APPENDIX I Data Sources
Foreign exchange reserves--this data was obtained from the International Monetary Fund’s survey of the currency composition of members’ foreign exchange reserves. In order to maintain the confidentiality of the data file, all regressions were run “blind” without any country specific parameters.
Exchange rate arrangements--these arrangements were classified according to the system used in the Fund’s Annual Report on Exchange Arrangements and Exchange Restrictions. The classifications prevailing at the end of 1985 were extended back through the period beginning in 1976.
Exports and imports--these variables were taken from the Fund’s Direction of Trade Statistics data file.
External debt--the currency denomination of public and publically guaranteed debt was taken from the World Debt Tables issued by the World Bank.
Eurodollar six-month deposit rate--this was taken from the International Financial Statistics.
APPENDIX II First Order Conditions for Optimal Net and Gross Foreign Asset Portfolio
Selecting N1, N2, A1, and A2 so as to maximize (7) yields:
or using A = A1 + A2
Thus, for a given total level of reserves, the holdings of a particular currency depend on the expected amount of transactions in that currency in comparison with the expected amount of transactions in other currencies, the cost of converting from one currency to another, and the differential net costs of borrowing reserves in the different currencies. Notice that, from the assumed distribution of transactions,
so that E(T1) increases with t1 and declines with t2, while the opposite occurs with E(T2).
Replacing (25) and (26) in either (22) or (23), it is possible to solve for the total level of reserves A. Thus
APPENDIX III Calculation of Symmetrically Censored Least Squares Estimates
As shown in Powell (1986), the symmetrically censored least squares estimates must satisfy:
where Xt = vector of independent variables at t.
1(A) = 1 if A is true
= 0 otherwise
The procedure starts with the tobit estimates of the β’s and uses them to calculate the right hand side (r.h.s.) of equation (30). This implies an initial vector of
The variance-covariance matrix for the SCLS estimates was calculated as:
where T = sample size
The test statistic (h) for the test of normality and homoskedasticity of the error terms was calculated (see Newey (1987)) as:
Amemiya, Takeshi, “Regression Analysis When the Dependent Variable is Truncated Normal,” Econometrica, Vol. 41 (1973), pp. 997–1016.
Ben-Bassat, Avraham, “The Optimal Composition of Foreign Exchange Reserves,” Journal of International Economics, Vol. 10 (May 1980), pp. 285–95.
Ben-Bassat, Avraham, “Reserve-Currency Diversification and the Substitution Account,” Essays in International Finance (Princeton, New Jersey), No. 53 (March 1984).
Branson, William, Hannu Halttuneu, and Paul Masson, “Exchange Rates in the Short Run: The Dollar-Duetschemark Rate,” European Economic Review, Vol. 10 (1977), pp. 303–24.
Dooley, Michael, “An Analysis of the Management of the Currency Composition of Reserve Assets and External Liabilities of Developing Countries” (Washington: International Monetary Fund), DM/83/49 (June 29, 1983).
Dooley, Michael, “An Analysis of Exchange Market Intervention of Industrial and Developing Countries,” Staff Papers (Washington: International Monetary Fund), Vol. 29, No. 2 (June 1982), pp. 233–69.
Dooley, Michael, and Peter Isard, “The Portfolio-Balance Model of Exchange Rates and Some Structural Estimates of the Risk Premium” (Washington: International Monetary Fund), DM/83/20 (March 1984).
Dornbusch, Rudiger, “Exchange Risk and the Macroeconomics of Exchange Rate Determination,” The Internationalization of Financial Markets and National Economic Policy, R. Hawkins, R. Levich, and C. Wihlborg, eds. (JAI Press, 1982).
Dhrymes, Phoebus J., “Limited Dependent Variables,” in Z. Griliches and M.D. Intriligator eds., Handbook of Econometrics (Amsterdam, North Holland, 1986), Vol. III.
Frankel, Jeffrey, “The Diversifiability of Exchange Risk,” Journal of International Economics, Vol. 9 (August 1979), pp. 379–93.
Frankel, Jeffrey, “A Test of Perfect Substitutability in the Foreign Exchange Market,” Southern Economic Journal, Vol. 49 (October 1982), pp. 406–16.
Goldberger, S., “Abnormal Selection Bias” in S. Karlin, J. Amemiya, and L. Goodman, eds., Studies in Econometrics, Time Series, and Multivariate Statistics (Academic Press: New York, 1983).
Healy, James, “A Simple Regression Technique for the Optimal Diversification of Foreign Exchange Reserves” (Washington: International Monetary Fund), DM/81/64 (August 1981).
Heller, H. Robert, and Malcolm Knight, “Reserve-Currency Preferences of Central Banks,” Essays in International Finance (Princeton, New Jersey), No. 131 (December 1978).
Horii, Akinari, “The Evolution of Reserve Currency Diversification,” The Bank for International Settelements Economic Papers, No. 18 (Basle, 1986).
Hurd, M., “Estimation in Truncated Samples When There is Heteroscedasticity,” Journal of Econometrics, Vol. 11 (Oct.-Nov. 1979), pp. 247–58.
Kouri, Pentti, “International Investment and Interest Rate Linkages Under Flexible Exchange Rates,” in The Political Economy of Monetary Reform, Robert Aliber, ed. (London, Macmillan, 1977), pp. 74–96.
Kouri, Pentti, and Jorge Braga de Macedo, “Exchange Rates and the International Process,” Brookings Papers on Economic Activity (1978), pp. 397–407.
Krugman, Paul, “Consumption Preferences, Asset Demands, and Distribution Effects in International Financial Markets,” NBER Working Paper No. 651 (March 1981).
Lizondo, J. Saul, and Donald J. Mathieson, “The Stability of the Demand for International Reserves,” Journal of International Money and Finance (September 1987), pp. 251–82.
Lizondo, J. Saul