Effects of Income and Price Changes on the U.S. Balance of Payments

Rudolf Rhomberg; LORETTE BOISSONNEAULT

doi:10.5089/9781451956054.024.A003

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Effects of Income and Price Changes on the U.S. Balance of Payments

Author: Rudolf Rhomberg and LORETTE BOISSONNEAULT

Publication Date:: 01 Jan 1964

eISBN:: 9781451956054

Language:: English

Keywords:: SP; price; import; export; forward rate; currency; price elasticity; U.S. dollar; foreign exchange; GNP price; price change; Imports; Export prices; Personal income; Western Europe

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This paper was given at the Winter Meeting of the Econometric Society, Boston, Massachusetts, December 29, 1963. Earlier versions of the paper were presented at Rice University (Houston, Texas), the University of Texas (Austin, Texas), and the Board of Governors of the Federal Reserve System (Washington, D.C.). The opinions expressed are entirely those of the authors.

Abstract

DURING THE LAST TWO YEARS, attention has been drawn to the likelihood, or at least the possibility, that the rate of growth of economic activity in the United States will rise, both absolutely and relative to the rate of growth in Western Europe, and that price developments may follow a somewhat different course in these two areas. While the average rate of growth of real gross national product (GNP) during the five years 1956-61 was 2.2 per cent in the United States and 4.3 per cent in the European countries in the Organization for Economic Cooperation and Development (OECD) taken as a group, present forecasts envisage growth at a rate of 4-5 per cent in both regions. A comparison of price movements shows that there has been a tendency in recent years for prices to rise more rapidly in continental Western Europe than in the United States.¹

In view of the balance of payments problems of the United States, it is important to assess the probable impact of these tendencies on the U.S. external accounts. Differential rates of economic expansion and of price movements in various parts of the world are likely to affect not only the current account balances but also the capital accounts of the regions in question. The present paper confines itself to the first part of this problem, considering chiefly the influence of income and price changes on trade in goods and services.

It is plausible to expect that an increase in the rate of growth of economic activity in the United States will, by itself, tend to worsen the current account of the U.S. balance of payments, and that a rate of increase in prices in Western Europe which exceeds that in the United States will tend to improve it. But it is difficult to estimate the probable net impact of simultaneous changes in economic activity and in prices in these two regions, with allowance made not only for direct effects but also for a number of roundabout, or “feedback,” relations. Such a task could hardly be undertaken without the help of some formal economic model, used partly as an aid in checking the logical consistency of the specified relations, and partly as a framework within which the numerical assumptions can be manipulated. A model of this sort consists of a number of equations, some of which may be identities stating accounting definitions and other known or assumed equalities, while others express economic “behavior,” that is, the reaction of members of various sectors of the economy to changes in incomes, prices, and other specified variables. The numerical values of the parameters of these behavior equations (that is, the magnitudes of the various marginal propensities and elasticities) may be derived in a more or less informal way from theoretical and empirical considerations, or estimated from past data through formal statistical analysis. The latter method has been adopted in this study. Sections I and II describe the logic and the statistical bases of the model.

Once the values of the parameters are obtained through statistical analysis, it is possible to make projections on the basis of assumed values of certain explanatory variables which are taken to be determined outside the model. Projections of this type are not unconditional “predictions” or “forecasts”; they are merely quantitative evaluations, on the basis of past experience, of the implications of certain assumptions about the future course of those magnitudes which are included in the model as autonomous, or “exogenous,” variables. Projections made from an earlier version² of the present model are described in a report³ to the Joint Economic Committee of the Congress of the United States published by the Brookings Institution (hereinafter referred to as Brookings Report). Section III presents projections for 1964 and 1968 from the revised model—with certain assumptions being made about the growth of U.S. and Western European economic activity and about the behavior of prices in the two areas—and compares the projections for 1968 with those made in the Brookings Report.

I. Nature of the Model

The model⁴ divides the trading world into three regions: (1) the United States, (2) Western Europe, and (3) the Rest of the World.⁵Exports from one of these regions to another are, in principle, identical with the latter region’s imports from the former, though in practice there is ordinarily some accounting discrepancy between corresponding entries in partner countries’balance of payments records.⁶ By accounting for the systematic influences of income and price changes on each region’s imports of goods and services during a particular period, the model at the same time “explains” the observed variations in each region’s exports of goods and services.

The two sectors of the model treating imports of goods and services of the United States and Western Europe (for short, the two “industrial regions”) are of similar design. The demand for merchandise imports (in 1954 prices) is taken to depend on real GNP and inventory investment, and on the ratio of domestic prices (GNP prices⁷) to the export prices of the region in which the imports originate. Payments for services, treated separately by category (transportation services, travel, interest and dividend payments, and other private services), are related to what was thought to be in each instance the most appropriate single variable.⁸

Imports of goods and services by the Rest of the World from the two industrial regions are treated in a different manner. In many of the countries in the Rest of the World group, variations in imports are determined not so much by changes in national income as by changes in the amount of foreign exchange receipts. As a first approximation, it may be assumed that these countries, as a group, use the total of their foreign exchange receipts from exports of goods and services to the two other regions and from net capital inflows and foreign aid to purchase imports from, or make payments for services to, the United States and Western Europe.⁹ The model does not, however, rely on the validity of this assumption. Increases (or decreases) in the Rest of the World’s exchange reserves can be treated as autonomous magnitudes and subtracted from (or added to) this region’s exchange receipts from exports, net capital inflows, and aid, to arrive at the amount spent for imports of goods and services. Apart from this accounting relation, the Rest of the World sector of the model is designed to make it possible to estimate the share which the United States receives of the Rest of the World’s expenditure on imports of goods and services. The principal behavior equation in this sector relates this share to the ratio of U.S. export prices to those of Western Europe.

The main relations of the model are shown schematically in Chart 1. In this chart, variables which are explained in the model (dependent, or “endogenous,” variables) are shown in circles, while variables whose magnitudes are determined outside of the model (“exogenous” variables) are shown in squares. The arrows indicate the lines of direct influence assumed in the model.¹⁰ The chart focuses on the U.S. current account balance, N₁, which is the sum of U.S. exports to the two other regions (M₁₂ and M₁₃) less the sum of U.S. imports from these two regions (M₂₁ and M₃₁). (In order to simplify the chart, payments for services have not been shown separately.) Imports into the United States and Western Europe are affected by GNP, inventory investment, and GNP prices of the importing region, as well as by export prices in the region of origin. All payments to the Rest of the World are shown as being collected in the receptacle marked E₃ (foreign exchange receipts of the Rest of the World) to be used as payment for the Rest of the World’s imports from the two other regions (M₁₃ and M₂₃).

Chart 1 thus indicates the mechanism by which an autonomous change in one of the variables in square boxes will affect some or all of the variables shown in circles. An increase in the U.S. GNP, for instance, will in the first place tend to raise U.S. imports from Western Europe and from the Rest of the World. It will thus lead to an increase in the Rest of the World’s foreign exchange earnings, and this region will in turn spend part of this increase on imports from the United States, and the other part on imports from Western Europe. The rise in U.S. imports will, therefore, be offset in part by an increase in U.S. exports to the Rest of the World.

It is indeed possible to go beyond this scheme in making allowance for roundabout, or feedback, effects. A more complete version of the model (which is described in the Appendix) allows for the effects of changes in the trade balance on GNP, and for the further repercussions of these effects on imports, in the two industrial regions. Furthermore, the effects of changes in domestic prices and in the export volume on export prices are made part of the mechanism of the larger model. The improvement, judged by statistical criteria, resulting from such an expansion of the model is, however, slight. For reasons discussed in the following section, the results presented in the text will, unless otherwise specified, be those obtained from the more limited version of the model, hereinafter called “Model 3” (see Appendix II, p. 106).

The econometric approach chosen in this study has inherent limitations. The parameters of the model, i.e., the marginal propensities to import, the coefficients showing the effects of price changes, etc., have been estimated from data over a period (generally 1948-62) which could hardly be called “normal.” This era includes the early phase of reconstruction in Europe—with limitations on the supply of European goods, extraordinary demands for imports (partly restrained by direct controls), and the financing of European imports by Marshall Plan aid—the Korean war, and the Suez crisis, to name but the most important of a number of special circumstances. However, disturbances of this sort neither make the task of statistical estimation of economic relationships impossible nor necessarily always work against the statistician. Some of them provide the sort of variation in the data which the econometrician must have in order to be able to estimate the individual effects of variables that exercise their influences jointly. Nevertheless, it is clear that tendencies which may not continue were present in the world economy during the 1950’s—tendencies such as the progressive liberalization of Europe’s trade, Europe’s improved position as a supplier to world markets, and the gradual discovery by consumers and businessmen in the United States of European sources of supply of industrial products. To the extent that such longer-run tendencies were present in the “sample period,” that is, the period used in the statistical estimation (1948-62), their effect is likely to have been ascribed to other variables moving in a trendlike fashion, most probably to GNP. Such statistical misrepresentation would cause no problem in the use of the model for projections, if these tendencies were to continue; but if they were to cease, or to continue at a reduced rate, the application of coefficients estimated from historical data would lead to error.¹¹

Apart from this difficulty, there can be no assurance that the structure of the world economy as represented in the numerical values of the parameters of the model will remain unchanged in the future. All that can be said is that, in the absence of specific information to the contrary, nothing better can be done than to assume that the past is a reasonably good guide for the future. But even if little credence is given to projections from such a model, its construction may still have served a useful function in the same sense in which any historical information is useful. By leading to a better understanding of the past, the model cannot fail to improve, at least in some measure, our ability to assess the forces which shape the present and the future.

II. Statistical Results

The equations of the model have been fitted by ordinary least-squares regression methods to annual data, generally for the period 1948-62. This period was chosen because of the desirability of basing the statistical analysis on as many observations as possible. For a number of key relations, however, one or several of the early years have ultimately been omitted from the regression equations because inspection of the initial results indicated that the values of the variables in question during these early years were not in accordance with the regularities observed for a somewhat shorter and more recent period. In particular, the equation for U.S. merchandise imports from Western Europe has been fitted for the period 1951-62, and that for Western European imports from the United States for the period 1950-61.¹² Although the supply shortages in Western Europe had not been completely overcome at the beginning of the 1950’s, the omission of earlier years in fitting these two import functions substantially reduces the disturbance of the import relations from this source.

The statistical results summarized in this section are presented in greater detail in Appendix I.

The computed income and price elasticities of the two industrial regions’ demand for imports are shown in Table 1.¹³ The magnitudes of these elasticities are on the whole in accordance with a priori expectations and with the results of other empirical studies. In the two industrial regions, the price elasticities of demand for imports from the Rest of the World are about −½. The price elasticity of demand for U.S. imports from Western Europe was estimated as −1.3, and that for Western Europe’s imports from the United States as −1. Both values appear somewhat lower¹⁴ than might have been expected. However, two points should be noted in this connection:¹⁵ First, Western Europe’s imports from the United States contain a considerable proportion of agricultural commodities, the demand for which is likely to be price-inelastic; the implied price elasticity of demand for U.S. manufactured products is, therefore, higher than −1, perhaps about −1.5. Second, calculated demand elasticities with respect to the ratios of import prices to GNP prices¹⁶ will tend to be lower than elasticities involving the ratios of import prices to the prices of import-competing goods.¹⁷ For these reasons, the calculated elasticities should not be considered unduly low. The findings do, at any rate, confirm the widely held view that the demand for primary products in industrial countries is rather price-inelastic, compared with the demand for industrial products.

Table 1.

Computed Income and Price Elasticities of Demand for Merchandise Imports¹

^¹Based on Appendix I (pp. 85-105). An asterisk indicates that the estimated coefficient is not statistically significant at the 95 per cent confidence level. The income elasticities of demand for imports (measured in 1954 prices) are taken with respect to real GNP excluding inventory changes (also measured in 1954 prices); the price elasticities of import demand are taken with respect to the ratio of export prices in the region of origin to domestic GNP prices.

Table 1.

Computed Income and Price Elasticities of Demand for Merchandise Imports¹

		Income Elasticity of Demand for Merchandise Imports by		Price Elasticities of Demand for Merchandise Imports by
		United States	Western Europe	United States	Western Europe
Imports from
	United States	—	0.9	—	−1.0*
	Western Europe	2.0	—	−1.3*	—
	Rest of World	0.8	0.9	−0.6	−0.4

Table 1.

Computed Income and Price Elasticities of Demand for Merchandise Imports¹

		Income Elasticity of Demand for Merchandise Imports by		Price Elasticities of Demand for Merchandise Imports by
		United States	Western Europe	United States	Western Europe
Imports from
	United States	—	0.9	—	−1.0*
	Western Europe	2.0	—	−1.3*	—
	Rest of World	0.8	0.9	−0.6	−0.4

Three of the four estimated income elasticities are slightly less than 1, a theoretically quite acceptable value. The income elasticity of U.S. demand for imports from Western Europe is found to have a value of 2, which is surprisingly high. This would mean that U.S. imports from Western Europe would tend to grow twice as fast as the U.S. GNP. Such a relation does indeed seem to have held for the past decade, even after a number of corrections have been made in the data for certain extraordinary influences, such as the boom in U.S. automobile imports during the late 1950’s. While U.S. real GNP rose by about 50 per cent from the beginning of the 1950’s to the beginning of the 1960’s, U.S. imports from Western Europe in constant prices increased during the same period by more than 100 per cent. If the principal factor causing such a rapid expansion had been the elimination of supply shortages in Western Europe, the growth of imports would have been expected to be greater in the early part of the decade than in the later part; but this was not true. Therefore, one is inclined to conclude that there is a longer-run tendency on the part of U.S. producers and consumers to “discover” European sources of supply of industrial products. Nobody can now say whether or not this tendency will continue.¹⁸ If it were to continue, it would be appropriate to use the income elasticity found for the recent past; but if this trend were to cease, a lower value would have to be substituted for the statistically estimated coefficient. For purposes of the computations reported in this paper, no such adjustment has been made.

The equation explaining the share of U.S. goods in total merchandise imports (in constant prices) by the Rest of the World indicates an elasticity of substitution between U.S. and Western European goods, with respect to the ratio of U.S. to Western European export prices, of —1.2. This means that a rise of 1 per cent in the ratio of export prices has tended to lower by 1.2 per cent the proportion of the Rest of the World’s imports originating in the United States; since this proportion has been about 40 per cent in recent years, the reduction would amount to about one half of one percentage point, or, expressed in absolute terms, to about $150 million.¹⁹

Acceptable statistical estimates have been obtained for the relations between various service categories and the factors presumed to be their principal determinants; they are discussed in Appendix I. For export prices in the three regions, satisfactory statistical explanations have been found for the sample period, but it is unlikely that these relations are suitable for longer-run projections. In the two industrial regions, export prices are affected slightly by the volume of exports, and they also fluctuate with, and more than in proportion to, domestic GNP prices; but their smaller long-run increase, in comparison with GNP prices,²⁰ is reflected in a trend factor with a negative sign. Since it is uncertain how long export prices can continue to increase more slowly than domestic prices, there is no assurance that reasonable long-run projections can be obtained from these relations.

A similar problem arises with respect to the domestic consumption functions included in the complete model, though not in the limited version. For both the United States and Western Europe, the estimates indicate a marginal consumption/GNP ratio of slightly more than compared with an average consumption/GNP ratio of slightly less than ⅔. This difference reflects the fact that the response of consumption to year-to-year changes in GNP is smaller than the corresponding long-run response. For long-run projections, it may be more appropriate to use the average consumption/GNP ratio instead of the estimated short-run “marginal propensity to consume out of GNP.”

For reasons given in the last two paragraphs, several versions of the model have been processed, some of which may be suitable for short-run forecasting and others for longer-run projections. These alternative versions differ with respect to the treatment of export prices and consumption.²¹ It is reassuring that these different versions of the model do not lead to substantial differences in the computed values of the dependent variables during the sample period, and, in particular, that the variable on which this study focuses, namely the U.S. balance on current account, is computed with roughly the same accuracy in all the alternative versions. As stated in the preceding section, the results given in the text will be those from the simplest form of the model (Model 3).

Before presenting the conclusions of this study as to the influence of income and price changes on the U.S. current account balance, it will be interesting to obtain an impression of the extent to which the model as a whole, as distinct from individual equations,²² fits the data for some recent years. The actual and computed values of the U.S. current account balance for the years 1958-62²³ are given in columns 1 and 2 of Table 2; the error of estimate for the year in question is shown in column 3; and this error as a percentage of the actual value is given in column 4. Estimation of a net balance from separate calculations of its components is typically not very successful, since relatively small errors in the estimates of the gross components lead to much larger percentage errors in the estimate of the balance. Therefore, a probable error of about $1 billion or slightly less—that is, some 3 per cent of current gross receipts or about 15 per cent of the current balance—is not surprising. Although the model correctly reflects the sharp reduction in the surplus from 1958 to 1959, the increase from 1959 to 1961, and the renewed decline from 1961 to 1962, Table 2 may serve as a warning that great accuracy in projections of the current account balance cannot be expected if an error of 20 per cent or more can occur even within the sample period.

Table 2.

U.S. Current Account Balance,¹ 1958-62: Actual and Computed Values

^¹Balance of merchandise trade (excluding exports under military grants) and private services (transportation, travel, investment income, and other private services).

^²Column 2 is computed, not from the individual equations but from the independent variables of Model 3 and the “multipliers” given in Table 12 (p. 109).

^³Figures for Western European GNP, inventory investment, and GNP price deflator have been estimated, since actual data are not yet available for 1962.

Table 2.

U.S. Current Account Balance,¹ 1958-62: Actual and Computed Values

	Actual Value	Computed Value²	Error in Computation (Col. 1 − Col. 2)	Error as Per Cent of Actual [(Col. 3 ÷ Col. 1) × 100]
				Error as Per Cent of Actual [(Col. 3 ÷ Col. 1) × 100]
	(1)	(2)	(3)	(4)
1958	5.48	6.41	−0.93	−17
1959	3.10	3.65	−0.56	−18
1960	6.64	8.05	−1.41	−22
1961	8.23	8.27	−0.05	−1
1962	7.41	6.65³	0.76	10

^¹Balance of merchandise trade (excluding exports under military grants) and private services (transportation, travel, investment income, and other private services).

^²Column 2 is computed, not from the individual equations but from the independent variables of Model 3 and the “multipliers” given in Table 12 (p. 109).

^³Figures for Western European GNP, inventory investment, and GNP price deflator have been estimated, since actual data are not yet available for 1962.

Table 2.

U.S. Current Account Balance,¹ 1958-62: Actual and Computed Values

	Actual Value	Computed Value²	Error in Computation (Col. 1 − Col. 2)	Error as Per Cent of Actual [(Col. 3 ÷ Col. 1) × 100]
				Error as Per Cent of Actual [(Col. 3 ÷ Col. 1) × 100]
	(1)	(2)	(3)	(4)
1958	5.48	6.41	−0.93	−17
1959	3.10	3.65	−0.56	−18
1960	6.64	8.05	−1.41	−22
1961	8.23	8.27	−0.05	−1
1962	7.41	6.65³	0.76	10

^¹Balance of merchandise trade (excluding exports under military grants) and private services (transportation, travel, investment income, and other private services).

^²Column 2 is computed, not from the individual equations but from the independent variables of Model 3 and the “multipliers” given in Table 12 (p. 109).

^³Figures for Western European GNP, inventory investment, and GNP price deflator have been estimated, since actual data are not yet available for 1962.

Similar information on both the current account balance and its components is given in Table 3 for annual averages of the years 1958-59 and 1961-62. This comparison constitutes an interesting test of the performance of the model because of the substantial improvement in the U.S. current account from the first to the second of these two-year periods. With the exception of the fairly large error in the computed value for merchandise exports in 1958-59, which is of course carried into the merchandise trade balance and the over-all current account balance, the model fits the data of these recent subperiods quite well. The fit of the model is improved if the computation is made for the average of two years rather than for a single year. If the model is used to project general tendencies of the current account balance, rather than its value in a particular future year, there is thus some hope, though there can never be any assurance, that the projection error, to the extent that it stems from imperfections of the model rather than from invalid assumptions about the values of the exogenous variables, may remain within acceptable limits.

Table 3.

U.S. Current Account Balance and Its Components: Actual and Computed Values, Annual Averages, 1958-59 and 1961-62

(In billions of current U.S. dollars)

^¹Military transactions and expenditures, and miscellaneous government services.

Table 3.

U.S. Current Account Balance and Its Components: Actual and Computed Values, Annual Averages, 1958-59 and 1961-62

(In billions of current U.S. dollars)

						Average, 1958-59			Average, 1961-62
						Actual value	Computed value	Residual (Col. 1 – Col. 2)	Actual value	Computed value	Residual (Col. 4 – Col. 5)
						(1)	(2)	(3)	(4)	(5)	(6)
Balance of goods and services (excluding
	transfers under militarv grants)					1.17	—	—	5.14	—	—
Less Balance of items not computed¹						−3.12	—	—	−2.68	—	—
Equals Balance of goods and services com-
	puted in the model					4.29	5.03	−0.74	7.82	7.46	+0.36
		Merchandise trade
			Exports
				To Western Europe		4.70	5.04	−0.34	6.95	6.44	+0.51
				To Rest of World		11.58	11.86	−0.28	13.24	13.53	−0.29
					Total exports	16.28	16.90	−0.62	20.19	19.97	+0.22
			Imports
				From Western Europe		3.91	3.88	+0.03	4.29	4.17	+0.12
				From Rest of World		10.22	10.09	+0.13	11.03	11.21	−0.18
					Total imports	14.13	13.97	+0.16	15.32	15.38	−0.06
		Trade balance				2.15	2.93	−0.78	4.87	4.59	+0.28
		Services
			Receipts
				From Western Europe		1.85	1.78	+0.07	2.35	2.24	+0.11
				From Rest of World		4.71	4.71	—	5.80	5.82	−0.02
					Total service receipts	6.56	6.49	+0.07	8.15	8.06	+0.09
			Payments
				To Western Europe		2.03	2.12	−0.09	2.53	2.45	+0.08
				To Rest of World		2.38	2.25	+0.13	2.68	2.74	−0.06
					Total service payments	4.41	4.37	+0.04	5.21	5.19	+0.02
		Service balance				2.15	2.12	+0.03	2.94	2.87	+0.07

^¹Military transactions and expenditures, and miscellaneous government services.

Table 3.

U.S. Current Account Balance and Its Components: Actual and Computed Values, Annual Averages, 1958-59 and 1961-62

(In billions of current U.S. dollars)

						Average, 1958-59			Average, 1961-62
						Actual value	Computed value	Residual (Col. 1 – Col. 2)	Actual value	Computed value	Residual (Col. 4 – Col. 5)
						(1)	(2)	(3)	(4)	(5)	(6)
Balance of goods and services (excluding
	transfers under militarv grants)					1.17	—	—	5.14	—	—
Less Balance of items not computed¹						−3.12	—	—	−2.68	—	—
Equals Balance of goods and services com-
	puted in the model					4.29	5.03	−0.74	7.82	7.46	+0.36
		Merchandise trade
			Exports
				To Western Europe		4.70	5.04	−0.34	6.95	6.44	+0.51
				To Rest of World		11.58	11.86	−0.28	13.24	13.53	−0.29
					Total exports	16.28	16.90	−0.62	20.19	19.97	+0.22
			Imports
				From Western Europe		3.91	3.88	+0.03	4.29	4.17	+0.12
				From Rest of World		10.22	10.09	+0.13	11.03	11.21	−0.18
					Total imports	14.13	13.97	+0.16	15.32	15.38	−0.06
		Trade balance				2.15	2.93	−0.78	4.87	4.59	+0.28
		Services
			Receipts
				From Western Europe		1.85	1.78	+0.07	2.35	2.24	+0.11
				From Rest of World		4.71	4.71	—	5.80	5.82	−0.02
					Total service receipts	6.56	6.49	+0.07	8.15	8.06	+0.09
			Payments
				To Western Europe		2.03	2.12	−0.09	2.53	2.45	+0.08
				To Rest of World		2.38	2.25	+0.13	2.68	2.74	−0.06
					Total service payments	4.41	4.37	+0.04	5.21	5.19	+0.02
		Service balance				2.15	2.12	+0.03	2.94	2.87	+0.07

^¹Military transactions and expenditures, and miscellaneous government services.

Price and income effects

From the estimated equations described in this section it is possible to compute the separate effects of changes in incomes, prices, and other exogenous variables on any of the variables explained in the model.²⁴These effects are conveniently recorded by giving in each case the number by which a change in one of the exogenous variables must be multiplied in order to arrive at the induced change of the endogenous variable in question, after all the repercussions throughout the system have worked themselves out. A table of the multipliers computed from Model 3 is presented in Appendix II (p. 109). In the text, only a selection of multiplier effects on the U.S. current account balance and on U.S. current gross receipts and payments is given.

In Table 4, column 1 indicates that a rise in U.S. real GNP by $1 billion, with all other exogenous variables remaining unchanged, would tend to worsen the U.S. current account balance by $34 million, that is, by 3.4 per cent of the increase in GNP. A similar increase in Western Europe’s real GNP²⁵ would improve the U.S. current account balance by $55 million. Since the multiplier effects shown in Table 4 are additive, a simultaneous increase in both U.S. and Western European real GNP by the same absolute amount would, other things being equal, lead to an improvement in the U.S. current account. Since the U.S. GNP exceeds Western Europe’s GNP approximately in the same proportion in which the magnitude (disregarding the sign) of the Western European GNP multiplier on the U.S. current account balance exceeds the corresponding U.S. GNP multiplier, an equal percentage growth of GNP in the two regions would tend to leave the U.S. current account balance approximately unchanged.

Table 4.

Estimated Effects of Changes in Incomes and Prices on the U.S. Current Account Balance

Source: Table 12 (p. 109).

^¹The estimated effects shown in this table are (1) proportional to the magnitudes of the “causal” changes, and (2) additive; the joint effect of simultaneous changes in several of the magnitudes listed in the stubs are obtained by adding their separate effects.

^²Column 2 minus column 3.

^³This item is the sum of net foreign exchange receipts by the Rest of the World on accounts not estimated in the model; it consists chiefly of (1) net receipts from the United States arising out of U.S. military expenditures and miscellaneous government services, (2) net payments (a negative item) to Western Europe on service account, (3) net receipts from the United States and Western Europe on capital account, including foreign aid, and (4) any reduction (minus, if increase) of the Rest of the World’s foreign exchange reserves. (See also p. 74, fn. 29.)

Table 4.

Estimated Effects of Changes in Incomes and Prices on the U.S. Current Account Balance

			Estimated Effect, in Millions of Current U.S. Dollars, on¹
			U.S. current account balance² (1)	U.S. exports of goods and services (2)	U.S. imports of goods and services (3)
Effect of a rise by $1 billion in
	GNP (in 1954 prices)
		United States	−34	+13	+46
		Western Europe	+55	+55	0
	Inventory investment (in 1954 prices)
		United States	−81	+50	+130
		Western Europe	+600	+600	0
	“Autonomous foreign exchange receipts”
		of Rest of World³	+450	+450	0
Effect of a rise by 1 percentage point in
	GNP Drices (1954 = 1)
		United States	−91	+36	+127
		Western Europe	+85	+85	0
	Export prices (1954 = 1)
		United States	−55	−68	−14
		Western Europe	+64	+65	+1
		Rest of World	+27	+72	+45

Source: Table 12 (p. 109).

^²Column 2 minus column 3.

Table 4.

Estimated Effects of Changes in Incomes and Prices on the U.S. Current Account Balance

			Estimated Effect, in Millions of Current U.S. Dollars, on¹
			U.S. current account balance² (1)	U.S. exports of goods and services (2)	U.S. imports of goods and services (3)
Effect of a rise by $1 billion in
	GNP (in 1954 prices)
		United States	−34	+13	+46
		Western Europe	+55	+55	0
	Inventory investment (in 1954 prices)
		United States	−81	+50	+130
		Western Europe	+600	+600	0
	“Autonomous foreign exchange receipts”
		of Rest of World³	+450	+450	0
Effect of a rise by 1 percentage point in
	GNP Drices (1954 = 1)
		United States	−91	+36	+127
		Western Europe	+85	+85	0
	Export prices (1954 = 1)
		United States	−55	−68	−14
		Western Europe	+64	+65	+1
		Rest of World	+27	+72	+45

Source: Table 12 (p. 109).

^²Column 2 minus column 3.

This conclusion must, however, be qualified with respect to the effect of changes in inventories. Whereas a rise in U.S. inventory investment leads to a relatively small worsening of the U.S. current account balance, an increase in Western Europe’s inventory investment induces a pronounced improvement. This asymmetry is due to the relatively strong effects of inventory changes on imports found in the estimated import equations of Western Europe, compared with the corresponding effects in the U.S. import equations.

Price changes in the United States and in Western Europe affect the U.S. current account in a roughly symmetrical manner. A 1 per cent rise in U.S. GNP prices results in a deterioration of the U.S. current balance by about $90 million; and a 1 per cent rise in Western European GNP prices results in an improvement by about $90 million in the U.S. balance. The corresponding effects of export price changes are somewhat smaller. An increase in export prices of the Rest of the World leads to a small improvement in the U.S. current account since it induces a somewhat larger rise in the value of U.S. exports, as a result of improved foreign exchange earnings of the Rest of the World, than in the value of U.S. imports.²⁶

Of particular interest is the net effect of a change in the Rest of the World’s “autonomous foreign exchange receipts”²⁷ on the U.S. current account balance. The relevant multiplier in Table 4 indicates that 45 per cent of any increase in the Rest of the World’s capital and aid receipts would be used to purchase exports from the United States and would, therefore, benefit the U.S. current account balance.²⁸ Some qualifications are necessary, however. First, it is in the nature of the model that the multiplicand in question is composed of a number of different items. From net capital and aid receipts by the Rest of the World (regularly a positive item) there must be subtracted the Rest of the World’s net payments to the two industrial regions on all those accounts not separately estimated in the model; in view of the Rest of the World’s large deficit in service transactions with Western Europe, this item is ordinarily a substantial offset to the Rest of the World’s capital and aid receipts. In addition, the multiplicand must be reduced by the amount of any increase, or increased by the amount of any reduction, in foreign exchange reserves held by the Rest of the World.²⁹ With allowance for this qualification, the multiplier must therefore be interpreted as follows: U.S. exports will tend to increase by 45 per cent of the amount of any increase in U.S. and Western European foreign aid and net capital payments to the Rest of the World, but only to the extent that such payments are not offset by a worsening of the Rest of the World’s current account deficit with the two industrial regions on various military expenditure and service accounts not separately estimated in the model or by an increase in the Rest of the World’s foreign exchange holdings. In this connection it is worth pointing out that the sum of net capital and aid receipts (which include short-term capital movements) by the Rest of the World shows considerable variability and may well be the item principally responsible for year-to-year changes in the U.S. current account balance. For instance, from 1961 to 1962 the estimated decline in net capital and aid receipts by the Rest of the World is $1-2 billion; moreover, the Rest of the World increased its reserves by $0.6 billion.³⁰ In terms of the mechanism of the model, these two changes would, by themselves, account for the worsening of the U.S. current balance from 1961 to 1962.

A second qualification concerns the effect of certain restrictions on the expenditure of foreign aid funds, commonly referred to as “tying” of aid. No separate allowance has been made in the model for the possibility that increased resort to tying of aid funds will raise the fraction by which U.S. exports will increase as a result of additional U.S. aid expenditures. The marginal effect on exports of the tying of aid is quite uncertain, and there is no good way of assessing its magnitude without an exhaustive country-by-country study of aid procedures. Also, much depends on the distribution of aid by type: aid in the form of shipments of surplus agricultural commodities under U.S. Public Law 480 entails little or no net balance of payments cost for the United States; on the other hand, tying of aid under the so-called irrevocable letter-of-credit procedure may not materially reduce the foreign exchange cost of the aid expenditure.³¹ For these reasons, it seems preferable to make allowance for the effect of tying of aid, to the extent necessary, outside the formal apparatus of the model.

A third qualification has to do with the geographical distribution of the Rest of the World’s autonomous foreign exchange receipts by recipient and, to some extent, by source. U.S. exports tend to benefit more from an additional dollar of foreign exchange received by Canada, Japan, or a Latin American country than from one received by, say, Australia.³² Again, capital and aid funds—especially, tied aid —are more likely to be spent in the region of origin than elsewhere. But until the model can be expanded by dividing the Rest of the World into a number of subregions it is not possible to allow formally for these geographic differences. For projection purposes, the model therefore operates on the implicit assumption of an unchanged distribution of the item “autonomous foreign exchange receipts” among the various recipient subregions of the Rest of the World and of an unchanged proportion of these funds originating in the United States.

III. Projections to 1964 and 1968

As emphasized in Section I, projections from an econometric model are not unconditional predictions; they merely show expected values of the endogenous variables on the condition that the exogenous variables take certain assumed values. In general, these assumed values are, themselves, not unconditional predictions but merely more or less plausible extrapolations of trends as seen at present. The projections from the model can be no more valid than these assumptions. Moreover, the structure of the economic system in question may change over time, so that the coefficients estimated from data for the sample period no longer reflect economic behavior during the projection period.

Nevertheless, it seems worthwhile for two reasons to conclude this paper by showing such projections. First, they may, and often do, serve as a point of departure for further analysis, in which elements left out of the formal apparatus of the model can be conveniently introduced as corrections of the initial results. Second, since projections made partly with the help of an earlier version of this model have been published in the Brookings Report, it may be interesting to ascertain the extent to which these projections might have been altered if the revised version of the model presented in this paper had been available when the Brookings study was in progress.

Three projections have been made. The first, to 1964, is included for reasons of the inherent interest in a proximate period for which the postulate of an unchanged economic structure is somewhat more defensible, and for which assumptions about the values of the exogenous variables can be made with somewhat greater assurance, than for a more distant year. In addition, two projections to 1968 are presented for the purpose of comparison with the results in the Brookings Report. They are based, as far as possible, on assumptions made in that Report, particularly with respect to expected income and price changes. This has been done in order to draw attention to the effects on the projected values of differences in the method of projection and in the coefficients used, and does not necessarily imply acceptance, in all respects, of the Brookings assumptions about price and income changes. The Brookings group started with a set of “initial” assumptions about income trends (1961-68) in the United States and in Western Europe, given to them as part of the terms of reference of their study, and added a set of “alternative” assumptions in which rates of economic growth in the United States and Western Europe were scaled down somewhat. To each of these sets of assumptions about income growth, the Brookings group added assumptions about trends in the number of man-hours, productivity, and several other factors, to arrive at a judgment about domestic and export price developments in the two industrial regions. Under the alternative assumptions, price increases in Western Europe, though not in the United States, are expected to proceed at a less rapid pace than under the initial assumptions. The changes from 1962 to 1964, assumed for purposes of the shorter-run projection made in this paper, are largely based on the Brookings group’s initial assumptions about prices and on their alternative assumptions about incomes, a combination which was thought to reflect present short-term trends fairly adequately. The three sets of assumptions³³ are given in Table 5. It should be added that some of the assumptions which must be made in these projections cannot reasonably be expected to hold for a particular future year, say 1964 or 1968, but should be interpreted as anticipations of average values at the time for which the projection is to be made, say, during the years 1963-65 or 1967-69.

Table 5.

Assumed Changes in Selected Items¹for Projections of U.S. Current Account Balance to 1964 AND 1968

^¹In addition to the assumptions shown in the table, the following assumptions have been made: (1) exchange rates and export prices of the Rest of the World will remain the same as in 1962; (2) inventory investment both in the United States and in Western Europe will remain approximately at the average value over recent years. Also, increases in international investment positions have been based in part on projections of long-term investment on page 150 in the Brookings Report (cited above, p. 60, fn. 3). For numerical assumptions, see Table 13 (p. 110).

^²The two sets of assumptions for 1968 about GNP and price changes are from the Brookings Report (p. 215). The assumption about the increase in the Rest of the World’s “autonomous foreign exchange receipts” is explained in the following footnote.

^³For a definition of “autonomous foreign exchange receipts” of the Rest of the World, see Table 4, footnote 3. The assumed increases in this item are based partly on the increases in the flow of capital and aid to the Rest of the World estimated in the Brookings Report (+$3.6 billion from 1961 to 1968), and partly on the authors’ estimate of the deterioration (−) of the Rest of the World’s net service balance with Western Europe (−$1.0 billion from 1961 to 1968) and on an assumed figure for the increase (−) in foreign exchange reserves of the Rest of the World during 1968 (−$0.3 billion). The assumed increase in autonomous foreign exchange receipts from 1962 to 1964 is large relative to that from 1961 to 1968 because of the very low value of this variable in 1962 compared with 1961.

Table 5.

Assumed Changes in Selected Items¹for Projections of U.S. Current Account Balance to 1964 AND 1968

		Assumed Changes for Projections to
		1964	1968
			“Initial” Assumptions²	“Alternative” Assumptions²
		Annual percentage increase from 1962 to 1964	Percentage increase from 1961 to 1968
Real GNP
	United States	4.5	43	36
	Western Europe	4.2	33	29
GNP prices
	United States	1.5	11	11
	Western Europe	2.75	20	11
Export prices
	United States	0.5	4	4
	Western Europe	1.5	11	7
		Excess of 1964 total over 1962 total, in billions of current U.S. dollars	Excess of 1968 total over 1961 total, in billions of current U.S. dollars
“Autonomous foreign exchange
	receipts” of Rest of World³	1.7	2.3	2.3

Table 5.

Assumed Changes in Selected Items¹for Projections of U.S. Current Account Balance to 1964 AND 1968

		Assumed Changes for Projections to
		1964	1968
			“Initial” Assumptions²	“Alternative” Assumptions²
		Annual percentage increase from 1962 to 1964	Percentage increase from 1961 to 1968
Real GNP
	United States	4.5	43	36
	Western Europe	4.2	33	29
GNP prices
	United States	1.5	11	11
	Western Europe	2.75	20	11
Export prices
	United States	0.5	4	4
	Western Europe	1.5	11	7
		Excess of 1964 total over 1962 total, in billions of current U.S. dollars	Excess of 1968 total over 1961 total, in billions of current U.S. dollars
“Autonomous foreign exchange
	receipts” of Rest of World³	1.7	2.3	2.3

Table 6 shows actual values for 1961 and 1962 and projected values for 1964 and 1968 of the U.S. current account balance and its major components. While all these components are expected to grow, increases on the receipts and payments sides between 1961 and 1964 approximately cancel one another, so that the current account balance projected to 1964 equals the actual balance of 1961. This means that the worsening of the current account in 1962 is, in this projection, expected to be reversed by 1964. The projections of the current account balance to 1968 under the initial and alternative assumptions show expected improvements over 1961 by $1.8 billion and $1.0 billion, respectively.

Table 6.

U.S. Current Account Balance: Actual, 1961 and 1962, and Projected, 1964 and 1968

(In billions of current U.S. dollars)

^¹Excluding military transactions and expenditures, and miscellaneous government services. (See also Table 3, p. 71.)

Table 6.

U.S. Current Account Balance: Actual, 1961 and 1962, and Projected, 1964 and 1968

(In billions of current U.S. dollars)

				Actual		Projected
				1961	1962	1964	1968
							“Initial” Assumptions	“Alternative” Assumptions
Current account balance¹				8.2	7.4	8.3	10.0	9.2
	Exports of goods and services¹
		Merchandise exports
			To Western Europe	6.8	7.1	7.5	9.2	8.5
			To Rest of World	13.1	13.4	15.3	20.0	18.9
				19.9	20.5	22.8	29.2	27.4
		Service receipts
			From Western Europe	2.2	2.5	2.5	3.2	3.0
			From Rest of World	5.6	6.0	6.7	8.4	8.1
				7.8	8.5	9.2	11.6	11.1
Total receipts				27.7	29.0	32.0	40.8	38.5
	ImDorts of goods and services¹
		Merchandise imports
			From Western Europe	4.0	4.5	5.2	7.3	6.8
			From Rest of World	10.5	11.6	12.5	15.4	14.8
				14.5	16.1	17.7	22.6	21.6
		Service payments
			To Western Europe	2.5	2.6	2.9	3.9	3.7
			To Rest of World	2.6	2.8	3.2	4.3	4.1
				5.1	5.4	6.1	8.2	7.8
		Total payments		19.6	21.5	23.7	30.8	29.3

^¹Excluding military transactions and expenditures, and miscellaneous government services. (See also Table 3, p. 71.)

Table 6.

U.S. Current Account Balance: Actual, 1961 and 1962, and Projected, 1964 and 1968

(In billions of current U.S. dollars)

				Actual		Projected
				1961	1962	1964	1968
							“Initial” Assumptions	“Alternative” Assumptions
Current account balance¹				8.2	7.4	8.3	10.0	9.2
	Exports of goods and services¹
		Merchandise exports
			To Western Europe	6.8	7.1	7.5	9.2	8.5
			To Rest of World	13.1	13.4	15.3	20.0	18.9
				19.9	20.5	22.8	29.2	27.4
		Service receipts
			From Western Europe	2.2	2.5	2.5	3.2	3.0
			From Rest of World	5.6	6.0	6.7	8.4	8.1
				7.8	8.5	9.2	11.6	11.1
Total receipts				27.7	29.0	32.0	40.8	38.5
	ImDorts of goods and services¹
		Merchandise imports
			From Western Europe	4.0	4.5	5.2	7.3	6.8
			From Rest of World	10.5	11.6	12.5	15.4	14.8
				14.5	16.1	17.7	22.6	21.6
		Service payments
			To Western Europe	2.5	2.6	2.9	3.9	3.7
			To Rest of World	2.6	2.8	3.2	4.3	4.1
				5.1	5.4	6.1	8.2	7.8
		Total payments		19.6	21.5	23.7	30.8	29.3

^¹Excluding military transactions and expenditures, and miscellaneous government services. (See also Table 3, p. 71.)

Since the sum of the current account balances of the three regions is by definition zero, it is easy to work out the implications of these assumptions and projections for Western Europe’s current account balance (see Table 7). Including those service transactions which are not estimated in the model, Western Europe’s current account balance in 1961 was $2.4 billion. The projected value for 1964 is also $2.4 billion, and for 1968 it is $4.0 billion and $4.8 billion under the initial and alternative assumptions, respectively. The projected balances for Western Europe and the United States add to the assumed amounts of the Rest of the World’s capital and aid receipts less reserve accumulation.

Table 7.

Current Account Balances of the Three Regions: Actual, 1961, and Projected, 1964 and 1968

(In billions of current U.S. dollars)

^¹Net exports of goods and services as given in the national income accounts, including items not estimated in the model (exogenous items).

Table 7.

Current Account Balances of the Three Regions: Actual, 1961, and Projected, 1964 and 1968

(In billions of current U.S. dollars)

				1968, Projected
		1961,	1964,	“Initial”	“Alternative”
		Actual	Projected	Assumptions	Assumptions
Rest of World		−6.9	−7.0	−10.2	−10.2
United States¹		+4.5	+4.6	+6.2	+5.4
	Endogenous items	+8.2	+8.8	+10.0	+9.2
	Exogenous items	−8.7	−8.7	−8.8	−8.8
Western Europe¹		+2.4	+2.4	+4.0	+4.8
	Endogenous items	−4.5	−5.6	−4.0	−8.2
	Exogenous items	+6.9	+8.0	+8.0	+8.0

^¹Net exports of goods and services as given in the national income accounts, including items not estimated in the model (exogenous items).

Table 7.

Current Account Balances of the Three Regions: Actual, 1961, and Projected, 1964 and 1968

(In billions of current U.S. dollars)

				1968, Projected
		1961,	1964,	“Initial”	“Alternative”
		Actual	Projected	Assumptions	Assumptions
Rest of World		−6.9	−7.0	−10.2	−10.2
United States¹		+4.5	+4.6	+6.2	+5.4
	Endogenous items	+8.2	+8.8	+10.0	+9.2
	Exogenous items	−8.7	−8.7	−8.8	−8.8
Western Europe¹		+2.4	+2.4	+4.0	+4.8
	Endogenous items	−4.5	−5.6	−4.0	−8.2
	Exogenous items	+6.9	+8.0	+8.0	+8.0

^¹Net exports of goods and services as given in the national income accounts, including items not estimated in the model (exogenous items).

The analysis of these computed changes by type of “cause” is perhaps more interesting than the projections themselves. The separate elements of the computed changes in the U.S. current account balance are listed in Table 8. The reason for choosing 1961 as the base period for the computations in this table is twofold: first, this is the year chosen as the base period in the Brookings Report; second, the current account balance for 1961 computed from the model is, by coincidence, almost exactly equal to the actual balance in that year, a circumstance which facilitates the presentation. It is found that the effect of the assumed growth in Western European GNP largely offsets that of the assumed increase in U.S. GNP, leaving only a comparatively small deterioration in the U.S. current account balance that is due to income effects. Price effects account for a small improvement in the projection to 1964 and in that to 1968 under the alternative assumptions, but for a somewhat larger improvement in the projection to 1968 under the initial assumptions. According to these computations, projected changes in the U.S. investment position (net) result in appreciable improvements in the U.S. current account, and so does the assumed increase between 1961 and 1968³⁴ in the “autonomous foreign exchange receipts” of the Rest of the World.

Table 8.

U.S. Current Account Balance: Analysis of Computed Changes from 1961 to 1964 and from 1961 to 1968

(In billions of current U.S. dollars)

^¹Excluding military transactions and expenditures, and miscellaneous government services. (See also Table 3, p. 71.)

^²Assumed changes are given in Table 5 (p. 78.)

^³The assumed change in Western Europe’s inventory investment is too small to produce effects in excess of $0.05 billion.

^⁴For definition, see Table 4 (fn. 3). See also page 80 (fn. 34).

Table 8.

U.S. Current Account Balance: Analysis of Computed Changes from 1961 to 1964 and from 1961 to 1968

(In billions of current U.S. dollars)

			1961 to 1964	1961 to 1968
			1961 to 1964	“Initial” Assumptions	“Alternative” Assumptions
Computed change in U.S. current
account balance¹			0	+1.8	+1.0
Effect of change in²
	U.S. real GNP		−2.4	−6.5	−5.4
	W.E. real GNP		+2.1	+5.2	+4.5
	U.S. inventory investment		−0.1	−0.2	−0.2
	W.E. inventory investment³		—	—	—
		Income and inventory effects	−0.4	−1.5	−1.1
	U.S. GNP prices		−0.4	−1.2	−1.2
	W.E. GNP prices		+0.9	+2.2	+1.2
	U.S. export prices		−0.1	−0.2	−0.2
	W.E. export prices		+0.2	+0.7	+0.5
		Price effects	+0.6	+1.5	+0.3
U.S. investment position (net)			+0.3	+0.7	+0.7
R.O.W. “autonomous foreign
exchange receipts”⁴			−0.5	+1.0	+1.0

^¹Excluding military transactions and expenditures, and miscellaneous government services. (See also Table 3, p. 71.)

^²Assumed changes are given in Table 5 (p. 78.)

^³The assumed change in Western Europe’s inventory investment is too small to produce effects in excess of $0.05 billion.

^⁴For definition, see Table 4 (fn. 3). See also page 80 (fn. 34).

Table 8.

U.S. Current Account Balance: Analysis of Computed Changes from 1961 to 1964 and from 1961 to 1968

(In billions of current U.S. dollars)

			1961 to 1964	1961 to 1968
			1961 to 1964	“Initial” Assumptions	“Alternative” Assumptions
Computed change in U.S. current
account balance¹			0	+1.8	+1.0
Effect of change in²
	U.S. real GNP		−2.4	−6.5	−5.4
	W.E. real GNP		+2.1	+5.2	+4.5
	U.S. inventory investment		−0.1	−0.2	−0.2
	W.E. inventory investment³		—	—	—
		Income and inventory effects	−0.4	−1.5	−1.1
	U.S. GNP prices		−0.4	−1.2	−1.2
	W.E. GNP prices		+0.9	+2.2	+1.2
	U.S. export prices		−0.1	−0.2	−0.2
	W.E. export prices		+0.2	+0.7	+0.5
		Price effects	+0.6	+1.5	+0.3
U.S. investment position (net)			+0.3	+0.7	+0.7
R.O.W. “autonomous foreign
exchange receipts”⁴			−0.5	+1.0	+1.0

^¹Excluding military transactions and expenditures, and miscellaneous government services. (See also Table 3, p. 71.)

^²Assumed changes are given in Table 5 (p. 78.)

^³The assumed change in Western Europe’s inventory investment is too small to produce effects in excess of $0.05 billion.

^⁴For definition, see Table 4 (fn. 3). See also page 80 (fn. 34).

In Table 9, the projected changes in the U.S. current account balance and its major components resulting from the application of the revised model are compared with those in the Brookings Report. The two sets of projections correspond more closely under the alternative assumptions than under the initial assumptions. Under the initial assumptions, the values for projected exports of goods and services are lower, and the values for projected imports of goods and services are higher, in the revised model than in the Brookings Report. Under the alternative assumptions, the differences in the two sets of projections are negligible.

Table 9.

Projected Changes from 1961 to 1968 in U.S. Current Account: Comparison of Brookings Report and Revised Model (Model 3)

(In billions of current U.S. dollars)

Sources: Columns 2 and 4 are based on Table 6; columns 1 and 3, on the Brookings Report (cited above, p. 60, fn. 3), Appendix Table 10, p. 289.

^¹Excluding exports transferred under military grants.

^²Including interest and dividend account.

^³Excluding military expenditures: the Brookings Report projects reductions in military expenditures of $0.4 billion and $0.5 billion under the initial and alternative assumptions, respectively. Including this item, the improvement in the current account balance projected in the Brookings Report is thus $4.2 billion and $1.7 billion under the two sets of assumptions.

^⁴See text, pages 80-81.

Table 9.

Projected Changes from 1961 to 1968 in U.S. Current Account: Comparison of Brookings Report and Revised Model (Model 3)

(In billions of current U.S. dollars)

				“Initial” Assumptions		“Alternative” Assumptions
				Brookings Report	Revised Model	Brookings Report	Revised Model
				(1)	(2)	(3)	(4)
Exports of goods and services¹
	Merchandise exports¹			+11.2	+9.3	+7.6	+7.5
	Service receipts²			+3.0	+3.8	+3.0	+3.3
			Total receipts	+14.3	+13.1	+10.6	+10.8
Imports of goods and services³
	Merchandise imports			+8.9	+8.1	+7.9	+7.1
	Service payments², ³			+1.6	+3.1	+1.5	+2.7
			Total payments	+10.5	+11.2	+9.4	+9.7
Current account balance¹, ³				+3.8	+1.8	+1.2	+1.0
	Memorandum
		Allowance for “EEC discrimination”		−0.6	—⁴	−0.6	—⁴
		Current account balance without EEC allowance⁴		+4.4	+1.8	+1.8	+1.0

Sources: Columns 2 and 4 are based on Table 6; columns 1 and 3, on the Brookings Report (cited above, p. 60, fn. 3), Appendix Table 10, p. 289.

^¹Excluding exports transferred under military grants.

^²Including interest and dividend account.

^⁴See text, pages 80-81.

Table 9.

Projected Changes from 1961 to 1968 in U.S. Current Account: Comparison of Brookings Report and Revised Model (Model 3)

(In billions of current U.S. dollars)

				“Initial” Assumptions		“Alternative” Assumptions
				Brookings Report	Revised Model	Brookings Report	Revised Model
				(1)	(2)	(3)	(4)
Exports of goods and services¹
	Merchandise exports¹			+11.2	+9.3	+7.6	+7.5
	Service receipts²			+3.0	+3.8	+3.0	+3.3
			Total receipts	+14.3	+13.1	+10.6	+10.8
Imports of goods and services³
	Merchandise imports			+8.9	+8.1	+7.9	+7.1
	Service payments², ³			+1.6	+3.1	+1.5	+2.7
			Total payments	+10.5	+11.2	+9.4	+9.7
Current account balance¹, ³				+3.8	+1.8	+1.2	+1.0
	Memorandum
		Allowance for “EEC discrimination”		−0.6	—⁴	−0.6	—⁴
		Current account balance without EEC allowance⁴		+4.4	+1.8	+1.8	+1.0

Sources: Columns 2 and 4 are based on Table 6; columns 1 and 3, on the Brookings Report (cited above, p. 60, fn. 3), Appendix Table 10, p. 289.

^¹Excluding exports transferred under military grants.

^²Including interest and dividend account.

^⁴See text, pages 80-81.

The Brookings Report makes allowance for the effect on U.S. exports of increased discrimination against U.S. dollar goods in the European Economic Community (EEC). In order to make the results of the Brookings Report and those obtained from an application of the revised model comparable, the last line of Table 9 shows the change in the current account balance projected in the Brookings Report, excluding the allowance for increased EEC discrimination. Under the initial assumptions, the improvement in the U.S. current account projected by the Brookings group exceeds the improvement computed from the revised model by $2.6 billion. Under the alternative assumptions, this excess is only $0.8 billion. These discrepancies are accounted for by a number of differences in approach, in the values of the coefficients of the two versions of the model, and in assumptions about variables other than incomes and prices. A rough quantitative allocation of these discrepancies to the various sources is given in Table 10.

Table 10.

U.S. Current Account Projections for 1968: Principal Sources of Differences Between the Brookings Report and the Revised Model (Model 3)

(In billions of current U.S. dollars)

^¹From Table 9.

^²See Table 5 (fn. 3) and text, pages 74-75.

Table 10.

U.S. Current Account Projections for 1968: Principal Sources of Differences Between the Brookings Report and the Revised Model (Model 3)

(In billions of current U.S. dollars)

				“Initial” Assumptions	“Alternative” Assumptions
Excess of improvement in U. S. current account
	balance as projected in Brookings Report over that
	projected from Model 3¹			2.6	0.8
Accounted for by
		Differences in income and price elasticities of
			merchandise trade	1.4	−0.6
		Differences in assumptions about size and effect
			of Rest of World’s “autonomous foreign ex
			change receipts”²	0.7	0.7
		Differences in projections of service receipts and
			payments	0.7	0.9
		Residual difference		−0.2	−0.2

^¹From Table 9.

^²See Table 5 (fn. 3) and text, pages 74-75.

Table 10.

U.S. Current Account Projections for 1968: Principal Sources of Differences Between the Brookings Report and the Revised Model (Model 3)

(In billions of current U.S. dollars)

				“Initial” Assumptions	“Alternative” Assumptions
Excess of improvement in U. S. current account
	balance as projected in Brookings Report over that
	projected from Model 3¹			2.6	0.8
Accounted for by
		Differences in income and price elasticities of
			merchandise trade	1.4	−0.6
		Differences in assumptions about size and effect
			of Rest of World’s “autonomous foreign ex
			change receipts”²	0.7	0.7
		Differences in projections of service receipts and
			payments	0.7	0.9
		Residual difference		−0.2	−0.2

^¹From Table 9.

^²See Table 5 (fn. 3) and text, pages 74-75.

Only the first of these discrepancies is accounted for by differences between the income and price elasticities of merchandise trade estimated in the revised model and those used by the Brooking group. In particular, the improvement in the U.S. current account that was due to price effects computed from Model 3 (+$1.5 billion and +$0.3 billion, respectively, under the two sets of assumptions)³⁵ is smaller than that projected in the Brookings Report (+$4.3 billion and +$1.4 billion, respectively).³⁶ This difference, particularly striking under the initial assumptions, stems chiefly from a larger Western European price elasticity of demand for merchandise imports from the United States assumed in the Brookings Report (—2.5, compared with −1 estimated in the model). On the other hand, income effects account for a somewhat smaller deterioration of the U.S. current balance in Model 3 than in the computations in the Brookings Report. The second discrepancy shown in Table 10 can be ascribed in large measure to the difference in the net total of the Rest of the World’s “autonomous foreign exchange receipts” (corrected for reserve changes) assumed in the present study and in the Brookings Report. The projections to 1968 shown in this paper do, while the Brookings Report does not, make allowance (1) for an increase (by $1.0 billion, over 1961), in accordance with recent trends, of the Rest of the World’s net deficit with the two industrial regions on various service accounts not separately estimated in the model, and (2) for an assumed annual increase (of $0.3 billion) in the Rest of the World’s foreign exchange holdings at the approximate annual rate at which this group of countries has accumulated foreign exchange reserves over the seven-year period ended in 1962. These two items imply a reduction of $1.3 billion in the Rest of the World’s expenditure on imports of goods and services compared with what it would otherwise have been; the U.S. share in this reduction (45 per cent, or $0.6 billion) accounts for the largest part of the difference between the two projections given in Table 10 under this heading.³⁷ The third difference shown in Table 10 is due, at least in part, to the fact that the Brookings Report confines its projection of receipts and payments for service transactions to those, between the United States and Western Europe, and assumes that the services balance of the United States with the Rest of the World remains unchanged.

The material presented in this section should not be interpreted as entailing criticism of the projections made in the Brookings Report. The Brookings group has studied the individual components of the U.S. current account balance with great care, and has had the benefit of advice from many agencies of the U.S. Government. Such projections can hardly fail to be in many ways superior to a more mechanical extrapolation of past relations of the type reported in this paper. It is, in fact, surprising that the two sets of projections correspond rather closely, especially the projections under the “alternative” assumptions. From the material presented in this section one would, nevertheless, be inclined to draw the conclusion that the Brookings projections of the U.S. current account balance are somewhat optimistic. This is especially true for the projection based on the initial assumptions; even if the validity of these assumptions is stipulated, the present study would lead one to expect an improvement in the U.S. current account which is some $2-3 billion less than that projected in the Brookings Report. The corresponding projection from Model 3 under the alternative assumptions is lower than the Brookings estimate by about $1 billion or slightly less. Both these differences, but especially the second one, are within the margin of error that must be expected in this type of projection. Since the margin of error is large relative to the size of the projected balance, any usefulness which such an exercise may have for policy formulation must be sought in what is learned from the study about the structure of the economic system in question rather than in the projected values themselves.

APPENDICES

The appendices present material of a technical nature (of interest chiefly to economists engaged in research in this field), and also some details about the model and its application, with which it was thought undesirable to burden the text. Appendix I lists and discusses the structural equations; II presents the multipliers of the model; III gives further detail about the projections; and IV consists of a tabulation of the data used in the study and a description of the sources of the data.

Before the structural equations are presented, a general comment about the method of estimation is in order. The equations have been estimated by the ordinary (single stage) least-squares method; the problem of the so-called least-squares bias in simultaneous equation models has been ignored.³⁸ The relative merits of various estimation methods for such models, when the number of observations is small, are still a matter of dispute.³⁹ Briefly, it is believed that the single stage least-squares method may give coefficient estimates which, though biased, have a smaller variance around their (biased) expected value than some of the principal alternative estimation methods.⁴⁰The smaller variance of the parameter estimates compensates to some extent for the undesirable property of bias. At any rate, it is unlikely that the least-squares bias is large enough to invalidate the general conclusions drawn from the model, or to cast substantial additional doubt on the projections, given the considerable uncertainty surrounding the assumptions about the values of the exogenous variables at various future dates.

I. The Structural Equations

The model consists of 29 structural equations, of which 3 are identities. The coefficients of the equations have been estimated from annual data, generally for the 15-year period 1948-62. Values for 1962 were not available for Western Europe’s GNP and related data when the computations were carried out, and in some equations one, two, or three of the early observations (1948-50) have been omitted; the fitting period is indicated next to the title of each equation. In the presentation below, the standard errors of the coefficients are given in parentheses below the point estimates. ${\bar{R}}^{2}$ denotes the coefficient of determination adjusted for degrees of freedom; s gives the standard error of estimate (root-mean-square error), corrected for the degrees of freedom, as a per cent of the sample mean of the dependent variable ; and d denotes the Durbin-Watson test statistic for serial correlation; a double asterisk (**) attached to the d value indicates the presence of serial correlation (at the 95 per cent confidence level); a single asterisk (*) indicates that the Durbin-Watson test is inconclusive. Subscripts 1, 2, and 3 refer to the three regions: United States = 1; Western Europe (European OECD countries) = 2; Rest of the World = 3.

List of variables

The data are shown, and the sources are described, in Tables 17–25 (pp. 116-22).

Jointly dependent variables

Exogenous variables

Equations

Region 1: United States

(1) U.S. GNP identity
$\begin{matrix} Y_{1} = & C_{1} + M_{12} + M_{13} + F_{12} + F_{13} + V_{12} + V_{13} + D_{12} + D_{13} \\ + O_{12} + O_{13} - M_{21} - M_{31} - F_{21} - F_{31} - V_{21} - V_{31} - D_{21} \\ - D_{31} - O_{21} - O_{31} + B_{1} + H_{1} + A_{1} \end{matrix}$
The GNP identity is stated in the conventional way, with GNP equal to the sum of consumption, domestic fixed and inventory investment, government expenditure on goods and services, and net exports of goods and services; but the last item is separated into the components individually estimated in the model and a residual item (B₁).
(2) U.S. consumption function (1948-62)
(a) Estimated:
$\begin{matrix} \frac{C_{1}}{P_{1}} = \underset{(0.07)}{1.23} \frac{Y_{1} - C_{1}}{P_{1}} - \underset{(4.1)}{24.8} W_{c} + \underset{(9.7)}{91.2} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.96 \end{matrix} & \bar{s} \end{matrix} = 2.6 % \end{matrix} & d = 1.00 * \end{matrix} \end{matrix}$
(b) Transformed:
$\frac{C_{1}}{P_{1}} = 0.552 \frac{Y_{1}}{P_{1}} - 11.1 W_{c} + 40.9$
Consumption is estimated as a function of GNP excluding consumption, and a dummy variable reflecting the lower level of consumption, partly as a consequence of higher personal tax rates, during the Korean war. The equation is then algebraically transformed into the form shown under (b), above.
(3) U.S. merchandise imports from Western Europe (1951-62)
$\begin{matrix} \frac{M_{21}}{P_{x 2}} - M_{21}^{a 8} = \underset{(0.0035)}{0.0144} \frac{Y_{1} - H_{1}}{P_{1}} + \underset{(0.0141)}{0.0427} \frac{H_{1}}{P_{1}} + \underset{(1.93)}{3.67} \frac{P_{1}}{P_{x 2}} - \underset{(0.82)}{6.78} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.97 \end{matrix} & \bar{s} \end{matrix} = 5.5 % \end{matrix} & d = 1.48 * \end{matrix} \end{matrix}$
Elasticities at the means of the respective variables:
With respect to income (final demand): 2.0
With respect to deflated European export prices (P_x2/P₁): −1.3
The price coefficient is not significant at the 5 per cent level. As indicated above, “extraordinary” imports, $M_{21}^{a 8}$ , of automobiles (during 1956-60) and steel (during and immediately following the 1959 steel strike), both in 1954 prices, have been subtracted from (M₂₁/P_x2) for purposes of estimating this equation. $M_{21}^{a 8}$ is regarded as an exogenous variable. See Table 25 (p. 122), column 5, and Chart 2 (p. 94).
Chart 2.
Adjustments of Merchandise Imports of the United States from Western Europe, 1951-62
(In billions of U.S. dollars in 1954 prices)
Citation: IMF Staff Papers 1964, 001; 10.5089/9781451956054.024.A003
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Chart 2.
Adjustments of Merchandise Imports of the United States from Western Europe, 1951-62
(In billions of U.S. dollars in 1954 prices)
Citation: IMF Staff Papers 1964, 001; 10.5089/9781451956054.024.A003
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Chart 2.
Adjustments of Merchandise Imports of the United States from Western Europe, 1951-62
(In billions of U.S. dollars in 1954 prices)
Citation: IMF Staff Papers 1964, 001; 10.5089/9781451956054.024.A003
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(4) U.S. merchandise imports from Rest of the World (1948-62)
$\begin{matrix} \frac{M_{31}}{P_{x 3}} = \underset{(0.0031)}{0.0197} \frac{Y_{1} - H_{1}}{P_{1}} + \underset{(0.021)}{0.101} \frac{H_{1}}{P_{1}} + \underset{(1.35)}{5.27} \frac{P_{1}}{P_{x 3}} - \underset{(0.66)}{3.93} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.97 \end{matrix} & \bar{s} \end{matrix} = 3.0 % \end{matrix} & d = 1.70 \end{matrix} \end{matrix}$
Elasticities at the means of the respective variables:
With respect to income (final demand): 0.8
With respect to deflated Rest of the World export prices (P_x3/P₁): −0.6
(5) U.S. payments to Western Europe for transportation services (1948-62)
$\begin{matrix} F_{21} = \underset{(0.017)}{0.204} M_{21} + \underset{(0.051)}{0.120} \\ \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.91 \end{matrix} & \bar{s} = 11.7 % \end{matrix} & d = 1.56 \end{matrix} \end{matrix}$
(6) U.S. payments to Rest of the World for transportation services (1948-62)
$\begin{matrix} F_{31} = \underset{(0.016)}{0.131} M_{31} - \underset{(0.148)}{0.541} \\ \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.83 \end{matrix} & \bar{s} = 14.1 % \end{matrix} & d = 1.06 \end{matrix} * \end{matrix}$
(7) U.S. payments to Western Europe for travel (1948-62)
$\begin{array}{l} V_{21} = \underset{(0.00018)}{0.00308} C_{1} - \underset{(0.049)}{0.404} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.95 \end{matrix} & \bar{s} \end{matrix} = 10.0 % \end{matrix} & d = 1.29 \end{matrix} \end{array}$
(8) U.S. payments to Rest of the World for travel (1950-62)
$\begin{array}{l} V_{31} = \underset{(0.00017)}{0.00466} C_{1} - \underset{(0.048)}{0.427} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.98 \end{matrix} & \bar{s} \end{matrix} = 3.7 % \end{matrix} & d = 0.71 * * \end{matrix} \end{array}$
(9) U.S. payments to Western Europe on investment income account (1948-62)
$\begin{array}{l} D_{21} = \underset{(0.0015)}{0.0184} I_{12} + \underset{(0.0258)}{0.0641} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.92 \end{matrix} & \bar{s} \end{matrix} = 10.3 % \end{matrix} & d = 1.73 \end{matrix} \end{array}$
(10) U.S. payments to Rest of the World on investment income account (1948-62)
$\begin{array}{l} D_{31} = \underset{(0.0026)}{0.0334} I_{13} + \underset{(0.032)}{0.163} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.93 \end{matrix} & \bar{s} \end{matrix} = 11.0 % \end{matrix} & d = 1.75 \end{matrix} \end{array}$
(11) U.S. payments to Western Europe for other private services (1949-62)
$\begin{array}{l} O_{21} = \underset{(0.000066)}{0.000644} Y_{1} + \underset{(0.027)}{0.098} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.88 \end{matrix} & \bar{s} \end{matrix} = 12.8 % \end{matrix} & d = 1.30 \end{matrix} \end{array}$
(12) U.S. payments to Rest of the World for other private services (1948-62)
$\begin{array}{l} O_{31} = \underset{(0.0022)}{0.0163} (M_{13} + M_{31}) - \underset{(0.045)}{0.174} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.78 \end{matrix} & \bar{s} \end{matrix} = 19.4 % \end{matrix} & d = 0.65 * * \end{matrix} \end{array}$
The independent variable is the total of merchandise trade between the United States and Rest of the World.
(13) U.S. export supply price (1949-62)
$\begin{array}{l} P_{x 1} = \underset{(0.23)}{1.69} P_{1} + \underset{(0.00258)}{0.00472} \frac{M_{12} + M_{13}}{P_{x 1}} - \underset{(0.0052)}{0.0253} t - \underset{(0.196)}{0.580} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.97 \end{matrix} & \bar{s} \end{matrix} = 1.1 % \end{matrix} & d = 1.71 \end{matrix} \end{array}$
The implied price elasticity of supply, at the mean of the variables, is +15.
The coefficient of the export volume is not significant at the 5 per cent level.

Region 2: Western Europe (W.E.)

(14) W.E. GNP identity
$\begin{matrix} Y_{2} = & C_{2} + M_{21} + M_{23} + F_{21} + V_{21} + D_{21} + O_{21} - M_{12} - M_{32} \\ - F_{12} - V_{12} - D_{12} - O_{12} + B_{2} + H_{2} + A_{2} \end{matrix}$
See note to equation (1). Data on Western Europe’s payments to, and receipts from, the Rest of the World for services are not available. Western Europe’s net receipts on service account are, therefore, included in the residual item, B₂.
(15) W.E. consumption function (1948-61)
(a) Estimated:
$\begin{array}{l} \frac{C_{2}}{P_{2}} = \underset{(0.02)}{1.11} \frac{Y_{2} - C_{2}}{P_{2}} - \underset{(0.91)}{3.97} W_{c} + \underset{(1.6)}{59.5} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.996 \end{matrix} & \bar{s} \end{matrix} = 0.9 % \end{matrix} & d = 2.52 \end{matrix} \end{array}$
(b) Transformed:
$\frac{C_{2}}{P_{2}} = 0.526 \frac{Y_{2}}{P_{2}} - 1.88 W_{c} + 28.2$
See equation (2). The dummy variable, W_c, improves the fit of this equation, though probably for reasons different from those discussed in connection with equation (2).
(16) W.E. merchandise imports from United States (1950–61)
$\begin{array}{l} \frac{M_{12}}{P_{x 1}} = \underset{(0.0070)}{0.0179} \frac{Y_{2} - H_{2}}{P_{2}} + \underset{(0.104)}{0.413} \frac{H_{2}}{P_{2}} + \underset{(5.29)}{4.56} \frac{P_{2}}{r_{2} P_{x 1}} - \underset{(4.15)}{5.36} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.87 \end{matrix} & \bar{s} \end{matrix} = 8.8 % \end{matrix} & d = 1.68 \end{matrix} \end{array}$
Elasticities at the means of the respective variables:
With respect to income (final demand): 0.9
With respect to deflated U.S. export prices corrected for exchange rates (P_x1r₂/P₂): −1.0
The price coefficient and the constant term are not significant at the 5 per cent level. The data for M₁₂ are not OECD reported imports from United States, but U.S. balance of payments data for exports to Western Europe. The correction for exchange rate variations (r₂) is necessary since P₂ is the implicit GNP price deflator derived from GNP data (in current and 1954 prices) expressed in 1954 exchange rates.
(17) W.E. merchandise imports from Rest of the World (1949−61)
$\begin{array}{l} \frac{M_{32}}{P_{x 3}} = \underset{(0.0045)}{0.0663} \frac{Y_{2} - H_{2}}{P_{2}} + \underset{(0.077)}{0.393} \frac{H_{2}}{P_{2}} + \underset{(1.29)}{5.95} \frac{P_{2}}{r_{2} P_{x 3}} - \underset{(0.78)}{4.77} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.99 \end{matrix} & \bar{s} \end{matrix} = 1.7 % \end{matrix} & d = 2.38 * \end{matrix} \end{array}$
Elasticities at the means of the respective variables:
With respect to income (final demand): 0.9
With respect to deflated Rest of World export prices corrected for exchange rates (P_x3r₂/P₂):: −0.4
On exchange rate correction (n), see note to equation (16).
(18) W.E. payments to United States for transportation services (1948-62)
$\begin{array}{l} F_{12} = \underset{(0.0095)}{0.0771} M_{12} + \underset{(0.049)}{0.279} \\ \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.82 \end{matrix} & \bar{s} = 7.6 % \end{matrix} & d = 1.86 \end{matrix} \end{array}$
(19) W.E. payments to United States for travel (1951–61)
$\begin{array}{l} V_{12} = \underset{(0.000071)}{0.000597} C_{2} - \underset{(0.012)}{0.030} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.88 \end{matrix} & \bar{s} \end{matrix} = 12.5 % \end{matrix} & d = 0.96 * \end{matrix} \end{array}$
(20) W.E. payments to United States on investment income account (1948-62)
$\begin{array}{l} D_{12} = \underset{(0.0040)}{0.0616} I_{21} - \underset{(0.065)}{0.483} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.94 \end{matrix} & \bar{s} \end{matrix} = 10.9 % \end{matrix} & d = 2.18 \end{matrix} \end{array}$
(21) W.E. payments to United States for other private services (1949-61)
$\begin{array}{l} O_{12} = \underset{(0.00011)}{0.00180} Y_{2} - \underset{(0.026)}{0.141} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.96 \end{matrix} & \bar{s} \end{matrix} = 9.7 % \end{matrix} & d = 0.80 * * \end{matrix} \end{array}$
(22) W.E. export supply price (1948-61)
$\begin{array}{l} P_{x 2} \cdot r_{2} = \underset{(0.21)}{2.18} P_{2} + \underset{(0.0067)}{0.0255} \frac{M_{21} + M_{23}}{P_{x 2}} - \underset{(0.0106)}{0.0899} t - \underset{(0.163)}{0.937} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.98 \end{matrix} & \bar{s} \end{matrix} = 1.5 % \end{matrix} & d = 1.74 \end{matrix} \end{array}$
The implied price elasticity of export supply, at the means of the respective variables, is +2.5.
The explained variable is the export price in “local” currency, i.e., the export price in U.S. dollars, P«₂, multiplied by the implicit W.E. exchange rate index r%. See also note to equation (16).

Region 3 : Rest of the World (R.O.W.)

(23) R.O.W. balance of payments identity
$\begin{array}{l} M_{13} + M_{23} + F_{13} + V_{13} + D_{13} + O_{13} - M_{31} - M_{32} - F_{31} - V_{31} \\ - D_{31} - O_{31} + B_{1} + B_{2} = K_{3} \end{array}$
The items to the left of the equality sign make up the region’s consolidated current account balance, including the net balance with the United States and Western Europe of items not separately explained in the model (B₁ + B₂); see notes to equations (1) and (14). As a result of this definition, the current account balance of all three regions taken together is zero. The right-hand side of equation (23), K₃, represents capital inflows, including foreign aid, plus any decumulation, or minus any accumulation, of gold and foreign exchange reserves of the Rest of the World. K₃, B₁, and B₂ are assumed to be exogenously determined.
(24) U.S. share of R.O.W. merchandise imports from United States and Western Europe (1949–62)
$\begin{array}{l} \frac{M_{13} / P_{x 1}}{(M_{13} / P_{x 1}) + (M_{23} / P_{x 2})} = \underset{(0.063)}{- 0.505} \frac{P_{x 1}}{P_{x 2}} + \underset{(0.063)}{0.940} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.83 \end{matrix} & \bar{s} \end{matrix} = 3.0 % \end{matrix} & d = 1.81 \end{matrix} \end{array}$
Elasticity of substitution of U.S. for W.E. goods in R.O.W. imports, at the means of the variables: −1.2
The equation implies that when the ratio of U.S. to W.E. export prices is unity, as in the index base year 1954, 43.5 per cent of R.O.W. imports would come from the United States and 56.5 per cent from Western Europe. The elasticity of substitution is defined as the proportionate change in the ratio of U.S. to W.E. exports to the Rest of the World, divided by the proportionate change in the ratio of U.S. to W.E. export prices.
(25) R.O.W. payments to United States for transportation services (1948-62)
$\begin{array}{l} F_{13} = \underset{(0.0091)}{0.0686} M_{13} + \underset{(0.0991)}{0.0965} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.80 \end{matrix} & \bar{s} \end{matrix} = 8.4 % \end{matrix} & d = 0.91 * * \end{matrix} \end{array}$
The constant term is not significant at the 5 per cent level.
(26) R.O.W. payments to United States for travel (1948-62)
$\begin{array}{l} V_{13} = \underset{(0.0032)}{0.0357} (M_{31} + M_{32}) - \underset{(0.086)}{0.331} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.90 \end{matrix} & \bar{s} \end{matrix} = 9.8 % \end{matrix} & d = 1.75 \end{matrix} \end{array}$
The explanatory variable is the value of total R.O.W. exports.
(27) R.O.W. payments to United States on investment income account (1948-62)
$\begin{array}{l} D_{13} = \underset{(0.0076)}{0.0393} I_{31} + \underset{(0.0198)}{0.0344} (M_{31} + M_{32}) - \underset{(0.320)}{0.034} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.96 \end{matrix} & \bar{s} \end{matrix} = 6.6 % \end{matrix} & d = 1.02 * \end{matrix} \end{array}$
R.O.W. interest and dividend payments depend, apart from the book value of U.S. investment, on the value of total R.O.W. exports. The coefficient of R.O.W. exports and the constant term are not significant at the 5 per cent level.
(28) R.O.W. payments to United States for other private services (1948-62)
$\begin{array}{l} O_{13} = \underset{(0.0015)}{0.0365} \frac{M_{31} + M_{32}}{P_{x 3}} - \underset{(0.041)}{0.405} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.98 \end{matrix} & \bar{s} \end{matrix} = 5.4 % \end{matrix} & d = 2.36 \end{matrix} \end{array}$
The explanatory variable is the volume of total R.O.W. exports.
(29) R.O.W. export supply price (1948-62)
$\begin{array}{l} P_{x 3} = \underset{(0.0072)}{0.0297} \frac{M_{31} + M_{32}}{P_{x 3}} + \underset{(0.022)}{0.174} W_{p} - \underset{(0.00053)}{0.00229} t^{2} + \underset{(0.147)}{0.361} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.88 \end{matrix} & \bar{s} \end{matrix} = 2.2 % \end{matrix} & d = 1.57 * \end{matrix} \end{array}$
The implied price elasticity of export supply, at the means of the respective variables, is +1.2.
The trend term in this equation involves the squared value of t; the coefficient of t itself was found not significantly different from zero. The dummy variable, W_P, corrects for the disturbance of primary product prices at the beginning of the Korean war.
In addition to these 29 equations, the following definitions are used in processing the model:
(a) The balance, N₁, of those U.S. current account items which are explained in the model
$N_{1} = M_{12} + M_{13} + S_{12} + S_{13} - M_{21} - M_{31} - S_{21} - S_{31}$
(b) U.S. receipts and payments on private service account
$\begin{matrix} \begin{matrix} \begin{matrix} S_{12} = F_{12} + V_{12} + D_{12} + O_{12} \\ S_{13} = F_{13} + V_{13} + D_{13} + O_{13} \end{matrix} \\ S_{21} = F_{21} + V_{21} + D_{21} + O_{21} \end{matrix} \\ S_{31} = F_{31} + V_{31} + D_{31} + O_{31} \end{matrix}$

Comments on the equations

Import functions

From the point of view of the operation of the model, the most important equations are the four functions explaining imports into the two industrial regions, equations (3), (4), (16), and (17). In all four, inventory changes have been found to be an important explanatory variable in addition to “final demand” (that is, GNP less inventory changes). The coefficients of final demand and inventory changes are significantly different from zero at the 95 per cent confidence level in all four equations. The coefficients attaching to the price ratios⁴¹ are significant only in the two demand functions of U.S. and Western European imports from the Rest of the World. These two equations also show, in general, a better fit to the sample data than do the two equations of demand in the two industrial regions for imports from one another.

U.S. merchandise imports from Western Europe have been adjusted for “extraordinary” U.S. imports of automobiles and steel. The nature of this adjustment is shown in Chart 2. There is little doubt that the boom in imports of foreign cars during the late 1950’s was an unusual experience that should not be allowed to influence the estimated parameters of this equation. For the same reason, an independent estimate of the additional steel imports into the United States at the end of 1959 and beginning of 1960 as a result of the 1959 steel strike has been deducted from U.S. imports from Western Europe. Chart 3 shows actual and computed values, 1951-62, of U.S. merchandise imports from Western Europe—equation (3)—as well as the contributions of the three explanatory variables. While it is possible that supply limitations in Western Europe exerted a depressing influence on U.S. imports from this region in the early part of the sample period, there is no detectable evidence of this in the data. These supply limitations had been overcome to a considerable extent by 1951, the beginning of the sample period for this particular equation, and have certainly not continued beyond the middle 1950’s. If postwar supply shortages⁴² had caused U.S. imports from Western Europe to be lower than would have been observed in the absence of such shortages, the growth of these imports during the first half of the 1950’s should have been more rapid and that in the later part of the 1950’s, slower. There is, however, no evidence of such behavior; if anything, the opposite was true.

Chart 4 shows actual and computed values of U.S. merchandise imports from the Rest of the World, equation (4). It is interesting that the largest residual, in both equations (3) and (4), is in 1955, when the rapid recovery from the recession in the United States gives rise to computed values of imports in excess of actual values.

Of the major equations of the model, that for U.S. merchandise exports to Western Europe⁴³ —equation (16)—is the least satisfactory from a statistical viewpoint. As can be seen from Chart 5, the effect of final demand is virtually that of a straight-line upward trend, while the variation of imports around such a trend is explained mainly by changes in inventory investment. The coefficient of this latter variable should not be interpreted too literally; it undoubtedly reflects not so much the marginal import content of inventory investment as the influence on imports of short-term variations in industrial production which do not find full expression in the GNP figures. When this equation was fitted, thought was given to the possibility of introducing certain adjustments similar to those made for U.S. imports from Western Europe. These adjustments, which would tend to reduce the residuals found for 1957 and for 1958-59, relate to extraordinary U.S. shipments of petroleum during 1957 following the Suez crisis, and to the deferment during 1958-59 of foreign demand for U.S. aircraft as commercial airlines changed from propeller to jet planes at a time when U.S. commercial jet aircraft were not available. An equation computed with such adjustments did indeed result in a better statistical fit. Unfortunately, the aircraft adjustment had to be very crudely estimated, since it was not possible to isolate U.S. exports of commercial aircraft to Western Europe from the global amount of such exports to all areas. Moreover, although ${\bar{R}}^{2}$ was higher, the estimated regression coefficients were not materially changed in the adjusted version. For these reasons, it was decided to retain the equation in unadjusted form.

In order to take account of the effect of the extraordinary demands and domestic supply limitations in Europe during the postwar reconstruction period, it had originally been planned to incorporate into this import demand function a variable expressing the progressive import liberalization in Europe, particularly with respect to U.S. dollar goods. There are, however, serious doubts about the appropriateness of the existing index (published in a number of Annual Reports of the Organization for European Economic Cooperation) as a measure of liberalization in the present context. The index shows imports of items on a “free list” as a proportion (by value) of total imports. The effect of liberalization on imports is, therefore, already reflected in the index value, and its use as an explanatory variable in the import function would be a questionable procedure. At any rate, a trial computation with this index showed that its coefficient is not statistically significant. From an inspection of the data and the fitted equation, one would be inclined to conclude that the effect of import restrictions in the early postwar years was not to reduce imports below what they would have been (given national income and price levels) in the absence of reconstruction difficulties, but rather to prevent the pressure of extraordinary demand from pushing imports substantially beyond this level. It is likely that import restrictions were reduced at a rate dictated by the pace at which exports could be expanded and at which domestic shortages were overcome. It is true that there can be no assurance that the coefficients of this equation reflect the true responsiveness of consumers and businesses in Western Europe to income and price changes; but the estimated values are not implausible and have, in the absence of persuasive reasons in favor of different ones, been accepted for purposes of the present model. In particular, it is not evident from Chart 5 that the relation of Western Europe’s imports from the United States to Western Europe’s GNP would have been very different if a shorter and more recent sample period had been chosen, provided that this period did not start from one of the troughs in imports. A similar comment applies to U.S. imports from Western Europe (Chart 3).

The equation for Western Europe’s merchandise imports from the Rest of the World, equation (17), fits the data of the sample period extremely well (see Chart 6). Here again, inventory changes explain much of the short-term variation in imports.

For reasons stated in the text, it is interesting to ascertain how these four import equations would be altered if GNP prices were replaced by wholesale prices in the numerator of the relative-price variable in each equation.⁴⁴

The four import functions are as follows (P_iw is the wholesale price index of region i):

(3′) U.S. merchandise imports from Western Europe (1951–62)⁴⁵

\begin{array}{l} \frac{M_{21}}{P_{x 2}} - M_{21}^{a 8} = \underset{(0.0019)}{0.0181} \frac{Y_{1} - H_{1}}{P_{1}} + \underset{(0.0143)}{0.0347} \frac{H_{1}}{P_{1}} + \underset{(2.07)}{3.70} \frac{P_{1 w}}{P_{x 2}} - \underset{(1.58)}{8.20} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.97 \end{matrix} & \bar{s} \end{matrix} = 5.6 % \end{matrix} & d = 1.49 * \end{matrix} \end{array}

(4′) U.S. merchandise imports from Rest of the World (1948–62)

\begin{array}{l} \frac{M_{31}}{P_{x 3}} = \underset{(0.0023)}{0.0219} \frac{Y_{1} - H_{1}}{P_{1}} + \underset{(0.0191)}{0.0930} \frac{H_{1}}{P_{1}} + \underset{(1.57)}{6.95} \frac{P_{1 w}}{P_{x 3}} - \underset{(1.04)}{6.45} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.98 \end{matrix} & \bar{s} \end{matrix} = 2.8 % \end{matrix} & d = 1.73 \end{matrix} \end{array}

(16’) W.E. merchandise imports from United States (1950–61)

\begin{array}{l} \frac{M_{12}}{P_{x 1}} = \underset{(0.0038)}{0.0241} \frac{Y_{2} - H_{2}}{P_{2}} + \underset{(0.095)}{0.366} \frac{H_{2}}{P_{2}} + \underset{(6.71)}{3.90} \frac{P_{2 w}}{r_{2} P_{x 1}} - \underset{(7.04)}{5.90} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.87 \end{matrix} & \bar{s} \end{matrix} = 9.1 % \end{matrix} & d = 1.67 \end{matrix} \end{array}

The data for Mu are U.S. balance of payments data for exports to Western Europe.

(17’) W.E. merchandise imports from Rest of the World (1949–61)

\begin{array}{l} \frac{M_{32}}{P_{x 3}} = \underset{(0.0027)}{0.0711} \frac{Y_{2} - H_{2}}{P_{2}} + \underset{(0.058)}{0.372} \frac{H_{2}}{P_{2}} + \underset{(1.22)}{7.73} \frac{P_{2 w}}{r_{2} P_{x 3}} - \underset{(0.98)}{7.59} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.996 \end{matrix} & \bar{s} \end{matrix} = 1.3 % \end{matrix} & d = 2.18 \end{matrix} \end{array}

The substitution of wholesale prices for GNP prices makes surprisingly little difference. The two functions for import demand by the United States and Western Europe from the Rest of the World, equations (4′) and (17′, give somewhat higher, and somewhat more reliable, price coefficients, and the statistical fit over the sample period is marginally improved over equations (4) and (17). The remaining regression coefficients of each of these two equations are, however, not substantially changed. In the two demand equations for U.S. and Western European imports from the other industrial region—equations (3′) and (16′)—the price coefficients are neither appreciably different nor statistically more significant, and the fit of these equations is not improved over that of equations (3) and (16). In view of these statistical results, there seems to be no compelling reason to substitute the equations involving wholesale prices for those which state the responsiveness of imports to price changes in terms of the ratios of GNP prices to export prices.

Moreover, it might be argued that there are no persuasive theoretical reasons for making such a substitution. Such concepts as “income elasticity” and “price elasticity” of demand, sufficiently commonplace to require no definition when employed in theoretical analysis, must be precisely defined when quantitative results are reported. What the theorist calls “income elasticity,” for short, may in a particular application be an elasticity with respect to disposable income, to GNP, or to yet other income measures. Matters are even worse when it comes to the concept of “price elasticity.” In general, “all other prices” neither remain constant nor change in the same proportion. There is thus, in principle, an indefinitely large number of (partial) price elasticities which would have to be stated to give a full description of demand behavior with respect to prices in a particular case. For statistical reasons, it is ordinarily possible to use only one, or at best two, price coefficients in one equation. It is true that the most interesting price elasticity, though not the only useful one, is the elasticity with respect to the ratio of the price of the commodity in question to the price of its closest substitute; but it is quite obvious that the only basis for designating a particular good, or a certain group of goods, as “closest substitute” is information— which is generally not available—about the cross elasticities of demand. On a priori grounds, it is by no means certain that the “basket” of commodities entering into the wholesale price index is a closer substitute for imports than the basket of commodities and services in general as reflected in the GNP price index. As has been mentioned in footnote 17 (p. 67), there is also the practical consideration that wholesale prices could not easily be projected for a number of years into the future except on the basis of factors which also underlie any projection of GNP prices.

In his comments on the Brookings Report, Professor Balassa suggests the possibility of using the ratio of export prices as the price variable in the U.S. and Western European demand functions for imports from one another.⁴⁶The argument supporting such a choice is that the range of goods exported by these two regions is fairly similar, so that the export price index is a better indicator than is the GNP price index of the price level of import substitutes. Reservations similar to those indicated above must also be made with respect to this suggestion. The equations have, nevertheless, been recomputed with this price, variable:

(3′) U.S. merchandise imports from Western Europe (1951-62)

\begin{array}{l} \frac{M_{21}}{P_{x 2}} - M_{21}^{a 8} = \underset{(0.0028)}{0.0164} \frac{Y_{1} - H_{1}}{P_{1}} + \underset{(0.0143)}{0.0384} \frac{H_{1}}{P_{1}} + \underset{(2.70)}{4.64} \frac{P_{x 1}}{P_{x 2}} - \underset{(1.80)}{8.50} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.96 \end{matrix} & \bar{s} \end{matrix} = 5.7 % \end{matrix} & d = 1.61 \end{matrix} \end{array}

(16′) WE. merchandise imports from the United States

\begin{array}{l} \frac{M_{12}}{P_{x 1}} = \underset{(0.0054)}{0.0234} \frac{Y_{2} - H_{2}}{P_{2}} + \underset{(0.098)}{0.370} \frac{H_{2}}{P_{2}} + \underset{(4.72)}{0.34} \frac{P_{x 2}}{P_{x 1}} - \underset{(5.55)}{2.24} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.86 \end{matrix} & \bar{s} \end{matrix} = 9.2 % \end{matrix} & d = 1.69 \end{matrix} \end{array}

The price coefficient in equation (3′′), though somewhat higher than that found in equation (3), is not significant, and the price coefficient in equation (16′′) is entirely unacceptable.

Thus, neither the a priori arguments in favor of using wholesale prices or export prices as deflators of “import” prices, nor the results of the recomputations, establish a persuasive case for altering the model in this respect so long as it is kept at the present level of aggregation.

Elasticity, of substitution between U.S. and Western European goods in Rest of World’s imports

Equation (24) shows the dependence of the share of U.S. goods in the Rest of the World’s merchandise imports on the ratio of U.S. to Western European export prices. Actual and computed values of this share are shown in Chart 7. The regression coefficient of the export price ratio is highly significant. From this equation, an elasticity of substitution, as customarily defined, of —1.2 can be computed. As Chart 7 shows, the increase in the U.S. share during 1956-57, which may have resulted from limitations of supply and shipping facilities in Western Europe in the course of the Suez crisis, is not reflected in the computed values. Nor is the slight rise in the U.S. share in 1962, which may be the consequence of a successful increase in the tying of foreign aid, explained by the equation.

Service equations

Since regional data on Western Europe’s service receipts and payments are not available, the model estimates only the service transactions of the United States with the two other regions but not the service transactions between Western Europe and the Rest of the World. (The balance of service transactions between Western Europe and the Rest of the World is part of the exogenous adjustment item, B₂ in the GNP identity for Western Europe.)

Payments of the two industrial regions for travel services and “other private services” are estimated as depending on consumption expenditure⁴⁷ and GNP, respectively. The same course cannot be followed in estimating payments for these services by the Rest of the World, since GNP and consumption figures for this region are not available. The Rest of the World’s payments for travel and “other private services” have therefore been estimated as functions of total exports, on the hypothesis that these services are to a considerable extent connected with the conduct of the region’s exporting business. Admittedly, a number of other variables, such as the total of exports plus imports or total foreign exchange receipts, might have been used with equal justification. In these eight equations, the regression coefficients exceed their standard errors by a factor of eight or more. Nevertheless, the standard errors of estimate (root-mean-square residuals) are quite high—frequently of the order of 10 per cent, and in some instances even higher.

Payments for transportation services have been estimated in all cases as functions of imports into the paying region. The comment made on the equations for travel and “other private services” regarding the significance of the regression coefficients and the standard errors of estimate applies also to these four equations.

Payments of interest and dividends are expressed as functions of the paying region’s total liabilities to the receiving region concerned. No distinction is made between liabilities of different type (direct investment, portfolio investment, government loans, etc.) or of different maturity. The regression coefficients show, in a sense, the marginal yields of additions to the relevant stock of foreign assets. These yield figures depend, of course, very much on the distribution of the receiving region’s holdings by type of asset. Projections from these equations will be successful only to the extent that the distribution of international assets by size of yield remains, for each of the regions, approximately the same as in the sample period. According to these investment income functions, the United States obtained in the past a marginal yield of about 6 per cent on its holdings in Western Europe (equation 20), while Western Europe obtained a marginal yield of only 2 per cent on its holdings in the United States (equation 9). The Rest of the World received a yield of somewhat over 3 per cent on its holdings in the United States (equation 10) and has paid to that region a yield of 4 per cent plus an additional amount of 3 per cent of total exports (equation 27). All of these “marginal yield” figures are statistically highly significant.

Export supply price equations

Export supply prices in the two industrial regions (equations 13 and 22) are taken to depend on GNP prices, the volume of exports, and a linear trend variable. The volume of exports was found to have a statistically significant influence in Western Europe, where the implied price elasticity of export supply is +2.5, whereas the corresponding coefficient in the U.S. export price equation is not statistically significant at the 95 per cent confidence level; in the latter, the price elasticity of export supply, computed at +15, is thus not significantly different from infinity. In both industrial regions export prices appear to respond strongly to changes in GNP prices. In the short run, they tend to vary more than in proportion to changes in GNP prices, but over the sample period export prices rose much less than GNP prices. Consequently, the trend terms are negative in both equations. These negative trend terms may be interpreted as reflecting the more rapid increase in productivity in the output of export commodities than in the output of goods and services in general.⁴⁸

The export price index of the Rest of the World is estimated as a function of the volume of exports and a trend variable. The export volume exerts a significant effect on the price index so that the implied elasticity of export supply is relatively low (+ 1.2). The trend term in this equation is t² (t = 1, 2, …) with a negative coefficient. This term should not be interpreted as expressing improvements in productivity; it is merely a reflection of the joint effect of a number of influences which have caused a fairly rapid decline in the prices of primary commodities over the five-year period ended in 1962, following a period of several years of stability in these prices. Such a progressive decline in primary product prices is, of course, not expected to continue. Equation (29) is, therefore, not likely to be suitable for extrapolation. The sharp rise in prices following the outbreak of the Korean war is not fully reflected in the explanatory variables and has been corrected for by the use of a dummy variable, whose value is 1 in 1951, 0.5 in 1952, and zero in other years (see p. 87).

Consumption Functions

The consumption functions for the two industrial regions have been estimated indirectly by regressing consumption on GNP minus consumption. The implied “marginal propensities to consume out of GNP” are in both regions slightly above 0.5 and statistically highly significant. In both functions, a dummy variable taking the value of unity during the years 1951-53 has been included, after inspection of the residuals from the equations initially fitted without such a dummy variable. For the United States it is plausible to assume that the implied shift in the consumption function reflects the 10 per cent increase in tax rates which was in force during those years. An interpretation of the role of this dummy variable in the Western European consumption equation would be possible only after study of consumption behavior and tax policies in individual countries.

II. Multipliers of Alternative Models

For purposes of further processing of the model the 16 service equations have been compressed into 4 equations, 1 each for U.S. receipts and payments from each of the two other regions. Furthermore, an identity defining the U.S. current account balance, as far as it is explained by the model, has been added. As a result, the full model (Model 1A) consists of 18 equations. The 18 dependent variables are the U.S. current account balance, its 4 merchandise components, its 4 service components, Western Europe’s imports from, and exports to, the Rest of the World, export prices of the three regions, and real GNP and real consumption in the two industrial regions.

As pointed out above,⁴⁹ it is unlikely that the export price equations, and particularly the export price function of the Rest of the World, are suitable for projection over a longer period. For this reason an alternative model (Model 2A) has been processed in which the 3 export price equations have been deleted and export prices are assumed to be exogenously determined. Moreover, as also stated above, the estimated consumption functions would seem to be more suitable for short-run projection than for extrapolation from the model over several years. It is well known that the average consumption-GNP ratio is a better forecasting device for long-run purposes than is the short-run marginal propensity to consume.⁵⁰ The consumption-GNP ratio in the United States has in recent years fluctuated narrowly around 0.65, and in Western Europe around 0.63. Each of the two models mentioned above have been processed in an alternative version (Models IB and 2B) in which these average consumption-GNP ratios have been substituted for the estimated consumption functions.

In the Brookings Report, parts of an earlier version of this model have been used in a manner which implies that GNP in the two industrial regions is exogenously determined. This follows simply from the fact that the values of various trade flows are projected with assumed values of GNP (and other variables). By suppressing the two consumption functions and the two GNP identities, Model 2, described in the preceding paragraph, can easily be altered to correspond in this respect to the method employed in the Brookings Report. This leaves Model 3, with 11 equations in as many endogenous variables (the U.S. current account balance, its 4 merchandise components, its 4 service components, and Western Europe’s imports from, and exports to, the Rest of the World), and with GNP in the two industrial regions joining the list of exogenous variables in lieu of the two variables expressing the sums of fixed investment and government expenditure. For this version of the model, the consumption variables in the equations for service payments by the United States and Western Europe have been replaced by the values of GNP multiplied, respectively, by 0.65 and 0.63, so that the consumption variables can be omitted from the model.

In order to “solve” these models (that is, express the endogenous variables as functions of the exogenous ones) by linear methods, any nonlinear variable combinations appearing in the equations have been replaced by linear approximations around the means of the variables.⁵¹ The resulting system of simultaneous linear equations may be written

\begin{matrix} (I I - 1) & B y^{'} = Γ z^{'} \end{matrix}

where y′ and z′ are column vectors of the endogenous and exogenous variables, respectively, and B and Γ are the matrices of coefficients associated with these two sets of variables.⁵² The solution for y′ is

\begin{matrix} (I I - 2) & y^{'} = B^{- 1} Γ z^{'} \end{matrix}

and B⁻¹Γ is the matrix of multipliers of z′ on y′.

Table 11 compares the standard errors of estimate from the equations originally fitted with similar standard errors derived from the solutions (the so-called reduced forms) of the linearized Models 1A and 3. In the reduced form calculations, the computed values of the endogenous variables have been derived solely from the actual values of the exogenous variables with the help of the multipliers, as indicated in equation (II—2). The standard errors of estimate from the reduced forms of Models 1A and 3 are, as would be expected, in many cases somewhat higher than those from the original equations. The comparison, nevertheless, suggests that the linearized model in its “reduced form” does not fit the data markedly worse than do the original equations. Also, the standard error of estimate of the U.S. current account balance (Ni) is about 13-14 per cent of the sample mean of this variable ($5.5 billion).

Table 11.

Standard Errors of Estimate (Root-Mean-Squared Errors) of variables

(In per cent of means of variables)

^¹The values during the fitting period of the listed dependent variables are computed from the values of the exogenous variables with the help of the respective tables of multipliers; the actual values of other dependent variables in the equation in question are not used in this computation.

^²The standard errors of estimate are here shown uncorrected for degree of freedom, to make them comparable with those in Columns 4 and 5, which are also uncorrected.

^³The standard errors of estimate for service receipts and payments (S_ij) are obtained by adding the residuals of the corresponding four equations (for F_ij, V_ij, D_ij, and O_ij) and computing the root-mean-squared error from these new net residuals.

^⁴The standard error of estimate for M₁₃ comes from an equation similar to equation (24) in which M₁₃ is estimated as a function of (M₁₃ + M₂₃) and (P_x1/P_x2). The corresponding standard error of estimate for Ma is not available.

Table 11.

Standard Errors of Estimate (Root-Mean-Squared Errors) of variables

(In per cent of means of variables)

From Fitted Equations		From Reduced Forms¹
			Standard error of estimate
	Standard error of
Variable	estimate²	Variable	Model 1A	Model 3
(1)	(2)	(3)	(4)	(5)
—	—	N₁	13.1	14.0
M₁₂/P_x1	7.2	M₁₂	7.4	7.6
S₁₂	5.1³	S₁₂	6.9	6.9
M₁₃	3.2⁴	M₁₃	4.3	4.0
S₁₃	2.9³	S₁₃	3.4	3.5
M₂₁/P_x2	4.5	M₂₁	6.1	4.4
S₂₁	5.8³	S₂₁	9.2	8.0
M₃₁/P_x3	2.6	M₃₁	3.1	2.6
S₃₁	5.1³	S₃₁	7.6	6.3
M₃₂/P_x3	1.4	M₃₂	2.5	1.5
—	—⁴	M₂₃	3.3	2.4
P_x1	1.0	P_x1	1.1	—
P_x2	1.3	P_x2	1.6	—
P_x3	1.9	P_x3	3.0	—
—	—	Y₁/P₁	1.4	—
C₁/P₁	2.3	C₁/P₁	2.2	—
—	—	Y₂/P₂	1.1	—
C₂/P₂	0.8	C₂/P₂	1.0	—

^²The standard errors of estimate are here shown uncorrected for degree of freedom, to make them comparable with those in Columns 4 and 5, which are also uncorrected.

Table 11.

Standard Errors of Estimate (Root-Mean-Squared Errors) of variables

(In per cent of means of variables)

From Fitted Equations		From Reduced Forms¹
			Standard error of estimate
	Standard error of
Variable	estimate²	Variable	Model 1A	Model 3
(1)	(2)	(3)	(4)	(5)
—	—	N₁	13.1	14.0
M₁₂/P_x1	7.2	M₁₂	7.4	7.6
S₁₂	5.1³	S₁₂	6.9	6.9
M₁₃	3.2⁴	M₁₃	4.3	4.0
S₁₃	2.9³	S₁₃	3.4	3.5
M₂₁/P_x2	4.5	M₂₁	6.1	4.4
S₂₁	5.8³	S₂₁	9.2	8.0
M₃₁/P_x3	2.6	M₃₁	3.1	2.6
S₃₁	5.1³	S₃₁	7.6	6.3
M₃₂/P_x3	1.4	M₃₂	2.5	1.5
—	—⁴	M₂₃	3.3	2.4
P_x1	1.0	P_x1	1.1	—
P_x2	1.3	P_x2	1.6	—
P_x3	1.9	P_x3	3.0	—
—	—	Y₁/P₁	1.4	—
C₁/P₁	2.3	C₁/P₁	2.2	—
—	—	Y₂/P₂	1.1	—
C₂/P₂	0.8	C₂/P₂	1.0	—

^²The standard errors of estimate are here shown uncorrected for degree of freedom, to make them comparable with those in Columns 4 and 5, which are also uncorrected.

Table 12 presents the multipliers, B⁻¹Γ, for Model 3.⁵³ To repeat, this table shows the changes induced in each endogenous variable (in the stub) when one of the exogenous variables (in the heading) changes by one unit. These effects must be interpreted in terms of the units in which the variables are stated (see List of Variables, p. 86).⁵⁴ The multipliers of the dummy variables, W_c and W_p, are not shown in this table.

Table 12.

Multipliers of Model 3: Multiplier Effects of Unit Changes in the Variables in the Column Headings on the Variables Appearing in the Stubs¹

^¹For list of variables see page 86.

^²B₃ = K₃ − B₁ − B₂.

^³Constant term.

Table 12.

Multipliers of Model 3: Multiplier Effects of Unit Changes in the Variables in the Column Headings on the Variables Appearing in the Stubs¹

	Y₁/P₁	Y₂/P₂	H₁/P₁	H₂/P₂	P₁	P₂	P_x1	P_x2	P_x3	r₂	I₁₂	I₁₃	I₂₁	I₃₁	B_s²	1³
N₁	−0.0336	0.0551	−0.0809	0.602	−9.10	8.48	−5.45	6.42	2.68	−8.25	−0.0184	−0.0185	0.0616	0.0217	0.448	8.37
M₁₂	0.0	0.0185	0.0	0.408	0.0	4.60	−0.290	0.0	0.0	−4.75	0.0	0.0	0.0	0.0	0.0	−0.520
S₁₂	0.0	0.00369	0.0	0.0315	0.0	0.835	−0.0224	0.0	0.0	−0.366	0.0	0.0	0.0616	0.0	0.0	−0.907
M₁₃	0.00990	0.0247	0.0353	0.122	2.83	2.28	−6.10	6.10	6.19	−2.35	0.0	0.0142	0.0	−0.0167	0.425	−7.99
S₁₃	0.00274	0.00865	0.0110	0.0426	0.758	0.798	−0.419	0.419	0.995	−0.824	0.0	0.000975	0.0	0.0382	0.0292	−2.04
M₂₁	0.0149	0.0	0.0292	0.0	3.67	0.0	−1.07	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	−5.88
S₂₁	0.00582	0.0	0.00596	0.0	1.76	0.0	−0.218	0.0	0.0	0.0	0.0184	0.0	0.0	0.0	0.0	−2.56
M₃₁	0.0193	0.0	0.0797	0.0	5.27	0.0	0.0	0.0	3.84	0.0	0.0	0.0	0.0	0.0	0.0	−7.62
S₃₁	0.00620	0.000402	0.0123	0.00198	1.98	0.0372	−0.0995	0.0995	0.665	−0.0383	0.0	0.0336	0.0	−0.000273	0.00693	−3.75
M₃₂	0.0	0.0650	0.0	0.320	0.0	6.00	0.0	0.0	10.7	−6.19	0.0	0.0	0.0	0.0	0.0	−9.02
M₂₃	0.0129	0.0321	0.0458	0.158	3.67	2.96	6.42	−6.42	8.03	−3.05	0.0	0.0185	0.0	−0.0217	0.552	−10.4

^¹For list of variables see page 86.

^²B₃ = K₃ − B₁ − B₂.

^³Constant term.

Table 12.

Multipliers of Model 3: Multiplier Effects of Unit Changes in the Variables in the Column Headings on the Variables Appearing in the Stubs¹

	Y₁/P₁	Y₂/P₂	H₁/P₁	H₂/P₂	P₁	P₂	P_x1	P_x2	P_x3	r₂	I₁₂	I₁₃	I₂₁	I₃₁	B_s²	1³
N₁	−0.0336	0.0551	−0.0809	0.602	−9.10	8.48	−5.45	6.42	2.68	−8.25	−0.0184	−0.0185	0.0616	0.0217	0.448	8.37
M₁₂	0.0	0.0185	0.0	0.408	0.0	4.60	−0.290	0.0	0.0	−4.75	0.0	0.0	0.0	0.0	0.0	−0.520
S₁₂	0.0	0.00369	0.0	0.0315	0.0	0.835	−0.0224	0.0	0.0	−0.366	0.0	0.0	0.0616	0.0	0.0	−0.907
M₁₃	0.00990	0.0247	0.0353	0.122	2.83	2.28	−6.10	6.10	6.19	−2.35	0.0	0.0142	0.0	−0.0167	0.425	−7.99
S₁₃	0.00274	0.00865	0.0110	0.0426	0.758	0.798	−0.419	0.419	0.995	−0.824	0.0	0.000975	0.0	0.0382	0.0292	−2.04
M₂₁	0.0149	0.0	0.0292	0.0	3.67	0.0	−1.07	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	−5.88
S₂₁	0.00582	0.0	0.00596	0.0	1.76	0.0	−0.218	0.0	0.0	0.0	0.0184	0.0	0.0	0.0	0.0	−2.56
M₃₁	0.0193	0.0	0.0797	0.0	5.27	0.0	0.0	0.0	3.84	0.0	0.0	0.0	0.0	0.0	0.0	−7.62
S₃₁	0.00620	0.000402	0.0123	0.00198	1.98	0.0372	−0.0995	0.0995	0.665	−0.0383	0.0	0.0336	0.0	−0.000273	0.00693	−3.75
M₃₂	0.0	0.0650	0.0	0.320	0.0	6.00	0.0	0.0	10.7	−6.19	0.0	0.0	0.0	0.0	0.0	−9.02
M₂₃	0.0129	0.0321	0.0458	0.158	3.67	2.96	6.42	−6.42	8.03	−3.05	0.0	0.0185	0.0	−0.0217	0.552	−10.4

^¹For list of variables see page 86.

^²B₃ = K₃ − B₁ − B₂.

^³Constant term.

III. Projections from Alternative Models

Table 13.

Assumed Values of Exogenous Variables for 1964 and 1968 Projections

^¹4.5 per cent growth per annum, 1962–64.

^²Brookings Report (cited above, p. 60, fn. 3), pp. 213 ff. and Table VIII-1.

^³4.2 per cent growth per annum, from 1961 on.

^⁴Partly based on Table V-9 (p. 150), in Brookings Report.

Table 13.

Assumed Values of Exogenous Variables for 1964 and 1968 Projections

	1964	1968
		“Initial” Assumption	“Alternative” Assumption
		Billion 1954 U.S. dollars
Y₁/P₁	518.5¹	640.2²	608.9²
Y₂/P₂	320.7³	376.8²	365.5²
A₁/P₁	177.8¹	216.2	205.6
A₂/P₂	114.0³	133.9	129.9
H₁/P₁	3.0	4.0	4.0
H₂/P₂	3.0	3.0	3.0
		Billion current U.S. dollars
I₁₂	28.5⁴	37.0⁴	37.0⁴
I₁₃	16.5⁴	20.0⁴	20.0⁴
I₂₁	23.0⁴	28.0⁴	28.0⁴
I₃₁	58.5⁴	75.0⁴	75.0⁴
B₁	−3.7	−3.8	−3.8
B₂	8.0	8.0	8.0
K₃	7.0	10.2	10.2
		1954 = 1
P₁	1.204²	1.285²	1.285²
P₂	1.377²	1.524²	1.409²
P_x1	1.120²	1.154²	1.154²
P_x2	1.070²	1.154²	1.113²
P_x3	0.922²	0.922²	0.922²
r₂	1.085²	1.085²	1.085²

^¹4.5 per cent growth per annum, 1962–64.

^²Brookings Report (cited above, p. 60, fn. 3), pp. 213 ff. and Table VIII-1.

^³4.2 per cent growth per annum, from 1961 on.

^⁴Partly based on Table V-9 (p. 150), in Brookings Report.

Table 13.

Assumed Values of Exogenous Variables for 1964 and 1968 Projections

	1964	1968
		“Initial” Assumption	“Alternative” Assumption
		Billion 1954 U.S. dollars
Y₁/P₁	518.5¹	640.2²	608.9²
Y₂/P₂	320.7³	376.8²	365.5²
A₁/P₁	177.8¹	216.2	205.6
A₂/P₂	114.0³	133.9	129.9
H₁/P₁	3.0	4.0	4.0
H₂/P₂	3.0	3.0	3.0
		Billion current U.S. dollars
I₁₂	28.5⁴	37.0⁴	37.0⁴
I₁₃	16.5⁴	20.0⁴	20.0⁴
I₂₁	23.0⁴	28.0⁴	28.0⁴
I₃₁	58.5⁴	75.0⁴	75.0⁴
B₁	−3.7	−3.8	−3.8
B₂	8.0	8.0	8.0
K₃	7.0	10.2	10.2
		1954 = 1
P₁	1.204²	1.285²	1.285²
P₂	1.377²	1.524²	1.409²
P_x1	1.120²	1.154²	1.154²
P_x2	1.070²	1.154²	1.113²
P_x3	0.922²	0.922²	0.922²
r₂	1.085²	1.085²	1.085²

^¹4.5 per cent growth per annum, 1962–64.

^²Brookings Report (cited above, p. 60, fn. 3), pp. 213 ff. and Table VIII-1.

^³4.2 per cent growth per annum, from 1961 on.

^⁴Partly based on Table V-9 (p. 150), in Brookings Report.

The assumed values of the exogenous variables used in the projections for 1964 and 1968 are listed in Table 13. For the assumptions for 1968, the figures for real GNP and all prices are obtained by translating the percentage changes assumed in the Brookings Report into absolute values.⁵⁵ In those variants of the model which require values for fixed investment plus government expenditure, this sum has been assumed to increase at the rate specified for GNP. Inventory investment is put at roughly the average value over recent years. With respect to the international investment positions, l_ij, the assumptions in the Brookings Report about private long-term investment have been supplemented, as required in the revised model, by rough guesses about government loans and short-term investment.

The variable B₁, the residual current account balance⁵⁶ of the United States, has been fairly stable during recent years and has been put down for 1968 at its average for 1955-62. Variable B₂, Western Europe’s residual current account balance,⁵⁷ has shown an intermittent upward trend during the postwar period; the figure for 1968 assumes an increase in B₂ of some 2 per cent per annum, a somewhat smaller rise than that over the seven years ended in 1961. The net capital inflow into the Rest of the World, K₃, is estimated for 1968 by adding to the 1961 value ($6.9 billion) the assumptions in the Brookings Report of an increase of $2.4 billion in U.S., and of $1.5 billion in Western European, foreign aid, and by subtracting the assumed reduction of $0.3 billion in the outflow of U.S. private long-term capital to the Rest of the World⁵⁸ and an equal amount to allow for an increase in the Rest of the World’s reserve holdings.

The assumptions for 1964 are essentially the Brookings assumptions carried forward over the shorter period. With respect to price changes, the 1964 figures reflect the “initial” assumptions in the Brookings Report, whereas the “alternative” assumptions have been used for the 1964 interpolation of real GNP and related variables.⁵⁹ The values for B₁, B₂), and K₃, have not been mechanically interpolated, but have been set down after account has been taken of the recent movements in the time series in question. As a result, B₂, has been assumed to rise between 1961 and 1964 by the full amount of its assumed increase from 1961 to 1968, while K₃ is assumed to reach by 1964 merely its 1961 value, after recovery from its 1962 low.

These choices concerning capital movements and foreign aid have been made without a detailed study of the figures in question. Indeed, it is not possible to forecast short-term capital movements or reserve changes over a period of several years. A large margin of error in any projection must be expected from this source alone. The Rest of the World’s net foreign exchange receipts on capital account and changes in this region’s reserve holdings, taken together, exert a very strong influence on the U.S. balance of goods and services and may account for a substantial part of its observed variation. The volatility of this variable is due in part to the fact that it includes changes in reserve holdings (which have in some years amounted to well over $1 billion), and in part to the variability of short-term capital movements, some of which undoubtedly take, at times, the form of capital flight from the Rest of the World. In the Brookings Report, the sum of these items was implicitly assumed to be zero in 1968; this may be the “expected” value, but a figure of +$1 billion or — $1 billion should not be considered out of the ordinary, even if the assumption relates to the annual average over a three-year period, 1967-69⁶⁰. Since the multiplier with which this item affects the U.S. current account is estimated at 0.45, any projection into the relatively distant future should, on this score alone, be interpreted as having a probable error of about $0.5 billion.

The projected values of the endogenous variables under these assumptions are shown in Tables 14–16. For reasons stated in the text, Models 1A and 2A may be considered more useful for short-term forecasting than for long-term projections; for the latter purpose, somewhat more faith may be placed on Models 2B and 3. All five versions of the revised model give very similar answers for the U.S. current account balance in 1964, and Models 2B and 3 do not differ appreciably in this respect for the two 1968 projections. Therefore, there was no good reason for not using the simplest version, Model 3, throughout the exposition in the text.

Table 14.

Projected Values of Dependent Variables in 1964¹

^¹Under assumptions given in Table 13.

^²In billions of 1954 dollars.

Table 14.

Projected Values of Dependent Variables in 1964¹

				Model 1A	Model IB	Model 2A	Model 2B	Model 3
				Billion current U.S. dollars
U.S. current account
	Balance, N₁			8.07	8.07	8.32	8.15	8.26
	Current receipts
		Merchandise exports
			M₁₂	7.32	7.52	7.31	7.52	7.49
			M₁₃	14.37	15.15	14.87	15.40	15.33
				21.68	22.67	22.18	22.92	22.82
		Service receipts
			S₁₂	2.47	2.51	2.47	2.51	2.51
			S₁₃	6.45	6.65	6.53	6.69	6.66
				8.92	9.16	9.00	9.20	9.17
		Total receipts		30.60	31.83	31.18	32.12	31.99
	Current payments
		Merchandise imports

Y_i	= GNP, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
C_i	= Consumption, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
Y_i	= GNP, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
P_xi	= Export price index in U.S. dollars (1954 = 1)
M_ij	= Value of merchandise imports into region j from region i, in billions of U.S. dollars
F_ij	= Payments for transportation services by region j to region i, in billions of U.S. dollars
V_ij	= Payments for tourist travel services by region j to region i, in billions of U.S. dollars
D_ij	= Payments of interest and dividends by region j to region i, in billions of U.S. dollars
O_ij	= Payments for other private services by region j to region i, in billions of U.S. dollars
S_ij	= F_ij + V_ij + D_ij + On (not used in the basic model)
N₁	= U.S. current account balance, excluding grant-financed military expenditures and government services (not used in the basic model)

Y_i	= GNP, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
C_i	= Consumption, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
Y_i	= GNP, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
P_xi	= Export price index in U.S. dollars (1954 = 1)
M_ij	= Value of merchandise imports into region j from region i, in billions of U.S. dollars
F_ij	= Payments for transportation services by region j to region i, in billions of U.S. dollars
V_ij	= Payments for tourist travel services by region j to region i, in billions of U.S. dollars
D_ij	= Payments of interest and dividends by region j to region i, in billions of U.S. dollars
O_ij	= Payments for other private services by region j to region i, in billions of U.S. dollars
S_ij	= F_ij + V_ij + D_ij + On (not used in the basic model)
N₁	= U.S. current account balance, excluding grant-financed military expenditures and government services (not used in the basic model)

A_i	= Fixed investment plus government expenditure on goods and services, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
H_i	= Change in inventories, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
P_i	= Implicit GNP price deflator (1954 = 1; i = 1, 2)
I_ij	= Investment position of region j in region i, at year end, i.e., total foreign assets, including short-term and nonprivate, held by region j in region i, in billions of U.S. dollars
r₂	= Implicit exchange rate of European OECD countries vis-à-vis U.S. dollar (1954 = 1); i.e., OECD countries^, GNP in current U.S. dollars and 1954 exchange rates divided by GNP in current U.S. dollars and current exchange rates (a rise in r₂ signifies a depreciation by Western Europe)
K₃	= Net capital imports into the Rest of the World, in billions of U.S. dollars
B_i	= Autonomous current account balance, i.e., net exports of goods and services from national income accounts less balance of endogenous current account items (i = 1, 2)
$M_{21}^{a 8}$	= “Extraordinary” imports of automobiles and steel from Western Europe into the United States, in billions of U.S. dollars in 1954 prices. This variable is used as an adjustment to M» (U.S. imports from Western Europe) and represents (1) the excess (for 1956-60) of automobile imports above a freehand trend line connecting automobile imports for 1955 and for 1961, and (2) an independent estimate for extraordinary steel imports at the end of 1959 and beginning of 1960 as a result of the steel strike in the United States.
t	= Calendar year minus 1947
W_e	= Korean-war “dummy” variable for consumption function; takes the value 1.0 in 1951, 1952, and 1953; in other years, it is zero.
W_p	= Korean-war “dummy” variable for equation of export prices of primary products; takes the values of 1.0 in 1951 and of 0.5 in 1952; in other years, it is zero.

A_i	= Fixed investment plus government expenditure on goods and services, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
H_i	= Change in inventories, in current prices and 1954 exchange rates, in billions of U.S. dollars (i = 1, 2)
P_i	= Implicit GNP price deflator (1954 = 1; i = 1, 2)
I_ij	= Investment position of region j in region i, at year end, i.e., total foreign assets, including short-term and nonprivate, held by region j in region i, in billions of U.S. dollars
r₂	= Implicit exchange rate of European OECD countries vis-à-vis U.S. dollar (1954 = 1); i.e., OECD countries^, GNP in current U.S. dollars and 1954 exchange rates divided by GNP in current U.S. dollars and current exchange rates (a rise in r₂ signifies a depreciation by Western Europe)
K₃	= Net capital imports into the Rest of the World, in billions of U.S. dollars
B_i	= Autonomous current account balance, i.e., net exports of goods and services from national income accounts less balance of endogenous current account items (i = 1, 2)
$M_{21}^{a 8}$	= “Extraordinary” imports of automobiles and steel from Western Europe into the United States, in billions of U.S. dollars in 1954 prices. This variable is used as an adjustment to M» (U.S. imports from Western Europe) and represents (1) the excess (for 1956-60) of automobile imports above a freehand trend line connecting automobile imports for 1955 and for 1961, and (2) an independent estimate for extraordinary steel imports at the end of 1959 and beginning of 1960 as a result of the steel strike in the United States.
t	= Calendar year minus 1947
W_e	= Korean-war “dummy” variable for consumption function; takes the value 1.0 in 1951, 1952, and 1953; in other years, it is zero.
W_p	= Korean-war “dummy” variable for equation of export prices of primary products; takes the values of 1.0 in 1951 and of 0.5 in 1952; in other years, it is zero.

Topics

Countries

Series

About

Resources

Abstract

I. Nature of the Model

II. Statistical Results

Price and income effects

III. Projections to 1964 and 1968

APPENDICES

I. The Structural Equations

List of variables

Equations

Region 1: United States

Region 2: Western Europe (W.E.)

Region 3 : Rest of the World (R.O.W.)

Comments on the equations

Import functions

Elasticity, of substitution between U.S. and Western European goods in Rest of World’s imports

Service equations

Export supply price equations

Consumption Functions

II. Multipliers of Alternative Models

III. Projections from Alternative Models