At the outset of the current floating exchange rate regime, expectations were widespread that the new system would allow countries a high degree of policy independence yet reduce strains on the free international movement of goods, services, and capital. Even long-standing critics of exchange rate flexibility seemed unable to oppose meaningfully the advent of flexible exchange rates in the face of the severe strains of reserve changes and international payments imbalances. Domestic financial policies and economic performance in the major industrial countries had diverged to such an extent that fixed relationships among currencies were obviously unfeasible. After several years’ experience with floating exchange rates, however, it is far from clear that exchange rate flexibility enhances the ability of countries to pursue their own chosen policies without contributing to severe disruptions in the international monetary system. In fact, as experience with the regime grows, a number of the fundamental tenets of flexible exchange rate advocates are being called into question.
The long-standing case for floating exchange rates has centered principally around the argument that exchange rate flexibility allows individual countries to choose financial policies independently while removing the burden of intervention on those countries whose policies deviate from the average. This argument has been summarized forcefully by Professor Harry G. Johnson:
The adoption of flexible exchange rates would have the great advantage of freeing governments to use their instruments of domestic policy for the pursuit of domestic objectives, while, at the same time, removing pressures to intervene in international trade and payments for balance-of-payments reasons. Both of these advantages are important in contemporary circumstances. On the one hand, a great rift exists between nations like the United Kingdom and the United States, which are anxious to maintain high levels of employment and are prepared to pay a price for it in terms of domestic inflation, and other nations, notably the West German Federal Republic, which are strongly averse to inflation. Under the present fixed exchange-rate system, these nations are pitched against each other in a battle over the rate of inflation that is to prevail in the world economy, since the fixed rate system diffuses that rate of inflation to all the countries involved in it. Flexible rates would allow each country to pursue the mixture of unemployment and price trend objectives it prefers, consistent with international equilibrium, equilibrium being secured by appreciation of the currencies of “price-stability” countries relative to the currencies of “full-employment” countries.1
The essential point made by flexible exchange rate advocates, and reflected in the above passage, is that exchange rates that are allowed to adjust freely to market forces provide an adjustment mechanism that insulates each economy from external influences that would, under fixed exchange rates, dominate its own policy decisions. Under flexible exchange rates, it is assumed that each domestic monetary authority controls the supply of an independent currency that is not a substitute for others. Each monetary authority can set a particular money growth rate for its currency, and excess demands for each currency will be eliminated by exchange rate and price level changes, with purchasing power parity (PPP) establishing the equilibrium relationship between the two. This process is in obvious contrast to a fixed rate system, which can be understood most easily in the context of a stylized model with one world money and one price level for goods in terms of money. In this case, differences among countries’ excess demands for money are eliminated through the balance of payments, which changes the physical distribution of world money among countries. There is, then, only one rate of inflation, and that is determined by the world excess demand for money.
This simple view of the distinction between fixed and flexible exchange rates leaves out a critical aspect of the differences between them. In the case of a fixed exchange rate regime, the concept of the world demand for money is clear. Yet, just as in the case of the world price level under fixed exchange rates, prices or exchange rates under a flexible exchange rate system are determined by the world excess demand for each particular currency. Thus, the fundamental distinction between the monetary approach to the balance of payments and the monetary approach to exchange rates lies in the fact that the former should be concerned with national demands for a world currency while the latter should be concerned with the world demand for a national currency.
This distinction between national and global demands for a currency takes on startling importance when the concept of the world demand for national currencies is examined more closely. Residents of any country may want to hold a variety of currencies in their portfolios, both to facilitate transactions in different currencies and to earn the rate of appreciation of a particular currency vis-à-vis others. As any one currency becomes less attractive as a store of value or medium of exchange, it is reasonable for portfolio holders to replace it with other stronger currencies. In addition, as the decline in the real value of a currency makes the losses involved in holding it larger, its role as a medium of exchange is likely to be taken over by stronger currencies. In the extreme case when currencies are highly substitutable and expectations of the continuing depreciation of a currency are held with certainty, the relative attractiveness of a strong currency will eliminate demand for a weak currency, and the exchange rate between the two will cease to exist.2
The lesson of this admittedly stylized conclusion is that, when currencies are substitutes, monetary authorities face similar types of constraints under flexible rates and under fixed rates. Under fixed exchange rates and unimpeded trade in capital and goods, excessive domestic credit creation results in a balance of payments deficit that eventually leads to a reversal of the expansionary policy. When exchange rates are permitted to change, monetary authorities may have more flexibility in the short run. In the long run, however, a continuing attempt to expand the money supply faster than demand for it grows will steadily erode demand and increase the rate of depreciation of the currency as money holders attempt to switch into other currencies. Thus, even with flexible exchange rates, there are limits to the policies available to monetary authorities. In the long run, excessively expansionary policies must be reversed or capital and trade restrictions will have to be imposed.3
In the short run, when an expansionary monetary policy is unlikely to drive a currency out of existence, a more complex relationship occurs among the different currencies which is, perhaps, equally limiting to the pursuit of an independent monetary policy. In particular, while the substitution between strong and weak currencies will still be important, complementarity or sub-stitutability with respect to third currencies may be equally influential. In this case, an expansionary monetary policy may not only weaken a country’s own currency but also weaken those currencies that have in the past tended to follow the weakening currency and strengthen those that have tended to diverge from it.
In modeling third-currency effects, the importance of uncertainty and its consequences on exchange rate determination should be emphasized. Indeed, uncertainty plays a central role in the development of an asset view of exchange rate determination, as it is the uncertainty of asset returns that induces a wealth holder to invest in a variety of assets with different expected returns. In particular, a wealth holder will hold cash as well as bonds even though the former has a lower expected rate of return because it has the offsetting advantage of being less risky. This principle of risk diversification can be extended in a more general model that includes various currencies as well as bonds and other financial instruments among the available assets. By aggregating across individual portfolios and assuming that domestic capital markets are well integrated in international capital markets, one can postulate a market portfolio that includes a number of national currencies. As in the case of an individual, the market holds a variety of currencies in order to diversify risk so that the prices of currencies will reflect their expected rates of return as well as their expected covariances. Thus, assuming that the supply of each currency is exogenously determined, changes in demand will normally affect the price of the currency or, in other words, its exchange rate. Since the demand for any one currency is tied to the demand for all other currencies by investors’ desire to diversify risk, changes in the demand for one currency and, hence, its exchange rate, will affect the demand for and exchange rate of all other currencies. This interdependence among currencies can produce quite interesting patterns of exchange rate movements. For example, policy changes in one country may induce an appreciation of another country’s currency, which in turn may induce a third currency to appreciate with it and a fourth to depreciate.
Such complex reactions to a policy shift are particularly likely to occur when investors use information from past behavior or policy announcements to anticipate particular relationships among exchange rate movements. While it may be difficult to predict which of several similarly behaving currencies will, say, appreciate, it is often easier to anticipate exchange rate movements for the group as a whole. Similarly, if the economic forces that tend to strengthen one currency weaken another, and one expects the first to appreciate, then it may be reasonable to expect the second to depreciate.
Since these third-currency effects are likely, even in the short run, to prevent floating exchange rates from insulating an economy from foreign shocks, it is important for policymakers to be aware of them. This paper is an attempt to measure the importance and nature of relationships between major currencies by examining them within the general framework of asset portfolio allocation decisions. From the general framework, an empirically manageable model is derived and estimated for eight currencies during the period March 1973-June 1978. The results show that currency substitution is an empirically significant phenomenon that must be accounted for in any modeling of exchange rate determination.
I. Empirical Measures of Rates of Return
Since empirical measures of the rate of return on each asset included in the model are not directly available, those used are based on a particular view of the characteristics of the rate of return on each of the three types of asset. The purpose of this Appendix is to describe, in more detail than in the text, the characteristics of the rates of return used in this paper. The rate of return on each currency,
In this paper, it is therefore assumed that each money, broadly defined, yields a nominal rate of return proportional to the interest rate on domestic nonmoney financial assets plus the change of its value in terms of U. S. dollars. Specifically, each country’s domestic currency is expected to yield ϕjij, where ϕj is a (constant) proportion of the yield on nonmoney financial assets and ij is the nominal interest rate on country j’s nonmoney financial assets. The second component of the return on currency j is simply the expected appreciation of the value of currency j in terms of U. S. dollars, Δ
In addition to its pecuniary return, money provides services in facilitating transactions in goods and asset markets. These services can be viewed as a nonpecuniary return which is typically captured in demand for money functions via a scale variable such as income or expenditure. Following this practice it is assumed that the nonpecuniary return (
The expected rate of return on currency j (
Although ij in equation (8) in principle should be the rates of return on bonds issued by the jth country, it is assumed that all noncurrency financial assets are perfect substitutes, so that there is effectively only one rate of return common to all of them; that is, the assumption of perfect substitutability implies that interest arbitrage equalizes the nominal yields on financial assets issued in any currency in terms of the numeraire. The yield on the jth country’s financial asset, ij, plus the expected rate of appreciation of the currency, Δẽj therefore, is assumed to equal the yield on financial assets in the numeraire currency, in.
Perfect substitutability among financial assets implies that the demand for financial assets denominated in any individual currency is indeterminate, so that it is possible only to determine the demand for the world aggregate of financial assets. In the model, therefore, the returns on individual financial assets are expressed collectively in terms of the yield on the financial asset of the numeraire currency, ĩn, deflated by the expected inflation rate of traded goods, also in terms of the numeraire.
Without the assumption of interest rate parity, it would be necessary to account for rates of return on comparable assets for each of the national capital markets—a difficult and cumbersome procedure. As a justification for the approach taken here, it should be noted that the assumption of interest parity is not unreasonable for most countries. It seems to fail only for currencies of countries that impose taxes or controls on capital transactions or that present sovereign risk in some other capacity.21 Even then, as long as such measures do not change over time, returns on assets should move together in a fixed relationship.
The rates of return on both money and nonmoney financial assets include components that cannot be directly observed but that can be determined by using another variable as proxy without a great loss of accuracy. Several recent papers provide evidence that the market forward premium for the jth currency (fj) is an unbiased forecast of the rate of appreciation of the currency, at least for the short maturities considered in this paper.22 Therefore, the forward premium has been used as a proxy for the expected rate of appreciation of a currency.
Finding a proxy for the expected rate of return on traded goods, ΔρT, is more difficult, although the relationship between expectations about the future inflation rate and rates of return on financial assets suggests a possible proxy. Given evidence that the interest rate is an unbiased forecast of the underlying inflation rate in the economy, 23 it is assumed that when interest parity holds the underlying inflation rate, expressed in a numeraire currency, is common to all countries. Since the inflation rate of nontraded goods is not equalized among all countries in the short run, the underlying inflation rate forecast by the interest rate must reflect only the inflation on traded goods. The expected change in the price of traded goods,
Relaxation of the purchasing power parity assumption for the short run implies that the relative price of nontraded and traded goods is not constant. Portfolio holders, therefore, face different returns on holdings of traded and nontraded goods. Although the nontraded goods of any one country, by definition, cannot be consumed in another country, it is possible to divorce the residence of a wealth holder from the storage place of a commodity that is purchased solely as a store of value. This is achieved simply by issuing titles to ownership of commodities, such as warehouse receipts and deeds. This separation of residence of the wealth holder from storage place of commodity stocks through the use of titles allows nontraded goods to enter the international portfolio, even though only the titles and not the goods themselves are internationally traded. Without titles to ownership the only real asset in the international portfolio would be traded goods, since nontraded goods could be included only in domestic asset portfolios.
While individual price indices of nontraded and traded goods are not available, the expression for the rate of return on nontraded goods requires only the expected differential rate of inflation between nontraded and traded goods. It is, therefore, possible to use as a proxy the difference between changes in two price indices, such as the consumer price index and wholesale price index, which include both traded and nontraded goods but with different weights, the former giving more weight to nontraded goods and the latter to traded goods. It is assumed that the expected differential change is equal to the current value, which is exogenous to the model.
II. Restrictions on General Portfolio Model
Since many of the restrictions are imposed directly on the functions expressing the equilibrium level of demand for each currency, it is convenient to rewrite the equilibrium equations (equation (2) in Section I) for the currency subset of the model in explicit functional form:
μk = constant term
All other variables are defined in Appendix I. The coefficient on real wealth is constrained to equal one, reflecting the assumption that the demand for real balances denominated in any currency is homogeneous of degree one in wealth.
The first set of restrictions results from the symmetric properties of the matrix of coefficients, αkj. These properties can be derived directly from utility maximization of wealth subject to a wealth constraint.24 The maximization process produces a term for the substitutability between any two assets that can be interpreted in the same way as a Slutsky equation in consumer demand theory, i.e., the effect on the demand for currency k of a change in the return on currency j when the investor is compensated for the change in expected wealth resulting from the new configuration of expected returns on his assets. Given the assumption that the covariance matrix of asset returns is symmetrical, it can be shown that these substitution effects are also symmetrical.
In practice, symmetry restrictions are imposed by requiring that the partial derivative of currency k with respect to the return on currency j is identical to the partial derivative of currency j with respect to the return on currency k. In terms of the notation,
where ωj,(ωk) is the mean share of currency j (k) in total currency holdings. Second, the coefficients on rates of return on nonmoney assets are restricted to be identical in each equation. In terms of the notation,
The implication of this restriction can be understood best by viewing the allocation of wealth among currencies as a two-step decision. In the first step, portfolio holders allocate their wealth among money (the aggregate of all eight currencies) and other assets (bonds and stocks of commodities). In the second step they allocate their money holdings among the eight currencies. Imposing this process on equation (14) results in an equation with the following form to describe the desired demand for total money holdings denominated in each of the eight currencies in the model:
μm = constant term
Given the total demand for money as a function of wealth and the rates of return on all assets, the restriction ηij implies that the desired share of each currency k in total money holdings is a function only of rates of return on currencies.
The rest of the restrictions are imposed on the dynamic structure of the model which, as developed in Section I of the text for the entire model, is easily applied to the currency subsection as follows:
dj = deviation of desired holdings of asset j from last period’s actual holdings,
Corresponding to the equilibrium demand for total money holdings defined in equation (17), an additional adjustment function is defined as follows:
θm = the mean share of money in total wealth
λm = rate of adjustment of actual to desired money holdings
We begin with the assumption that changes in currency holdings are not affected by disequilibria in holdings of nonmoney assets. Lack of stock data for these assets makes this assumption unavoidable. In terms of the model, the adjustment coefficients on all nonmoney assets in the money demand subset of the full model are set equal to zero.
The second set of restrictions on the dynamic structure requires that adjustments to the desired shares of currencies in total money holdings take place instantaneously. In other words, for any given level of total money holdings, the desired and actual shares of each currency are always equal. Algebraically, equality between desired and actual shares of currencies implies:
In estimating the model with these dynamic restrictions, two approaches are feasible. First, it is possible to derive the restrictions implied by (22) on the individual dynamic money demand equations, (19). This is done by subtracting ak(–1) and m (–1) from both sides of equation (22), rearranging, and substituting for Am in equation (20) to get
Since m has been defined as
In terms of the original equation (19), these restrictions imply
One approach to estimation, then, is to estimate money demand equations of the form (19) with the restrictions given by (25), (26), and (27) imposed directly. A second approach, which was used here, is to estimate an overall money demand equation of the form (20) and seven currency share equations of the form (22). The two approaches obviously yield identical results in terms of the structural equation (19), and the choice was made solely for convenience.
III. Data Sources
Exchange rates are defined as U.S. dollars per domestic currency units. The U.S. interest rate is the rate on 30-day Eurodollar deposits. The forward premiums and discounts are the rates on 30-day contracts. The data for these rates are taken from Weekly Review, International Money Markets and Foreign Exchange Rates, Harris Bank, Chicago, Illinois. The observations used correspond to the rate available on the last Friday of the month.
The nominal stock of each currency is measured by the stock of broad money in each country.25 For most countries, the data are constructed by adding seasonally adjusted money (line 34 … b) and quasi-money (line 35, seasonally adjusted), both taken from International Monetary Fund, International Financial Statistics (IFS). For the United Kingdom, a broader concept, M3, taken from the Bank of England, Quarterly Bulletin and seasonally adjusted, is used.
Real income is measured as gross national or gross domestic product in 1975 prices, depending on the country. These data are obtained from IFS For Italy and Switzerland, 1978 data are Fund staff estimates of gross domestic product. Since the data are available only on a quarterly basis (with the exception of Switzerland), monthly estimates were made by interpolating the quarterly data using monthly industrial production indices as benchmarks. For Switzerland, the yearly data were interpolated to a quarterly frequency using industrial production and to a monthly frequency using a quadratic interpolation of the quarterly series. Real incomes in national currencies were converted into U.S. dollars using the average 1975 exchange rate.
Wholesale and consumer price indices were taken from IFS. The index of industrial country export unit values (line Ml1075 … d from IFS), seasonally adjusted, was used as a proxy for the price index of traded goods.
Aliber, Robert Z., “The Interest Rate Parity Theorem: A Reinterpretation,” Journal of Political Economy, Vol. 81 (November/December 1973), pp. 1451–59.
Bilson, John F.O., “The Monetary Approach to the Exchange Rate: Some Empirical Evidence,” Staff Papers, Vol. 25 (March 1978), pp. 48–75.
Brainard, William C, and James Tobin, “Pitfalls in Financial Model Building,” American Economic Review, Vol. 58 (May 1968), pp. 99–122.
Brillembourg, Arturo, “The Role of Savings in Flow Demand for Money: Alternative Partial Adjustment Models,” Staff Papers, Vol. 25 (June 1978), pp. 278–92.
Cornell, Bradford, “Spot Rates, Forward Rates and Exchange Market Efficiency,” Journal of Financial Economics, Vol. 5 (August 1977), pp. 55–65.
Dooley, Michael P., “Note on Interest Parity, Eurocurrencies and Capital Controls,” International Finance Discussion Paper No. 80, Board of Governors of the Federal Reserve System (Washington, January 1976).
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Grauer, Frederick L.A., Robert H. Litzenberger, and Richard E. Stehle, “Sharing Rules and Equilibrium in an International Capital Market Under Uncertainty,” Journal of Financial Economics, Vol. 3 (June 1976), pp. 233–56.
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Johnson, Harry G., “The Case for Flexible Exchange Rates, 1969,” Further Essays in Monetary Economics, ed. by Harry G. Johnson (Harvard University Press, 1973), pp. 198–222.
Kareken, John, and Neil Wallace, “International Monetary Reform: The Feasible Alternatives,” Federal Reserve Bank of Minneapolis, Quarterly Review (Summer 1978), p.2.
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Levich, Richard, “On the Efficiency of Markets for Foreign Exchange,” in International Economic Policy: Theory and Evidence, ed. by Rudiger Dornbusch and Jacob A. Frenkel (Johns Hopkins University Press, forthcoming).
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Royama, Shoichi, and Koichi Hamada, “Substitution and Complementarity in the Choice of Risky Assets,” in Risk Aversion and Portfolio Choice, ed. by Donald D. Hester and James Tobin (New York, 1967), pp. 27–40.
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Wymer, Clifford R., “Full Information Maximum Likelihood Estimation with Nonlinear Restrictions and Computer Programs: resimul Manual” (mimeographed, International Monetary Fund, 1977).
Mr. Brillembourg, economist in the Special Studies Division of the Research Department, is a graduate of Harvard University and of the University of Chicago.
Ms. Schadler, economist in the Special Studies Division of the Research Department, holds degrees from Mount Holyoke College and the London School of Economics and Political Science.
In a simple theoretical model of the demand for two currencies, Girton and Roper (1976) develop the implications of different degrees of currency substitution for the stability of the system and for policy independence.
Kareken and Wallace (1978) in fact argue that insofar as currencies are intrinsically useless they are necessarily perfect substitutes. They argue that perfect substitutability among currencies, while not always evident, implicitly requires that countries choose between the options of harmonizing financial policies and imposing prohibitive controls on capital and trade flows.
It is assumed that either there are no legal impediments to the exchange of assets across national borders, or changes in any impediments that exist are negligible over the observation period. In principle, taxes or nonprohibitive controls could be included in the model, but the process of accounting for them would add considerably to the complexity of the model, perhaps without proportionate rewards.
Smith (1975) gives a concise explanation of the necessity for the general disequilibrium specification and of its correct functional form.
Throughout the paper, notations are as follows: Upper and lower case letters in the Roman alphabet denote levels and logarithms, respectively, of variables (with the exception of interest rates). Upper and lower case letters in the Greek alphabet denote functions and parameters, respectively. Upper case deltas (Δ) denote first differences. Stars (*) and tildes (˜;) as superscripts denote desired and expected variables, respectively. Nominal and real interest rates are denoted by i and r, respectively. All assets are evaluated in terms of the numeraire currency (U. S. dollars) and deflated by an index of traded goods prices (industrial country export prices), also in terms of the numeraire. The real rates of return are nominal rates less the expected inflation rate of traded goods prices.
Because a logarithmic rather than a linear functional form is used, the speeds of adjustment (Δkj) must be weighted by θj in order to preserve the usual constraint that
As explained below, all rates of return are evaluated in terms of the return on traded goods, so that the real return on traded goods is its rate of depreciation, which is neglected here.
It should be noted that the assumptions of a constant real rate of interest on bonds and continuous interest rate parity imply that (r), the vector of real rates of return on bonds issued by each country, is a scalar. In the formulation of the model for estimation, therefore, the term to the real rate of return on bonds is subsumed in the constant term.
Tobin (1958) uses a similar type of portfolio allocation process in which wealth holders first allocate their liquid asset holdings between the general categories of cash and interest-bearing financial assets and then allocate the latter among the various interest-bearing assets. The two-step process is made simpler in his analysis than it is here because he assumes cash to be riskless. Nevertheless, he defends the general idea of dividing the portfolio allocation process into decisions at different levels of aggregation as a seemingly “permissible and perhaps even indispensible simplification both for the theorist and for the investor himself.”
The time trend is included as an independent term although theoretically it constitutes part of the proxy for the rate of return on currencies. This specification is necessary because the structural coefficient relating the time trend to the rate of return on money cannot be identified when the time trend is specified directly as a part of that term.
Note that for notational convenience θm λm ≡ λ.
Recall from the discussion of the rate of return on currencies that the proxy is composed of the expected rate of appreciation of the jth currency, measured by the forward rate (fj), plus a fixed proportion of the jth country’s treasury bill rate, which given interest arbitrage is equal to the difference between the Eurodollar (in) and the forward rates, a fixed proportion of the volume of transactions in the jth currency proxied by real income (Yj) less the expected rate of inflation of traded goods prices, proxied by the Eurodollar rate.
The program was developed by Clifford Wymer, and its general properties are described fully in Wymer (1977).
The advantage of formulating an explicit nonpecuniary return is that it clearly divorces the role of income as a proxy for transactions from that of income as a proxy for wealth. Furthermore, this formulation imposes strong restrictions on the income parameters. Income enters the functions for non-pecuniary returns in levels rather than logarithms because the level formulation gives a marginally better fit in estimation. Real income is measured in 1975 prices and converted into U.S. dollars using the average 1975 exchange rate.
See Royama and Hamada (1967) for a rigorous derivation of symmetry restrictions in the context of a portfolio allocation model of the type developed in this paper. Parkin (1970) has applied these restrictions in a similar way to an empirical model of U. K. discount house portfolio selection.
Although it would have been desirable to introduce some measure of Eurodeposits in the money supply figures to account for what is probably an important channel of currency substitution, no reliable data were available.