OVER THE LAST TWENTY YEARS, and especially since the end of World War II, there have appeared a large number of statistical estimates of the numerical values to be assigned to the main structural parameters governing international trade relationships, i.e., the various foreign trade “elasticities” and “propensities.” These estimates, which are of importance to all those concerned with studying the mechanism of balance of payments adjustments, are, however, scattered in many publications. An economist interested in knowing, for instance, the magnitude of the income elasticity of demand for imports by a certain country, or the price elasticity of its demand for the import of a certain commodity, might have some difficulty in tracking down the various estimates that have been made. There is as yet no published study that gathers together existing estimates of elasticities and propensities on international trade and presents them in a systematic way for convenient reference.
The present paper is intended as a contribution toward meeting this need. Part I is an index, according to country or area, of estimates of elasticities and propensities taken from 42 books and articles published in the period 1937 to 1957. These sources are described in Part II. The numbers in parentheses—e.g., exports of food (30), (31), under United Kingdom—in Part I, are references to the sources given in Part II for the estimated elasticities or propensities related to the topic.1 Each description in Part II sets forth the purpose and scope of the study, the variables and the methods used in the statistical estimation, the tests of significance used (if any), and the conclusions drawn by the author. A quick look at these notes may help the reader to decide whether a study is likely to give him the information that will be useful to him.
No attempt is made to evaluate the validity and usefulness of the various studies examined. In the first place, the basic statistical data underlying the estimates may not be entirely accurate, adequate, or appropriate. Moreover, a full description of the statistical data used in the studies is often lacking. Secondly, the question of the technique of estimation is still unsettled. Discussions on methodology have not led to general acceptance of any given technique of estimation.2 Hence proper caution must be exercised in making use of any of the estimates presented in these studies.
No claim is made as to the comprehensiveness of this collection. In fact, with only one exception, it is confined entirely to the literature published in English, or, if published in some other language, accompanied by a summary in English; and even within these limits, the coverage must still be far from complete.
Mr. Hang Sheng Cheng, economist in the Special Studies Division, is a graduate of the National Tsing Hwa University, Peiping, and of the George Washington University, Washington, D.C. He is currently engaged in postgraduate studies at the Johns Hopkins University, Baltimore, Md.
Owing to limitation of space, it is not possible to present in this paper the numerical estimates extracted from the studies examined. A collection of these estimates, however, has been mimeographed and is available upon request to the Secretary, International Monetary Fund, Washington 25, D.C. The mimeographed paper also contains a classification of the estimates by commodity.
For some of the issues involved in estimating price elasticities in international trade, see Guy H. Orcutt, “Measurement of Price Elasticities in International Trade,” The Review of Economics and Statistics, Vol. XXXII (May 1950), pp. 117-32; Fritz Machlup, “Elasticity Pessimism in International Trade,” Economia Internationale (February 1950), pp. 118-37; and Arnold C. Harberger, “A Structural Approach to the Problem of Import Demand,” American Economic Review, Vol. XLIII (May 1953), pp. 148-60. Some rather disheartening experiences in applying various techniques to the estimation of price elasticities in international trade are related in 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, CXIV, Part III (1951), pp. 307-52. On some theoretical aspects of measuring substitution elasticities, see J.J. Polak, “Note on the Measurement of Elasticity of Substitution in International Trade,” The Review of Economics and Statistics, Vol. XXXII (February 1950), pp. 16-20, and Irving Morrissett, “Some Recent Uses of Elasticity of Substitution—A Survey,” Econometrica, Vol. 21 (January 1953), pp. 41-62. A comprehensive but technical discussion of the commonly used least squares method is to be found in Richard Stone, The Measurement of Consumers’ Expenditure and Behaviour in the United Kingdom, 1920-1938 (Cambridge, England, 1954), Vol. I, Chap. XIX, pp. 279-309.
Weighted average of industrial production indices of ten European countries (viz., United Kingdom, Germany, France, Italy, Netherlands, Belgium, Sweden, Denmark, Norway, Czechoslovakia) and three non-European countries (viz., Canada, Japan, and Chile), the weights being each country’s share in the total value of U.S. exports for the period 1920-38.
Weighted average of industrial production indices of European countries, excluding the Soviet Union. The weights and the countries included are not explained.
The eight regions are European Recovery Program countries, other European countries, Scandinavia, total Europe, North America, Latin America, overseas sterling area, and rest of world. The nine countries are Belgium, France, Germany, Greece and Turkey taken together, Italy, Netherlands, Portugal, Switzerland, and United Kingdom. The four economic classes are crude foodstuffs, manufactured foodstuffs, crude and semimanufactured materials, and finished manufactures.
Arnold C. Harberger, “Index Number Problems in Measuring the Elasticity of Demand for Imports,” paper presented at the joint meeting of the Econometric Society and the American Statistical Association, December 27, 1949.
Canada, dollar Latin America, sterling OEEC, continental Western Europe, overseas territories of continental Western Europe, overseas sterling area, non- dollar Latin America, Eastern Europe (including China), and others (excluding United States).
These ratios are average propensities to import (with respect to total exports) of the respective sectors from the various regions. By assuming constant elasticities of demand (with respect to total exports) for imports from the individual regions during the period, the average propensities are then regarded as indicators of the marginal propensities to import.
See (33), below.
Radios, motor vehicles, paper, footwear, cotton goods, woolen and worsted goods, rayon yarn, rubber tires, soap, pig iron, steelwork products, cement, linoleum, and oilcloth.
The index of world real income is obtained by combining the real income (money income deflated by cost of living index) of 14 countries weighted by the average percentages of the various countries in the total world real income for the period 1925-34 as given in Colin Clark, The Conditions of Economic Progress (1st ed.), p. 56. The 14 countries and their respective weights are Australia (10), Canada (8), Denmark (5), France (15), Germany (20), Hungary (20), Japan (10), Netherlands (6), New Zealand (6), Norway (5), Sweden (5), Union of South Africa (5), United Kingdom (30), and United States (75).
Two other regressions are also given, taking the ratio of Netherlands exports to total world trade as linear functions of the world price and of Netherlands domestic wholesale prices.
Butter, cheese, onions, bacon, bulbs, coal, coke, cotton manufactures, shoes, and bicycles.
The method of trend adjustment is to add US$1 billion cumulatively to the value of national income for each year prior to 1930 and to subtract US$1 billion cumulatively for each year after 1930, while leaving the value for 1930 unchanged. It is explained that the value US$1 billion is an average of the year-to-year changes in national income during the 19-year period, i.e., the algebraic sum of the year-to-year changes divided by 19.
Weighted by the country’s share in the total value of the exports of manufactured goods by all the countries in the group in the base year.
West Germany is excluded from some of the calculations, as its behavior was found to be exceptional.
Adjustment to eliminate effects of changes in commodity composition (or market structure) was made by dividing the actual change in each country’s volume of exports of manufactured goods by an index of a hypothetical value of the country’s exports of these goods on the assumption that the commodity composition (or market structure) of world demand for these goods was the same in the current year as in the base year. The adjusted export volume index for the country was then divided by the weighted average of the adjusted export volume indices of all the countries in the group, the weights used being those indicated in footnote 15. The combination of commodity and market adjustments was made on the assumption that the two effects are independent of each other.
Confidence intervals have been computed for the estimated substitution elasticities.
This belief is based on the existence of large import-competing home production in the United States. The author suggests that import demand in this case should be viewed as a residual between the total demand curve and the supply curve of import-competing home production. Consequently, any slight shift in the total demand curve or the domestic supply curve will be magnified in the shift of the import demand curve.
United Kingdom, Netherlands, United States, Canada, Australia, New Zealand, Union of South Africa, and Sweden,
Based on income elasticities of import demand estimated by Polak; see (33), below.
See (25), below.
Raymond E. Zelder, “The Elasticity of Demand for Exports, 1921-1938,” doctoral dissertation (unpublished), University of Chicago, 1955.
United States, Canada, United Kingdom, Sweden, Norway, Denmark, France, Italy, Belgium-Luxembourg, Netherlands, Germany, Switzerland, Australia, and India.
United States, Canada, Latin America, overseas sterling area, United Kingdom, Scandinavia, France and Italy, Benelux countries, Germany and Austria, Switzerland, and rest of world.
Two alternative weighting systems have been used, one based on the assumption of equal substitutability of imports from all sources, the other on the assumption of equal substitutability between imports from manufacturing countries but zero substitutability between imports from manufacturing countries and from primary producing countries.
It is further shown that the elasticity of export receipts with respect to the exporting country’s exchange rate, derived in abstraction from the cross elasticities of the demand and supply of related goods, can be taken as the upper limit, and the elasticity of export receipts with respect to world income, similarly derived, as the lower limit, of the respective elasticities considered in conjunction with the cross elasticities.
The magnitudes of the elasticities are shown to vary at different price levels. For instance, the elasticity of export receipts with respect to the exporting country’s exchange rate tends to be higher, and the elasticity of export receipts with respect to world income tends to be lower, at higher price levels than at lower price levels.
G.H. Orcutt asserts that simultaneous shifts in the same direction in the demand and supply curves would result in underestimates of the elasticity of demand by the least-squares method; see “Measurement of Price Elasticities in International Trade,” The Review of Economics and Statistics, Vol. XXXII (February 1950), pp. 117-32. Liu points out that an estimate of demand elasticity known to be an underestimate is still useful information if the estimated value is greater than unity, and that Orcutt’s criticism of the least-squares method should be extended to the really serious situation in which one is not sure whether the estimates are overestimates or underestimates.
This regression is a modification of an original regression in Adler et al.; see (3), above.
The series is so computed as to square the absolute year-to-year changes in the price ratio, while leaving the algebraic signs of these changes unaffected.
More specifically, it is the Federal Reserve Board index of manufacturing production adjusted to exclude three component series—iron and steel, cotton consumption, and manufactured food products—which are thought to require little in the way of raw material imports other than food.
The index is based on the quantities of output, valued at 1937 prices, of 12 commodities: aluminum, copper, lead, zinc, crude petroleum, residual fuel oil, vegetable oils, lumber, woodpulp, rayon, wool, and synthetic rubber.
The inventory data have been adjusted for price variations by arbitrarily assuming that one third of the reported inventories of manufacturers’ purchased materials were valued at constant prices (i.e., last in, first out method) and the remaining two thirds at prices equal to the average wholesale prices of the five months preceding the inventory reporting date.
The index is unity where the pattern of exports of the two countries in question is exactly the same. It is zero where the exports are entirely different. For details, see Appendix C to the article (Vol. LXII, p. 513).
For criticism of the concept of product elasticity of substitution, and MacDougall’s rejoinder, see (31), below.
See (20), above.
The price elasticities of U.S. demands for newsprint and woodpulp during the period are not statistically significant on a 5 per cent level.
The prewar relationship between the volume of exports (X) and terms of trade (P) is represented by the equation X = 2P-100. For the postwar period 1948–54, the modified equation is X = 2P-85.
The authors, however, do not believe that the ordinary significance tests of the correlation coefficient are applicable to time series of this nature.
The resultant regression coefficient for this variable is considered an estimate of the difference between the income elasticities of demand for the imports from the two sources under consideration.
Two alternative models using variables expressed in natural units instead of logarithms have also been computed for Model IV (i.e., U.K. imports of butter from various sources).
Cotton piece goods, raw cotton, vehicles, chemicals, hardware, tobacco, dyes, and machinery.
Groundnuts, raw skins, raw hides, tanned hides and skins, tea, jute manufactures, linseed, and pepper.
The index of world real income is derived by combining the per capita real income of the working population of eight countries—United Kingdom, United States, Japan, Germany, France, Australia, Netherlands, and Canada—for the period 1924-37. These eight countries were selected since they accounted for about 68 per cent of India’s total exports during the five years ended 1938/39.
The world price index is a weighted average of price indices of the eight countries mentioned in footnote 45, the weights being each country’s contribution to world real income in the period 1925-34.
Austria, Belgium, Czechoslovakia, Italy, Japan, Sweden, and Switzerland.
The rest of the world excluding the U.S.S.R.
See (25), above.
The author states that, in situations where the foreign elasticity of demand is the only relevant elasticity, the elasticity of supply of foreign exchange equals the foreign elasticity of demand less unity.
The three groups together accounted for 40 per cent of U.S. imports from Mexico.
National income data for Mexico were available only on an annual basis. Half-year figures were interpolated from a regression of income on industrial production for 1947-50.
See (7), above.
The income factor used in the total demand equation for investment goods is money income other than wages; that used in the total demand equation for consumption goods is not explained.
It is shown that the quota elasticity equals the substitution elasticity when the usual weights are used in the construction of the quantum and price indices of world trade.
For bulbs, see (12), above, pp. 33-34; for rubber, see J.B.D. Derksen, De Uraag naar Rubber (De Nederlandsche Conjunctuur, August 1936), p. 19; for tin, see M.J. Schut, Tinrestrictie en Tinprijs (Haarlem, 1940), pp. 26-27.
For the 1929-32 depression, each of the three years is treated as a separate observation. This is permissible, the author asserts, since the relationship between the rate of changes of imports and the rate of changes of production is essentially linear.