchange rates can be attributed in part to the limitations of this particular representation of the portfolio-balance model and in part to the fact that observed changes in exchange rates can differ from the changes expected by portfolio managers. In Dooley and Isard (1982 a), a different estimation procedure was employed, using a modified version of the model described earlier;10 the resulting estimates of the risk premium, however, are again capable of explaining only a small part of observed changes in exchange rates. Thus, the authors have failed to find empirical evidence that portfolio managers have expected the major portion of observed changes in exchange rates.

IV. Extensions of the Portfolio-Balance Framework

Section I emphasized that the portfolio-balance framework in its streamlined form determines the relative levels of current and expected future exchange rates but cannot explain the absolute levels of either. A number of papers have “resolved” this difficulty by assuming that exchange rate expectations are static or autoregressive, but several approaches for modeling expected future exchange rates “rationally” have also been suggested in the literature. One approach is the method of repeated substitution, which was used by Mussa (1976) in an analytic model of exchange rate determination and earlier by Sargent and Wallace (1973) in a study of hyperinflation, and which was applied empirically by Dooley and Isard (1982 a) in estimating a model of the deutsche mark/dollar exchange rate. Under this approach, the exchange rate at time t is expressed as a linear function of the time-t expectation of the exchange rate at time t+ 1, along with other explanatory variables. This procedure implies that the time-t expectation of the exchange rate at time t + 1 is a linear function of the time-t expectation of the exchange rate at t + 2, along with time-t expectations of the other explanatory variables. Thus, by repeated substitution, the exchange rate at time t can be expressed as a linear function of the time-t expectation of the exchange rate at the time t+ T, for any T, along with time-t expectations of the time paths of the other explanatory variables. One of the difficulties in employing this procedure empirically is the necessity of truncating the repeated substitutions at some choice of T, and hence of arbitrarily tying down the time-t expectation of the exchange rate at t + T. Rodriguez (1980) has suggested an analytic model in which the truncation error converges to zero as T approaches infinity, but the speed of convergence can be shown to vary inversely with the degree of substitutability between assets denominated in domestic currency and foreign currency, and convergence can be ruled out in the important benchmark case of perfect substitutability (Dooley and Isard (1982 b)).

A second “rational expectations” approach for extending the portfolio-balance framework is to tie expectations about the long-run real exchange rate to a steady-state value that solves a goods market or balance of payments equilibrium condition. This approach was taken in the influential papers by Dornbusch (1976) and Kouri (1976), and has been discussed by Mussa (1982), Isard (1983 b), and Dooley and Isard (1983). Many contributions to the literature assume that expectations about the long-run level of the real exchange rate are time invariant, which is a strong form of the long-run purchasing power parity assumption. Such an assumption facilitates regression analysis by absorbing the expected long run real exchange rate into the constant term. The assumption of time-invariant expectations about the long-run real exchange rate sidesteps the issue, however, of specifying the conditions on which long-run expectations are based, which in turn precludes a scientific evaluation of the assumption. In principle, it seems important to seek a sensible specification of the long-run balance of payments constraint. In this context, Dooley (1982) has emphasized that the constraint should be viewed basically as reflecting the risk that debtor countries will not fully repay borrowings from creditor countries, rather than any direct increases in exchange risk associated with the currency denomination of borrowings, since countries with persistent balance of payments deficits generally do not denominate their international borrowings in their own currencies. An implication is that the interaction between exchange risk and country risk deserves further attention in the portfolio-balance framework.11

V. Conclusions

There is now a growing body of evidence rejecting the joint hypothesis that exchange markets are efficient and exchange risk premiums are nonexistent. Much of the evidence is based on studies of time-series data on spot and forward exchange rates and interest differentials,12 rather than tests of structural exchange rate equations. The time-series evidence, however, has heightened interest in obtaining structural estimates of the exchange risk premium and, more generally, of the parameters of portfolio-balance models that describe the extent to which exchange rates respond to exchange market intervention and the creation of outside assets through fiscal budget deficits. This study has found weak evidence of a risk premium based on a structural model, but provides little insight into the values of the relevant portfolio-demand parameters.13

Part of the difficulty in obtaining structural estimates of portfolio-demand parameters may reflect deficiencies in specifying the portfolio-balance framework. This paper has emphasized that the portfolio-balance model in its streamlined version can be solved for the expected rate of change of the exchange rate, but that an additional expectations framework is required to solve for the absolute levels of current and expected future exchange rates. A relatively attractive method of extending the portfolio-balance framework is to base expectations of the long-run real exchange rate on the solution to a long-run goods market or balance of payments constraint. As Dooley (1982) has argued, however, the essence of any long-run balance of payments constraint must involve credit risk attached to debtor countries, which has received little emphasis in portfolio-balance models developed to date. In Dooley and Isard (1983) a one-currency, two-country model has been developed that focuses on both economic and political sources of country risk and the interdependence between country risk and the exchange rate has been emphasized.

In addition to extending the portfolio-balance model to recognize the role of country risk and to provide a solid anchor for long-run exchange rate expectations, it seems important for studies of exchange rate behavior to distinguish carefully between expected and unexpected changes in explanatory variables. The empirical results of this paper support the view that observed changes in exchange rates have been predominantly unexpected—that is, have predominantly reflected unexpected changes in (or revisions in expectations about) explanatory variables. In view of the limited attempts that have been made to specify exchange rate equations in this spirit, it is not surprising that empirical exchange rate models of the 1970s have been found to predict poorly out of sample, even under perfect foresight of explanatory variables.14

The empirical results presented in this paper also support the view that current account imbalances do not have substantial “wealth effects” on exchange rates, which is an implication of the evidence that risk premiums are small. In view of the important deficiencies of the portfolio-balance framework as developed to date, however, the supporting evidence must be regarded as tentative. Until the portfolio-balance model is renovated to provide an understanding of the interdependencies between exchange risk and country risk, it would seem difficult to reach a clear judgment on the relative importance of the different channels through which current account imbalances may influence exchange rates.

DATA APPENDIX

Exchange rates are measured on the last Friday of the quarter, taken from the data files of the Federal Reserve System. Interest rates are 90-day Eurocurrency rates measured on or near the last day of the quarter, taken from Morgan Guaranty’s World Financial Markets and the data file of the Bank of America. DEF represents the change in the stock of U.S. Government securities held by the public, as published in the Federal Reserve Board, Annual Statistical Digest and (monthly) Bulletin. Forward premiums are constructed to equal Eurocurrency interest differentials. CAS is the U.S. current account surplus published in Survey of Current Business. MB, represented by Federal Reserve data, is adjusted for breaks that are due to changes in reserve requirements. DEF* represents the budget deficit of the Federal Republic of Germany, taken from the Bundesbank, Monthly Report, Reihe 4; MB* and that country’s current account surplus (CAS*) are from the same source. Private U.S. wealth (WH) is constructed as $400 billion + Í(DEF + CAS). Private German wealth (WF) is constructed as DM 200 billion + ∫(DEF* + CAS*). The initial values of WH and WF are estimated from end-of-1972 stocks of federal debt, monetary bases, and net claims on foreigners, as published in the Federal Reserve Board, Annual Statistical Digest and Bulletin and the Bundesbank, Monthly Report. The dollar value of the wealth of the rest of the world (WROW) is constructed by subtracting the combined cumulative current account surpluses of the United States and the Federal Republic of Germany from an estimated initial value (WROW0).

WROW=WROW0(CAS+sCAS*)

The market-clearing conditions of the model have been relied on to provide estimates of WROW0 under the alternative assumptions (i) that the risk premium was zero at the end of 1976, which was the middle of a long interval of relatively small fluctuations in the dollar-deutsche mark rate, or (ii) that on average during the entire sample period the dollar-bond market cleared at a zero risk premium. In case (i), the authors solve for WROW (1976Q4) and then WROW0 by setting B¯(1976Q4) = B(1976Q4) in equation (27); in the second case, they solve for the WROW0 that is consistent with the assumption that B¯B has a zero mean over the entire 24-quarter sample. In each case, WROW0 is estimated as a function of the prespecified values of the triplet (b¯H,b¯F,b¯R). Table 1 is based on the former choice of WROW0. However, the goodness-of-fit statistics and mean (ɸ) estimates are quite insensitive to this choice of WROW0, and the estimates of ϵ are lower in case (ii) than in case (i).

REFERENCES

  • Aliber, Robert Z.,The Interest Rate Parity Theorem: A Reinterpretation,Journal of Political Economy, Vol. 81 (November/December 1973), pp. 145159.

    • Search Google Scholar
    • Export Citation
  • Breeden, Douglas T.,An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities,Journal of Financial Economics, Vol. 7 (September 1979), pp. 26596.

    • Search Google Scholar
    • Export Citation
  • Cumby, Robert E., and Maurice Obstfeld,A Note on Exchange-Rate Expectations and Nominal Interest Differentials: A Test of the Fisher Hypothesis,Journal of Finance, Vol. 36 (June 1981), pp. 697703.

    • Search Google Scholar
    • Export Citation
  • Danker, Deborah, Richard Haas, Steven Symansky, and Ralph Tyron,Small Empirical Models of Exchange Market Intervention: Applications to Canada, Germany and Japan,Federal Reserve Board, Staff Study No. 135 (Washington, scheduled for issue in 1984).

    • Search Google Scholar
    • Export Citation
  • Dooley, Michael P. (1974), “A Model of Arbitrage and Short-Term Capital Flows,International Finance Discussion Papers, No. 40, Board of Governors of the Federal Reserve System (Washington, January 4, 1974).

    • Search Google Scholar
    • Export Citation
  • Dooley, Michael P. (1982), “An Analysis of Exchange Market Intervention of Industrial and Developing Countries,Staff Papers, Vol. 29 (June 1982), pp. 23369.

    • Search Google Scholar
    • Export Citation
  • Dooley, Michael P., and Peter Isard (1980), “Capital Controls, Political Risk, and Deviations from Interest-Rate Parity,Journal of Political Economy, Vol. 88 (April 1980), pp. 37084.

    • Search Google Scholar
    • Export Citation
  • Dooley, Michael P., and Peter Isard (1982 a), “A Portfolio-Balance Rational-Expectations Model of the Dollar-Mark Exchange Rate,Journal of International Economics, Vol. 12 (May 1982), pp. 25776.

    • Search Google Scholar
    • Export Citation
  • Dooley, Michael P., and Peter Isard (1982 b), “The Role of the Current Account in Exchange-Rate Determination: A Comment on Rodriguez,Journal of Political Economy, Vol. 90 (December 1982), pp. 129194.

    • Search Google Scholar
    • Export Citation
  • Dooley, Michael P., and Peter Isard (1983), “Country Risk, International Lending, and Exchange Rate Determination,International Finance Discussion Papers, No. 221, Board of Governors of the Federal Reserve System (Washington, May 10, 1983).

    • Search Google Scholar
    • Export Citation
  • Dooley, Michael P., and Jeffrey R. Shafer,Analysis of Short-Run Exchange Rate Behavior: March, 1973 to November, 1981,” in Exchange Rate and Trade Instability, ed. by David Bigman and Teizo Taya (Cambridge, Massachusetts, 1983).

    • Search Google Scholar
    • Export Citation
  • Dornbusch, Rudiger (1976), “Expectations and Exchange Rate Dynamics,Journal of Political Economy, Vol. 84 (December 1976), pp. 116176.

    • Search Google Scholar
    • Export Citation
  • Dornbusch, Rudiger (1983), “Exchange Risk and the Macroeconomics of Exchange Rate Determination,” in The Internationalization of Financial Markets and National Economic Policy, ed. by Robert G. Hawkins, Richard M. Levich, and Clas G. Wihlborg (Greenwich, Connecticut, 1983).

    • Search Google Scholar
    • Export Citation
  • Frankel, Jeffrey A. (1979), “The Diversifiability of Exchange Risk,Journal of International Economics, Vol. 9 (August 1979), pp. 37993.

    • Search Google Scholar
    • Export Citation
  • Frankel, Jeffrey A. (1982 a), “A Test of Perfect Substitutability in the Foreign Exchange Market,Southern Economic Journal, Vol. 49 (October 1982), pp. 40616.

    • Search Google Scholar
    • Export Citation
  • Frankel, Jeffrey A. (1982 b), “In Search of the Exchange Risk Premium: A Six-Currency Test Assuming Mean-Variance Optimization,Journal of International Money and Finance, Vol. 1 (December 1982), pp. 25574.

    • Search Google Scholar
    • Export Citation
  • Geweke, John, and Edgar Feige,Some Joint Tests of the Efficiency of Markets for Forward Foreign Exchange,Review of Economics and Statistics, Vol. 61 (August 1979), pp. 33441.

    • Search Google Scholar
    • Export Citation
  • Girton, Lance, and Dale W. Henderson,Central Bank Operations in Foreign and Domestic Assets Under Fixed and Flexible Exchange Rates,” in The Effects of Exchange Rate Adjustments, The Proceedings of a Conference Sponsored by OASIA Research, Department of the Treasury, April 4 and 5, 1974, ed. by Peter B. Clark, Dennis E. Logue, and Richard James Sweeney (Washington, 1977), pp. 15179.

    • Search Google Scholar
    • Export Citation
  • Hansen, Lars Peter, and Robert J. Hodrick (1980), “Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis,Journal of Political Economy, Vol. 88 (October 1980), pp. 82953.

    • Search Google Scholar
    • Export Citation
  • Hansen, Lars Peter, and Robert J. Hodrick (1983), “Risk Averse Speculation in the Forward Foreign Exchange Market: An Econometric Analysis,” in Exchange Rates and International Macroeconomics, ed. by J. A. Frenkel (University of Chicago Press, 1983).

    • Search Google Scholar
    • Export Citation
  • Herring, Richard J., and Richard C. Marston,The Forward Market and Interest Rates in the Eurocurrency and National Money Markets,” in Eurocurrencies and the International Monetary System, ed. by Carl H. Stem, John H. Makin, and Dennis E. Logue (Washington, 1976), pp. 13963.

    • Search Google Scholar
    • Export Citation
  • Isard, Peter (1983 a), “What’s Wrong with Empirical Exchange Rate Models: Some Critical Issues and New Directions,International Finance Discussion Papers, No. 226, Board of Governors of the Federal Reserve System (Washington, August 1983).

    • Search Google Scholar
    • Export Citation
  • Isard, Peter (1983 b), “An Accounting Framework and Some Issues for Modelling How Exchange Rates Respond to the News,” in Exchange Rates and International Macroeconomics, ed. by J. A. Frenkel (University of Chicago Press, 1983).

    • Search Google Scholar
    • Export Citation
  • Kouri, Pentti J.K.,The Exchange Rate and the Balance of Payments in the Short Run and in the Long Run: A Monetary Approach,Scandinavian Journal of Economics, Vol. 78 (No. 2, 1976), pp. 280304.

    • Search Google Scholar
    • Export Citation
  • Kouri, Pentti J.K., and Jorge Braga de Macedo,Exchange Rates and the International Adjustment Process,Brookings Papers on Economic Activity: 1 (1978), pp. 11150.

    • Search Google Scholar
    • Export Citation
  • McKinnon, Ronald I.,Portfolio Balance and International Payments Adjustment,” in Monetary Problems of the International Economy, ed. by Robert A. Mundell and Alexander K. Swoboda (University of Chicago Press, 1969), pp. 199234.

    • Search Google Scholar
    • Export Citation
  • McKinnon, Ronald I., and Wallace E. Oates, The Implications of International Economic Integration for Monetary, Fiscal, and Exchange-Rate Policy, Princeton Studies in International Finance, No. 16, International Finance Section, Princeton University (1966).

    • Search Google Scholar
    • Export Citation
  • Meese, Richard A., and Kenneth Rogoff (1983 a), “Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?Journal of International Economics, Vol. 14 (February 1983), pp. 324.

    • Search Google Scholar
    • Export Citation
  • Meese, Richard A., and Kenneth Rogoff (1983 b), “The Out-of-Sample Failure of Empirical Exchange Rate Models: Sampling Error or Misspecification?” in Exchange Rates and International Macroeconomics, ed. by J. A. Frenkel (University of Chicago Press, 1983).

    • Search Google Scholar
    • Export Citation
  • Meese, Richard A., and Kenneth J. Singleton,On Unit Roots and the Empirical Modeling of Exchange Rates,Journal of Finance, Vol. 37 (September 1982), pp. 102935.

    • Search Google Scholar
    • Export Citation
  • Merton, Robert C.,Optimum Consumption and Portfolio Rules in a Continuous-Time Model,Journal of Economic Theory, Vol. 3 (December 1971), pp. 373413.

    • Search Google Scholar
    • Export Citation
  • Mussa, Michael (1976), “The Exchange Rate, the Balance of Payments and Monetary and Fiscal Policy Under a Regime of Controlled Floating,Scandinavian Journal of Economics, Vol. 78 (No. 2, 1976), pp. 22948.

    • Search Google Scholar
    • Export Citation
  • Mussa, Michael (1979), “Empirical Regularities in the Behavior of Exchange Rates and Theories of the Foreign Exchange Market,” in Policies for Employment, Prices, and Exchange Rates, ed. by Karl Brunner and Allan H. Meltzer, Carnegie-Rochester Conference Series on Public Policy, A Supplementary Series to the Journal of Monetary Economics, Vol. 11 (Amsterdam, 1979), pp. 957.

    • Search Google Scholar
    • Export Citation
  • Mussa, Michael (1982), “A Model of Exchange Rate Dynamics,Journal of Political Economy, Vol. 90 (February 1982), pp. 74104.

  • Rodriguez, Carlos Alfredo,The Role of Trade Flows in Exchange Rate Determination: A Rational Expectations Approach,Journal of Political Economy, Vol. 88 (December 1980), pp. 114858.

    • Search Google Scholar
    • Export Citation
  • Rogoff, Kenneth,On the Effects of Sterilized Intervention: An Analysis of Weekly Data” (unpublished, International Monetary Fund, May 23, 1983).

    • Search Google Scholar
    • Export Citation
  • Sargent, Thomas J., and Neil Wallace,Rational Expectations and the Dynamics of Hyperinflation,International Economic Review, Vol. 14 (June 1973), pp. 32850.

    • Search Google Scholar
    • Export Citation
  • Solnik, Bruno Henri, European Capital Markets: Towards a General Theory of International Investment (Lexington, Massachusetts, 1973).

  • Stulz, René M.,A Model of International Asset Pricing,Journal of Financial Economics, Vol. 9 (December 1981), pp. 383406.

*

Mr. Dooley, Senior Economist in the Financial Studies Division of the Research Department, is a graduate of Duquesne University, the University of Delaware, and the Pennsylvania State University.

Mr. Isard, Chief of the U.S. International Transactions Section in the International Finance Division of the Federal Reserve Board, is a graduate of the Massachusetts Institute of Technology and Stanford University. The views expressed in this paper should not be interpreted as reflecting the views of the Federal Reserve System.

1

The simple textbook model of an exchange rate that balances the current account flow within a single period is thus replaced with the notion of an expected future exchange rate that balances the current account flows that are expected in the long run (or, on average, over time).

2

This portfolio structure follows the tradition of assuming that the allocation between money and bonds is independent of the expected yields on equities and other assets, which are complicated to model. In addition, by assuming that current account flows measure the shifts of money and bond portfolios between domestic and foreign residents, the authors follow a preference for treating equities as substitutes for bonds rather than as substitutes for goods.

3

Conditions (10)–(15) do not treat the degree of substitution as a variable. In particular, it is assumed implicitly that subjective perceptions of the variance of π either are constant or do not affect desired portfolio shares.

4

This equivalence is well established for Eurocurrency differentials; see Aliber (1973), Dooley (1974), or Herring and Marston (1976).

6

The authors have also used conditions (3) and (8) in deriving the factor that multiplies ds in the numerator of condition (22).

7

See Mussa (1979). With regard to end-of-quarter data on the dollar-deutsche mark rate during the period 1973–78, for example, the coefficient of correlation between the percentage forward premium (measured as the Eurocurrency interest differential) and the subsequently observed percentage change in the exchange rate was 0.19; the root-mean-square error of predictions based on the forward premium exceeded the mean aosolute value of the observed changes; and in 10 of the 24 quarters the forward premium mispredicted the direction of exchange rate change. Moreover, the average absolute value of the change in the exchange rate was 4.9 percent a quarter during this period—seven times the average absolute value of the forward premium.

8

The fact that the mean estimated risk premium is constant (up to two significant digits) in all cases merely reflects the fact that the mean of the fitted values from any regression is generally a close approximation to the mean of the dependent variable, which is identical in all these cases.

9

None of these conclusions is sensitive to the initial value of the wealth of the rest of the world, which it was necessary to estimate arbitrarily. See the Data Appendix.

10

In particular, (i) the rest of the world was disaggregated into OPEC (Organization of Petroleum Exporting Countries) and non-OPEC wealth holders in order to pay particular attention to the dramatic growth of OPEC wealth since 1973, and (ii) it was assumed that desired portfolio shares reflected the type of risk-averse behavior pictured by the shapes of the BH and BF curves in Figure 1, in contrast to the linear curves that are implied by assumptions (23). That is, it was assumed that successive unit increases in the risk premium lead to positive but successively smaller increments in the shares of financial portfolios that are allocated to dollar-denominated bonds.

11

See Aliber (1973) and Dooley and Isard (1980; 1983) for previous studies that have addressed the issue of country-specific risks.

13

See Frankel (1982 a; 1982 b), Rogoff (1983), and Danker and others (1984) for other attempts to find structural evidence of the exchange risk premium.

14

Evidence on the poor predictive power of the empirical models of the 1970s is presented by Meese and Rogoff (1983 a; 1983 b). See Isard (1983 a) for further discussion of the inadequacies of empirical exchange rate models.