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:
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