Journal Issue

The Elasticity of U.S. Import Demand: A Theoretical and Empirical Reappraisal

International Monetary Fund. Research Dept.
Published Date:
January 1954
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Ta-Chung Liu*

Much useful research, both empirical and theoretical, has recently been undertaken on the elasticity of demand for imports. While so far the results have been mainly negative, considerable insight into this subject has been gained.1

All of the statistically derived demand functions for imports yield elasticity estimates that are exceedingly low, much lower than “informed opinion” would expect them to be. These surprisingly low estimates have stimulated many students to a rigorous examination, in relation to the least squares method of estimation, of the nature of the problem and of the data available for its solution. The main conclusion has been either that an estimate by the least squares method is impossible or that the results obtained are gross underestimates. This paper endeavors to show, however, that, at least for certain cases, such as imports of finished manufactures into the United States, meaningful estimates can be derived by the least squares method.

A Theoretical Analysis

The most important contributions to the critical examination of the least squares estimates of import demand have been made by Professor Orcutt.2 After summarizing his criticisms, we shall endeavor to show that, if his analysis is carried to its logical conclusion, one will find still in the least squares method more serious difficulties than he has indicated. The main part of this section, however, is devoted to a defense of this method against his criticisms.

Orcutt’s criticisms of the least squares estimates

Orcutt points out first that no method of estimation and no amount of effort could yield a satisfactory estimate for the price elasticity of demand if, after parallel movements between income and prices have been allowed for, relative prices have in fact not changed sufficiently to exert an influence on imports. However, the relevant data for such a case simply do not exist, and there is no basis for any estimate. This is a point of fact which, for any given problem, can be verified. An estimate should be attempted only for cases where there has been a wide range of changes in relative prices, after allowing for parallel movements with income. Two such cases are dealt with in the second section of this paper.

Orcutt then gives four reasons why a least squares estimate would in any event necessarily yield an underestimate for the elasticity of demand. One of these reasons will be discussed in detail later. The others are that (1) a greater degree of error of observation is involved in prices and income than in quantities of imports; (2) low-elasticity products are more heavily weighted in historical data than high-elasticity prod-ucts;3 and (3) estimates obtained from data on year-to-year changes could not reveal the higher long-run elasticities. All these criticisms are valid. The fact that, as a result of these considerations, elasticities are likely to be underestimated does not, however, in itself preclude a useful attempt to derive a least squares estimate. Whether the attempt would be justified or not depends upon the result obtained. If a low figure of, say, 0.4 were obtained, it would not be very useful as an indication of the lower limit of the elasticity in question. A figure higher than unity would mean that the demand was confirmed as definitely elastic, and this would be useful information. The higher the figure obtained, the higher would be the lower limit to be placed on the probable figure of true elasticity.

The discussion in Orcutt’s paper of the shifts of the demand and the supply curves of imports needs to be examined in detail. Chart 1 has been drawn from Orcutt’s Chart 3, which depicts the simultaneous shifts of the demand and the supply curves of imports in the same direction. Orcutt gives a number of reasons to explain why the demand curve for imports (a “derived demand” obtained by deducting domestic supply of the importing country from its total domestic demand) and the supply curve for imports (a “derived supply” obtained by deducting home demand in the supplying country from its total supply) tend to shift upward and downward together. The chart and the analysis presented by him are applicable, strictly speaking, only to a situation where the product imported by Country 1 from Country 2 is homogeneous with a product produced in Country 1 itself and hence, abstracting from the exchange rate and the cost of movement, only one price rules in the markets of the two countries.

Chart 1.Orcutt’s Version of Simultaneous Shifts in Import Demand and Supply1

1 This chart has been drawn from Chart 3 in G. H. Orcutt‘s article, “Measurement of Price Elasticities in International Trade”, The Review of Economics and Statistics, Vol. XXXII (1950), pp. 117-32.

Chart 2.Changes in Price and Shifts in Supply

Chart 3.Perfect Elasticity and Independent Shifts in Supply

The following equations explain clearly the simultaneous shifts of the demand and the supply curves of imports by Country 1 from Country 2. Let D1 and D2 denote the quantities demanded of the product in the two countries, respectively; S1 and S2 represent the quantities supplied by the domestic producers of the two countries, respectively; Y1 and Y2 stand for real incomes; and P be the price of the product, deflated by the general price level. On the usual assumption that demand is a linear function of Y and P and that supply is a function of P, we have the equations listed below, (a, b, c, d, and e are constants. The u‘s, representing the influences of variables other than Y and P, would give rise to the “shifts” in the demand and the supply curves.)

Country l’s demand for imports (“derived” from equations 1 and 3):

Supply of imports to Country 1 (“derived” from equations 2 and 4):

The simultaneous shifts in the Dm and Sm functions in the same direction, pointed out by Orcutt, are brought about by certain patterns of change in the u’s. If, for instance, there were an improvement in techniques of production in both Country 1 and Country 2, uSl and uS2 would both be greater, Dm would be smaller, and Sm greater at the same values of Yi, Y2, and P. There would be a simultaneous shift of the Dm and Sm curves downward to Dfm and S’m. On the other hand, if there were a general increase in the taste or preference for this product in the world, uDl and uD2 would both become larger. As a result, Dm would be bigger, and Sm smaller, at the same values of , Y2, and P. In terms of Chart 1, there would be a simultaneous shift of the D’m and S’m curves upward to Dm and Sm. As Orcutt has pointed out, these simultaneous shifts in the demand and the supply curves would result in an underestimate of the elasticity of demand by the least squares method as represented by the curve E. If the shifts were perfectly correlated, we would obtain a misleading underestimate with a unity correlation coefficient. Furthermore, even if the shifts were random (the Dm, D’m, Sm, and S’m curves may now be taken to represent the outside limits of the “shifting” positions, with points of intersections of the two curves scattered more or less evenly in the black area), an E curve which underestimated elasticity would still be obtained.

Orcutt’s criticisms extended

If there were no difficulties in this situation other than those which Orcutt has pointed out, the complications raised by the simultaneous shifts of the demand and supply curves would be no more serious than those resulting from the other three biases mentioned on p. 417, above; whether one could make a useful least squares estimate would again depend upon how high the estimate (known to be an underestimate) that is obtained may be. Following the same general approach used by Orcutt, one can, however, conceive many situations where the simultaneous changes in uDl and uDi (or in uS1 and uS2) may not be in the same direction. For instance, the same industry may be a growing and progressive one in Country 1 but a deteriorating or dying one in Country 2. While uS1 may increase during a given year, uS2 may at the same time become smaller. Also, with Countries 1 and 2 at different stages of economic development, the demand for one type of goods may have passed its peak in Country 1 at the same time when Country 2 feels greater need for it. Hence uD1 may increase at a time when uD2 increases. All these changes may proceed during different years at irregular speeds, so that no statistically significant trend term in the demand or supply functions will take account of them. In such cases, the shifts in the Dm and Sm curves would be in the opposite directions; they would also not be random. In such a situation, we would not be sure at all whether the estimates were underestimates or overestimates.

When imports and nonhomogeneous home substitutes are considered, the demand and supply functions of imports can no longer be treated simply as “derived functions”. More functions, more variables, and more “shifts” come into the picture. This is then the standard situation of a system of simultaneous equations in which the same variables enter into more than one relation. It is now well known that the least squares method of estimating one of the equations in isolation would not yield consistent estimates of the regression coefficients. It would be even more difficult to say whether a given least squares estimate is an underestimate or an overestimate. Here, then, we have a real problem of “identification”. The method proposed by the Cowles Commission publications is designed to solve this difficulty; and recently an empirical study has been made which uses this approach.4 The method, however, has its own theoretical limitations. In addition, there is the practical difficulty of obtaining “reduced form” relations of sufficiently high goodness of fit. The correlation coefficients of these relations are usually quite low, unless the number of “predetermined” variables included is too large for the number of observations. In either case, the “identified” regression coefficients would have large standard errors. It will, therefore, be some time before the difficulty can actually be resolved by any improvement in statistical techniques.

A defense of the least squares method

A re-examination of the nature of the historical data used in making the statistical estimates, however, raises doubts as to whether the difficulties arising from the simultaneous shifts in the demand and the supply curves of imports are really important or even relevant. There are strong reasons for believing that these difficulties need not really give us concern—at least in the case of aggregate demand functions for imports, into a country such as the United States, of those finished manufactures for which there are no homogeneous domestic substitutes5—and that a least squares estimate of the demand function can be useful and meaningful. These conclusions are reached on the grounds, supported by some empirical evidence, that the shifts in the supply curves of imports are determined largely by the changes in the general price levels in the exporting countries and are therefore quite independent of the shifts in the demand curve of imports, and that the supply price is largely independent of the quantity imported.6

(1) Provided that many important factors are assumed to remain unchanged, one can usually draw a supply curve giving the relationship between the supply price and quantity produced, often an increasing function such as the S curve in section (a) of Chart 2. Thus, if the quantity produced changes from q1 to q2, the supply price will increase from P1 to P2. In fact, however, the prices of the raw materials and manufactured products purchased by suppliers change from year to year; so do the levels of wages paid by these suppliers. If, while q1 changes to q2, there is a rise in prices and wages that suppliers have to pay, the supply curve will shift upward and Pi will rise to the higher point P’2 instead of to P2. On the other hand, P1 will fall to P”2, in spite of the increase in quantity, if, in the meantime, the prices and wages that the suppliers have to pay fall and the supply curve shifts downward.

When an aggregate supply function of some kind is considered, such as the supply function of exports as a whole or of a subclass of exports, the raw materials and the manufactured products the suppliers buy will cover a wide range of goods, and the shifts in the supply curves will be governed by the changes in the general price level (such as the wholesale price level) and the levels of wage rates in the respective industries. The general price level is largely determined by such broad factors as the relative magnitudes of aggregate money income and total real output. Wage levels in the different industries are determined mainly by the cost of living (another kind of general price level) and the relative bargaining strengths of managements and unions in the respective fields. Hence the shifts in the supply curves are governed by factors that have no direct relationship with the quantities of output of the particular suppliers.

As can be seen from section (a) of Chart 2, whether the change in P is primarily dominated by movement along the curve or by the shifts of the curve depends upon the relative magnitudes of these two factors. During a period such as the past three decades, when there were, all the time, extensive upward and downward swings in the general price and wage levels, it would be reasonable to assume that the level of the supply price of exports was predominantly determined by the changing levels of prices and wages, the effects of the quantity of exports being rather unimportant. Some empirical evidence in support of this position is found in the fact that an almost perfect fit is found between the export price level (Px) on the one hand, and the indices of wholesale price (Pw) and the cost of living (Pcl) on the other, for the United Kingdom, as given in the following equation for the period 1930-51:

Undoubtedly, the fit would be even better if Pc l were replaced by an index of wage rates prevailing in the export industries. Given the wholesale price and the relevant wage levels at a given time, one can tell what the export price level is with almost complete accuracy without knowing anything about the quantity of exports. It might be thought that such a good correlation between Px on the one hand and Pw and Pc l on the other is obtained only because Pw and Pc l are also highly correlated with the quantity of exports. This is not the case, as the correlation coefficient of the quantity of exports with Pw is only 0.46 and that with Pc l is only 0.49 for the same period of time.7

A similar relation is found for France for the period 1923-51, excluding the years 1939-45:

The correlation coefficient of the quantity of exports with Pw is only 0.15 and that with Px is 0.18.

(2) That the export price level can be determined without knowing the quantity of exports implies that the supply curve of exports is perfectly elastic, or nearly so, within a wide range around the quantities actually supplied. This situation is depicted in section (b) of Chart 2. The supply curves are horizontal at the different levels of export prices, which are determined by the general price and wage levels, around the quantities determined by the intersection of these shifting supply curves and the demand curves. The demand function will be discussed in detail later. We must first explain why the implied hypothesis of perfect elasticity of supply is reasonable, at least in the case of finished manufactures.

The price and quantity data used for estimating demand functions are annual averages. While in any given year a considerable change from the volume of exports in the preceding year may be observed, the change in the monthly rate may have been decisive only somewhere in the middle or the latter part of the year. The quantity of current output may indeed fall short of (or exceed) the demand from time to time; but within the next few months, these differences would be taken care of through adjustments in stocks without changing the rate of output. In fact, if the change in demand is temporary, there need not be any lasting effects at all. Hence, the inventory is the first cushion which tends to maintain perfect elasticity of supply within a range. The larger the inventory, the greater would be the cushion effect. Hence, for a small shift of the demand curve from one year to the next, the possibility of adjustments through stocks would by itself be sufficient to bring about an unchanged price for the different quantities in two successive years, if there were no substantial changes in the general price and wage levels.

When a longer period of time is allowed for the adjustment of supply to demand, there are, in the case of finished manufactures, two considerations in favor of high elasticities of supply. First, returns are more likely to be constant, regardless of the scale of operations, in manufacturing industries than in raw material industries, as in the former none of the factors of production, except perhaps entrepreneurship, is really fixed if sufficient time is allowed. Second, the well-known “kinked” demand curve facing an individual producer in an imperfect market will result in an unchanged price even when there is a substantial change in output brought about by a shift in the demand curve.8 Furthermore, especially for finished manufactures, the volume of exports will be only a portion of total home production. The change in the volume of exports will be a still smaller portion of the total output; and the smaller the proportional change in output, the smaller will be the effects of such a change on prices. This factor takes on added force when the supply of exports to a given country (in contrast to the whole world) is considered, as the exports to a given country will be an even smaller portion of the total supply.9

In any case, historical evidence shows that the effects of changes in the general price and wage levels on the export price level tend to overwhelm whatever small effects the volume of exports and other factors may have on the export price level. This is, of course, not to deny the obvious fact that at times there would be a few export commodities the supply prices of which would be out of line with the general price level and the relevant wage levels. The supplies of these commodities might not be perfectly elastic within any important range of output. However, it is reasonable to believe, and the little empirical evidence we have presented tends to indicate, that the great majority of the prices of the components of an aggregate export supply function would tend to follow the general price level. This is in fact a partial answer to the objections raised by Harberger and Machlup against estimating the elasticity of an aggregate function. Machlup’s illustrations of absurd results were based on the assumption that the price movements of various components of the aggregate were very divergent.10 If the movements of important sectors of the export price level in equation (1) should show a wide divergence, the chances are that the export price level could not be fitted so well with the average wholesale price and cost of living indices.

(3) From the standpoint of the importing countries, therefore, the import price level is primarily determined by the various general price levels in the exporting countries. It may be expected to undergo frequent and substantial shifts, fluctuating with the movements in the general price levels of the exporting countries and largely independently of the quantity of imports. For entirely similar reasons, the year-to-year changes in the general price levels (including wage levels) are by far the most important factor determining the aggregate price level of domestic substitutes for imported manufactures. One hears from time to time of isolated cases of deliberate price reductions by domestic suppliers to meet price reductions of competitive imported manufactures. Such evidence as there is, however, tends to show that these matching price changes are, insofar as their position in the whole picture is concerned, of very minor importance in the case of finished manufactures. Adler, Schlesinger, and van Westerborg have constructed a wholesale price index for a group of goods (P8) which are as similar as possible to the finished manufactures imported from ERP countries (Pw). P8 is correlated with both the general wholesale price index in the United States (P) and Pm in the following equation, in order to obtain some indication of the relative influences of the last two on the first.

While the influence of P on Ps is definitely significant, that of Pm on P8 is very uncertain. With a standard error as large as 0.24, compared with an estimated magnitude of 0.35 for the coefficient, the chances are not negligible that the true value of the coefficient is zero.

(4) We may therefore venture to say that both Pm and P8, and the ratio PmP8, are, in the case of finished manufactures, largely determined by the respective domestic price levels, and are quite independent of the quantity of imports. In contrast to raw materials, where the demand for imports is some kind of “derived demand” (the difference between the importing country’s total demand and domestic supply), the form of the demand function to be fitted statistically for imports of finished manufactures may reasonably be written in one of the following ways, with real income and various relative prices as independent variables:

Equation (10) should be used if the substitution effects are primarily limited to those between imports and close substitutes. If there are no close substitutes or if the substitution effects are more general, equation (11) may be preferable. Which equation is appropriate to a given situation is a problem to be determined on the basis of empirical evidence.11 The important point is that Pm, Ps, and P are all determined independently of m, and may be considered as given values in equation (10) or (11).12 In other words, the supply of m is perfectly elastic within a wide range around the current quantity. This horizontal “supply curve” would then fluctuate in accordance with the changes in PmPs or PmP as determined primarily by the changes in the respective general price levels and wage levels. There is no longer any reason why these changes should be correlated with u, representing shifts in the demand curve after the effects of the changes in real income and relative prices are allowed for. This is quite different from the situation outlined on pp. 417-21, above, where the shifts (uD1uS1) in the demand curve for imports (equation 5) and the shifts (uS2—uD2) in the supply curve for imports (equation 6) are likely to be brought about by the same set of factors and are therefore likely to be correlated with each other.

The new situation represented by equation (10) or (11) is described in Chart 3. The horizontal axis measures the quantity of imports after the income effects are allowed for. The “true” demand curve is represented by the solid line, with the “shifted positions” given by the broken lines. The points 1, 2, etc., give the historical quantity and price data in successive years. The rectangle represents the outer limit of the shifting demand and supply curves. Whether a satisfactory estimate of the demand function can be obtained depends upon whether there is a wide enough fluctuation in the price ratios and whether the variance of u is sufficiently small. The horizontal “supply curves” given in the chart would also save us from the embarrassment of necessarily obtaining an underestimate of the elasticity of the demand curve by the least squares method if the supply curves had finite elasticity. As explained by Chart 1, the estimated slope would be too steep even if the “shifts” in the demand and supply were random. As shown in Chart 3, the estimated slope obtained by the least squares method would be unbiased if the supply curves were perfectly elastic within a wide range and if the shifts in the supply curves were independent of the shifts in the demand curve.

Empirical Findings

In the light of the preceding theoretical discussion, it seems worth while to re-examine the least squares estimates of import demand for the cases where there is a reasonable chance of success. Such cases would include, for instance, the estimated demand functions for imports of those finished manufactures whose prices did undergo considerable changes relative to prices and income in the importing country or relative to prices of competitive goods from other sources of supply. One such case is found in the recent estimate, by Adler, Schlesinger, and van Westerborg,13 of the U.S. demand function for imports of finished manufactures from ERP countries.

Prewar period

The function as originally fitted for 1923-37 by Adler, Schlesinger, and van Westerborg is as follows:14

  • m: Quantity index of U.S. imports of finished manufactures from ERP countries, 1935-39 = 100

  • gnp: Index of U.S. real gross national product, 1935-39 = 100

  • P”:PmP+Pr+P0, where Pm is the index of import prices of finished manufactures from ERP countries adjusted for duty payments (1935-39 = 100); P is the U.S. Bureau of Labor Statistics wholesale price index for finished manufactures (1935-39 = 100); Pr is the index of U.S. wholesale prices for finished manufactures reweighted to conform with the composition of imports of finished manufactures from ERP countries (1935-39 = 100); P0 is the index of prices adjusted for duty payments of U.S. imports of finished manufactures from origins other than ERP countries (1935-39 = 100).

The P” term represents, of course, an attempt by the authors to derive a relative price series such that “… a fair representation of the most important pertinent price relationships has been achieved”.15 The denominator of P”, an unweighted average of three price indices, presumably covers the prices of both close and less close substitutes. The “average” price elasticity16 (the regression coefficient of the P” term multiplied by the ratio of the mean values of P” and m) is as high as 2.38.

Three competing price indices enter into the denominator of P” with equal weights. Weights, however, should be assigned to the different indices in accordance with their relative importance as explanatory variables for the movement in imports. For an aggregate of imports, it is quite impossible to decide on a priori grounds the relative importance of substitution with U.S. products or with products from other countries. Any one or two of the components of the denominator of the P” index may not even have any significant bearing on the problem. It is possible (and, indeed, it turns out to be so in the present case) that the unweighted average of the three indices in the denominator of P” would yield a correlation poorer than that obtained by using one price index only.

The only practical way to judge the relative importance of the influences of the three price ratios PmP,PmPr,and PmP0 on m during the period investigated is to include all these price ratios in the regression. Those that prove to be irrelevant or insignificant can then be dropped, and the reasons for their irrelevance and insignificance sought. If more than one significant ratio remains in the equation, the relative importance of their influences on imports during the period investigated would be indicated by the regression coefficients and the respective standard errors. If this is done, the following equation is obtained:

The only significant price term is PmP0. Hence PmP and PmPr and are dropped in turn in the following two equations. It is seen that, while PmPr has the “wrong” sign in equation (13), all signs in the following two equations are correct:

It is seen that the regression coefficients of gnp and PmP0 are about the same in all three equations. Neither PmP nor PmPr is significant, even after each is omitted in turn in equations (14) and (15). That these two terms did not have much “independent” influence on imports is clearly shown by the fact that the correlation coefficient remains as high as 0.981 after they are dropped:

The correlation coefficient in equation (16) is higher than that of the original Adler-Schlesinger-van Westerborg equation (R = 0.96 for equation 12). Thus, the inclusion of PmP and PmPr in the relative price series actually results in a relation poorer than without them.

It is therefore seen that substitutions took place mainly between imports of finished manufactures from ERP countries and those from other countries. While these “other countries” include very few industrialized countries (Japan, Canada, Czechoslovakia, etc.), they supplied $161 million worth of finished manufactured goods to the United States in the prewar year 1937, a substantial amount in comparison with the $227 million worth of imports from the ERP countries.

The impression prevails that there is very little possibility of substitution between imports from these two groups of countries even though they all belong to the “finished manufactures” category. However, even a rough check of the detailed trade statistics in Foreign Commerce and Navigation of the United States reveals that this is not so. Perhaps 80 per cent of the U.S. imports from Czechoslovakia were finished manufactures; these alone accounted for $30 million in the total of $161 million cited above for the year 1937. Practically all of these items are substitutes for similar items from ERP countries. For both Japan and Canada, a very substantial number of items fulfill the following conditions: (1) they bear the same detailed import classification numbers as the corresponding items from ERP countries; (2) they are subject to the same rate of tariff as the corresponding ERP items; and (3) they represent substantial dollar values in comparison with the corresponding ERP items. These conditions indicate substitution possibilities.

One method of checking the validity of equation (16) is to find the relationship between imports of finished manufactures from these “other countries” and the same independent variables used in equation (16), i.e., gnp and PmP0 Since the coefficient of PmP0 is significantly negative in equation (16), the coefficient of PmP0 should be significantly positive in the new relationship if there is substitution between imports from these two sources. Such a result is obtained in the following relationship:

The fact that substitution effects between imports of ERP finished manufactures and U.S. domestic products did not play a visible role in the determination of these imports during 1923-37, however, does not necessarily mean that such substitutions would not be of importance in other periods. The lack of substitution between ERP finished manufactures and U.S. domestic goods during 1923-37 was mainly due to the fact that the price ratios PmP and PmPr did not fluctuate sufficiently to bring such substitutions into play. This can be seen from a comparison of the small standard deviations, calculated as percentages of their respective means, of PmP and PmPr with the standard deviation of PmP0 : for PmP,4.73103.64=4.6 Per Cent; for PmPr,6.9797.27=7.2 per cent; for PmP0,18.0074.01=24.3 per cent.

It may therefore be concluded that equation (16) merely confirms the existence of substitution between ERP manufactures and those from other origins; it does not disprove the possibility of substitution between ERP manufactures and U.S. domestic products. In fact, it will be shown later that there was some substitution of the latter kind during the postwar years.

The demand schedule of imports of finished manufactures from ERP countries with respect to the ratio of ERP prices to those of other countries, as implied in equation (16), is plotted in Chart 4. It relates the quantity of imports, net of income effects (i.e., m’ = m—2.22 gnp), with PmP0

Chart 4.U.S. Demand for Imports of Finished Manufactures from ERP Countries, 1923-37

It is observed in Chart 4 that, from 1929 to 1937, there was a more or less consistent decline in imports of finished manufactures from ERP countries, after allowance for income effects. It might be argued that this consistent decline is the manifestation of a trend through time and, therefore, that the “nice” negative correlation with the increasing price ratio PmP0 is spurious. The suspected spuriousness cannot be proved or disproved by the statistical evidence presented here. Suffice it to say that it is rather difficult to explain the trend away from ERP finished

manufactures except on the basis of the unfavorable price developments. It is also clear from the chart that the substitution of a trend term in place of PmP0 in equation (16) would give an equation that would not provide so good a fit as equation (16).

The “average” elasticity of demand, as computed from equation (16), is only 1.13. This “average” figure, however, is not very instructive, since a linear relation such as equation (16) assumes a variable elasticity throughout the range of variations. The elasticity of demand for ERP finished manufactures with respect to the relative prices in the ERP and the “other countries” was as high as 2.76 in 1934 and as low as 0.56 in 1929. It was approximately 2 in 1937. The variations in the price elasticity during 1923-37 are plotted in Chart 5, together with the series for gnp, the quantity of imports (m), and the relative price ratio (PmP0).

Chart 5.Price Elasticity of U.S. Demand for Imports of Finished Manufactures from ERP Countries with Respect toPmP0

Prewar and postwar period as a whole

While the ratio of import prices of finished manufactures from ERP countries to the prices of U.S. manufactured products did not fluctuate greatly in the prewar years, it did move with a considerable amplitude after the war. The movement of the relative price series PmP is plotted in Chart 6.17 The range of the changes in relative prices in the postwar years 1946-51 was certainly great enough to bring about substitutions between ERP and U.S. manufactures in the U.S. market, if such substitutions are possible at all. It is regrettable that figures for PmPr and PmP0 (see equation 16) are not available for most of the postwar years, so that the following analysis has to be confined to the PmP series.

Chart 6.Ratio of Unit Value of U.S. Imports of Finished Manufactures from ERP Countries (pm) to Domestic Wholesale Price (P) (1939 = 100)

The postwar data alone, however, are not sufficient to produce a reliable statistical equation. There would be a much larger number of observations to rely upon, if a way could be found to include both the pre-war and the postwar data in one relationship. Such a method is suggested by Chart 7, which gives the scatter diagram between real gnp and the quantity of imports of finished manufactures (m) from the ERP countries. While there were several shifts in the relationship, especially a

Chart 7.U.S. Imports of Finished Manufactures from ERP Countries and Gross National Product, 1927-51

downward shift from the prewar years to the postwar years, the mean slope of the m-gnp relationship in the postwar period does not appear to be significantly different from the prewar one. Deviations from the mean slope might perhaps be due to changes in relative prices. Hence we may set up the hypothesis that the year-to-year changes in imports (Δm = mtmt-1) are a function of the year-to-year changes in the gross national product (Δgnp = gnpt—gnpt-1) and the year-to-year changes in relative prices [ΔPmP=(PmP)t(PmP)t1], both for the prewar and the postwar years, as follows:

In connection with the independent variable ΔPmP, an experiment to

test whether the dependence of Δm on ΔPmP is linear or not would be of interest. There are reasons for believing that the changes in imports associated with larger changes in relative prices would tend to be pro-portionately greater than those associated with smaller changes in relative prices. If a five-point change in the index of relative prices PmP results in a change of imports of an amount x, it is highly probable that a ten-point change in PmP would lead to a change in imports by an amount more than 2x, while a one-point change in PmP would give rise to a negligible change in imports very much less than x5 Many of the finished manufactures of the ERP countries are imported into the United States for use by manufacturers. Most of the rest are purchased by consumers through importers and retailers. There are always “costs” involved in a change of the things a business firm has become accustomed to purchase. New contacts must be made; the quality of the new product tested; certain risks taken in the sale of a new product; and sometimes, the process of production modified to suit the new product. A one-point change in relative prices may not justify the change-over at all. A five-point change may make a partial or complete switch-over unavoidable for some importers. A ten-point change would not only increase the extent of substitution for those who had made a partial change, but also increase the number who must for the first time make a shift.

There are many ways of testing this hypothesis. We propose to do it by introducing both a linear term ΔPmP and a square term (Δ˜PmP)2 into the equation and then examining whether only one of the two terms is significant.18 The result obtained for the period 1927-39 and 1947-51 as a whole is as follows, Δm and Δgnp being increments in any given year over the preceding year in millions of 1939 dollars:

Relative to the respective regression coefficients, the standard error of the (Δ˜PmP)2 term is much smaller than that of the ΔPmP term. The assumption that the change in imports is a function of (Δ˜PmP)2, therefore, has a much stronger basis in fact than the linear assumption. In fact, the omission of the ΔPmP term from the equation does not reduce the correlation coefficient to any noticeable extent.

While the regression coefficient of the (Δ˜PmP)2 term is highly significant, it can be shown that the influence of the ratio of the prices of imported finished manufactures from the ERP countries to the prices of U.S. manufactures was effective only during the postwar years. In Chart 8, the change in imports, net of income effects,19 is plotted against (Δ˜PmP)2. It is seen that the postwar points 1947-51 scatter along the regression line quite well; but the prewar points, with the exception of 1932 and 1935, tend to cluster along a vertical line at 0 < (Δ˜PmP)2 < 50. This, of course, means that during most of the prewar years the changes in the ratio of ERP prices to U.S. prices were not of sufficient magnitude to affect the quantity of finished manufactures imported from the ERP countries. The reasons for the changes in import quantities, net of income effects, during these years must be sought elsewhere. This is quite consistent with the conclusion reached in the first part of this section that it was the changes in the ratio of ERP prices to the prices of finished manufactures imported from other origins (i.e., PmP0) that were significant in influencing the quantity of finished manufactures imported from the ERP countries during the prewar years.

Chart 8.U.S. Demand for Imports of Finished Manufactures from ERP Countries, 1927-39 and 1947-51

It might be argued that the “nice” quantity-price relationship during the postwar years, after income effects have been allowed for, was spurious for two reasons: (1) the gradual improvement in the supply situation in ERP countries in the years immediately after the war, and (2) the effects of the Korean war. The increase in Δm from 1947 to 1948 might perhaps be attributed to the improvement in supply rather than

to the decline in the price ratio;20 but it is important to observe that there was a decline in Δm’ from 1948 to 1949. This latter development runs counter to the easing-of-supply theory; but it was also accompanied by an increase in ΔPmPd. The large increase in Δm’ in 1950 and the equally large decrease in Δm’ in 1951 apparently tend to justify the argument that these abrupt changes were due to the sudden rise and the consequent tapering off of demand on account of the Korean war. It must not be forgotten, however, that Δm’ represents the change in imports after income effects have been allowed for; the influence of the Korean war might therefore be expected to have been allowed for through the income effects. It is difficult, then, to believe that the rise and the subsequent fall in Δm’ are unrelated to the accompanying fall and rise in the price ratio.

From equation (20) the elasticity of demand for imported finished manufactures from the ERP countries can be calculated. Since Δm a function of (Δ˜PmP)2, the elasticity varies with the magnitude of the change in relative prices (ΔPmP) itself, as shown in the following formula:

The greater the change in relative price, the greater will be the elasticity of demand. On the basis of the 1949, 1950, and 1951 figures of m and PmP, the elasticity of demand for imports of finished manufactures from the ERP countries with respect to the ratio of ERP and U.S. domestic prices is estimated for various magnitudes of ΔPmP in Table 1.

Table 1.Price Elasticity at Various Values ofPmP/mfor Various Price Ratio Changes
ΔPmP(per cent)1949PmP/m=0.7051950PmP/m=0.2081951PmP/m=0.214

It is seen that, with the ratio PmP/ m at the 1949 level of 0.705, a ten point reduction of relative prices would yield an elasticity of demand greater than unity, and a thirty-point reduction, an elasticity greater than three. On the other hand, a thirty-point reduction in 1950 would yield only about unity elasticity. The reason is, of course, that, with the reduction in PmP and the large increase in m from 1949 to 1950, the magnitude of the ratio PmP / m is much smaller (0.208), and this results in a smaller elasticity. For equal price changes, elasticities are about the same in 1951 as in 1950, as the ratio PmP / m has not changed much.

Finally, it would be of interest to compare the two estimates of income elasticity of demand obtainable from equations (16) and (20). In spite of the difference in the price terms and in the years covered by the equations, confidence in the income terms would be enhanced if the two elasticity estimates were close to each other. The two figures are, respectively, 1.34 and 1.68. The difference of 0.34 amounts to about 20 per cent of the higher figure and is not unreasonably large.

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Mr. Liu, economist in the Special Studies Division of the Research Department, is a graduate of National Chiao-Tung University, and received graduate training at Cornell University. He was formerly Assistant Commercial Counselor, Chinese Embassy, Washington, D.C., and Professor of Economics, National Tsing-Hua University, Peiping. He is the author of National Income of China, 1931-36 (The Brookings Institution, 1946) and of several articles in economic journals.

Positive empirical contributions to the subject have been made by John H. Adler, Eugene R. Schlesinger, and Evelyn van Westerborg in The Pattern of United States Import Trade Since 1923: Some New Index Series and Their Application (Federal Reserve Bank of New York, May 1952); and by Arnold C. Harberger in “A Structural Approach to the Problem of Import Demand”, American Economic Association, Papers and Proceedings of the Sixty-Fifth Annual Meeting (American Economic Review, Vol. XLIII, May 1953), pp. 148-66. The section on Empirical Findings in the present paper deals with one of the results of the study by Adler, Schlesinger, and van Westerborg.

Guy H. Orcutt, “Measurement of Price Elasticities in International Trade”, The Review of Economics and Statistics, Vol. XXXII (1950), pp. 117-32.

Professor Arnold C. Harberger has made a more comprehensive examination of the aggregation problem in an unpublished paper, “Index Number Problems in Measuring the Elasticity of Demand for Imports”. A review of his paper is found in Fritz Machlup’s article, “Elasticity Pessimism in International Trade”, Economia Internazionale, Vol. Ill (1950), pp. 118-41.

D. J. Morgan and W. J. Corlett, “The Influence of Price in International Trade: A Study in Method”, Journal of the Royal Statistical Society, Series A, Vol. CXIV, Part III (1951), pp. 307-58.

In contrast with most raw materials and foodstuffs.

Adler, Schlesinger, and van Westerborg (op. cit., p. 41) have also defended the least squares estimates of demand for imports of finished manufactures. They believe that “… there are certain instances where supply and demand changes are sufficiently independent of each other to enable the investigator to assume that a downward bias of the Orcutt type is operationally unimportant.” No explanation, however, is given by them as to why and in what way the shifts in the demand and the supply curves are independent. Later on the same page they point out that “… the supply for the American market can be considered as almost perfectly elastic … Perfectly elastic supply and independent shifts are, however, quite different things. A least squares estimate would still be biased if the perfectly elastic supply curve shifts in the same direction as the demand curve.

The simple correlation coefficients of Px with Pw and Pcl are, respectively, 0.982 and 0.985. The correlation coefficient between the quantity and the price of exports is 0.43.

The “kinked” demand curves would result in a discontinuous marginal revenue curve. Hence, in spite of a shift of the demand curve, price may remain constant. See R. L. Hall and C. J. Hitch, “Price Theory and Business Behaviour”, Oxford Economic Papers, No. 2 (1939), pp. 12-45.

Adler, Schlesinger, and van Westerborg have also given the smallness of the ratio of exports to aggregate home production as the reason for the perfectly elastic supply of exports. See footnote 6.

Fritz Machlup, op. citp. 130.

See pp. 429-33, below, for an empirical study of this problem.

In terms of the Cowles Commission terminology, PmPs and PmP may legitimately be considered as “predetermined variables” in equations (10) and (11). For imports into a country such as the United States, y may also be considered as a “predetermined variable”. Hence the regression coefficients obtained by the least squares estimates are “consistent”. The problem of “identification” does not arise.

Op. cit., pp. 48-49.

The standard errors of the regression coefficients have been computed on the basis of data kindly provided by the authors, and are given in parentheses under the respective regression coefficients.

Adler, Schlesinger, and van Westerborg, op. cit., p. 48.

For a linear equation, such as equation (12), the “average” elasticity is not very instructive. See pp. 433 and 434, below.

As explained on p. 428, above, Pm is after adjustment for duty payments. Since the data for 1949-51 provided by Adler, Schlesinger, and van Westerborg are before duty adjustments, an approximation to figures after adjustment for duty payments was obtained for those years on the basis of the ratio of before-and-after duty figures for 1948.

The sign ͠ indicates that the square term (Δ˜PmP)2 takes the same sign as that of ΔPmP for any given year. Thus, (ΔPmP)1937=(PmP)1937(PmP)1936=2.7,and (Δ˜PmP)2 = -7.29. The PmP series is the same as defined on p. 428, above, with the base shifted to 1939. ΔPmP is the increment in any given year over the preceding year.

That is Δm’ = Δm -0.00624 Δgnp, measured along the vertical axis in Chart 8.

This is quite doubtful, as exports to the United States are merely a rather small part of total exports and a still smaller portion of the total output of finished manufactures in the ERP countries, which were quite anxious to earn dollars by shifting supply from other purchasers to U. S. buyers.

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