Relationship Between Sources and Uses of Financial Wealth
The definition and measurement of wealth in this paper may be illustrated by the following set of highly simplified balance sheet identities:
First, private sector wealth (W) is defined as the sum of three assets: money (M), private holdings of government debt (Sp), and assets denominated in foreign currencies (F). Second, ignoring intermediation by the banking system, the stock of money equals the stock of bank reserves, which in turn is equal to the sum of the central bank’s holdings of government debt (Sc) and its net claims on the rest of the world (Z).27 Third, the total stock of government debt (S) is held by nonresidents (Sf) as well as by domestic residents and the central bank. Finally, from the balance of payments constraint, the net stock of external claims—the right-hand side of equation (15)—must be equal to the cumulated balance on the current and direct investment accounts (−K). For convenience, it is assumed that all external claims are denominated in the currency of the issuer, except that Z is denominated in the home currency regardless of the issuer; that is, all assets in the model except F are denominated in the home currency.
That is, rather than aggregating the uses of wealth, as in equation (12), one can equally well aggregate the sources, with a substantial gain in data availability. In practice, of course, the aggregate balance sheets are more complex than those described here; a much more detailed model is set out in Boughton (1983). From that larger model, it may be shown that the appropriate domestic source of private financial wealth is not just S, but the stock of central government debt held outside the central bank, plus the nonborrowed domestic components of the monetary base, minus government deposits in commercial banks. That is the measure employed in this paper.
Comparing equations (12) and (15) demonstrates the critical distinction between the cumulated external balance (K) and the net stock of foreign-currency assets (F). When the rest of the world accumulates claims on the home country through an increase in K, there is no automatic effect on the outstanding stock of foreign-currency assets. Whether asset holders choose to retire a portion of those assets (reducing F) or increase their holdings of home-country debt (increasing Sf and reducing Sp) is an endogenous decision depending on expected relative returns.
Bomhoff, Edward J., and Pieter Korteweg, “Exchange Rate Variability and Monetary Policy Under Rational Expectations: Some Euro-American Experience, 1973–1979,” Journal of Monetary Economics (Amsterdam), Vol. 11 (March 1983), pp. 169–206.
Boughton, James M. (1981), “Recent Instability of the Demand for Money: An International Perspective,” Southern Economic Journal (Chapel Hill, North Carolina), Vol. 47 (January 1981), pp. 579–97.
Boughton, James M. (1983), “Conditions for an Active Exchange Rate Policy with a Predetermined Monetary Target,” Staff Papers, International Monetary Fund (Washington), Vol. 30 (September 1983), pp. 461–90.
Branson, William H., Hannu Halttunen, and Paul Masson, “Exchange Rates in the Short Run: The Dollar-Deutschemark Rate,” European Economic Review (Amsterdam), Vol. 10 (December 1977), pp. 303–24.
Dooley, Michael, and Peter Isard, “A Portfolio-Balance Rational-Expectations Model of the Dollar-Mark Exchange Rate,” Journal of International Economics (Amsterdam), Vol. 12 (May 1982), pp. 257–76.
Frankel, Jeffrey A. (1979), “On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials,” American Economic Review (Nashville, Tennessee), Vol. 69 (September 1979), pp. 610–22.
Frankel, Jeffrey A. (1983), “Monetary and Portfolio-Balance Models of Exchange Rate Determination,” in Economic Interdependence and Flexible Exchange Rates, ed. by Jagdeep S. Bhandari and Bluford H. Putnam (Cambridge, Massachusetts: MIT Press, 1983), pp. 84–115.
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)| false ( Frankel, Jeffrey A. 1983), “ Monetary and Portfolio-Balance Models of Exchange Rate Determination,” in Economic Interdependence and Flexible Exchange Rates, ed. by ( Jagdeep S. Bhandariand Bluford H. Putnam Cambridge, Massachusetts: MIT Press, 1983), pp. 84– 115.
Hatanaka, M., “An Efficient Two-Step Estimator for the Dynamic Adjustment Model with Autoregressive Errors,” Journal of Econometrics (Amsterdam), Vol. 2 (September 1974), pp. 199–220.
Hooper, Peter, and John Morton, “Fluctuations in the Dollar: A Model of Nominal and Real Exchange Rate Determination,” Journal of International Money and Finance (Guilford, England), Vol. 1 (April 1982), pp. 39–56.
Knight, Malcolm D., and Donald J. Mathieson, “Economic Change and Policy Response in Canada Under Fixed and Flexible Exchange Rates,” in Economic Interdependence and Flexible Exchange Rates, ed. by Jagdeep S. Bhandari and Bluford H. Putnam (Cambridge, Massachusetts: MIT Press, 1983), pp. 500–29.
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)| false , “ Knight, Malcolm D., and Donald J. Mathieson Economic Change and Policy Response in Canada Under Fixed and Flexible Exchange Rates,” in Economic Interdependence and Flexible Exchange Rates, ed.by ( Jagdeep S. Bhandariand Bluford H. Putnam Cambridge, Massachusetts: MIT Press, 1983), pp. 500– 29.
Meese, Richard A., and Kenneth Rogoff, “Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?” Journal of International Economics (Amsterdam), Vol. 14 (February 1983), pp. 3–24.
Mussa, Michael, “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, Vol. 11 of the Carnegie-Rochester Conference Series on Public Policy (Amsterdam: North-Holland, 1979), pp. 9–57.
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)| false “ Mussa, Michael, 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 Vol. Karl Brunnerand Allan H. Meltzer, 11of the Carnegie-Rochester Conference Series on Public Policy ( Amsterdam: North-Holland, 1979), pp. 9– 57.
Tobin, James, “A General Equilibrium Approach to Monetary Theory,” Journal of Money, Credit and Banking (Columbus, Ohio), Vol. 1 (February 1969), pp. 15–29.
von Furstenberg, George M., “Changes in U.S. Interest Rates and Their Effects on European Interest and Exchange Rates,” in Exchange Rate and Trade Instability: Causes, Consequences, and Remedies, ed. by David Bigman and Teizo Taya (Cambridge, Massachusetts: Ballinger, 1983), pp. 257–82.
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)| false “ von Furstenberg, George M., Changes in U.S. Interest Rates and Their Effects on European Interest and Exchange Rates,” in Exchange Rate and Trade Instability: Causes, Consequences, and Remedies, ed.by ( David Bigmanand Teizo Taya Cambridge, Massachusetts: Ballinger, 1983), pp. 257– 82.
Mr. Boughton, Assistant Chief of the External Adjustment Division of the Research Department, holds advanced degrees from the University of Michigan and Duke University and was formerly Professor of Economics at Indiana University. He has published two books on monetary economics, as well as a number of articles in economic journals.
For convenience, the yield on money balances is ignored. For a more detailed model that incorporates interest rates paid on bank deposits, see Boughton (1983).
The relationship between the sources and uses of financial wealth is described for a detailed set of sectoral balance sheets in Boughton (1983). A simplified version is included in the appendix to this paper.
Substitution between money and goods—which would involve including the expected inflation rate as an argument—is omitted. This omission reflects the simplifying assumption that utility functions are separable between financial and real assets.
This formulation is in contrast to asset-market models such as Frankel (1979) and Hooper and Morton (1982) that treat money stocks as exogenously fixed by the authorities. For examples of other models employing reaction functions, see Branson, Halttunen, and Masson (1977) and Knight and Mathieson (1983).
This effect, however, also depends on the additional necessary condition that the intervention be large enough to alter the cumulated private capital balance by a sufficient amount and that it not produce offsetting effects on expectations.
The endogeneity of this stock is described further in the appendix.
This variable enters equation (4) as the ratio of the cumulated external capital balance, which may be denoted by K, to domestic financial wealth, W. If K were restricted to be negative, then the supply function could be written in the same form as the demand function, with the supply divided by (-K) as a measure of the home country’s claims on the rest of the world; that is, one would have Fs/(−K) = g’(r − rf − e), where F is the stock of foreign-currency assets. Multiplying both sides of this equation by (−K)/W and dropping the assumption of linear homogeneity—which is necessary to accommodate the possibility of positive values of K—gives the form of equation (4).
See, however, Bomhoff and Korteweg (1983) for a model that dispenses with long-run PPP on the grounds that currencies are subject to differing degrees of risk in predictions of their purchasing power.
A different approach by which this same result is obtained is to assume that the expected level of the exchange rate is a function of the level of the interest rate differential and that the rate of change in the exchange rate is related to the difference between this expected level and the actual lagged level. See von Furstenberg (1983).
The relationship between the parameters of equation (9) and the structural parameters is as follows:
α0 = λ1(f0 − g0), α1 = λ1(f1 + g1), α2 = λ1g2, and α3 = α2κ.
With goods prices exogenous, stability of this function requires 0 < α3 ≤ 1.
Expected inflation is measured in this study as a moving average of the rate of change in the deflator for private domestic demand. In practice there is likely to be some feedback from the exchange rate to expected inflation. The estimate of α1 is thus expected to be biased, to an unknown extent; nonetheless, for major industrial countries the extent of this bias should be relatively small.
These parameters are derived as follows:
β0 = γ(l0 − m0), β1 = γm2, β2 = γm3, β3 = γl2,
β4 = γm1, and β5 = γ/λ2, where γ = λ2/[1 + λ2(l1 + m2)].
Data on money, income, prices, and financial wealth are seasonally adjusted.
For example, in the MERM, the U.S. dollar has a weight of 50 percent in the computation of the effective exchange rate for the Japanese yen and less than 25 percent for the other three major currencies. The weight for the dollar in computing the value of the SDR was set in 1981 at 42 percent.
An SDR-weighted effective exchange rate is not the same as the SDR value of a currency. The latter is a variable-weight value based on a fixed basket of currencies. The index developed here is a fixed-weight value based on the SDR weights established at the time that the SDR was reconstituted as a five-currency basket in 1981.
If the equations for the four bilateral rates are combined to solve for the effective rate for the U.S. dollar, one obtains an equation similar to equation (9) except that the U.S. private capital balance is replaced by a weighted average of the capital balances for the other four countries, and the weights on the foreign interest rates depend on the parameters of the bilateral equations as well as the exchange rate weights.
The Hatanaka estimator uses two-stage least squares, with the lagged dependent variable treated as endogenous because of the presence of serially correlated residuals, to obtain an initial estimate of the autocorrelation coefficient. An ordinary least squares regression is then run on quasi-differences of the data, plus the residuals from the first regression. The coefficient on the residuals is added to the initial estimate to give the final estimate of the autocorrelation coefficient (p).
The problems with the equation for the pound sterling most likely reflect the instability of demands for financial assets in the United Kingdom, as has long been evident in studies of the demand for money. For a discussion of that issue, see Boughton (1981). The ending of capital controls in the second half of 1979 may have had a particularly destabilizing effect on the exchange market equations for the pound sterling.
Recall that the predicted values of interest rates from the equations shown in Table 1 have been used as instruments in these equations, so that these coefficients should be relatively free of reverse causation bias.
As is shown in footnote 10, the coefficient on the lagged real exchange rate is the product of three structural coefficients: the lag operator in the market for foreign-currency assets (λ1), the coefficient on the cumulated private capital balance in the supply function for those assets (g2), and the Marshall-Lerner coefficient (k).
Mussa (1979) has asserted that a model should be judged “successful” if it explains “10 percent of the actual quarter-to-quarter changes in exchange rates” (p. 50). The criterion applied here, using significance level of 0.05, is roughly equivalent to Mussa’s for the present sample.
Compare Table 2 with the interest rate equations in Table 1. In both cases the average R2 for levels is about 0.88. However, the average R2 for first differences of interest rates is 0.47, while for exchange rates it is 0.26. The F-statistics are omitted from Table 1; all of the equations in that table are significant at the 0.01 level.
This version of the model is simplified somewhat from the functions estimated in Hooper and Morton (1982); for example, their version included the current account as well as the capital account, with both deflated by trend gross national product rather than by wealth. Also, income here is measured by private domestic demand rather than by gross national product.
The failure of relative money stocks to explain exchange rates has been observed in a number of recent papers; see Frankel (1983).
In the full model, money is defined as currency plus most bank deposits; excluded bank liabilities and—as an offsetting item—bank loans to the private sector are ignored throughout this paper.