Export Norms and Their Role in Compensatory Financing
Author:
J. MARCUS FLEMING
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Rudolf Rhomberg
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LORETTE BOISSONNEAULT
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Publication Date:
01 Jan 1963
eISBN:
9781451956023
Language:
English
Keywords:
SP; export; export norm; Japan; export receipt; export cycle; root mean square percentage deviation; moving average; regression calculation; Exports; Export fluctuations
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Marcus Fleming, Rudolf Rhomberg, and Lorette Boissonneault*

Abstract

Marcus Fleming, Rudolf Rhomberg, and Lorette Boissonneault*

Marcus Fleming, Rudolf Rhomberg, and Lorette Boissonneault *

There are many purposes, both of national and of international policy, for which it may be necessary to isolate short-term fluctuations in an economic variable by establishing a medium-term norm, or trend value, from which positive and negative deviations can be measured. In recent years, this need has presented itself especially with respect to fluctuations in the export prices or proceeds of countries exporting primary products. The purpose in question may be to devise a national export marketing scheme that aims, through fiscal action, to stabilize the prices or proceeds received by domestic producers; or an international commodity arrangement that aims, through buffer stocking, at stabilizing the prices or proceeds received by producing countries; or a compensatory financing scheme whereby short-term fluctuations in the export receipts of primary producing countries would be automatically offset, in whole or in part, by some form of international transfer. Under all these schemes, prices or proceeds would have to be stabilized with reference to some medium-term norm, or trend.

Part I of this study considers what are the desirable characteristics of a medium-term norm, having in mind such purposes as those described above, and how such a norm can best be estimated in practice, given the limited amount of relevant information available at the time when the estimate has to be made. For purposes of illustration, attention is confined to export proceeds. Similar problems would, however, arise, and a similar treatment be appropriate, in arriving at suitable norms for export prices.

Part II of the study concentrates attention on international schemes, of a more or less “automatic” character, for compensating short-term fluctuations in exports, with special emphasis on the manner in which the norm can in practice be determined. Alternative schemes are then evaluated by tests based respectively on the “ideal” norm discussed in Part I, suitably adjusted for the purpose of compensatory financing, and on a criterion of “smoothness.”

Part I. A Comparison of Formulae for Determining Export Norms

For various types of stabilization activities, of the kind indicated above, it is desirable to find a moving norm, or trend, which will yield positive deviations (excesses) and negative deviations (shortfalls) that approximately balance over a fairly short period (say three to five years). For this purpose, the norm, ideally, should fulfill two conditions:

  • 1. It should respond to medium-term trends or movements in the original series (i.e., for the data under consideration, in export proceeds). The shorter the period within which an approximate balance between positive and negative deviations is to be attained, the more responsive the norm must be to the movements in actual exports.

  • 2. Its movements should be synchronized with the medium-term tendency of movements in actual exports; that is, the norm should reflect not only the actual exports of the more or less recent past but also those of the more or less immediate future. Otherwise, if the movement in actual exports has a persistent tendency in one direction, the movement in the norm will lag continuously behind actual exports. If the persistent trend is upward, positive deviations of actual exports from the norm will predominate; if the trend is downward, negative deviations will be the rule.

This statement of desiderata strongly suggests the selection, as the ideal export norm for any particular year, of a moving average of actual exports over a number of years symmetrically distributed before and after the year in question. The choice probably lies between a centered seven-year and a centered five-year moving average. For the purpose of this paper we shall take as the definition of the ideal norm an unweighted moving average of actual exports for the five years beginning two years before and ending two years after the year in question.1 This definition seems—from the charts shown below (pp. 112–24)—to yield deviations that correspond reasonably well with what economists usually have in mind when they speak of short-term export fluctuations.

Any attempt, however, to apply plans for stabilization or financial compensation on the basis of an ideal norm, as thus defined, runs into the difficulty that the value of the norm for any year cannot be derived from export data that are already established at the time when action has to be taken. For practical purposes, therefore, the norm for any year has to be estimated on the basis of data relating to the same or previous years. Indeed, it has usually been assumed that such “practical” norms can be based on data relating only to previous years and not to the year for which the norm is calculated. This, however, seems to be an unnecessary restriction. Certainly, the data must relate to periods prior to the time when the estimate is made, but that estimate may well be made after the year to which the norm relates. In any event, any estimate of a deviation from normal exports involves estimating not only the norm but also the actual amount of exports for the year in question; and whatever estimate is made for actual exports can also be used in the calculation of the norm. If a preliminary estimate of actual exports for any year is made on a partially forecast basis before the end of that year, the same preliminary estimate can be used in calculating the norm; this will reduce the effect of any errors in estimating actual exports on the measurement of the compensable variation.

The question arises of how to assess the relative merits of alternative methods of estimating the practical norm. In a general sense, it would seem that the more closely such a norm approximates the ideal norm, the more satisfactory it will be. This opens up the possibility of a statistical testing of alternative practical norms in terms of their closeness of fit, as determined by least-squares regression, to the ideal norm. However, it must be borne in mind that the ideal norm has been chosen as such by reason of a complex of qualities—notably a certain degree of smoothness and an approximate balancing of shortfalls and excesses within a fairly short period of years, etc.—which are difficult to measure or even to define precisely. It is quite possible, as we shall see, that the result of one formula may deviate slightly less, in a statistical sense, from the ideal norm than another, and yet constitute on the whole a less satisfactory practical norm.

In this part of the paper we therefore seek to evaluate alternative formulae for determining practical norms, partly by comparing their closeness of fit to the ideal norm (as defined) and partly by comparing their movements on time charts relative to the movements of actual exports and of the ideal norm, respectively.

For some purposes, particularly that of determining appropriate national policies, estimates of export norms can be made on the basis of a combination of quantitative and qualitative information relating to the circumstances of the particular country. Even in such cases it may be helpful, if only as a stage in the process of arriving at a practical norm, to combine relevant statistical data for immediately preceding years in dynamic formulae derived by statistical regression. The formulae, however, can be tailored to fit the circumstances of each country and may differ, in respect to both the determining variables and the relative weights assigned to them, from country to country. Moreover, though the actual exports of immediately preceding years will always bulk large in the estimation of export norms, data reflecting other economic magnitudes likely to affect future exports, e.g., domestic cost trends or the level of economic activity in other countries, might well find a place in such calculations.

For most international purposes, however, there is need of a formula of a type that is recognizably uniform as between countries, and that can be applied to an individual country both quickly and without resort to potentially controversial statistical manipulations. The present paper deals exclusively with formulae of this relatively simple and uniform type. These formulae are tested for their relative degree of approximation to ideal export norms as defined above. The approximation can never be as close for formulae applied uniformly to all countries as for formulae that are tailored to suit the circumstances of individual countries.

The relationships tested

Practical norms have been calculated for 48 primary exporting countries2 over the period 1951–61 according to a variety of formulae. In all of these, the practical export norm, x, is expressed as a weighted sum of actual exports, x, in the current year and in preceding years, i.e.,

x ¯ t = a 0 ⁢ x t + a 1 ⁢ x t − 1 + a 2 ⁢ x t − 2 ,   etc.,

where the subscript signifies the year to which the variable refers and a0, a1, a2, etc., are constant coefficients. These formulae fall into two main categories:

  • A. Those in which the coefficients a0, a1, a2, etc., measuring the extent to which the practical norm for year t is influenced by the actual exports of years t, t-1, t-2, etc., respectively, are determined a priori; and

  • B. Those in which the coefficients a0, a1, a2, etc., are determined, by least-squares regression analysis, so as to minimize the percentage discrepancy between xt and Nt, the ideal norm (defined as a centered five-year moving average).3

For certain countries, the practical norms so calculated have been charted (pp. 112–24); for a somewhat larger group of schemes, the norms are given in Table 1 (p. 103); and for a still larger group, they are presented in Table 3 (p. 110).

Table 1.

Extent of Discrepancy Between “Practical” Export Norm (on Alternative Definitions) and “Ideal” Export Norm (Define as a Centered Five-Year Moving Average of Actual Exports) for 48 Primary Producing Countries, Selected Formulae

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Root mean square percentage deviation of “practical” norm from “ideal” norm.

Table 2.

Coefficients by Which Actual Exports in Each of the Years Covered by a Category B Formula are Multiplied to Yield a “Practical” Export Norm for the Current Year1

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Fitted over the period 1961–59.

Table 3.

Extent of Discrepancy Between “Practical” Export Norm (on Alternative Definitions) and the “Ideal” Export Norm (Defined as a Centered Five-Year Moving Average of Actual Exports) for 48 Primary Producing Countries

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Weights determined by regression. The weights given refer to the period 1951–59 or the first sub-period for which the calculation could be made. The regression weights for the other subperiods are shown as Table 4.

Weights implied by extrapolation from moving trends. See discussion in the Appendix, (p. 108).

Root mean square percentage deviation of “practical” norm from “ideal” norm.

Table 4.

Weights Determined by Regression

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Category A formulae

In one type of Category A formula, equal weights are given to the exports in such years as are included. Thus, in the examples set forth in Table 1, the practical export norm of any year is equal, respectively, to

  • (1) the actual exports in the current year, [xt = xt],

  • (2) the actual exports in the preceding year, [xt = xt-1],

  • (3) the “unweighted” (i.e., equally weighted) mean4 of the exports in the two preceding years, [xt = ½ (xt-1 + xt-2)],

  • (4) the “unweighted” mean of the exports in the three preceding years, [xt = ⅓ (xt-1 + xt-2 + xt-3)],

  • (5) the “unweighted” mean of exports in the current year and preceding year, [xt = ½ (xt + xt-1)], and

  • (6) the “unweighted” mean of exports in the current year and two preceding years, [xt = ⅓ (xt + xt-1 + xt-2) ].

Norms based on the “unweighted” means for longer periods of years than those given above show a poorer approximation to the ideal norm and are generally less satisfactory.5

Table 1 also shows

  • (7) a particular unequally weighted mean for the current year and the two previous years, [xt = ½xt + ¼xt-1 + ¼xt-2]. This particular formula is not, strictly speaking, of an a priori character, since it represents a rounding of one of the formulae arrived at by least-squares regression.

A second type of Category A formula is also shown in Table 1, namely, one in which the practical export norm for any year is equal to

  • (8) a figure arrived at by extrapolating a straight-line trend fitted (by least squares) to actual exports over the preceding seven years, and

  • (9) the value for the current year of a straight-line trend fitted to actual exports over a five-year period ending in the current year.

Trends for longer or shorter periods than those shown here yield practical norms that approximate less closely to the ideal norms (Table 3). As is demonstrated in the Appendix to Part I, norms arrived at by trend fitting as in (8) and (9) above can be expressed as weighted means of actual exports, over the years in question, with unequal coefficients or weights. They therefore belong, where we have put them, in Category A.

Category B formulae

For each practical norm in Category B, the coefficients expressing the influence on the practical norm for any year of actual exports in the several preceding or current years have been arrived at by a single least-squares regression calculation including all countries. More precisely, the coefficients are such as to minimize the average squared percentage discrepancy between xt and Nt for all 48 countries and all the years covered in the calculation in question. Of the practical export norms of Category B, four are included in Table 1, viz., those expressing the practical norm for any year as a weighted sum of actual exports in

  • (1) the two preceding years,

  • (2) the three preceding years,

  • (3) the current year and the preceding year, and

  • (4) the current year and two preceding years.

In all these examples, the regressions have been calculated (to permit comparison) over the same period, 1951 to 1959 inclusive. Formulae including a larger number of previous years’ exports could have been—and some have been—calculated (Table 3). With each addition of a year to the formula, the “fit” between xt and Nt necessarily improves. But with each such additional year, the number of years that can be included in the regression calculation declines, and one can feel less and less confident of the validity of the results. As can be seen from Table 3, the closeness of fit does not in fact increase very materially even when the number of years for which exports are included rises from three to seven. It has therefore been decided to stop short, in Table 1, at the former figure.

Table 2 sets forth the coefficients or weights assigned by regression analysis under the various Category B formulae to actual exports in each of the years covered by each formula.

As shown by the table, all the coefficients are positive, and the later the year, the higher is the coefficient. (These features are not implicit in the nature of the calculation.) For formulae including year t-4, the regressions yielded coefficients for that year that were both small in magnitude and statistically of low significance. In general, the coefficients add to more than unity, and the further back in time is the average year covered by the formula, the higher is the sum of the coefficients. In this way, the general upward trend in the exports of the 48 countries is reflected in the calculation.

Coefficients for Category B formulae have been worked out by regression analysis not only for the period 1951–59 but also for overlapping subperiods. As shown in Table 4, the coefficients arrived at for the various formulae are remarkably stable in the various subperiods.

Comparison of formulae

In Table 1, the standard percentage deviations of the selected practical norms from the ideal norm are shown both for the period 1951–59 as a whole and for the subperiod 1955–59.6 This has been done largely to facilitate comparison between the results for formulae A.8 and A.9 (which are not available for the earlier part of the period) and those for other formulae, but it also shows how stable, as between different periods, is the ranking of the different practical norms with respect to the magnitude of their standard deviations—a fact that is brought out even more convincingly in Table 3, where standard deviations are given for various subperiods. The general decline in the standard deviation in successive subperiods results from the greater stability of export earnings as the disturbances following the Korean war were left behind.

Evaluation of the tests

1. Formulae that give a substantial weight to the current year’s exports in the computation of the practical norm fit the ideal norm more closely than those that exclude the current year.

2. From the nature of the mathematical process involved, it follows that formulae for which the coefficients or weights are assigned by least-squares regression yield a better fit than those for which weights are assigned a priori. The reason why the results of formula A.7 in Table 1 are close to those of B.4 is that the weights of the former were specifically chosen as an approximation to those of the latter. On the other hand, the results of A.5 are close to those of B.3, because the least-squares coefficients of the latter happen to be close to the equal weights of the former.

3. Among the formulae using “unweighted” means, a closer fit to the ideal norm is obtained by using the exports of the preceding two years (A.3) than by using the exports of the preceding three years (A.4). This is somewhat to be expected in view of the definition of the ideal norm itself, which gives weight to the last preceding and second last preceding years but not to the third last preceding year.

4. Similar considerations help to explain the fact that formula A.6 gives a closer fit than formula A.5. However, the fact that formulae A.7 and B.4 give a closer fit than formula A.6 (i.e., the fact that a better fit is obtained when the current year is given an especially large weight) does not follow from the definition of the ideal norm, but indicates that the current year is a better predictor of the years immediately following than are past years.

5. The “unweighted” arithmetic means of the previous two years (A.3) and of the previous three years (A.4) lie, in general, further from the ideal norm than does the current level of actual exports (A.l). This does not mean that A.3 and A.4 fluctuate more widely than A.l. On the contrary, such moving averages of several years’ exports necessarily pursue a smoother course than do the exports of a single year. Their wider deviation from the ideal norm results from the fact that where the long-term trend of exports is upward (downward) the practical norms A.3 and A.4 may lie for extended periods substantially below (above) the ideal norm.

6. Over the 1951–59 period, the standard percentage deviation of the practical with respect to the ideal norm for the closest fitting of the practical norms (A.7 and B.4) is 50 to 51 per cent less than for the practical norm with the poorest fit (A.4), and 36 to 38 per cent less than for current actual exports.

7. Even for the practical norm showing the closest fit to the ideal norm (B.4), the standard deviation over the 1951–59 period is more than 8 per cent, and of the a priori norms other than A.7, those showing the closest fit have a standard deviation for the same period of about 10 per cent.

Comments on the charts

The charts in this paper show, for 13 primary producing countries, the movements over the period 1950–61 of four different practical norms, together with actual exports and (up to 1959) the ideal norm. The four practical norms selected for charting are not confined to those which best fit the ideal norm but include some of those most frequently considered as practical norms in connection with schemes of compensatory financing, together with some that show a better approximation to the ideal norm. They are, running from top to bottom of the charts,

  • A.4—Preceding three years’ exports: equal weights,

  • A.3—Preceding two years’ exports: equal weights,

  • A.6—Current year’s and preceding two years’ exports: equal weights, and

  • B.4—Current year’s and preceding two years’ exports: weights determined by least-squares regression.

Examination of the charts illustrates certain features of the various practical norms that are not revealed by the single statistical measure of standard percentage deviation from the ideal norm, discussed in the previous section.

Thus it is clear that, where the long-term trend in actual exports is definitely upward, the deviations of actual exports from the practical norm are in all cases predominantly negative; and that where the long-term trend is downward, the deviations are positive. Of course, this is the more serious, the greater (up to a point) is the average length of time between the years on whose exports the practical norm for the current year is based and the current year itself, i.e., the larger are the weights given to the more distant preceding years.

The practical norms all lag to some extent behind actual exports. Here, again, the lag is the longer, the larger are the weights given to the more distant preceding years. Of the formulae illustrated in the charts, the lag is greatest for the scheme shown in the top panel of each chart (A.4), where the practical norm is the unweighted mean of the exports of the three preceding years. In this case, the average lag (of two years) appears to correspond roughly to half the length of the average export cycle in many countries, and in those countries the practical norm therefore appears to move countercyclically to actual exports. Any attempt to stabilize or compensate on the basis of such a practical norm would tend to overshoot the mark.

Though the practical norm shown in the second panel of each chart (A.3), representing the unweighted mean of the exports of the two preceding years, fits the ideal norm more closely than does that shown in the top panel (A.4), its movements are more abrupt and it is doubtful whether, on balance, it is superior to A.4. A similar objection could be brought against the practical norm shown in the fourth panel (B.4), an unequally weighted function of the current and two previous years, compared with that shown in the third (A.6), an unweighted mean of the same years. In the latter comparison, however, it is arguable that the lesser smoothness of the unequally weighted norm is outweighed by the better timing of its movements and by the resulting better balance of surpluses and deficits of actual exports with respect to it.

Conclusion

As we have seen, the merits of different formulae for arriving at a practical export norm cannot be assessed by any single measure. However, a very important measure would appear to be the smallness of the deviation of the practical norm in question from an ideal norm defined as a centered five-year moving average of actual exports. Judged by this test as well as by other characteristics, such as smoothness, promptness of response to changes in long-term trend, etc., formulae that give weight to the current year and the two preceding years appear to be preferable to those giving no weight to the current year. As the weight assigned to the current year’s exports rises above one third, the practical norm will move still closer to the ideal norm, but with some loss of smoothness.

APPENDIX TO PART I

This Appendix sets out the procedure by which the standard deviations given in Tables 1 and 3 have been computed and the methods by which the coefficients in Tables 2 and 4 have been derived.

The normal level of exports, or the ideal norm, N, for country j at time t is defined as the centered five-year moving average of exports, x:

N j ⁢ t = 1 5 ⁢ ( x j ⁢ . ⁢ t + 2 + x j ⁢ . ⁢ t + 1 + x j ⁢ . ⁢ t + x j ⁢ . ⁢ t − 1 + x j ⁢ . ⁢ t − 1 + x j ⁢ . ⁢ t − 2 ⁢ ) .

A particular practical norm, x, of the form

x ¯ j ⁢ t = a 0 ⁢ x t + a 1 ⁢ x t − 1 + … + a n ⁢ x t − n ( 1 )

will differ from the value of the ideal norm for the country and year in question by a discrepancy or “error,” Ujt = Njt – xjt. The criterion of goodness of fit which has been chosen in this study uses these deviations expressed as fractions (ujt) of the respective values of the ideal norm (ujt = Ujt/Njt). This procedure makes the errors for different countries comparable and permits an evaluation of the closeness with which a particular practical norm approximates the ideal norm, on the average, for all countries and for all years included in the computation. The measure of the average discrepancy given in Table 1 is the root mean square of the “errors” ujt (j = 1, 2,…, 48; t = 1951, 1952, …, 1959).

Since this procedure does not distinguish between the errors for different countries and for different years, the notation may be simplified accordingly. We write ui for the difference between the two norms for any year-country, expressed as a fraction of the ideal norm,

u i = N i − x ¯ i N i = 1 − x ¯ i N i

where the subscript i runs over all countries and all years. We can write

u i = 1 − a 0 ⁢ X i 0 − a 1 ⁢ X i ⁢ 1 − a 2 ⁢ X i ⁢ 2 − … − a n ⁢ X i n ( 2 )

where Xi0 stands for the ratio of the exports of the country and the year to which i refers to the respective ideal norm, and Xi1, Xi2, …, Xin stand for the corresponding ratios of the country’s exports in the first, second, …, nth, preceding year to the ideal norm of the current year. The coefficients a0, a1, …, an are the same as in equation (1).

To determine the root mean square deviation σ for any chosen practical norm we compute

σ = Σ i = 1 m ⁢ u i 2 m

where m is the number of countries (in the present study 48) multiplied by the number of years for which the computation is carried out (for instance, nine years when the period is 1951–59). These calculations are facilitated by obtaining the expression Σui2 from equation (2) in terms of the coefficients ak (k = 0, 1,…, n), their squares and cross-products, and of the sums, the sums of squares, and the sums of cross-products of the Xik (i = 1, 2, …, m; k = 0, 1, …, n). After we have obtained these moments once, the goodness of fit of any (linear) practical norm can be derived by substituting the numerical weights of this norm, including zeros where applicable, into the expression for Σui2. For instance, for the practical norm that gives equal weights to the preceding three years we would have

Σ u i 2 = m − 2 ( a 1 Σ X i 1 + a 2 Σ X i 2 + a 3 Σ X i 3 − a 1 a 2 Σ X i 1 X i 2 − a 1 a 3 Σ X i 1 X i 3 − a 2 a 3 Σ X i 2 X i 3 + a 1 2 Σ X i 1 2 + a 2 2 Σ X i 2 2 + a 3 2 Σ X i 3 2 ( 3 )

with a1 = 0.33, a2 = 0.33, and a3 = 0.33.

In order to find the set of weights, ak*, which will minimize σ for a practical norm that takes account of a given number, n’, of current or past years’ exports, we set the first derivative of Σui2 with respect to each of the weights equal to zero and obtain n’ equations of the form

∂ Σ ⁢ u i 2 ∂ a k = 2 ⁢ Σ ⁢ ( 1 − a 0 ⁢ X i ⁢ 0 − … − a n ′ ⁢ X i ⁢ n ′ ) ⁢ ( − X i ⁢ k ) = 0 ( k = 0 ,   1 ,   … , n ′ )

which are similar to the so-called normal equations of standard least-squares regression procedure. These n’ equations can be solved for the n’ values of ak*:

{ a k * } = [ Σ i ⁢ X i ⁢ k ⁢ X i ⁢ j ] − 1 ⁢ { Σ i ⁢ X i ⁢ k } ( k = 0 ,   1 ,   … ,   n ′ ;   j = 0 ,   1 ,   … , n ′ )

where braces enclose column vectors and the brackets contain the matrix of the second moments around the origin of the Xik. It follows from the method of their derivation that these “optimal” weights, ak*, yield the smallest possible percentage deviation of any practical norm from the ideal norm for the period over which they have been fitted.

Table 4 shows the weights ak* which were computed for the different sub-periods. Optimal weights have been derived for three overlapping subperiods, 1951–55, 1953–57, and 1955–59, in addition to the computations for the full period 1951–59. It is seen that the optimal weights remain fairly stable from one fitting period to another. The standard errors of these weights have been found to range from 0.01 to 0.06. The weights that apply to the current year and to the two preceding years are generally at least 5 to 10 times their standard errors.

Another type of practical norm mentioned in the text is the extrapolation of a straight-line trend fitted over the preceding θ years. For instance, if θ = 6, we compute a trend equation from the exports of years 1 to 6 and make the extrapolated value for year 7 our practical norm for that year; similarly, extrapolation to year 8 of a trend equation fitted to years 2 to 7 gives the norm for year 8, etc. Alternatively, the practical norm can be defined as the trend value for the current year computed from a trend equation fitted to the export data for the current and the (θ – 1) preceding years.

While this method appears at first sight to be quite different from the one discussed previously, it can easily be reduced to similar terms. The practical norm may be expressed as a linear function of the β preceding years’ exports with coefficients which are given by the standard regression procedure of fitting a linear trend.

In fitting a trend line to θ observations of a variable yt, we get the estimated trend values, ŷt:

y ^ t = c 0 + c 1 ⁢ t , where c 0 = Σ ⁢ t 2 ⁢ Σ ⁢ y t − Σ ⁢ t ⁢ Σ ⁢ y t ⁢ t θ ⁢ Σ ⁢ t 2 − ( Σ ⁢ t ) 2 ⁢ and c 1 = θ ⁢ Σ ⁢ y t ⁢ t − Σ ⁢ t ⁢ Σ ⁢ y t θ ⁢ Σ ⁢ t 2 − ( Σ ⁢ t ) 2 ⁢ ( t = 1 ,   2 ,   … ,   θ ) ⁢ .

all summations being from 1 to θ. The extrapolation one year beyond the fitting period is

y ^ θ + 1 = c 0 + c 1 ⁢ ( θ + 1 ) ⁢ .

By substituting for c0 and c1 and rearranging terms, we obtain

y ^ θ + 1 = A θ Σ y i + B θ Σ y i t = ( A θ + B θ ) y 1 + ( A θ + 2 B θ ) y 2 + … + ( A θ + θ B θ ) y θ where A θ ⁢           ⁢     = Σ t 2 − ( θ + 1 ) Σ t θ Σ t 2 − ( Σ t ) 2 and B θ = θ ( θ + 1 ) − Σ t θ Σ t 2 − ( Σ t ) 2 ( t = 1 ,   2 ⁢ , . ⁢ . ⁢ . ⁢ , θ ) .

We can now apply this formula to our problem by supplying the appropriate coefficients in equation (2). The proportional deviation of the ideal norm from the practical norm, defined as the extrapolated value of the straight-line trend over the preceding θ years, is then

u i = 1 − [ A θ + θ ⁢ B θ ] ⁢ X i ⁢ 1 + [ A θ + ( θ − 1 ) ⁢ B θ ] ⁢ X i ⁢ 2 + . ⁢   . ⁢   . ⁢ + [ A θ + B θ ] ⁢ X i ⁢ θ ⁢ . ( 4 )

A similar formula applies when the practical norm is taken to be the trend value computed over θ years ending in the current year. For any given trend period θ—say, a seven-year trend—Aθ and Bθ are given constants and the coefficients of the X’s in (4) are given coefficients. From the moments of the X’s and a formula analogous to (3), the standard percentage deviations, σ, for different moving trends can be immediately derived without actually fitting the individual trend equations.

This approach to the problem shows that the moving-trend extrapolation method of determining the practical norm is merely one of an indefinitely large number of possible weighting schemes of the past θ export values. Such a set of weights can never be superior to the set ak* (k = 1, 2, …, θ), which is derived by minimizing Σui2, and it could be equally good only by coincidence. The weights implied by the various moving-trend methods of defining a practical norm are given in Table 3, where they can be compared with the corresponding optimal weights determined by least squares and with the a priori weights that have been considered.

uA03fig01

ARGENTINA

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig02

BOLIVIA

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig03

CEYLON

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig04

COLOMBIA

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig05

GHANA

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig06

HAITI

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig07

INDONESIA

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig08

MALAYA

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig09

PAKISTAN

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig10

SUDAN

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig11

TUNISIA

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig12

UNITED ARAB REPUBLIC

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

uA03fig13

URUGUAY

Citation: IMF Staff Papers 1963, 001; 10.5089/9781451956023.024.A003

Part II. Statistical Testing of Alternative Schemes of Compensatory Financing

In this part of the paper, we apply certain statistical tests, based on the concept of the ideal norm employed in Part I and on a concept of “smoothness,” to a number of schemes for the compensatory financing of export fluctuations. These comprise the scheme for an International Fund for Stabilization of Export Receipts, prepared by an Expert Group of the Organization of American States (OAS), and 136 alternatives.

The OAS scheme7 envisages a permanent organization administering a revolving fund from which low-income primary producing countries would be entitled to borrow when their export proceeds fell short of the average of such proceeds over the preceding three years, and to which they would be obliged to repay outstanding loans when their export proceeds exceeded this average. In the terminology of Part I, the average value of exports over the preceding three years is thus the practical norm of the OAS scheme. In any year, countries would be entitled to borrow, in the form of “stabilization credits,” two thirds of the shortfall of exports below the practical norm up to a limit on the cumulative outstanding debt of 20 per cent of average exports over the three preceding years. Similarly, countries with outstanding stabilization credits (excluding the “deferred credits” referred to below) would repay an amount equal to two thirds of the excess of exports over the practical norm. Debts are to be repaid in the order in which they were contracted. “Interim credits” may be obtained before the final determination of the value of exports for any year; these would be adjusted after the final export data become known. Stabilization credits that have not been repaid out of excess exports within three years from the date of issue would be converted into “deferred credits,” which would be repaid in two equal installments in the fourth and fifth calendar years after the original borrowing.

The alternative schemes considered below have been arrived at by altering various features of the OAS scheme, notably the formula used to determine the practical norm. The schemes in question have been tested with respect to the export movements, over the period 1951–61 inclusive, of the 48 primary exporting countries examined in Part I. The results of these tests are presented in Table 5 (inserted between pp. 132 and 133) and analyzed in subsequent tables.

Since the selection of variants of the OAS scheme has depended in part on the way in which initially chosen alternatives performed under the tests that have been applied, and in part on the logic of the tests themselves, it is convenient to discuss these tests before describing the variants.

Description of tests and measurements

The principal test that is applied to the OAS scheme and its variants is designed to measure the extent to which the transactions under such a scheme, had it been in operation during the period 1951–61, would have improved the time pattern of foreign exchange receipts in the sense described below. We define as “foreign exchange availabilities” (or simply as “availabilities”) the actual value of exports plus any borrowings permitted, less any repayments required, under the scheme. The test is a measure of the extent to which the availabilities under a particular scheme approximate a desired or preferred level, called the “target level” (to be defined presently), compared with the degree to which availabilities in the absence of any compensation scheme—i.e., actual exports—approximate this target level. The test statistic used is the ratio of the standard percentage deviation of availabilities from the target level for all years and countries to the standard percentage deviation of actual exports from the same target. This statistic, which we call the “target deviation ratio,” will have the value of unity, if exports and availabilities are identical, so that there are neither compensatory borrowings nor repayments. A target deviation ratio close to zero would indicate that the deviations of the availabilities from the target are very small when compared with those of actual exports from the target; a value in excess of unity would indicate that the availabilities lie, on the whole, further away from the target than do the actual exports. As far as this test is concerned, therefore, the success of a compensation scheme is measured by the smallness of its target deviation ratio.

In specifying a target level of availabilities for any year and country, we take as the starting point the ideal norm described in Part I, i.e., the five-year moving average centered on the year in question. As has been argued there, a centered five-year moving average provides as fair a version as can be found of what most people would regard as the medium-term trend of exports, and effects a reasonable smoothing out of short-term fluctuations. The inclusion in the average of exports of years following, as well as of those preceding, the year in question is the only way to ensure the equality of surpluses and deficits with respect to the norm that is necessary if compensatory receipts based on deficits are to be balanced by compensatory repayments based on surpluses. The inclusion of five rather than any other number of years in the average thus centered appears to bring about an approximate balance of deficits and surpluses within the sort of period—three to five years—that might be considered appropriate for a compensatory lending scheme.

For the purpose of compensatory financing8 the ideal norm requires, however, further adjustment before it can be regarded as an acceptable target at which to aim. Variations in exports inevitably carry with them certain variations in the need, and effective demand, for imports. For this reason, the degree of compensation of export deviations from the ideal norm should be only partial. Most developing countries will be able neither to avoid a decline of imports when exports fall, nor to prevent a rise in imports when export earnings increase. Their additional foreign exchange requirements will thus be smaller than the shortfall in exports below the ideal norm, and their ability to repay borrowed reserves will be less than the excess of their export receipts above the ideal norm. The target level of export availabilities chosen in this study is a figure that lies between the actual exports and the ideal norm in such a way as to diverge from actual exports by two thirds, and from the ideal norm by one third, of the difference between actual exports and the norm. In other words, the target reflects the view that ideally two thirds of the deviations of actual exports from the ideal export norm should be compensated. A fuller discussion of the considerations underlying the degree of compensation arrived at is given in the Appendix to Part II.

Target deviation ratios based on a target compensation of two thirds are shown in column 8 of Table 5. Deviation ratios with respect to a target level of export availabilities that coincides with the ideal norm or five-year moving average are given in column 9; these ratios, based on a target compensation of 100 per cent, are shown merely for purposes of comparison with column 8.9

The degree of approximation of actual to target export availabilities does not by itself supply a fully satisfactory criterion of the excellence of a compensation scheme. As has been pointed out in Part I, movements in all the norms that can in practice be calculated for the purpose of defining compensable export deviations, based as they necessarily are on formulae relating to past and present years’ exports only, tend to lag behind the movements in the ideal norm. For this reason, movements in actual availabilities under the various schemes also tend to lag behind movements in target availabilities. Changes in the schemes whereby availabilities are made to conform more closely to the movements over time of target availabilities will beyond a certain point involve some diminution in the smoothness of the actual availabilities. A certain degree of smoothing out of availabilities, however, is part of what is sought in a compensation scheme. Therefore, in column 11 of Table 5 a measure of the “smoothness” of availabilities, relative to the need for foreign exchange for import and other foreign payments, has been supplied to provide an auxiliary, though subordinate, criterion of excellence to that provided by the target deviation ratio. This “smoothness ratio,” as the measure in question might be called, consists in the standard percentage deviation of actual availabilities from a centered five-year moving average of availabilities (corrected for the deviation of the target availabilities from the ideal norm), divided by the standard percentage deviation of exports from the ideal norm (similarly corrected).10

In addition to these measures, data showing the total for all borrowing countries of the maximum indebtedness outstanding at the end of any year from 1951 to 1961, as estimated under the various plans, are given in column 12 of Table 5. Since the maxima in 1953 or 1954 reflect the rather abnormal conditions prevailing in the early years of the period—when exports were falling after the post-Korean boom—and since by these dates the repayment features of some of the schemes had not yet had time to exercise their effect on total indebtedness, data are also given (column 14) for the amount of total indebtedness outstanding at the end of 1958, a year when indebtedness under most schemes was at its second highest level, and under some, at its highest level.

Nature of the schemes examined

All the schemes examined are based on the OAS scheme for an International Fund for Stabilization of Export Receipts, in the sense that each one shares all features of the OAS scheme other than those explicitly mentioned in Table 5; with respect to the latter it may or may not differ from that of the OAS.

Three features of the OAS scheme have been subjected to variation: (a) the weights assigned to the current and previous years in determining the current year’s practical norm, (b) the proportion which each country’s maximum permitted cumulative indebtedness under the scheme bears to the amount of its average exports over the three preceding years (the “debt limit”), and (c) the provisions governing the repayment of indebtedness under the scheme.

In regard to (a), the practical export norm for any year, calculated in the OAS scheme as the arithmetic mean of actual exports in the three preceding years, has been varied by eliminating the weight in the third preceding year, and at the same time assigning to the current year weights amounting, in different variants, to 33% per cent, 45 per cent, 50 per cent, 55 per cent, 60 per cent, 65 per cent, 70 per cent, and 75 per cent, respectively. In all schemes, the first and second preceding year are given equal or approximately equal weights, in such a fashion that the weights sum to 100 per cent. A slightly closer approximation to target availabilities might have been obtained had the weights been allowed to sum to 101 per cent so as to allow for the general upward trend in export receipts over the period in question. It was found, however, that this improvement in fit was obtained at the cost of a disproportionately large increase in the maximum outstanding indebtedness resulting from the increased entitlement to borrow combined with the diminished obligation to repay, and it was decided to discard schemes involving weights exceeding 100 per cent.

In general, it has been assumed that, subject to the limits imposed, borrowings and repayments other than repayments on deferred credits are equal to two thirds of any shortfalls or excesses of actual exports, compared with the practical export norm. In other words, the compensation ratio applicable to deviations from the practical norm has been kept at two thirds as in the original OAS scheme. As long as the compensation ratio applies equally to surpluses and deficits,11 there is no point in varying it experimentally, since the effects of a change in the compensation ratio are exactly the same as those of a change in the weight assigned to the current year, compared with other years, in the determination of the export norm. Thus it makes no difference to either borrowings or repayments whether the weights assigned to the present year’s and two preceding years’ exports in the formula determining the practical export norm are 0, 40 per cent, and 60 per cent with a compensation ratio of 40 per cent, or whether the weights are 50 per cent, 20 per cent, and 30 per cent with a compensation ratio of 80 per cent, or whether the weights are 60 per cent, 16 per cent, and 24 per cent with a compensation ratio of 100 per cent.12 The higher the compensation ratio, the higher must be the weight assigned to the current year in the determination of the practical norm, if the same results are to be obtained.

In some ways it might be more elegant to assume a compensation ratio of 100 per cent in all schemes and to adjust the weight in the current year accordingly, or to assume a zero weight on the current year’s exports in all schemes and to adjust the compensation ratio accordingly. However, to assume a two thirds compensation ratio has the advantage not only of facilitating comparison with the OAS scheme, which has such a ratio, but also of corresponding to the target degree of compensation of two thirds (with respect to deviations from the ideal norm) that is implicit in the definition of the target level of availabilities. Roughly speaking, we may say that the partial compensation with respect to export deviations from the practical norm provided in the compensation ratio reflects the partial compensation with respect to deviations from the ideal norm aimed at in the target availabilities, while the weight assigned to the current year in the practical norm affects the extent to which the latter approximates the ideal norm.

In regard to (b), the limit of the cumulative indebtedness beyond which a country is not permitted to contract new indebtedness under the OAS scheme is 20 per cent of average exports over the preceding three years. One set of alternative schemes has also been examined under which the limit is one third of such average exports, and another in which there is no limit.

In regard to (c), six alternative repayment systems (RS) have been considered:

(1) RS 1 is based on an interpretation of the Proposed Articles of Agreement of the International Fund for Stabilization of Export Receipts.13 All borrowings are assumed to take place (in the form of interim credits) in the calendar year for which the borrowing entitlements accrue. Automatic repayments on stabilization credits (i.e., repayments the amount of which is dependent on export excesses) are likewise assumed to take place—or are treated as if they took place—in the calendar year for which the repayment obligation accrues, the earliest stabilization credits being repaid first. Such part of any stabilization credit as remains unpaid in the first and second calendar year following the year in which the borrowing took place is assumed to be converted into a deferred credit in the course of the third calendar year, and in that year no repayment, automatic or otherwise, takes place with respect to those credits, though if there have been later stabilization credits any automatic repayment obligations will be applied to them. Deferred credits are repaid in two equal installments occurring in the fourth and fifth calendar years after the original borrowing.

Literal interpretation of the Proposed Articles of Agreement (Article V, Sections 2 to 5) results in the peculiar feature that under these provisions no repayment of any kind, other than a voluntary repayment, would in practice be made in the third calendar year following the year in which a debt was contracted. RS 2, which has been designed so as to eliminate this peculiarity, is thought to correspond to what the authors of the OAS scheme intended to achieve. Therefore, in Table 5 and subsequent tables, RS 1 has not been fully worked out, though two schemes of the RS 1 type are given in Table 5.

(2) RS 2 is the same as RS 1, except that stabilization credits are not converted into deferred credits until the end of the third calendar year following the year in which, and with respect to which, the borrowing took place. Automatic repayment obligations are applied to the repayment of outstanding credits in the third, as well as in the first and second, calendar year following the year of borrowing, and only what remains unpaid at the end of the third calendar year is repaid in installments in the fourth and fifth years. Total repayment in any year then equals the total amount of any five-year-old (deferred) credits outstanding plus half the amount of any four-year-old (deferred) credits outstanding plus either the maximum automatic repayment obligation (two thirds of the export excess) or the total amount of stabilization credits outstanding, whichever is the less.

(3) RS 3 is the same as RS 2, except that automatic repayment obligations are applied, in the first instance, to the repayment of any four-year-old (deferred) credits before being applied to the repayment of any subsequent (stabilization) credits.14 Compulsory repayments are made on any five-year-old (deferred) credits and also any four-year-old (deferred) credits to the extent that less than one half of the latter has been repaid out of automatic repayments. Total repayments in any year will equal total outstanding five-year-old deferred credits, plus an amount that equals the maximum automatic repayment obligation, save that it may not fall short of half the amount of four-year-old deferred credits outstanding nor exceed the total amount of credit outstanding of a maturity of four years or less.

(4) RS 4 is the same as RS 2, except that stabilization credits are not converted into deferred credits until the end of the fourth calendar year following the year of borrowing, and that the amounts so converted are repaid in two equal installments in the fifth and sixth years. The amount repaid in any year will then be all of any six-year-old credits, half of any five-year-old credits, and an amount equal to either the maximum automatic repayment obligation or the total stabilization credits outstanding (four years old or less), whichever is the less.

(5) RS 5 is an entirely automatic system of repayment without any deferment of credits or compulsory repayment of such credits. But while borrowing entitlements amount to only two thirds of any export shortfalls, repayment obligations amount to 100 per cent of any export excesses. Repayments are applied to outstanding credits in the order in which they were contracted.

(6) RS 6 is the same as RS 5, except that repayment obligations amount to only two thirds of any export excesses.

Evaluation of schemes

The results presented in Table 5 and subsequent tables relate to the performance of the various schemes considered, for all countries taken together, that is to say, in the average country. This synoptic view enables us to reach broad conclusions regarding the effects of varying certain features of the compensatory arrangements, though a close appraisal of the schemes would call for an examination of the results country by country. The following appear to be the main conclusions drawn from the tables:

(1) The extent to which any of the schemes bring export availabilities closer to the target is limited. This would be true even if the target had aimed at a 100 per cent compensation, rather than a two-thirds compensation, of deviations from the ideal norm; the deviation ratios with respect to the two targets are indeed rather similar in order of magnitude. Some of the variants examined have deviation ratios in excess of unity, showing that availabilities under these schemes deviate from the target more than do actual exports, i.e., more than availabilities in the absence of any scheme whatsoever. The deviation ratio of the OAS scheme as drafted (scheme l)15 is as high as 0.92, and the lowest deviation ratio for any scheme is no lower than 0.77. This implies that only 23 per cent of the deviations of actual exports from target availabilities would be cut out by the scheme in question (scheme 132). These figures, however, may give too negative an impression. It should be borne in mind that none of the schemes purports to do anything to improve export availabilities during years when there are neither automatic borrowing entitlements nor repayment obligations—e.g., in years of generally rising exports prior to any shortfalls. Roughly 40 per cent of all country-years fall in this category. A deviation ratio corrected for this factor can be roughly estimated by taking one and two thirds of the deviation ratio as given in Table 5 and subtracting the figure 0.67. The corrected deviation ratio for the OAS scheme would then amount to 0.86, and that for the scheme with the lowest ratio would be 0.62, implying that, in those years for which the schemes affect the level of availabilities at all, some 38 per cent of deviations from target are eliminated. Furthermore, it may be considered that the extent to which a compensation scheme relieves the hardships caused by export fluctuations is understated by the percentage reduction of export deviations, since the detrimental influence of export deviations varies more than in proportion to their size.

(2) All the schemes examined enhance the smoothness of export availabilities. This follows from the fact that all the smoothness ratios are below unity. These ratios vary from almost 0.87 in the OAS scheme as drafted (scheme 1) to 0.66 (scheme 129). In the latter case, deviations in availabilities from their own moving average are reduced by one third for all country-years, i.e., by more than one half for those country-years for which the schemes affect the level of availabilities at all.

(3) The schemes examined vary considerably with respect to the maximum total indebtedness involved, from $2,770 million for scheme 129 to $590 million for scheme 92. A similar range between the different schemes is found with respect to the 1958 peak of indebtedness. There is no clear inverse correlation, as one might at first sight expect, between the expensiveness of a scheme and the extent to which it achieves a close approximation to target. On the contrary, by and large, the more expensive schemes are further from target than the less expensive. It will be possible to get a closer insight into this relationship after the effects of varying specific features of the schemes have been examined. As has already been observed, the maximum level of indebtedness in most schemes occurs in 1953 or 1954, because of the heavy borrowing in 1952 and 1953. In these schemes, there is a secondary peak in 1958; in some, however, the 1958 peak is the absolute maximum.

(4) Perhaps the most striking of the conclusions that emerge from a perusal of Table 5 is the extent to which the inclusion of a weight on the current year in the formula determining the practical export norm, and the raising of that weight, not only reduce the volume of outstanding indebtedness occasioned by the scheme, but also, up to a point, improve the fit of actual to target availabilities. It is noteworthy that these effects appear whatever the degree of limitation on each country’s cumulative indebtedness and whatever the repayment system adopted, though, as can be seen from Tables 6 and 7, they are more pronounced where the limits on indebtedness are wide than where they are narrow. There is, of course, some weight on the current year’s exports that permits the closest approximation of actual to target availabilities. (If the weight on the current year were to rise to 100 per cent there would, in effect, be no compensation at all and the deviation ratio would rise to unity.) The weight can be determined only by trial and error; it depends to some extent on the other features of the scheme. It appears to be higher for schemes with low debt limits and compulsory repayments of deferred credits than for schemes without such limits and such repayments. Naturally, too, it is higher, the nearer target availabilities are to actual exports—e.g., higher for our target that seeks to compensate for two thirds of export deviations from the ideal norm than it would be for a target incorporating the aim of 100 per cent compensation. In almost all the schemes, however, the weight on the current year’s exports that gives the closest approximation of actual to target availabilities is to be found within the 50–75 per cent range. When it is borne in mind that, after the practical norm has been determined, only two thirds of any deviations are subject to compensation, it will be clear that, in the schemes which best approximate to target availabilities, actual availabilities will fluctuate to a very considerable extent with exports. In such schemes the peak of total indebtedness is generally less than $1,200 million.

Table 6.

Decline in Deviation Ratio (for ⅔ Compensation Target) as Weight on Current Year’s Exports Rises from Zero to 75 Per Cent and from Zero to Optimal Weight

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Table 7.

Decline in Maximum Total Indebtedness and in Total Indebtedness at 1958 Peak as Weight on Current Year’s Exports Rises from Zero to 75 Per Cent

(In millions of U.S. dollars)

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The reason why “optimal” weights on current exports are so large is, in part (as was shown in Part I), that, in any formula for determining a practical norm on the basis only of past and current data, considerable weight has to be given to the current year’s exports if that norm is to approximate as closely as possible a moving average centered on the current year; and, in part, for schemes that involve debt limits and compulsory repayments, that any addition to the weight on the current year reduces the importance of these restrictive factors and the irregularities in the flow of export availabilities to which they give rise. Thus, for example, a high weight on the current year, by reducing the amount of compensation paid during a year of shortfall, may reduce the compulsory repayments that will be necessary four or five years later, which may also be years of shortfall, or may make it possible to compensate later severe shortfalls that would otherwise have had to remain uncompensated owing to the operation of the limit. Broadly speaking, a 50 per cent weight on the current year is necessary to make the practical norm a good predictor of the ideal norm; higher weights are rendered desirable only by the need to mitigate the consequences of the limit and of compulsory repayments.

The circumstance that the deviation ratio is more sensitive to changes in the weight assigned to the current year when debt limits are low than when they are high or nonexistent is associated with the fact, discussed below, that such limits tend to improve the fit when the weight on the current year is low and to worsen it when that weight is high.

(5) The effect of the weighting system on smoothness of availabilities is different from its effect on the closeness of availabilities to target. Broadly speaking, among schemes that are without limits on indebtedness or compulsory repayments the smoothness of availabilities will be the higher, the greater the number of years’ exports entering into the formula for the practical norm and the more equal the weights assigned to those years.16 Among schemes that involve both limits and compulsory repayments, however, those resulting in the smoothest trend of availabilities have fairly high weights (one third or one half) on the current year—though not so high as the weights of the schemes that show the best fit of availabilities with respect to target. The effect, therefore, of introducing smoothness as an auxiliary criterion of the relative excellence of schemes will be to reduce slightly—but only slightly—the optimal weight attached to the exports of the current year in the determination of the practical norm, compared with what it would have been on the criterion of closeness to target alone.

(6) Repayment systems have been arranged in Table 5 in order of diminishing reliance on compulsory repayments and increasing reliance on automatic repayments. Broadly speaking, it can be said that the greater the reliance on automatic and the less on compulsory repayments, the more closely will actual availabilities approximate to target availabilities (and the greater will be the smoothness of the availabilities), but the larger also will be the maximum levels of aggregate indebtedness and hence the amount of resources required by the scheme.17 The data shown in column 8 of Table 5, on the one hand, and in column 12, on the other, understate the influence that variations in the automaticity of the repayment system are likely to exercise in the longer run on the deviation ratio and on the maximum aggregate indebtedness, respectively. The influence on the deviation ratio is understated because, for the first four years of the nine-year period under examination, no compulsory payments on deferred credits could occur under any of the repayment systems and therefore no difference could appear in the availabilities arising under the different repayment systems with the exception of RS 5 (where automatic repayments amount to 100 per cent of export excesses, compared with two thirds in other systems). For this reason, column 10 has been added to the table showing the average deviation ratios under the various schemes for the years 1955–59 only, though the shortness of the period makes for some irregularity in the results. The influence of repayment systems on the maximum amount of outstanding indebtedness has likewise been understated because for many of the schemes the maximum indebtedness occurs in the year 1954, at a time when—except for RS 5—the influence of the differences between the repayment systems had not yet come into play. A sounder idea of the importance of this influence can be obtained by noting the difference that a change in the repayment system makes, not on the highest aggregate level of indebtedness but on the level of indebtedness in 1958, which for some schemes is the absolute peak and for others a secondary peak.

As can be seen from Tables 8 and 9, the influence of the degree of automatism of the repayment system both on the fit of actual to target availabilities and on the level of aggregate indebtedness will be the greater, the wider are the debt limits, and—where debt limits are wide or nonexistent—the less is the weight assigned to the current year’s exports in the determination of the export norm.18 Both wide limits and low weights on the current year tend to increase the amounts borrowed and the amounts due for repayment, and thus give the repayment mechanism greater scope for exercising its influence on aggregate indebtedness. Inasmuch as automatism tends to improve the fit of availabilities, it is natural that whatever gives automatism a greater quantitative effect on repayments will also enhance its beneficial effect on the fit.

Table 8.

Effect on Deviation Ratios of Changes in Repayment System with a Two-Thirds Compensation Target, 1955–59

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Table 9.

Effect on Total Indebtedness in 1958 of Changes in Repayment System with a Two-Thirds Compensation Target

(In billions of U.S. dollars)

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(7) The widening, or removal, of the limits on the indebtedness of individual countries always has the effect of increasing the aggregate amount of indebtedness contracted at peak years (Table 11). This effect is much more important when the weight assigned to the current year’s exports in the definition of the practical norm is low than when it is high, since a high weight on the current year itself tends to keep the indebtedness of individual countries from attaining the limits. The effect of widening the limits is also more important when repayment is on a more automatic than when it is on a less automatic basis.

Table 10.

Effect on Deviation Ratios of Changes in Debt Limits With Two-Thirds Compensation Target

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Table 11.

Effect on Maximum Indebtedness of Changes in Debt Limits with Two-Thirds Compensation Target

(In billions of U.S. dollars)

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The effect of varying the limits on the fit of actual to target availabilities cannot be expressed so simply (Table 10). When the weight assigned to the current year’s exports in the determination of the practical norm is high (45 per cent or more), a widening of the limits tends to improve the fit. When no weight at all is assigned to the current year’s exports, a widening of the limits markedly worsens the fit, to the point at which availabilities diverge more from the target than do unadjusted exports. Where a weight of one third is assigned to the current year’s exports, the influence of the limits is doubtful. A complete removal of all limits produces a better fit than either a 20 per cent or a 33 per cent limit, but an expansion of the limit from 20 per cent to one third will be clearly beneficial only where the repayment system is entirely automatic. The conclusion is that when current year’s exports receive a low weight the norm is so distorted that it is better, as well as cheaper, to have a limit on each country’s indebtedness.

This conclusion is slightly modified when account is taken of the effect on smoothness of availabilities. Expansion of the debt limit fairly generally tends to increase smoothness; but even here, for schemes on which the current year’s exports receive a zero weight in the definition of the practical norm, a widening of the limit from 20 per cent to one third tends to reduce, rather than to increase, smoothness.

(8) It would seem to be of interest to extract from the set of 137 schemes a short list of schemes which give the “best” results (in a sense to be defined) for a given “cost” or, to put the same thing in another way, have the lowest cost for a given degree of “excellence.”

In this paper we have used two criteria of excellence—a measure of closeness of fit to target availabilities (the deviation ratio) and a measure of smoothness of availabilities (the smoothness ratio). We have also two measures of cost, the maximum indebtedness outstanding at any time from 1951 to 1961, and the indebtedness outstanding at the end of 1958. For the purpose of compiling the short list of schemes, a composite criterion of excellence has been calculated in which the deviation ratio is given twice the weight of the smoothness ratio, and a composite measure of cost in which maximum indebtedness and end-1958 indebtedness are given equal weights. Table 12 lists, in increasing order of the deviation ratio, 17 schemes selected in such a fashion that all schemes other than those included in Part A are, by these composite criteria, both “inferior” to and “more expensive” than at least one of the schemes included in the list.

Table 12.

Selected Schemes Showing the “Best” Results for a Given “Cost” or the Smallest “Cost” for a Given Result

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All the schemes listed in Part A show a closer approximation to the target, and all except the last two show greater smoothness (in relation to need), than scheme 3, the OAS scheme reinterpreted so as to permit automatic repayments in the third year.19 Only the “best” scheme (132) costs more than scheme 3. All the listed schemes attach a high—usually a very high—weight to the current year’s exports in defining the practical export norm, and those which show a relatively close fit of availabilities to target, as well as great smoothness, have wide or no debt limits. Those showing the best fit have neither debt limits nor compulsory repayments of deferred credits.

If schemes without debt limits and with repayment system 6 were excluded from consideration, the top ten schemes and the twelfth scheme would disappear from the list, and there would be no additions. Scheme 100 is the best of all the schemes with debt limits and with repayment systems other than repayment system 6.

If, in addition to schemes without debt limits and schemes with repayment system 6, all schemes with weights on the current year’s exports exceeding 50 per cent were excluded from consideration, we would have a completely different short list of schemes, as shown in Part B of Table 12. All the schemes appearing in Part B give the highest “permissible” weight, viz., 50 per cent, to the current year’s exports; and they are all closer to target, smoother (in relation to need), and cheaper than scheme 3, the reinterpreted OAS proposal, shown in Part C of Table 12.

APPENDIX TO PART II

The objective of a compensatory financing scheme is to supply participating countries with additional foreign exchange resources at times of falling export receipts in order to make it unnecessary for them to restrict imports and foreign exchange payments for other purposes to the level of current foreign exchange earnings. This, however, does not mean that the compensation should equal the full amount of the reduction in export receipts, since imports of goods and services will themselves tend to decline as a result of the fall in exports. Similarly, under the scheme countries should not be required to repay past credits to the full extent of a rise in exports, since part of the additional foreign exchange earnings will be absorbed by the expansion of imports which is induced by the increase in exports.

In this Appendix, we shall assess the extent to which foreign exchange payments would tend to fluctuate with fluctuations in exports as a result of the normal economic relationships in underdeveloped countries and, consequently, the extent to which these countries would be able to absorb available resources for compensatory financing of export fluctuations when exports decline, and to repay loans contracted for this purpose when exports recover, without drastic changes in their economic and financial organization.

Table 13 brings together ratios for 29 countries20 from which an estimate is made of the ratio of the change in foreign exchange expenditure (M’, the prime being used to indicate a concept wider than imports alone) to the change in exports (X), which is considered to be the autonomous variable. With the help of these figures, a judgment is made about the time pattern of foreign exchange expenditure induced by export fluctuations.

Table 13.

Effect of a Change in Exports on Foreign Exchange Expenditures, and Underlying Ratios1

(Average 1958–60)2

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Columns 1 and 2: Imports are merchandise imports. Income is national income or, in some cases, gross national product; the computation in column 5, however, is independent of the concept of income used. General taxes are government tax revenue less export taxes and oil royalties paid to the government.

Column 3: Taxes are those levied on exports and oil royalties paid to the government. Exports are merchandise exports.

Column 4: Investment income paid abroad is direct investment income remitted. For some countries, the figures include unspecified amounts of reinvested earnings. For Ecuador, Haiti, Indonesia, and Turkey, it has been assumed that one half of investment income is actually paid abroad. For the Philippines and Venezuela, reinvested profits of U.S. firms have been deducted from direct investment income debits in the balance of payments of these countries. For some other countries, it has been assumed that total investment income debits constitute remitted profits.

Columns 5 and 6: In the computation of column 5, the propensity not to spend (s) is assumed to be zero; in column 6, it is assumed to be .05. The formula used in the computation is

Δ ⁢ M ′ Δ ⁢ X = m ⁢ ( 1 − x p − t x ) m + t y + s + x p

Data for national income are from United Nations, Statistical Yearbook, 1961, and Monthly Bulletin of Statistics, and also Fund staff estimates.

Imports and exports are from International Monetary Fund, International Financial Statistics.

Export taxes, general taxes, and oil royalties are from United Nations, Statistical Yearbook, 1961, and country publications.

Investment income paid abroad is from International Monetary Fund, Balance of Payments Yearbook.

Or nearest years available.

Exports affect exchange expenditure in the first place through the remission abroad of profits of the export industry, particularly when that industry is conducted by foreign companies. For foreign oil companies, a related item is royalties paid abroad. The ratio (xp) of investment income paid abroad to exports is shown in column 4. This ratio runs as high as 0.40 for some oil producing countries and is 0.07 on the average for the 29 countries.21 A second deduction from export income is made by government taxation levied directly on exports. The ratio (tx) of these taxes to exports is indicated in column 3. The tax figures have been derived from the detailed information about government receipts provided in the Statistical Yearbook of the United Nations. The ratio is quite large for oil producing countries and also for a number of others, in particular, some of the underdeveloped countries of the Commonwealth. On the average this ratio is 0.10. The remainder of the gross value of exports represents private domestic income from exports, and this is spent and respent, except insofar as it “leaks out” by way of taxation, imports, or private saving.

An estimate of the ratio (ty) of taxes (other than taxes on exports) to income is shown in column 2. For the 29 countries, the average is 0.11. In further use of this ratio, it is assumed that all nonexport taxes fluctuate proportionately to income, which is probably an overestimation of their degree of flexibility. The ratio of imports to income (m) is shown in column 1. The figure used here is the average propensity to import, limited to goods. Allowance has not been made for imports of services or for any difference between the marginal and the average propensity to import. The former adjustment would certainly, and the latter probably, raise the ratios computed in columns 5 and 6. On the average for all countries listed, the import/income ratio is 021. No data are available on the response of private saving and private investment to changes in income. The calculation in column 5 has been made on the assumption that the private marginal propensity to spend (1—s) in the countries concerned equals unity. An alternative calculation in column 6 is based on the assumption that the private marginal propensity to spend equals 0.95, a figure which would almost certainly be a low estimate for most underdeveloped countries.22

As far as the government is concerned, however, the assumption has been made that its marginal propensity to spend in the short run equals zero, i.e., that declines in tax receipts lead to equal government deficits and increases in tax receipts to equal surpluses. It may be assumed that governments would like to operate at least to this extent in a compensatory manner, although in fact they may in many cases not have been financially able to follow such a policy. This assumption23 does not, however, represent the maximum degree of stabilization that the government could practice. The government might raise government expenditure (or lower its rate of taxation) when exports and incomes decline, and it might contract expenditure (or raise tax rates) when exports and incomes rise. Few underdeveloped countries, however, have at their disposal the institutional arrangements that would permit them to do this except where they run commodity schemes of their export products in such a manner as to achieve these additional compensatory effects. Indeed, many developed countries have found it difficult in practice to follow a policy of this nature.

Applying the assumptions made above, we come as follows to the computed effect shown in column 6: The initial impact on private domestic income of a change in exports will be equal to the amount of the export change multiplied by the coefficient (1–xp‒tp). With allowance made for the leak through imports and “income” taxes, this sum will give rise, according to standard multiplier theory, to a total effect on imports equal to mm+tv+s times the original impact. When the direct impact on foreign exchange expenditures of profits remitted abroad is added, the total effect of a change in exports on foreign expenditure is as follows:

Δ ⁢ M ′ Δ ⁢ X = m ⁢ ( 1 − x p − t x ) m + t v + s + x p ⁢ .

It will be seen from column 5 that the ratios are narrowly concentrated, with almost two thirds falling in the range of 0.50 to 0.65. Perhaps most surprising is the fact that the oil countries do not fall far outside this range. This is attributable not only to the fact that the oil countries remit large profits abroad, but also to the fact that the ratio of export taxes to exports is higher for these countries than it is for other countries; the effects of these two unusually high ratios approximately cancel out in the result. The alternative computation in column 6 assumes a marginal propensity to spend of 0.95 rather than of unity. Recomputation of the figures in column 5 with this allowance yields corrected ratios which are, on the average, lower by 0.08.

The ratios in columns 5 and 6 show the changes in imports between an initial equilibrium situation and the final equilibrium which is re-established eventually after a change in exports. During the year in which the change in exports occurs, the induced change in imports would be much smaller. Moreover, since imports adjust with a lag to an equilibrium level which itself fluctuates with exports, the adjustment will always remain incomplete. Using the average ratios of imports to income, of export taxes to exports, etc., given in Table 13, and assuming that imports and income tax collections lag three months behind the receipt of income, one can determine the time pattern of imports produced by a regular cyclical movement of exports. Export cycles with a duration of three to four years result in import fluctuations whose amplitude is approximately one third of the amplitude of the underlying export fluctuations.

It is obviously impracticable to tailor the provisions of an international compensatory scheme to the precise time pattern with which each country’s imports react to changes in its exports. The data given in this Appendix and the argument in the preceding paragraph nevertheless, suggest that for many primary producing countries foreign exchange expenditures fluctuate on the average by as much as one third of the fluctuations of exports, even in the absence of variations in exchange control measures. This conclusion, it must be remembered, is based on the assumption that government expenditures and the money supply remain roughly constant in the face of export fluctuations. If government expenditures were to vary with the changes in tax collections that are induced by variations in exports, or if a similar influence of exports on domestic economic activity were allowed to occur through induced changes in the money supply, the effect of export changes on imports would be more pronounced and the scope for compensatory export financing would be correspondingly reduced. On the other hand, if domestic financial policies were to offset part of the impact of export changes on economic activity and thus on imports, international compensatory action could be more extensive. For reasons given earlier it would seem, however, that countries would not be able to use safely a compensatory scheme that finances more than two thirds of the short-term fluctuations in their exports, unless they were in a position to reform their internal financial system in the direction of offsetting much more fully the domestic effects of fluctuations in exports.

Les normes d’exportations et leur rôle dans le financement compensatoire

Résumé

Pour de nombreuses raisons qui relèvent à la fois de la politique économique nationale et internationale, il peutêtre souhaitable d’isoler les fluctuations à court terme dans une variable économique en établissant une norme à moyen terme, ou une valeur représentative de tendance, à partir de laquelle des écarts positifs et négatifs pourraient être mesurés. Le besoin d’un tel instrument a été ressenti au cours des dernières années, notamment en raison des fluctuations dont les prix ou recettes d’exportations des pays exportateurs de matières premieres ont été l’objet. La première partie de cette étude examine quelles devraient étre les caractéristiques d’une norme à moyen terme et quelles seraient, en pratique, les meilleures méthodes d’estimation á employer pour obtenir celle-ci, compte tenu du nombre limité d’indications utilisables avec certitude au moment où l’on doit établir cette estimation. A titre d’exemple, on a limité le domaine des recherches aux recettes d’exportations. Toutefois, la détermination de normes appropriées pour les prix d’exportations poserait les mêmes problèmes et appellerait les mêmes solutions. On a vérifié plusieurs formules, dont certaines sont le résultat d’une analyse de régression, en raison de leur utilité pour le calcul de la moyenne mobile des exportations sur une période de cinq ans, calcul effectué á partir des seules données relatives aux exportations de l’année en cours et des années precedentes. Ces vérifications sont fondées sur les exportations de 48 pays producteurs de matières premieres au cours de l’après-guerre.

La deuxième partie de l’étude s’attacheà l’examen de plans interna-tionaux de caractère plus ou moins “automatique” visant à compenser les fluctuations à court terme des exportations, en particulier à la suite d’une proposition récemment formulée par l’Organisation des Etats Américains. Elle met surtout l’accent sur la manière dont la norme peut, en pratique, être déterminée. On essaye de dégager des critères permettant d’évaluer l’efficacité des divers plans de compensation considérés. Pour vérifier un grand nombre de variantes de la proposition de l’Organisation des Etats Américains on applique ces critères aux chiffres des exportations des 48 pays producteurs de matières premières. II en ressort que ces variantes du plan qui, dans la formule de calcul de la norme d’exportation, attachent peu d’importance, voire aucune, aux exportations de l’année en cours, sont dans l’ensemble moins propres à assurer une meilleure distribution chronologique des recettes de devises et plus coüteuses en terme de dette non réglée, que les plans qui dans la formule accordent davantage d’importance aux recettes d’exportations pour l’année en cours.

Las normas de exportación y el papel que desempeñan en el financiamiento compensatorio

Resumen

Muchos son los fines, tanto de política nacional como internacional, por los que puede ser conveniente aislar las fluctuaciones de una variable económica estableciendo una norma a mediano término o valor de tendencia, para poder medir las desviaciones positivas y negativas. En los últimos años la necesidad de hacerlo se ha presentado particularmente en lo que respecta a las fluctuaciones de los precios o ingresos de exportación de los países exportadores de materias primas. En la Parte I de este artículo se trata de cuáles son las características que debería tener la norma a mediano término y como podría ésta estimarse mejor en la práctica dada la escasa información pertinente de que se dispone al tiempo en que hay que efectuar la estimación. Para fines de ilustración, el estudio se circunscribe a los ingresos de exportación. Sin embargo, problemas semejantes surgirían, y el procedimiento que cabría emplear sería parecido, si se tratara de obtener normas apropiadas de los precios de exportación. Se examina una serie de fórmulas, algunas de las cuales han sido derivadas por medio del análisis de regresión, para averiguar su utilidad para la estimación de la media móvil quinquenal de las exportaciones, usando solamente los datos de las exportaciones del año en curso y de los años precedentes. Las pruebas se basan en las exportaciones realizadas durante la posguerra por 48 países productores de materias primas.

La Parte II del artículo se ocupa de los esquemas internacionales de un carácter más o menos “automático” para compensar las fluctuaciones a corto plazo de las exportaciones, particularmente en lo que respecta a la propuesta presentada por la Organización de los Estados Americanos (OEA). Se ha puesto especial énfasis en la forma en que puede determinarse la norma en la práctica, y se han desarrollado criterios que permiten evaluar la eficacia de diversos esquemas de compensación. Se analiza un gran número de variantes de la propuesta de la OEA mediante la aplicación de dichos criterios a los datos de exportación de 48 países productores de materias primas. Se comprueba que las variantes del esquema en que se da poca o ninguna ponderación a las exportaciones del año en curso en la fórmula para el cálculo de la norma de exportación, resultan en general menos eficaces para la mejor distribución cronológica de los ingresos de divisas extranjeras y más costosas en términos de la deuda pendiente, que en los esquemas en que se da una mayor ponderación al producto de las exportaciones del año en curso.
*

Mr. Fleming, Advisor in the Department of Research and Statistics, is a graduate of Edinburgh University. He was formerly a member of the League of Nations Secretariat, Deputy-Director of the Economic Section of the U.K. Cabinet Offices, U.K. representative on the Economic and Employment Commission of the United Nations, and Visiting Professor of Economics at Columbia University. He is the author of numerous articles in economic journals.

Mr. Rhomberg, economist in the Special Studies Division, is a graduate of the University of Vienna and of Yale University and has been a member of the faculty of the University of Connecticut.

Miss Boissonneault, economist in the Special Studies Division, is a graduate of George Washington University.

1

This is identical with the statistical definition of normal exports adopted in an earlier article, “Fund Policies and Procedures in Relation to the Compensatory Financing of Commodity Fluctuations,” Staff Papers, Vol. VIII (1960–61), pp. 1–76.

2

The 48 countries are Argentina, Bolivia, Brazil, Burma, Ceylon, Chile, China (Taiwan), Columbia, Costa Rica, Cyprus, Dominican Republic, Ecuador, El Salvador, Ethiopia, Ghana, Greece, Guatemala, Haiti, Honduras, India, Indonesia, Iran, Iraq, Jordan, Korea, Lebanon, Libya, Malaya, Mexico, Morocco, Nicaragua, Nigeria, Pakistan, Panama, Paraguay, Peru, Philippines, Saudi Arabia, Sudan, Syria, Thailand, Tunisia, Turkey, United Arab Republic, Uruguay, Venezuela, Viet-Nam, and Yugoslavia.

3

The precise method by which these coefficients have been arrived at is set forth in the Appendix to Part I.

4

The term “mean” signifies that the coefficients sum to unity.

5

For “unweighted” means covering four years, see Table 3.

6

The Category B formulae for which standard deviations are shown for the subperiod 1955–59 have coefficients arrived at by regression for that subperiod, not for the period 1951–59. For a comparison of the two sets of regression weights, see Table 4.

7

Organization of American States, Final Report of the Group of Experts on the Stabilization of Export Receipts, Doc. 59 (English, mimeographed), Rev. 5, April 18, 1962, and Proposed Articles of Agreement of the International Fund for Stabilization of Export Receipts, Doc. 64 (English, mimeographed), Rev. 4, April 3, 1962.

8

In other applications, e.g., with respect to buffer stock policy, or income stabilization through fiscal means, either no adjustment to the ideal norm or a different adjustment might be required.

9

Since the value of the target, or of the ideal norm, cannot be calculated for the last two years in the data series, the deviation ratios shown in columns 8 and 9 of Table 5 apply only to the nine-year period 1951–59.

10

The formula for the smoothness ratio is as follows:

Σ r = 1 s ⁢ ( a r − m r n r ) 2 Σ r = 1 s ⁢ ( x r − m r n r ) 2

where a represents the deviation of availabilities from the centered five-year moving average of availabilities, x the deviation of exports from the centered five-year moving average of exports, m the deviation of target availabilities (based on a target compensation of two thirds) from the ideal export norm, n the ideal export norm, r the country-year in question, and s the number of countries times the number of years included in the calculation. Since a cannot be calculated for 1951 or 1952, the smoothness ratios shown in column 11 of Table 5 apply only to the seven years 1953–59.

11

In certain schemes, while the borrowing ratio has been kept at two thirds, the repayment ratio has been assumed to be 100 per cent.

12

More generally, it makes no difference to either borrowings or repayments whether there are weights on the present year and the two preceding years of a, b, and c, respectively, with a compensation ratio of unity (i.e., 100 per cent), or weights of [1−1r⁢(1−a)],  br⁢  and  cr, respectively, with a compensation ratio of r, or, again, weights of zero, b1−a, and   c1−a

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, respectively, with a compensation ratio of (1 – a).

13

See footnote 7

14

This system was suggested to the authors by Miss Gertrud Lovasy.

15

The OAS scheme as drafted (scheme 1) and the reinterpreted OAS scheme (scheme 3), which permits automatic repayments in the third year (see p. 131 above), differ only slightly. The deviation ratio of the latter scheme is also 0.92.

16

It is not clear why the smoothness of availabilities under scheme 129 is greater than under scheme 130. One would have expected approximate equality in the smoothness ratios in the two schemes. The difference may be in part explained by the fact that the computation of the practical norm for scheme 129 involves export data for 1948 but not those for 1961, while the practical norm for scheme 130 involves export data for 1961 but not those for 1948.

17

From column 12 of Table 1, RS 5 appears to involve lower aggregate indebtedness than RS 4. This, however, is because of the atypical character of maxima occurring in 1953 and 1954, which took place too early in the period to be affected by compulsory repayments under any scheme. In 1958, the year of the secondary maximum under both schemes, RS 5 involves higher aggregate indebtedness than does RS 4.

18

Where debt limits are narrow, the influence exercised by the weighting of the present year on the effectiveness of automaticity is not uniform.

19

See page 131 above.

20

It was not possible to obtain the required data for all 48 primary producing countries treated in this paper.

21

The figures used for remitted profits represent total direct investment income remitted abroad and may, for a few countries, include payments of profits of non-export industries; for some countries, reinvested earnings may also be included.

22

For some evidence on this, see J. J. Polak, An International Economic System (Chicago, 1953), especially pp. 163–64.

23

A second assumption about government policy is implicit in the computation shown in Table 13. It is assumed that the monetary authorities keep the quantity of money in circulation constant by offsetting the effect of fluctuations in foreign exchange receipts (“availabilities”) on the money supply through variations in central bank credit.

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Cover IMF Staff Papers
IMF Staff Papers: Volume 10, No. 1
Author:
International Monetary Fund. Research Dept.
Volume/Issue:
Volume 1963: Issue 001
Publisher:
International Monetary Fund
ISBN:
9781451956023
ISSN:
1020-7635
Pages:
230
DOI:
https://doi.org/10.5089/9781451956023.024