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 MB_H, B_H, F_H and $M{B}_F^{*}$, B_F, F_F, such that

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

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)

Similarly,

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

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.

Similarly, the division of W_F 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*).

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

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

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.

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 = r − r* + 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

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 $b_H^{ʹ}$ and $b_F^{ʹ}$ 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 B_H + B_F 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 B_H or the B_F curve to the right, and the associated rightward shift in the B_H + B_F 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

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Market for Bonds Denominated in Domestic Currency

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

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where $b_H^{ʹ}$, $b_F^{ʹ}$, 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

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

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,

condition (18) can be shown to be equivalent to⁶

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 DEF – dMB, 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 b_H – b_F > 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 $b_H^{ʹ}$ and $b_F^{ʹ}$ 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 DEF – dMB 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 $b_H^{ʹ}$ and $b_F^{ʹ}$. For the limiting case in which domestic bonds and foreign bonds are perfect substitutes, $b_H^{ʹ}$ = $b_F^{ʹ}$ = ∞ 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:

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. W_ROW is the dollar valuation of the net money and bond holdings of the rest of the world, and b_R(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

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

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

Condition (24) can then be expressed as

where the notation

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

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

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 $\overline{B}$ that correspond to a broad range of plausible assumptions about ${\overline{b}}_H,{\overline{b}}_F,\mathrm{a}\mathrm{n}\mathrm{d}{\overline{b}}_R$. 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 (${\overline{b}}_H,{\overline{b}}_F,{\overline{b}}_R$) using a grid of the 200 combinations of ${\overline{b}}_H$ = 0.95, 0.90, 0.85, 0.80, 0.75; ${\overline{b}}_F$ = 0.05, 0.10, 0.15, 0.20, 0.25; and ${\overline{b}}_R$ = 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 (${\overline{b}}_H,{\overline{b}}_F,{\overline{b}}_R$) = (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

¹Ratio of the root-mean-square prediction error to mean absolute value of the independent variable.

²Coefficient of correlation between the estimated risk premium and the dependent variable.

³Number of observed changes in the dependent variable (of 24 total observations) that are predicted correctly in sign.

⁴Average absolute value of the estimated risk premium divided by the average absolute value of the dependent variable.

⁵Mean of the estimated risk premium.

⁶These are t-statistics associated with the regression estimates ɸ₀ and ɸ₀/ϵ.

⁷Coefficient of first-order autocorrelation in the residuals from the regressions after the Cochrane-Orcutt correction.

Table 1.

Goodness-of-Fit Statistics and Parameter Estimates

Prespecified Parameters			Goodness-of-Fit Statistics				Regression Estimates
${\overline{b}}_H$	${\overline{b}}_F$	${\overline{b}}_R$	RMSE1	RHO12	Signs3	Scale4	Mean ɸ5	∊	ɸ0	ɸ0/∊	tɸ06	tɸ0/∊6	RHO27
0.85	0.15	0.1	1.10	0.289	14	0.320	–0.62	0.025	–2.04	–81.5	–1.33	–1.22	–0.077
0.85	0.15	0.2	1.09	0.308	15	0.330	–0.62	0.029	–2.39	–80.9	–1.44	–1.33	–0.075
0.85	0.15	0.3	1.09	0.315	16	0.324	–0.62	0.034	–2.56	–73.8	–1.48	–1.37	–0.077
0.85	0.15	0.4	1.09	0.316	16	0.317	–0.62	0.040	–2.62	–64.9	–1.49	–1.37	–0.082
0.85	0.15	0.5	1.09	0.313	15	0.308	–0.62	0.046	–2.62	–56.6	–1.48	–1.35	–0.087
0.85	0.15	0.6	1.09	0.310	14	0.299	–0.62	0.052	–2.59	–49.6	–1.46	–1.32	–0.092
0.85	0.15	0.7	1.09	0.306	14	0.294	–0.62	0.058	–2.55	–43.8	–1.44	–1.30	–0.096
0.85	0.15	0.8	1.09	0.313	16	0.305	–0.62	0.064	–2.54	–34.3	–1.48	–1.33	–0.109
0.85	0.05	0.4	1.09	0.326	16	0.310	–0.62	0.043	–2.71	–62.2	–1.54	–1.42	–0.091
0.85	0.10	0.4	1.09	0.323	15	0.315	–0.62	0.041	–2.69	–64.5	1.53	–1.41	–0.086
0.85	0.15	0.4	1.09	0.316	16	0.317	–0.62	0.040	–2.62	–64.9	–1.49	–1.37	–0.082
0.85	0.20	0.4	1.09	0.304	16	0.317	–0.62	0.039	–2.48	–63.1	–1.43	–1.31	–0.080
0.85	0.25	0.4	1.10	0.289	15	0.311	–0.62	0.039	–2.28	–59.0	–1.35	–1.22	–0.080
0.95	0.15	0.4	1.13	0.163	14	0.192	–0.62	0.067	–0.90	–134.6	–0.741	–0.308	–0.119
0.90	0.15	0.4	1.12	0.241	15	0.277	–0.62	0.037	–1.72	–91.8	–1.11	–0.918	–0.091
0.85	0.15	0.4	1.09	0.316	16	0.317	–0.62	0.040	–2.62	–64.9	–1.49	–1.37	–0.082
0.80	0.15	0.4	1.08	0.341	16	0.323	–0.62	0.049	–2.84	–57.5	–1.62	–1.51	–0.095
0.75	0.15	0.4	1.08	0.341	17	0.332	–0.62	0.060	–2.72	–45.2	–1.62	–1.50	–0.110
0.80	0.25	0.1	1.08	0.353	15	0.357	–0.62	0.029	–2.85	–99.6	–1.66	–1.61	–0.066
0.75	0.25	0.1	1.06	0.393	18	0.354	–0.62	0.037	–3.34	–90.0	–1.89	1.83	–.080

¹Ratio of the root-mean-square prediction error to mean absolute value of the independent variable.

²Coefficient of correlation between the estimated risk premium and the dependent variable.

³Number of observed changes in the dependent variable (of 24 total observations) that are predicted correctly in sign.

⁴Average absolute value of the estimated risk premium divided by the average absolute value of the dependent variable.

⁵Mean of the estimated risk premium.

⁶These are t-statistics associated with the regression estimates ɸ₀ and ɸ₀/ϵ.

⁷Coefficient of first-order autocorrelation in the residuals from the regressions after the Cochrane-Orcutt correction.

View Table

Table 1.

Goodness-of-Fit Statistics and Parameter Estimates

Prespecified Parameters			Goodness-of-Fit Statistics				Regression Estimates
${\overline{b}}_H$	${\overline{b}}_F$	${\overline{b}}_R$	RMSE1	RHO12	Signs3	Scale4	Mean ɸ5	∊	ɸ0	ɸ0/∊	tɸ06	tɸ0/∊6	RHO27
0.85	0.15	0.1	1.10	0.289	14	0.320	–0.62	0.025	–2.04	–81.5	–1.33	–1.22	–0.077
0.85	0.15	0.2	1.09	0.308	15	0.330	–0.62	0.029	–2.39	–80.9	–1.44	–1.33	–0.075
0.85	0.15	0.3	1.09	0.315	16	0.324	–0.62	0.034	–2.56	–73.8	–1.48	–1.37	–0.077
0.85	0.15	0.4	1.09	0.316	16	0.317	–0.62	0.040	–2.62	–64.9	–1.49	–1.37	–0.082
0.85	0.15	0.5	1.09	0.313	15	0.308	–0.62	0.046	–2.62	–56.6	–1.48	–1.35	–0.087
0.85	0.15	0.6	1.09	0.310	14	0.299	–0.62	0.052	–2.59	–49.6	–1.46	–1.32	–0.092
0.85	0.15	0.7	1.09	0.306	14	0.294	–0.62	0.058	–2.55	–43.8	–1.44	–1.30	–0.096
0.85	0.15	0.8	1.09	0.313	16	0.305	–0.62	0.064	–2.54	–34.3	–1.48	–1.33	–0.109
0.85	0.05	0.4	1.09	0.326	16	0.310	–0.62	0.043	–2.71	–62.2	–1.54	–1.42	–0.091
0.85	0.10	0.4	1.09	0.323	15	0.315	–0.62	0.041	–2.69	–64.5	1.53	–1.41	–0.086
0.85	0.15	0.4	1.09	0.316	16	0.317	–0.62	0.040	–2.62	–64.9	–1.49	–1.37	–0.082
0.85	0.20	0.4	1.09	0.304	16	0.317	–0.62	0.039	–2.48	–63.1	–1.43	–1.31	–0.080
0.85	0.25	0.4	1.10	0.289	15	0.311	–0.62	0.039	–2.28	–59.0	–1.35	–1.22	–0.080
0.95	0.15	0.4	1.13	0.163	14	0.192	–0.62	0.067	–0.90	–134.6	–0.741	–0.308	–0.119
0.90	0.15	0.4	1.12	0.241	15	0.277	–0.62	0.037	–1.72	–91.8	–1.11	–0.918	–0.091
0.85	0.15	0.4	1.09	0.316	16	0.317	–0.62	0.040	–2.62	–64.9	–1.49	–1.37	–0.082
0.80	0.15	0.4	1.08	0.341	16	0.323	–0.62	0.049	–2.84	–57.5	–1.62	–1.51	–0.095
0.75	0.15	0.4	1.08	0.341	17	0.332	–0.62	0.060	–2.72	–45.2	–1.62	–1.50	–0.110
0.80	0.25	0.1	1.08	0.353	15	0.357	–0.62	0.029	–2.85	–99.6	–1.66	–1.61	–0.066
0.75	0.25	0.1	1.06	0.393	18	0.354	–0.62	0.037	–3.34	–90.0	–1.89	1.83	–.080

¹Ratio of the root-mean-square prediction error to mean absolute value of the independent variable.

²Coefficient of correlation between the estimated risk premium and the dependent variable.

³Number of observed changes in the dependent variable (of 24 total observations) that are predicted correctly in sign.

⁴Average absolute value of the estimated risk premium divided by the average absolute value of the dependent variable.

⁵Mean of the estimated risk premium.

⁶These are t-statistics associated with the regression estimates ɸ₀ and ɸ₀/ϵ.

⁷Coefficient 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.