APPENDIX: Statistical Analysis
The background to the results previously described are presented in this Appendix, which is divided into seven sections. The first defines the basic notation. The second and the third, respectively, deal with the statistical analysis of export earnings and export shortfalls. The fourth provides the rationale for the relation between shortfalls in aggregated earnings and the sum of country shortfalls. The fifth and sixth deal with two possible modifications in the definition of shortfalls—namely, taking the trend value as a geometric, instead of an arithmetic, average, and conducting calculations in real (instead of nominal) terms. The seventh consists of statistical tables.
Artus, Jacques R., “Measures of Potential Output for Eight Industrial Countries, 1955-78,” Staff Papers, Vol. 24 (March 1977), pp. 1–35.
de Vries, Jos, “Compensatory Financing: A Quantitative Analysis,” World Bank Staff Working Paper No. 228 (mimeographed, December 1975).
International Monetary Fund, Selected Decisions of the International Monetary Fund and Selected Documents (Washington, Eighth Issue, 1976).
Krishnamurty, K., and Ke-young Chu, “Export Earnings of Primary Commodity Exporting Countries and Business Cycles in Industrial Countries” (unpublished, International Monetary Fund, July 5, 1977).
Morrison, Thomas K., and Lorenzo Perez, “Analysis of Compensatory Financing Schemes for Export Earnings Fluctuations in Developing Countries,” World Development, Vol. 4 (1976), pp. 687–94.
United Nations Conference on Trade and Development, Trade and Development Board, “An Integrated Programme for Commodities: Compensatory Financing of Export Fluctuations,” TD/B/C.1/195 (October 16, 1975).
Mr. Goreux, Assistant Director in the Research Department, holds doctorates from the Universities of Paris, Louvain, and Chicago. Before joining the Fund staff, he held various positions in the Food and Agriculture Organization and in the World Bank. He is the author of Interdependence in Planning and Agricultural Productivity and Economic Development in France.
For reasons that will be explained later, the amount drawn is often lower than the amount of the shortfall.
Shortfall years are taken here as calendar years. Under the Fund facility, the shortfall year is based on the latest available data and can end in any month. For a brief description of the facility, see Goreux (1977).
When export earnings are below trend, the member experiences a shortfall. When exports are above trend, the member experiences an excess. The maximum amount that can be drawn under the facility is defined by the sum of the country shortfalls. When that sum is larger (or smaller) than the sum of the country excesses, the value of aggregated country earnings is below (or above) trend; the deviation from the trend measures the shortfall in (or excess of) the aggregated export earnings of the group of countries. (See Chart 1.)
None of the 26 countries classified in the Fund’s publication, International Financial Statistics, as either industrial countries or oil exporting countries has made use of the facility since it was liberalized by Executive Board Decision No. 4912-(75/207), adopted December 24, 1975 and reproduced in Selected Decisions of the International Monetary Fund and Selected Documents (Washington, Eighth Issue, 1976), pp. 62-66.
Forecasts for 1977 were required to calculate shortfalls experienced in 1975. The forecasts were made in February 1977.
This equation can be interpreted as the reduced form of a three-equation model defining the import demand by industrial countries and the export supply from the 71 sample countries. (See section II in the Appendix.)
In an attempt to minimize the impact of subjective factors on the estimation of the shortfall, Executive Board Decision No. 4912-(75/207)—cited in footnote 5—provides an extrapolation formula. The decision, however, specifies that the extrapolated value of post-shortfall earnings should be replaced by a judgmental forecast if the extrapolated value is not considered reasonable. In practice, a judgmental forecast is always made.
Little was gained by replacing the two world economic indicators by country-specific indicators. In one case, the business cycle indicators relating to each of the eight industrial countries were weighted by their relative shares in the imports of the primary exporting country concerned. In the other case, commodity spot prices were weighted according to the shares of each commodity in export earnings of the country. A detailed analysis of export earnings based on semiannual data for 48 countries between 1957 and 1975 is given by Krishnamurty and Chu (1977).
When shortfalls are defined in relation to an arithmetic average and the arithmetic forecasting equation is used, the sum of squares of the forecasting errors increases from 14 to 42 per cent of the variance in shortfalls.
See Section 4 in the Appendix.
See Section 5 in the Appendix.
See Section 6 in the Appendix.
More precisely, the rates of change in the value of the deflator.
All equations in this paper are estimated by ordinary least-squares techniques.
A circumflex (^) above a variable denotes its estimated value.
The values of the business cycle coefficients are about the same whether export earnings or export shortfalls are used as dependent variable. However, the estimated price coefficients are lowered in the shortfall equation; the value estimated in the earnings equation was affected by the correlation between the price and trend variables.
When the regression coefficients are alternately constrained to remain the same for all countries, the coefficients of determination comparable to those shown in rows 2-4 of Table 5 become, respectively, 0.24 (for ai, b, ci), 0.18 (for ai, bi, c), and 0.17 (for a, b, c).
When the trend is taken as the deviation from an arithmetic trend and the regression equation is expressed in the arithmetic form, the coefficient of determination is reduced to 0.58.
The dependent variable of equation (6i) is the dependent variable of equation (50 multiplied by the percentage share of country i in aggregated earnings, namely 100 Xit/Xt.
Calling ΔB the error made in forecasting B, the resulting errors δSB, δx, and δy can be calculated as follows:
δ(Bt+1 + Bt+2)/2Bt = 0.05 → δSBt/Bt = 0.02 → δxt = 1.3 δSBt/Bt = 0.026.
For xt = 10, dy/dx = 0.95 → δy = 0.025
xt = 0, dy/dx = 0.50 → δy = 0.013
xt = −10, dy/dx = 0.05 → δy = 0.0013
Consider the five consecutive values 1, 1, x, 1, 1 so that the calculated shortfall is S = x0.2 − x. Its derivative dS/dx = 0.2x−0.8 − 1 is positive for 0 < x < (0.2)⅛ = 0.134. When the value of export earnings x declines from 0.134 to zero, the amount of the calculated shortfall also declines, from 0.535 to zero.