APPENDIX Data Used in the Model
The following variables were used for estimating the model:
is Short-term interest rates: rates on money-market instruments with maturities of about three months—United States, certificates of deposit; Japan, discount rate on two-month private bills: Federal Republic of Germany and United Kingdom, interbank deposits; France, money rate against private paper
it Long-term interest rates: yields on government bonds with maturities of ten to twenty years—United States, twenty-year constant maturities; Japan, over-the-counter sales of interest-bearing government bonds with maturities of ten years or more; Germany, public authority bonds; France, national equipment bonds of 1965, 1966, and 1967: United Kingdom, twenty-year maturities
i* Foreign interest rates: for the countries other than the United States, the U.S. rate serves as the foreign rate; for the United States, the foreign rate is a weighted average of the rate for the four other countries listed above, with the weights based on the relative weights used in the SDR basket of currencies as of end-1980—0.3276 for Germany and 0.2241 each for Japan, France, and the United Kingdom
K The cumulated balance on private capital, as a percentage of total private portfolios: first, each country’s balance of payments is separated into ten to twelve components (merchandise exports and imports, service transactions, transfers, direct and portfolio capital transactions, official transactions); second, wherever monthly data are not available for one or more components, each series is benchmarked on a closely related series or interpolated; third, the balance on private capital is derived as the negative of the sum of the current account and official transactions; fourth, this balance is cumulated from the beginning of 1965 to obtain the numerator of k; fifth, the denominator is the stock of government debt held by domestic nonbank sectors, minus the numerator (that is. plus the cumulated balance on the current account and official capital); for further description of the role of k in the model, and the basis for this measure of k, see Boughton (1984)
μ The targeted rate of monetary growth: on the assumption that the authorities seek, other things being equal, to maintain steady downward pressure on the rate of monetary growth, this variable is defined here as c [2 ln (Mt-1 - ln (Mt-2)], where c (0 < c < 1) is an arbitrary constant that becomes embedded in the regression coefficients; the money stock (M) is broadly defined—United States. M2; Japan. M2 plus certificates of deposit; Germany, M3; France, resident M2; United Kingdom, sterling M3
π The expected inflation rate: for calculating long-term real interest rates, a nine-month centered average of actual inflation rates; for short-term real rates, a three-month average; prices are measured by the deflator for private domestic demand in each country
ρ Real exchange rates: relative price levels (p, domestic demand deflators) adjusted for exchange rate changes; exchange rates are end-period; for the U.S. effective rate, weights are the same as those used for foreign interest rates(i*)
y Real income: natural logarithm of the deflated level of private domestic demand.
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Mr. Boughton, an Advisor in the Research Department, holds advanced degrees from the University of Michigan and Duke University and was formerly Professor of Economics at Indiana University. He has published two books on monetary economics and numerous articles in economic journals.
The author thanks Joshua Aizenman, Assaf Razin. and his colleagues in the Research Department for comments on earlier drafts.
The interest rate data used in this paper are yields to maturity in domestic markets; real interest rates are calculated with reference to inflation in domestic goods-price indices. The conditions for constant yield-curve differences with these data are presumably stronger than would be the case for Euro-currency markets or for holding-period yields. The analysis could be extended usefully in that direction, but empirical estimation would be problematic for long-term assets
These assumptions underlie the models developed by Frenkel (1976), Mussa (197), Bilson (1978), and others. Note that the hypothesis of perfect substitut-ability requires uncovered as well as covered interest rate parity.
These assumptions characterize the Dornbusch-Frankel extension of Frenkel’s model; for an exposition, see Frankel (1983) and Boughton (1988). The implied term-structure relationship is also discussed briefly in Frankel (1979).
See footnote 51 in Shafer and Loopesko (1983, p. 57) for a list of reasons that the strict version might not hold.
A third possibility is that market participants might have maturity-dependent expectations of the inflation rate while simultaneously having a single expected path for the exchange rate. This possibility does not seem as realistic as the two mentioned here and so is ignored in the following discussion.
This hypothesis is consistent with the long-run equilibrium of the model, as long as the equilibrium real exchange rate is constant over time.
In the steady state, when Δk = 0 and ρ is at its long-run equilibrium value
In versions of this model discussed in earlier papers (Boughton (1983,1984)), the supply function for foreign-currency assets was explicitly introduced as a function of relative returns as well as of the cumulated capital balance. In that more general formulation, the structural parameters were less well-identified, but the form of the block solution was similar to equation (13).
The simple correlation coefficients between short- and long-term nominal interest differentials are 0.69, 0.70, and 0,78 for the United States, the Federal Republic of Germany, and Japan, respectively. The correlations between nom-inal short-term differentials and real long-term differentials are -0.06,0.46, and -0.09 for these same countries.
The conditions for, and the implications of. this assumption are discussed in Tobin (1969). Without this assumption, the reduced-form equation for i, (equa-tion (17)) would include a term in i, with an expected negative coefficient.
This formulation assumes slow adjustment of a financial-market price; alter-native hypotheses would be that goods prices adjust gradually in response to excess money demand or that the money stock adjusts gradually. The former would require a more general equilibrium framework than has been developed here, whereas the latter would seem to be inconsistent with the view expressed in equation (15)—-that the monetary authorities control the money stock through a reaction function. Tests of these alternatives would constitute a useful extension of the estimates presented below.
The structural parameters of equations (14)—(16) may be recovered from the reduced-form estimates of equation (17) as long as one parameter is determined independently. A convenient choice is which may be estimated from other studies of the income elasticity of the demand for money. Equation (17) also imposes the same elasticity on real output and the price level by using nominal income (V); note that money, income, and prices are all expressed as natural logarithms.
Identities are required for the nominal and real short-term foreign interest rates and for the real long-term foreign interest rate.
The program is SIMUL, developed by Clifford R. Wymer of the Fund.
The F-statisties for these three equations are 5.17 (the U.S. dollar effective rate), 4.39 (the dollar-deutsche-mark rate), and 3.50 (the dollar-yen rate). These statistics may be compared with those reported in Table 1 of Boughton (1987, pp. 46-47), where the model was similar to the present one except that short-term interest differentials were omitted; the sample period was the same, al-though the current data set has been updated. The corresponding statistics in the earlier paper were 6.63, 3.25, and 2.70, respectively; the last two were significant only at the 95 percent confidence level.
Dynamic simulation “cannot discriminate between models in terms of the validity of their estimated parameters, nor their congruity with the sample evi-dence.... In fact, what dynamic simulation tracking accuracy mainly reflects is the extent to which the explanation of the data is attributed to non-modelled variables” (Chong and Hendry (1986, p. 673)).
During the first two years of the simulation period, U.S. short-term interest rates were quite high. Consequently, the co unterf actual experiment results in correspondingly high long-term rates; during the later years, the effect is to reduce long-term rates, but by relatively smaller amounts. For the other coun-tries, the experiment reduces long-term rates over most or all of the simulation period.