Article

Statistical Estimates of Elasticities and Propensities in International Trade A Survey of Published Studies

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1959
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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.

I. Index of Statistical Estimates According to Area or Country

Page
World Trade109
Europe109
European Recovery Program Countries109
Continental Western Europe109
Benelux Countries109
France and Italy109
Germany and Austria109
Scandinavia109
Eastern Europe109
Latin America109
Latin America, Dollar109
Latin America, Non-Dollar109
Sterling Area109
Sterling OEEC Countries110
Sterling Area, Overseas110
Industrial Countries110
Industrial Countries, “Major”110
Primary Producing Countries110
Algeria110
Argentina110
Australia110
Austria110
Belgium110
Brazil111
Bulgaria111
Canada111
Ceylon111
Chile111
China111
Colombia111
Czechoslovakia111
Denmark111
Egypt111
Estonia111
Finland111
France111
Germany112
Greece112
Hungary112
Iceland112
India112
Indonesia112
Ireland112
Italy112
Japan112
Latvia113
Malaya113
Mexico113
Netherlands113
New Zealand113
Norway113
Philippines113
Portugal113
Rumania113
Spain113
Sweden113
Switzerland114
Turkey114
Union of South Africa114
United Kingdom114
United States115
Uruguay116
Yugoslavia116

As noted on page 107, the numbers in parentheses refer to the stubs described in Part II.

  • WORLD TRADE

    • Total (4), (7), (10)

    • Primary products (33)

    • Manufactures (33)

  • EUROPE

    • Exports to U.S.

      • Crude foodstuffs (3)

      • Crude and semimanufactured materials (3)

  • European Recovery Program Countries

    • Exports to U.S.

      • Crude foodstuffs (3)

      • Manufactured foodstuffs (3)

      • Crude and semimanufactured materials (3)

      • Finished manufactures (3), (23)

  • Continental Western Europe

    • Exports, total (4)

    • Exports to U.S.

      • Total (42)

  • Benelux Countries

    • Exports, total (16)

  • France and Italy

    • Exports, total (16)

  • Germany and Austria

    • Exports, total (16)

  • Scandinavia

    • Exports, total (16)

  • Eastern Europe

    • Exports, total (4)

  • LATIN AMERICA

    • Exports, total (16)

    • Exports to U.S.

      • Total (42)

      • Crude foodstuffs (3)

      • Manufactured foodstuffs (3)

      • Crude and semimanufactured materials (3)

  • Latin America, Dollar

    • Exports, total (4)

  • Latin America, Non-Dollar

    • Exports, total (4)

  • STERLING AREA

    • Exports to U.S.

      • Total (42)

      • Crude foodstuffs (3)

      • Crude and semimanufactured materials (3)

  • Sterling OEEC Countries

    • Exports, total (4)

  • Sterling Area, Overseas

    • Exports, total (4), (16)

    • Exports to U.S.

      • Total (42)

      • Crude foodstuffs (3)

      • Crude and semimanufactured materials (3)

  • Industrial Countries (Austria, Belgium, Czechoslovakia, France, Germany, Italy, Japan, Sweden, Switzerland, U.K., and U.S.)

    • Imports of raw materials from Primary producing countries (30)

    • Imports of manufactures from Primary producing countries (30)

      • France (30)

      • Germany (30)

      • U.K. (30)

      • U.S. (30)

  • Industrial Countries, “Major” (Belgium, Canada, France, West Germany, Italy, Netherlands, Sweden, Switzerland, U.K., and U.S.)

    • Exports of manufactures (14)

  • Primary Producing Countries (total world excluding U.S.S.R. and countries listed in “Industrial Countries” group above)

    • Exports of food (30)

    • Exports to

      • Primary producing countries

        • Raw materials (30)

        • Manufactures (30)

      • Industrial countries

        • Raw materials (30)

      • Industrial countries excluding U.K.

        • Manufactures (30)

      • U.K.

        • Manufactures (30)

    • Imports

      • Food (30)

      • Raw materials (30)

      • Manufactures (30)

    • Imports of manufactures from

      • Germany (30)

      • U.K. (30)

      • U.S. (30)

  • Algeria

    • Exports to U.K.

      • Iron ore (28)

  • Argentina

    • Exports

      • Total (7), (37)

      • Wheat (7), (28), (37)

    • Exports in competition with Australia (7)

    • Exports to U.K.

      • Wheat (7), (28)

  • Australia

    • Exports

      • Total (7), (33), (37)

      • Butter (12), (20)

      • Wheat (7), (20), (28), (37)

      • Wool (7), (20), (28)

    • Exports in competition with

      • Argentina (7)

      • Denmark (7)

      • Ireland (7)

      • New Zealand (7)

    • Exports to U.K.

      • Butter (12)

      • Wheat (7), (28)

      • Wool (7), (28)

    • Imports

      • Total (7), (8), (16), (33)

      • Asphalt (28)

      • Hemp (28)

      • Newsprint (28)

      • Rosin (28)

      • Tea (28)

    • Receipts from exports of wool, wheat, and butter (20)

    • Net payments on current account (excluding merchandise trade) (7)

  • Austria

    • Exports to U.S.

      • Total (11)

    • Imports

      • Total (7)

      • Raw materials (30)

  • Belgium

    • Exports to

      • India

        • Glass (28)

      • U.K.

        • Leather gloves (28)

      • U.S.

        • Total (11)

      • Imports, raw materials (30)

      • Imports from Netherlands

        • Agricultural products (12)

        • Cheese (12)

        • Coal (12)

        • Coke (12)

  • Brazil

    • Exports to

      • U.K.

        • Cotton (7)

      • U.S.

        • Coffee (28)

  • Bulgaria

    • Imports, total (7)

  • Canada

    • Exports

      • Total (4), (7), 16), (26)

      • Cheese (7), (12)

      • Iron ore (26)

      • Newsprint (26), (28)

      • Wheat (7), (26), (37)

      • Woodpulp (26)

    • Exports to

      • Australia

        • Newsprint (28)

      • U.K.

        • Cheese (12)

        • Copper ores (28)

        • Wheat (37)

      • U.S.

        • Total (10), (42)

        • Crude foodstuffs (3)

        • Crude and semimanufactured materials (3)

      • Imports, total (7), (10), (16), (33)

      • Imports from

        • U.K.

          • Coal (28)

        • U.S.

          • Total (10)

          • Coal (28)

      • Net interest and dividend payments (7)

      • Net shipping payments (7)

      • Net tourist receipts (7)

  • Ceylon

    • Exports to Australia

      • Tea (28)

  • Chile

    • Exports, total (7), (33)

    • Imports, total (7), (33)

  • China

    • Exports, total (33)

    • Imports

      • Total (33)

      • Cotton fabric (7)

  • Colombia

    • Exports to U.S.

      • Coffee (28)

  • Czechoslovakia

    • Exports, total (33)

    • Imports

      • Total (7), (33)

      • Raw materials (30)

  • Denmark

    • Exports

      • Total (7), (33)

      • Butter (7), (12), (28)

    • Exports in competition with Australia (7)

    • Exports to

      • U.K.

        • Butter (7), (12), (28)

        • Eggs (28)

      • U.S.

        • Total (11)

      • Imports, total (7), (33)

  • Egypt

    • Exports, cotton (7), (28), (37)

    • Exports to U.K.

    • Cotton (7), (28)

  • Estonia

    • Exports, total (7)

    • Imports, total (7)

  • Finland

    • Exports, total (7), (33)

    • Imports, total (7), (33)

  • France

    • Exports

      • Total (7), (33)

      • Food (30)

      • Raw materials (30)

      • Primary products (33)

      • Manufactures (16), (25), (30), (33)

    • Exports to

      • Industrial countries

        • Total (30)

      • Primary producing countries

        • Total (30)

      • Australia

        • Rosin (28)

      • Belgium

        • Cheese (12)

      • Netherlands

        • Automobiles (38)

      • U.K.

        • Leather gloves (28)

        • Sardines (28)

      • U.S.

        • Total (11), (32)

    • Imports

      • Total (7), (33)

      • Raw materials (30)

  • Germany

    • Exports

      • Total (7), (33), (37)

      • Food (30)

      • Raw materials (30)

      • Manufactures (16), (25), (30)

      • Pig iron (41)

    • Exports to

      • Industrial countries

        • Total (30)

      • Primary producing countries

        • Total (30)

      • Sweden

        • Steel plates (28)

        • U.K.

          • Total (30)

        • U.S.

          • Total (32)

      • Imports

        • Total (7), (33)

        • Food (30)

        • Raw materials (30)

        • Manufactures (30)

  • Greece

    • Exports to U.S.

      • Total (11)

  • Hungary

    • Exports, total (7), (33), (37)

    • Imports, total (7), (33)

  • Iceland

    • Exports to U.S.

      • Total (11)

  • India

    • Exports

      • Total (29), (33)

      • Cotton (37)

      • Groundnuts (29)

      • Hides and skins (29)

      • Leather (29)

      • Linseed (29)

      • Pepper (29)

      • Tea (29)

    • Exports to U.S.

      • Jute manufactures (29)

    • Imports

      • Total (29), (33)

      • Automobiles (29)

      • Chemicals (29)

      • Cotton, raw (29)

      • Cotton fabric (7), (29)

      • Dyes (29)

      • Glass (28)

      • Hardware (29)

      • Machinery (29)

      • Tobacco (29)

  • Indonesia (formerly Netherlands East Indies)

    • Exports, total (33)

    • Exports to Australia

      • Hemp (28)

      • Tea (28)

    • Imports, total (33)

    • Imports from Netherlands

      • Bicycles (12)

      • Cotton fabric (12)

      • Shoes (12)

  • Ireland

    • Exports

      • Total (7), (33)

    • Exports in competition with Australia (7)

    • Exports to U.S.

      • Total (11)

    • Imports, total (7), (33)

  • Italy

    • Exports, total (7), (33)

    • Exports to U.S.

      • Total (11)

    • Imports

      • Total (7), (33)

      • Raw materials (30)

  • Japan

    • Exports

      • Total (7), (33), (37)

      • Manufactures (16)

        • In competition with U.S. (25)

    • Exports to

      • China

        • Cotton fabric (7)

      • India

        • Cotton fabric (7)

      • U.S.

        • Cotton fabric (11)

    • Imports

      • Total (7), (33)

      • Raw materials (30)

  • Latvia

    • Exports, total (7)

    • Imports, total (7)

  • Malaya

    • Exports, total (7)

  • Mexico

    • Exports to

      • Australia

        • Asphalt (28)

      • U.S.

        • Metals and manufactures (34)

    • Imports from U.S.

      • Total (34)

    • U.S. income from direct investment in Mexico (34)

    • U.S. tourist expenditure in Mexico (34)

  • Netherlands

    • Exports, total (12), (33)

    • Exports to

      • Belgium

        • Agricultural products (12)

        • Cheese (12)

        • Coal (12)

        • Coke (12)

      • Netherlands East Indies (Indonesia)

        • Bicycles (12)

        • Cotton fabric (12)

        • Shoes (12)

      • U.K.

        • Bacon (12)

        • Bulbs (12)

        • Butter (7)

        • Cheese (7)

        • Onions (12)

      • U.S.

        • Total (11), (32)

        • Bulbs (12)

        • Herring (38)

    • Imports

      • Total (33)

      • Raw materials (36), (39), (40)

      • Finished manufactures (36), (39), (40)

      • Consumption goods (36), (39)

      • Investment goods (36), (39)

      • Automobiles (38)

  • New Zealand

    • Exports

      • Total (7), (33)

      • Butter (7), (12), (28)

      • Cheese (7), (12)

      • Wool (7)

    • Exports in competition with Australia (7)

    • Exports to

      • Australia

        • Hemp (28)

      • U.K.

        • Butter (7), (12), (28)

        • Cheese (12)

        • Dairy products (5), (7), (12), (28)

        • Eggs (28)

        • Lamb (5)

        • Mutton (5)

        • Wheat (28)

    • Imports, total (7), (33)

  • Norway

    • Exports, total (7), (33)

    • Exports to U.S.

      • Total (11), (32)

    • Imports, total (7), (16), (33)

  • Philippines

    • Exports to Australia

      • Hemp (28)

  • Portugal

    • Exports to

      • U.K.

        • Sardines (28)

      • U.S.

        • Total (11)

  • Rumania

    • Imports, total (7)

  • Spain

    • Exports to U.K.

      • Copper ore (28)

      • Iron ore (28)

  • Sweden

    • Exports

      • Total (7), (33)

    • Exports in competition with U.K. (7)

    • Exports to U.S.

      • Total (32)

    • Imports

      • Total (7), (21), (33)

      • Food (30)

      • Raw materials (30)

      • Manufactures (30)

      • Consumption goods (21)

      • Cast iron (37)

      • Metal plates (37)

      • Potatoes (37)

      • Steel plates (28)

      • Syrup (28)

      • Imports from U.S.

      • Automobiles (28)

    • Income from shipping (7)

  • Switzerland

    • Exports, total (7), (16), (33)

    • Exports to U.S.

      • Total (11)

      • Manufactures (3)

    • Imports

      • Total (7), (33)

      • Raw materials (30)

  • Turkey

    • Exports to U.S.

      • Total (11)

  • Union of South Africa

    • Exports

      • Total (7), (33), (37)

      • Wool (7)

    • Exports to U.K.

      • Wool (28)

    • Imports, total (7), (16), (33)

  • United Kingdom

    • Exports

      • Total (7), (16), (19), (27), (33), (37)

      • Food (30), (31)

      • Raw materials (30)

      • Primary products (33)

      • Manufactures (6), (16), (25), (30), (33)

    • Exports in competition with

      • Sweden (7)

      • U.S. (7)

    • Exports to

      • Primary producing countries

        • Manufactures (30)

      • Australia

        • Newsprint (28)

      • Canada

        • Coal (28)

      • China

        • Cotton fabric (7)

      • India

        • Cotton fabric (7)

        • Glass (28)

      • Sweden

        • Steel plates (28)

        • Syrup (28)

      • U.S.

        • Total (11), (18), (32), (42)

        • Manufactures (3)

        • Textile manufactures (3)

        • Pig iron (41)

    • Imports

      • Food (7), (22), (30)

      • Raw materials (7), (22), (30)

      • Manufactures (7), (22), (30)

      • Animals (live, for food) (7)

      • Apparel (7)

      • Automobiles (7)

      • Bacon (12)

      • Bulbs (12)

      • Butter (7), (12), (28)

      • Cheese (12)

      • Copper ores (28)

      • Cotton, raw (7), (28)

      • Cotton manufactures (7)

      • Dairy products (5), (7), (12), (28)

      • Eggs (28)

      • Electrical apparatus (7)

      • Feed (7)

      • Fruits and vegetables (7)

      • Gloves, leather (28)

      • Grain and flour (7)

      • Hardware, cutlery, etc. (7)

      • Hides and skins (7)

      • Iron ores (7), (28)

      • Iron and steel manufactures (7)

      • Lamb (5)

      • Machinery (7)

      • Meat (5), (7)

      • Metalliferous (nonferrous) ores and scrap (7)

      • Metals (nonferrous) and manufactures (7)

      • Mutton (5)

      • Oils and fats (7)

      • Oilseeds and nuts (7)

      • Onions (12)

      • Papermaking materials (7)

      • Pottery, glassware, etc. (7)

      • Sardines (28)

      • Silk (7)

      • Tobacco (7)

      • Vehicles (7)

      • Wheat (7), (28)

      • Wood and timber (7)

      • Wood manufactures (7)

      • Wool (7), (28)

      • Wool manufactures (7)

    • Imports from

      • Primary producing countries

        • Manufactures (30)

      • Canada

        • Cheese (12)

        • Copper ores (28)

        • Wheat (37)

      • France

        • Sardines (28)

      • Germany

        • Manufactures (30)

      • Netherlands

        • Bacon (12)

        • Bulbs (12)

        • Butter (7)

        • Cheese (7)

        • Onions (12)

      • New Zealand

        • Butter (7), (12), (28)

        • Cheese (12)

        • Dairy products (5), (7), (12), (28)

        • Eggs (28)

        • Lamb (5)

        • Mutton (5)

        • Wheat (28)

      • Portugal

        • Sardines (28)

      • U.S.

        • Manufactures (30)

        • Cotton (7), (28)

      • Uruguay

        • Wheat (7)

    • Long-term overseas investment (7)

    • Receipts from interest and dividends (7), (19)

    • Receipts from shipping (7), (19)

  • United States

    • Exports

      • Total (2), (7), (16), (33), (37), (38)

      • Food (30), (31)

      • Raw materials (30)

      • Primary products (33)

      • Manufactures (16), (25), (30), (33)

      • Semimanufactures (33)

      • Cotton (7), (28), (37)

      • Pig iron (41)

      • Wheat (37)

    • Exports in competition with U.K. (7)

    • Exports to

      • Primary producing countries

        • Manufactures (30)

      • Australia

        • Asphalt (28)

        • Rosin (28)

      • Canada

        • Total (10)

        • Coal (28)

      • Mexico

        • Total (34)

      • Netherlands

        • Automobiles (38)

      • Sweden

        • Automobiles (28)

        • Syrup (28)

      • U.K.

        • Manufactures (30)

        • Cotton (7), (28)

    • Imports

      • Total (1), (7), (8), (10), (11), (13), (15), (16), (18), (33), (38), (42)

      • Food, total (30)

      • Food, crude (3), (7), (15), (42)

      • Food, manufactured (3), (7), (15), (42)

      • Crude materials (7), (11), (17), (30), (42)

      • Crude and semimanufactured materials (3), (15), (24)

      • Manufactures (3), (7), (15), (17), (23), (30), (42)

      • Semimanufactures (7), (17)

      • Alcoholic beverages (11), (30)

      • Aluminum (11)

      • Art, works of (10)

      • Beef and cattle (11)

      • Books (10)

      • Burlap (11)

      • Cheese (38)

      • Coffee (28), (30)

      • Cotton cloth (11), (38)

      • Fish (11), (38)

      • Iron and steel manufactures (11)

      • Lead (11)

      • Leather (11)

      • Machinery (11)

      • Manganese ore (11)

      • Oils and fats (11)

      • Pig iron (41)

      • Pork and hogs (11)

      • Rayon staple fiber (11)

      • Rubber (38)

      • Sugar (38)

      • Textile manufactures (3)

      • Tin (38)

      • Tungsten (11)

      • Watches, jeweled (11)

      • Whiskey (11)

      • Woolen yarns (38)

      • Woolen fabric (38)

      • Zinc (11)

    • Imports from

      • Europe

        • Crude foodstuffs (3)

        • Crude and semimanufactured materials (3)

        • European Recovery Program Countries

          • Crude foodstuffs (3)

          • Manufactured foodstuffs (3)

          • Crude and semimanufactured materials (3)

          • Finished manufactures (3), (23)

        • Continental Western Europe

          • Total (42)

        • Latin America

          • Total (42)

          • Crude foodstuffs (3)

          • Manufactured foodstuffs (3)

          • Crude and semimanufactured materials (3)

        • Sterling area

          • Total (42)

          • Crude foodstuffs (3)

          • Crude and semimanufactured materials (3)

        • Sterling area, overseas

          • Total (42)

          • Crude foodstuffs (3)

          • Crude and semimanufactured materials (3)

        • Austria

          • Total (11)

        • Belgium

          • Total (11)

        • Brazil

          • Coffee (28)

        • Canada

          • Total (1), (42)

          • Crude foodstuffs (3)

          • Crude and semimanufactured materials (3)

          • Colombia

          • Coffee (28)

        • Denmark

          • Total (11)

        • France

          • Total (11), (32)

        • Germany

          • Total (32)

        • Greece

          • Total (11)

        • Iceland

          • Total (11)

        • India

          • Jute manufactures (29)

        • Ireland

          • Total (11)

        • Italy

          • Total (11)

        • Japan

          • Cotton fabric (11)

        • Mexico

          • Metals and manufactures (34)

        • Netherlands

          • Total (11), (32)

          • Bulbs (12)

          • Herring (38)

        • Norway

          • Total (11), (32)

        • Portugal

          • Total (11)

        • Sweden

          • Total (32)

        • Switzerland

          • Total (11)

          • Manufactures (3)

        • Turkey

          • Total (11)

        • U.K.

          • Total (11), (18), (32), (42)

          • Manufactures (3)

          • Textile manufactures (3)

          • Pig iron (41)

    • Interest and dividends (7), (34)

    • Net immigrants’ remittances (7)

    • Net shipping payments (7)

    • Tourist expenditures abroad (7), (10), (34)

  • Uruguay

    • Exports to U.K.

      • Wheat (7)

  • Yugoslavia

    • Exports, total (33)

    • Imports, total (33)

II. Bibliographical Notes

(1) J.H. Adler, “United States Import Demand During the Interwar Period,” American Economic Review, Vol. XXXV (June 1945), pp. 418-30.

This article studies U.S. demand for imports from 1922 to 1937 by means of regression analysis. The regression equation is one of import volume on real national income and relative prices. “Relative prices” is not found to be a significant explanatory variable.

Assuming that this is due to a structural change in U.S. demand for imports occurring around 1930, the author splits the period in two parts, 1922-29 and 1930-37, and computes a separate regression equation for each. In the resulting regressions, the relative price term is found to be negative and significant for the first period, and positive and insignificant for the second period.

The author attributes the finding for the second period to the rise in U.S. tariff rates. To confirm this hypothesis, he computes another regression equation for the explanation of duty-free imports, again on real income and relative prices, for the whole period 1922-37. The coefficient for relative prices turns out to be negative and significant.

(2) J.H. Adler, “The Postwar Demand for United States Exports,” The Review of Economic Statistics, Vol. XXVIII (February 1946), pp. 23-33.

This article starts with an analysis of the demand for U.S. exports in the interwar period. Several regression equations are fitted to explain the volume of U.S. exports, first as a function of an industrial production index for the “outside world”3 and of a linear trend, and then as a function of an industrial production index for Europe4 only and of a linear trend. The years covered are 1920-38 in some cases and 1922-38 (omitting 1926) in others. The linear trend is designated to reflect the “degree of trade barriers” in each year, assuming that the “degree of trade barriers” rose in a systematic fashion from zero in 1929 to 1 in 1930, to 2 in 1931, etc. This analysis of conditions in the interwar period leads to some speculation about the conditions of postwar demand for U.S. exports.

Partial correlation coefficients of the regressions are given in the article, but no test of significance was made.

(3) J.H. Adler, E.R. Schlesinger, and E. van Westerborg, The Pattern of United States Import Trade Since 1923 (Federal Reserve Bank of New York, May 1952).

An important contribution of this publication to the empirical study of U.S. import trade is its computation of new indices of unit value and quantum of U.S. imports. The indices are calculated for the years 1923 through 1950 (1935-39=100) for U.S. imports as a whole and for U.S. imports from eight regions and nine individual countries, with the total imports and the imports from each region or country classified into four economic classes.5

These new indices are computed to serve as basic tools in deriving “rules” for U.S. import demand during the interwar period. The “rules” are obtained by least-squares regressions of the quantity of U.S. imports of crude foodstuffs, manufactured foodstuffs, and crude and semi- manufactured materials from each of the geographical regions, and of finished manufactures from the European Recovery Program countries in general and from the United Kingdom and Switzerland in particular, as functions of an index of U.S. real income (represented by real gross national product or industrial production) and an index of relative prices. The data used are the new indices for the period from 1923-37.

The authors claim that there are several salient merits in this study: first, it takes cognizance of the diverse patterns of U.S. imports from different origins; second, it mitigates the index number problem6 commonly encountered in estimations of demand elasticities of imports; and third, the index of relative prices is so constructed in each case as to bear more relevance to the fact of competing products. They concede that the regressions do not yield demand functions where the changes in supply and demand are interdependent. Nevertheless, the regressions are said to “reveal what is perhaps the equally meaningful pattern of demand and supply adjustments to changes in the determinant variables.” In the case of U.S. imports of finished manufactures of Western European origin, they assert that the supply can be considered as almost perfectly elastic and that the income and price elasticities are therefore true demand elasticities.

Tests of significance have been made for the correlation coefficients by using a table of critical values of the correlation coefficients based on R.A. Fisher’s z-distribution. In addition to the multiple correlation coefficients, the partial correlation coefficients and the simple correlation coefficients between the income and price variables are given.

(4) W. Beckerman, “The World Trade Multiplier and the Stability of World Trade, 1938 to 1953,” Econometrica, Vol. 24 (July 1956), pp. 239-52.

This article presents the results of an application of the techniques of matrix operation (familiar in input-output analyses) to the study of world trade. Its purpose is to calculate the effects on world trade of hypothetical changes in U.S. imports, given the trade patterns prevalent in the years 1938, 1948, and 1953.

The pattern of world trade in a particular year is based upon a “world trade matrix” in which are entered the values of merchandise trade during that year between various regions of the world. The world is divided into ten sectors. For each of nine of these sectors,7 its imports from each of the other sectors are assumed to vary in proportion to its total exports in the current year; the tenth sector, viz., the United States, is an “autonomous” sector, whose imports from the others are assumed to be independent of its current exports. The world trade matrix can be considered as consisting of three parts: a nine-by-nine “matrix of the minor” for the intertrade of the nine sectors; a row vector for U.S. exports to the individual sectors; and a column vector for individual sector’s exports to the United States.

After the matrix is set up, the rest of the operation is as follows: The matrix of the minor for the intertrade of the nine sectors is converted into a “coefficient matrix,” and the column vector for the nine sectors’ exports to the United States is converted into a “coefficient vector.” The elements in the coefficient matrix for the nine nonautonomous sectors are the ratios between (1) each sector’s imports from each of the nine sectors and (2) that importing sector’s total imports.8 The elements in the coefficient vector for the column vector of the nine sectors’ exports to the United States are ratios of U.S. imports from the respective sectors to total U.S. imports. By multiplying the inverse of the coefficient matrix for the nine sectors by the coefficient vectors for the nine sectors’ exports to the United States, the author obtains another vector, whose elements are called sector multipliers, for the respective sectors. These sector multipliers are used as indicators of the final changes in each sector’s total exports induced by a change in total U.S. imports, after the effects on all the other sectors and all the interactions between the nine sectors have been taken into consideration. The total world trade multiplier, defined as the ratio of the final change in world exports to the autonomous change in total U.S. imports, is simply the sum of the nine sector multipliers.

From the inverse matrix, the “reflection ratio” of any sector (say sector j) with respect to any other sector (sector i) can be directly obtained. This ratio is defined as the ratio of the final change in sector i’s total exports to an autonomous change in U.S. imports from sector j alone. It is simply the element in row i and column j of the inverse matrix. By summing all the elements in column j, one obtains the international reflection ratio9 for sector j, defined as the ratio of the final change in total world exports to an autonomous change in U.S. imports from sector j alone.

Some interesting observations are made concerning the statistical results of this study. It is shown, for instance, that the world trade multiplier fell significantly from 1938 to 1953. The author states that the reduction is attributable, on the one hand, to the tendency to import more from the United States and, on the other hand, to the shift in the pattern of U.S. imports from sectors with high reflection ratios (e.g., sterling OEEC and continental Western Europe) toward sectors with low reflection ratios (e. g., Canada and dollar Latin America).

(5) A.R. Bergstrom, “An Econometric Study of Supply and Demand for New Zealand’s Exports,” Econometrica, Vol. 23 (July 1955), pp. 258-76.

This article attempts to estimate the parameters of the supply and demand equations for New Zealand’s exports of dairy products, lamb, and mutton to the United Kingdom. The estimates are obtained from data for the years 1922-38, using both the limited-information, maximum-likelihood method and the least-squares method.

The U.K. demand equations and the New Zealand supply equations constitute the core of a model of 27 equations with 9 predetermined variables. (An alternative model with 8 predetermined variables shows less satisfactory results.) In addition, there are New Zealand demand equations explaining livestock numbers in New Zealand, equations explaining the supply and demand for labor and the determination of wage rates in New Zealand, a New Zealand income generating equation, various margin and adjustment equations, and an identity. All the equations are assumed to be linear, and the variables are expressed in logarithms of their year-to-year changes.

The results estimated for the U.K. demand equations and the New Zealand supply equations by the limited-information method are found to be much superior to those estimated by the least-squares method, from the viewpoint both of economic theory and of their predictive power when judged by postwar data.

The demand and supply elasticities thus obtained are all short-term, since the data used are first differences of the variables under consideration. However, the author shows, by the relationships between the supply equations and some dynamic equations explaining the livestock numbers in New Zealand, that the long-run supply elasticities can also be derived.

It is interesting to note that the results obtained suggest negative supply elasticities (both short-run and long-run) for dairy products and mutton in New Zealand, presumably indicating dominant income effects in the supply of these products. The income elasticities of U.K. demand for New Zealand lamb and mutton also turn out to be negative. This is explained as an indication that the New Zealand lamb and mutton, being frozen meat, are regarded as inferior substitutes for home-produced fresh lamb and mutton in the U.K. market.

Standard errors of the estimated elasticities have been computed. Their size relative to those of the respective estimates casts doubt on the significance of the estimates. The Van Neumann ratios have also been computed and are seen to be not significant in most cases, i.e., the residuals do not seem to be autocorrelated.

(6) A.J. Brown, “The Fundamental Elasticities in International Trade,” in Oxford Studies in the Price Mechanism (T. Wilson and P.W.S. Andrews, editors, London, 1951), pp. 91-106.

This paper purports to make a survey of main contributions to the measurement of fundamental elasticities in international trade. It is divided into three sections: demand elasticity of exports, demand elasticity of imports, and supply elasticities of both exports and imports.

In regard to demand elasticity of exports, the author suggests that, because of the various difficulties in the measurement of partial demand elasticity, a more profitable approach is to measure the elasticity of substitution between a country’s exports and other countries’ exports of similar goods. Estimates of substitution elasticities made by various authors are then discussed. It is indicated that a major difficulty still exists in that the effect of relative prices is often obscured because of collinearity between the price series and other variables (e.g., income) in a multiple regression equation. The method of confluence analysis is suggested as a means of determining whether the effects of the independent variables can be estimated separately. As an example, a multiple correlation of the British share of world manufactured exports on the corresponding price ratio and a world industrial production index is presented, and, with the aid of confluence analysis, it is found that the price effect can be measured separately from the effect of the variations in world income (represented here by world industrial output). Two variant forms of this regression equation are also given, one for the same relationship but with a one-year distributed lag in the independent variables, and the other for a simple correlation between the quantity ratio and the price ratio, both being expressed as deviations from their three-year moving averages.

Two other methods of estimating elasticity of substitution are also tried. One is that developed by G.D.A. MacDougall; see (25), below. A mean static elasticity of substitution between U.K. and U.S. exports of manufactures is obtained by correlating, in a logarithmic equation, the quantity ratios of the exports of some 14 manufactured articles10 from the two countries on their relative direct labor costs of production, as measured in man-hours during a given (unspecified) year. The other method tried is to compare the changes in the volume of total exports of 16 countries with the changes in their corresponding prices between the year 1937 and the third quarter of 1948. Six industrial countries—the United States, the United Kingdom, Switzerland, France, Sweden, and the Netherlands—are seen to lie on a very good line with a correlation of 0.87 and an elasticity of—1.98.

In the conclusion to his study of the measurement of demand elasticities for exports, the author states that the results seem to indicate that the elasticities of substitution are quite high; furthermore, that the demand elasticity for a country’s exports is not expected to be much lower than the average elasticity of substitution between its exports and other countries’ exports of similar goods.

The rest of the paper deals with the measurement of demand elasticities of imports and of supply elasticities of internationally traded goods. On the former, he reviews the contributions made by Chang and by Neisser, and agrees with them on the general orders of magnitude of their estimates. On the supply elasticities, he confines himself to a theoretical speculation about their magnitudes because of the lack of available data and empirical studies.

(7) Tse Chun Chang, Cyclical Movements in the Balance of Payments (Cambridge, England, 1951).

This book presents the results of a statistical study of the cyclical movements in the balance of payments of different types of country, based on data for the period 1924-38. In addition to new material, it consists of revised versions of several of the author’s articles published earlier.

The countries examined are classified into five types, as follows: the highly industrialized and deficient, the highly industrialized and self-sufficient, the less industrialized, the purely agricultural, and the mining type. For each type, one representative country is selected and the cyclical pattern of its balance of payments is studied. The countries selected to represent the five types are, respectively, the United Kingdom, the United States, Sweden, Australia, and Chile. In addition, the Canadian balance of payments is studied because of the mixed nature of the Canadian economy.

The author has fitted a large number of least-squares regressions to explain the cyclical behavior both of the balance of payments of these countries and of the merchandise trade of many other countries. From these regressions, many elasticity estimates are obtained. Broadly speaking, these elasticities may be classified into three categories: income or price elasticity of demand with respect to various aspects of a country’s merchandise trade, such as total exports or total imports, or exports or imports of individual commodities or groups of commodities; elasticities concerning nontrade items in the balance of payments; and elasticities of substitution between exports of different countries in certain markets.

In general, the regressions for demand equations of trade items are logarithmic regressions of quantity of imports or exports on an income variable and a price variable. The income variable in import functions is real national income or an index of home employment, and in export functions it is an index of world real income.11 The price variable is generally a ratio of two prices, such as an import price index (including tariff duties) relative to a domestic price index, in the import function; or, in the export function, an export price index relative to a world export price index or to an average export price index for a number of competing exporting countries. The regressions for nontrade items in the balance of payments are generally expressed in money values, using an income series as the explanatory variable. Finally, the regressions for functions expressing substitution relationships are usually logarithmic functions of the relative quantities on the corresponding relative prices and the real income in the market concerned.

Estimates are also made for the elasticities of U.K. demand for 36 individual commodities. In these cases, the regression equations are logarithmic functions of the quantity of imports on a home employment index, an import price index corrected for tariffs, and in some cases a price index for competing home-produced goods.

In addition to the elasticity of demand for imports, the marginal propensity to import (in money values) is computed for many countries.

The trend is eliminated from each series used in the regressions, so that the results show only the cyclical fluctuations. No measures of the significance of the numerous regressions are given.

(8) Colin Clark and J.G. Crawford, The National Income of Australia (Sydney, 1938).

There is in this book an incidental estimate of Australia’s marginal propensity to import, calculated for the derivation of a national income multiplier. Imports and national income, both in millions of Australian pounds, are drawn, respectively, on the vertical and the horizontal scales of a chart. It is shown that the points representing the fiscal years 1922/23-1926/27 form a very good linear relationship, and that those representing the years 1930/31-1937/38 scatter along another straight line with approximately the same slope but on a lower level. The two slopes are estimated to be 0.21 and 0.25, respectively. The method of estimation is not stated. The intervening years, viz., 1927/28-1929/30, are regarded as a transitional period, presumably associated with the rise in tariffs.

(9) Colin Clark, “A System of Equations Explaining the United States Trade Cycle, 1921 to 1941,” Econometrica, Vol. 17 (April 1949), pp. 93-123.

The author presents in this paper a model of seven empirical equations explaining the U.S. trade cycle from 1921 to 1941. The parameters are estimated by the single-equation least-squares method.

Among the seven structural equations, one expresses the volume of U.S. imports as a function of U.S. gross national product, with both variables measured in billions of wage units per quarter, i.e., billions of dollars per quarter divided by average hourly wage rate. A structural change in the import-income relationship is seen to have occurred in the early part of the 1930’s. Thus, the period under study is divided into two subperiods, 1921-33 and 1934-41, and a regression equation is fitted for each. The marginal propensities to import for the two sub- periods are seen to be of about the same magnitude, but the average propensity to import is lower in the second than in the first sub- period.

(10) Imre de Vegh, “Imports and Income in the United States and Canada,” Review of Economic Statistics, Vol. XXIII (August 1941), pp. 130-46.

This article presents an empirical study of the relationships between imports and income in the United States and in Canada based on data for the interwar period. A large number of regression equations are fitted, using different series of import data (e.g., general imports and retained imports), different income series (e.g., gross national product and income payments), and assuming different forms of equations (e.g., linear, logarithmic, first differences, and percentage changes). In addition to total imports of the United States and Canada, regressions are made for U.S. imports of works of art, U.S. imports of books, and U.S. tourist expenditures abroad, as functions of personal income of various income groups in the United States. Regressions of the quantum of world trade on world industrial production are also computed to show the decline in world trade in relation to world industrial output during the interwar period.

In general, when imports are expressed in value the explanatory variable is money income, but when the volume of imports is under consideration an index of industrial production is used instead of national income. No measure of significance is given; however, the correlation coefficients are quite high in all cases.

(11) Barend A. de Vries, “Price Elasticities of Demand for Individual Commodities Imported into the United States,” Staff Papers, Vol. I (1950-51), pp. 397-419.

This paper is based on the U.S. Tariff Commission’s study in 1945 of the long-run effects of a 50 per cent reduction and of a 50 per cent increase in the U.S. tariff rates of 1939 on the postwar volumes and values of U.S. imports of individual commodities. Since a change in a tariff rate is equivalent to a shift in the demand curve, the estimated levels of imports and import prices corresponding to the assumed tariff rates determine three points on the supply curve of the commodity in question. From these points on the supply curve and from the given changes in the tariff rates, the author arrives at the points through which the implicit demand curve has to pass. A pair of elasticities of demand then can be measured for each commodity, one corresponding to the reduction and the other to the increase in the tariff rate. This has been done for 176 individual commodities.

Using these elasticity estimates for individual commodities, the author has computed an average elasticity of U.S. demand for the major imports from each of the European Recovery Program countries, each commodity elasticity being weighted by the value of U.S. imports of the commodity from the country concerned in 1948.

Similar average elasticities are also computed for U.S. imports of all 176 commodities and for 27 raw materials from all countries, weighted by the values of U.S. imports of the commodities in 1939.

(12) J.B.D. Derksen and A. Rombouts, The Influence of Prices on Exports (De Nederlandsche Conjunctuur, Special Memorandum No. 1, The Hague, June 1939—in Dutch with English summary).

This paper attempts to measure the elasticities of substitution between Netherlands exports and exports of other countries both in the world market and in the markets of certain importing countries. The data used are those for the interwar period.

For Netherlands exports to the world, the linear-approximation method is used to convert an equation relating the ratio of Netherlands exports to total world trade to a ratio of the corresponding prices into a linear form, i.e., one that treats the algebraic difference between an index of the volume of Netherlands exports and an index of the volume of total world trade as a linear function of the Netherlands export price and the world price.12

Netherlands exports of agricultural products to Belgium, expressed as a ratio to total Belgian imports of agricultural products, are studied in another regression as a function of a ratio of the corresponding prices.

The rest of the article is devoted to estimating substitution elasticities for some ten commodities13 exported from the Netherlands in competition with similar exports from other countries in certain importing markets. The regression equations consist in general of a quantity ratio correlated directly with the corresponding price ratio. However, in a few cases, hyperbolic or parabolic functions are assumed. In cases where the Netherlands is the sole supplier of the commodity in a market (e.g., bulbs to the United Kingdom), the regression equation relates the quantity of imports with the price of the commodity and the money income of the importing country.

In some cases, the quantity ratio used in the regression is not the ratio of Netherlands exports to exports of competing exporters but the share of the Netherlands in the total imports of the importing country. The elasticities derived from these equations are called elasticity of competition, as distinguished from elasticity of substitution, which is used to indicate the substitution between the imports from the Netherlands and the imports from all other countries. By using the same price ratio in the definition of each elasticity, the authors are able to show that the elasticity of substitution can be readily derived from the elasticity of competition, given the Netherlands’ share in the total imports of the market.

The bunch-map method has been used to provide some indication of the reliability of the estimates.

(13) Stephen Enke, “America, Britain, and the Dollar,” Proceedings of the Twenty-First Annual Conference of the Pacific Coast Economic Association (December 30-31, 1946), pp. 32-35.

A simple regression is given in this paper to show the relationship between U.S. national income and expenditure on foreign goods and services in the interwar period. The marginal propensity to import and the income elasticity of imports thus obtained are then used to provide some guidance in a discussion on the problem of dollar supply in the postwar world.

More specifically, the dependent variable in the regression is the sum of the value of U.S. imports, gross service payments, and tourist expenditure abroad. The explanatory variable is U.S. national income in money value adjusted for trend. The author explains that the trend adjustment was made to eliminate a steady tendency for the average propensity to import to decline during the years 1921-39.14

(14) J.M. Fleming and S.C. Tsiang, “Changes in Competitive Strength and Export Shares of Major Industrial Countries,” Staff Papers, Vol. V (1956-57), pp. 218-48.

The purpose of this paper is to estimate an average elasticity of substitution in world demand between the manufactured exports of major industrial countries. The estimate is derived by correlating the changes in the export shares of the individual countries in the total volume of exports of manufactured goods by all the countries in the group between a given pair of years with the changes in the ratios of the export prices of the respective countries to the average15 export price for the group between the same pair of years. The countries included in the group are the United States, the United Kingdom, France, West Germany,16 Canada, Italy, Belgium, the Netherlands, Switzerland, and Sweden. The years compared are 1948 with 1953 and 1953 with 1954.

In selecting a proper index to indicate price changes, both the unit value for exports of manufactured goods and the efficiency wage costs, i.e., wage rate adjusted by productivity, in manufacturing have been considered. It is found that the unit value provides a better explanation for changes in the export share in almost all the calculations. Hence, the unit value of exports of manufactured goods is used as the price variable.

Consideration has also been given to the changes in export shares induced not by price changes but by changes in market demand, viz., changes in the commodity composition or in the geographical pattern of world demand for manufactured exports. Steps were taken to eliminate these influences from the changes in export shares.17 It is found that elimination of these effects tends to improve the correlation between the changes in export shares and the price changes for the 1948-53 comparison, but tends to reduce the correlation coefficient for the 1953-54 comparison.

The authors state that the results of the correlations indicate that the average elasticity of substitution between the exports of manufactured goods of major industrial countries is greater than unity even in the short period (such as 1953-54), but more so in the long period (such as 1948-53). They add the caution, however, that these estimates are subject to a considerable margin of error.18 Furthermore, greater errors would arise if they were applied to any particular country.

(15) Arnold C. Harberger, “A Structural Approach to the Problem of Import Demand,” American Economic Review, Vol. XLIII (May 1953, Papers and Proceedings of the 65th Annual Meeting of the American Economic Association), pp. 148-59.

The purpose of this article is to show that empirical estimates of U.S. import demand elasticities obtained by the traditional least-squares method are generally underestimates. Least-squares estimates of demand elasticities are said to be based on the assumption that either there is no shift in the demand function, or if there is any the shift is uncorrelated with changes in the independent variables. Both assumptions are asserted to be implausible, especially in the case of the U.S. demand for imports. The author believes first, that the U.S. import demand function is likely to be highly unstable,19 and, second, that the shifts are positively correlated with the price changes.

Therefore, he proposes a different approach based on the assumption that shifts in the demand function are positively correlated with price. In addition, several other assumptions are alternatively introduced in his estimations, and the results are shown to vary with the assumptions postulated. Thus, when it is further assumed that demand shifts are uncorrelated with income changes, the lower limit of plausible price elasticities coincides with the least-squares estimate (the upper limit being negative infinity). If, in this case, a range of plausible income elasticities is also postulated, the resultant range of estimated price elasticities becomes finite and the lower limit is still the least-squares estimate. A different range of plausible price elasticities is obtained, corresponding to the assumptions that the income elasticity is given and that shifts in the demand function are positively correlated with both price changes and changes in the quantity of imports not explained by income. Still another range of results is obtained if it is assumed that there is a positive partial correlation of demand shifts with price changes (income held constant) and that there is a maximum conceivable amount of “shiftability” in the demand function. The resultant estimates vary considerably in their ranges, but they are invariably centered far above the least-squares estimates.

The empirical data used in making these estimates are those for the period 1923-39. The import data refer to the volume of U.S. total imports and of U.S. imports of crude and semimanufactured materials, crude and manufactured foodstuffs, and finished manufactures; the price data are ratios of import price to domestic wholesale price; and the income data are gross national product in real terms. All variables are expressed in year-to-year percentage changes. Thus the elasticities estimated are, admittedly, short-run elasticities.

No test of significance is performed, because, as the author explains, the assumptions postulated are intended to apply to the actual period of observation, not to a population from which the actual observations may be regarded as a sample.

(16) Arnold C. Harberger, “Some Evidence on the International Price Mechanism,” The Journal of Political Economy, Vol. LXV (December 1957), pp. 506-21. (An abstract of this article, together with comments by Warren L. Smith and Hans Neisser, appeared in The Review of Economics and Statistics, Vol. XL, No. 1, Part 2, Supplement [February 1958], pp. 123-32.)

This article seeks for evidence of the effectiveness of the price mechanism in international trade. The author does not believe that with the existing tools exact measurement is possible. He tries to collect the results of independent experiments in the hope that, “when all or most of a set of uncertain and imprecise pieces of evidence point in the same direction, we have the sort of situation where ignorance turns into hunch, hunch into belief, and, ultimately, belief into knowledge.”

He starts with estimating import demand elasticity by an admittedly crude experiment of his own. The 1954 imports of eight countries20 are compared with their respective 1937 or 1938 imports. The changes in imports unexplained by income changes21 are all attributed to changes in prices. Six of the eight demand elasticities thus estimated turn out to be negative and range in value from—0.56 to—2.12.

The second piece of evidence is gathered by estimating demand elasticities of exports on the basis of studies that had been made by MacDougall22 and by Zelder.23 MacDougall’s estimate of the substitution elasticity of U.S. and U.K. exports was based on a comparison of the relative quantities and relative prices of about 100 commodities exported by the two countries in a given year. Harberger points out that this estimate becomes meaningful only when it can be assumed to represent the common substitution elasticity of all the commodities in the sample. The validity of this assumption is said to be supported by Zelder’s study, which finds that the calculated substitution elasticities of 39 commodities exported by the United States and the United Kingdom do cluster around the value of MacDougall’s estimate. Harberger then feels assured in the use of MacDougall’s estimate of the substitution elasticity of U.S. and U.K. exports to derive elasticities of demand for the two countries’ exports from an ingenious formula using the properties of the Hicksian concept of substitution effect. The results give the demand elasticities for the exports of the United States and the United Kingdom as at least—1.65 and—1.35, respectively. If the substitution elasticities between the exports of the United States, the United Kingdom, France, Germany, and Japan estimated by MacDougall are all used in the formula, the resultant estimates of the elasticities of demand for the exports of these countries will range from—1.30 to—1.90.

The third experiment is to derive export demand elasticities based on the results of an unpublished study by Arnold Harberger and Michel Verhulst made at the International Monetary Fund in 1950. In this study, the effect of the 1949 devaluations on the world trade pattern is assessed by comparing the trade pattern of the first quarter of 1949 with that of the first quarter of 1950. The relative change in the percentage distribution of imports of each of 14 importing countries24 from a particular source of exports is regarded as measuring the net substitution by the importing country for or against that exporting source. The average net substitution of all 14 importing countries from an exporting source is then compared with the change in the dollar price of the exports from the same source. For the 11 exporting sources25 into which the world is divided, there seems to be a good rank correlation between the average net substitution series and the dollar export price indices. By identifying this concept of net substitution with the Hicksian substitution effect, another formula is obtained for deriving the export demand elasticities from the average net substitution and the changes in the relative prices of the respective sources. The deflators in the relative-prices term are weighted averages of the export prices of the other exporting sources.26 Aside from two estimates with the wrong sign, the results show the elasticities of export demand to be generally higher than—1.

The author goes on to summarize the results of several other statistical studies of price elasticities in international trade. From these estimates and from the results of his own experiments, presented in this article, he arrives at the conclusion that “the price mechanism works powerfully and pervasively in international trade.” He offers his judgment that “in the relatively short run the elasticity of import demand for a typical country lies in or above the range of—0.5 to—1.0, while its elasticity of demand for exports is probably near or above—2.”

(17) J.A. Hargreaves, “U.S. Import Propensities Since the War,” Bulletin of the Oxford University Institute of Statistics, Vol. 12, Nos. 1 and 2 (January and February 1950), pp. 60-64.

The purpose of this article is to present a numerical formulation of the decline of U.S. imports in relation to national income in the postwar period, compared with the same relationship in the prewar period. The years 1934-37 are considered to be normal representatives of the decade prior to the war, and the postwar years under consideration are 1945-49. The data for the postwar period are quarterly for the period from the second quarter of 1945 to the first quarter of 1949; the nature of the data for the prewar period, however, is not explained.

For each period, quarter-to-quarter changes in the value of U.S. imports of crude materials, semimanufactures, and manufactures, respectively, are correlated in a linear regression with the corresponding changes in U.S. national income in money value and a wholesale price index (to represent import price) of the particular economic group. However, only the regression coefficients for national income are given in the paper.

No measures of significance are given.

(18) Randall Hinshaw, “American Prosperity and the British Balance of Payments Problems,” The Review of Economic Statistics, Vol. XXVII (February 1945), pp. 1-9.

This article presents a study on the determination of the levels of U.S. total imports and of U.S. imports from the United Kingdom in the interwar period.

The volume of U.S. total imports is correlated in a multiple regression with U.S. national income in money value and an index of U.S. import prices. The author does not believe that a price elasticity of demand for imports can be estimated from this regression, which is said to reflect the results of shifts in both demand and supply curves during the period under study. He suggests that the true demand elasticity can be measured from a simple regression of imports on price, with the influence of income changes eliminated from both series. It is asserted that, after income effects on both imports and price are eliminated, the resulting relationship can be assumed to represent the true shape of the demand curve.

In the case of U.S. imports from the United Kingdom, the volume of imports is again correlated with U.S. money income and a specially constructed price index of U.S. imports from the United Kingdom. In this case, the price elasticity of demand is apparently obtained directly from this equation, as no other regressions are mentioned.

(19) Randall Hinshaw and Lloyd A. Metzler, “World Prosperity and the British Balance of Payments,” The Review of Economic Statistics, Vol. XXVII (November 1945), pp. 156-70.

A number of simple linear regressions are presented in this article to describe the fluctuation in various elements of the U.K. balance of payments in the period 1932-37 as functions of income. First, the volume of U.K. imports is correlated with U.K. real national income. Second, the volume of U.K. exports is correlated with world real income. Third, some nontrade items in the U.K. balance of payments, viz., net income from overseas investment, net shipping income, and net income from short-term interest and commissions, are each correlated with world money income. All the variables are expressed in index numbers, 1937=100. The index of world income is derived from income series for 21 countries, including all the major industrial countries except Russia.

No measure of significance is given. The correlation coefficients of the simple regressions are, however, quite high in all cases.

(20) F.B. Horner, “Elasticity of Demand for the Exports of a Single Country,” The Review of Economics and Statistics, Vol. XXXIV (November 1952), pp. 326-42.

A new approach to the measurement of various elasticities relating to the exports of a country is suggested in this article. The central idea is that the various elasticities relating to the export of a commodity by a given country are best derived by calculating the basic elasticities of demand and supply for that commodity in home and world markets, respectively, and by assigning appropriate weights to these basic elasticities.

The basic elasticities needed for the derivation of export elasticities are comparatively few in number and are said to be “formally capable of measurement.” They are the supply elasticities of the commodity in the exporting country and in competing countries, the demand elasticities of the commodity with respect to price and income in the world market, and the demand elasticities of the commodity with respect to price and income in the exporting country. The weights needed in the derivation are as follows: proportions of the export market supplied by the competing countries, proportion of the export in the total production, and proportion in the total consumption of the commodity in the exporting country. Government commercial policies and transport costs are also taken into consideration in the choice of proper weights.

The author shows that, based on these data, a large variety of elasticities relating to the export of the commodity by the given country can be obtained; for example, the elasticity of world demand for the country’s export of the commodity, the elasticity of the country’s supply of the commodity for export, and the elasticities of world demand for the country’s export of the commodity with respect to the country’s exchange rate and world income, respectively.27

This approach is then applied to an estimation of the elasticities relating to Australian exports of wool, wheat, and butter. Among the basic elasticities needed for the derivation, only the demand elasticities of the United Kingdom and the United States for wool, and of the United States for wheat and butter, are empirically estimated; the values of the others are all arbitrarily assumed. The empirically estimated elasticities are obtained by observing the general tendencies of the results of some 34 correlations. The basic demand functions assumed in these correlation analyses are, in general, a logarithmic equation relating the quantity demanded with real income, the price of the commodity, a price index of all other commodities, and a time trend. The confluence analysis method has been used to examine the reliability of the results. The weights used in the derivation of the export elasticities are calculated on the basis of trade, production, and consumption data for each country in the export market during the three years ended 1938. The export elasticities refer specifically to the average prices for 1938.28

(21) Konjunkturinstitutet, “Regression Analyses of Swedish Imports During the Interwar Period,” Ekonomiska Utredningar (Meddelanden, Series B:10 [Spring 1949]), pp. 56-72 (in Swedish with a summary in English).

A number of regression equations are computed to explain the volume of Swedish total imports and that of imports of consumer goods in the period 1922-39. The equations assumed are logarithmic, relating the volume of imports to real national income and relative prices, all variables being expressed as percentage deviations from their respective average values over the whole period. The results of some 30 regressions of this general pattern but using different statistical series are given in the article.

It is found that better results are obtained if a structural change is assumed to have occurred around 1931-32 (the Swedish krona was depreciated in September 1931). Two methods of allowing for this are tried in the studies of Swedish total imports: first, by making separate calculations for the periods 1922-31 and 1932-39, and second, by assuming different values of “structural factor” for these two periods in the analysis of the whole period 1922-39. In the studies of Swedish imports of consumer goods, the correlation coefficient is found to be greater if the structural factor, instead of being represented by two arbitrary constants, is represented by a three-year moving average (with a two-year lag) of the ratio between the price index for imported consumer raw materials and imported consumer goods. The theory is that a lower ratio will indicate improvement in the competitive position of Swedish home industries in comparison with foreign export industries, and, consequently, in due time lead to an expansion of the former.

In presenting the results of three-variable regressions, both the square of the multiple correlation coefficients and the square of the simple correlation coefficients between imports and income are given. Comparison of the two magnitudes is intended to provide some indication of the significance of the third variable (either a relative price term or a structural factor) in the regression. Thus, the estimates of the price elasticities, when judged by this criterion, are described as uncertain.

(22) A. Kubinski, “The Elasticity of Substitution Between Sources of British Imports, 1921-1938,” Yorkshire Bulletin of Economic and Social Research, Vol. 2 (January 1950), pp. 17-29.

This paper describes an attempt to estimate the elasticity of substitution between sources of U.K. imports by measuring the individual substitution elasticities of a large number of commodities imported by the United Kingdom from different sources in the period 1921-38, and then by examining the general characteristics of these estimates.

The imported commodities included in this study are classified as follows: 69 commodities in the food, drink, and tobacco group; 63 in the raw materials, etc., group; and 159 in the manufactures group.

Substitution elasticities of individual commodities are measured by correlating the logarithms of the relative quantities of U.K. imports from two sources with the logarithms of their relative prices. In many cases efforts are made to improve the correlations by using distributed time lags, by breaking up a period of time into subperiods, by eliminating trend from the variables, or by measuring the variables as deviations from their moving averages.

Of the elasticity estimates thus obtained, 265 are found to have a negative sign, 145 to be statistically significant, and 133 to be both negative and statistically significant. From an examination of the arithmetic means and the median values of these elasticity estimates, the author concludes that there seemed to be a fairly high degree of substitutability between goods imported into the United Kingdom from different sources in the interwar years.

(23) Ta-Chung Liu, “The Elasticity of U.S. Import Demand: A Theoretical and Empirical Reappraisal,” Staff Papers, Vol. III (1953-54), pp. 416-41.

This paper presents a theoretical and empirical reappraisal of the least-squares regression method used in the estimation of elasticities of demand for imports.

In the theoretical section, it is pointed out that the least-squares method is especially inadequate when it is used to estimate the demand for imports in a situation where both the import demand curve and the import supply curve have shifted simultaneously in opposite directions. For then one cannot be sure at all whether the resultant estimates are underestimates or overestimates.29 However, the author continues, the least-squares estimate of the demand function can still be useful and meaningful if one can ascertain empirically that the shifts in the supply curve are independent of the shifts in the demand curve, and that the supply curve is perfectly elastic within a wide range. Under these conditions, the least-squares estimates are shown to be unbiased estimates.

Some empirical evidence is presented to show that these conditions are satisfied in the case of U.S. imports of finished manufactures. The author then proceeds to make an estimate of U.S. demand for imports of finished manufactures from the European Recovery Program countries. For the prewar years 1923-37, he correlates the quantity index of these imports with an index of U.S. real gross national product and a ratio of a price index of these imports to a price index of U.S. imports of finished manufactures from other origins30—the 1935-39 average being the base for all the indices. The price elasticity estimated from this linear regression varies from year to year. Its movement over the period is plotted in a chart in the article.

For the prewar years 1927-39 and the postwar years 1947-51 as a whole, the author has calculated a correlation of the year-to-year changes in the quantity of U.S. imports of finished manufactures from the European Recovery Program countries with the year-to-year changes in U.S. real gross national product and the square31 of the year-to-year changes in a ratio of the price index of these imports to the wholesale price index of finished manufactures in the United States. The quantity of imports and real gross national product are expressed in millions of constant (1939) dollars. The derivation of price elasticities from this second-degree regression equation is based on a formula given in the article.

Standard errors of the regression coefficients have been computed and used extensively throughout the paper to assist in selecting proper variables in the regressions.

(24) G. Lovasy and H.K. Zassenhaus, “Short-Run Fluctuations in U.S. Imports of Raw Materials, 1928-39 and 1947-52,” Staff Papers, Vol. III (1953-54), pp. 270-89.

A number of least-squares regressions are presented in this paper as a basis for studying the short-run fluctuations in U.S. imports of raw materials in the periods 1928-39 and 1947-52, respectively. Quarterly data have been used in all the regressions.

The import series is the sum of the values of U.S. imports of raw materials and semimanufactures (as defined by the U.S. Department of Commerce) deflated by the corresponding unit value indices and then combined into one index. For explanatory variables, several statistical series have been specially computed. First, there is an index covering that part of domestic production of manufactures which is deemed to absorb imports of raw materials from abroad.32 Second, there is an index of domestic output of raw materials that compete with imports of raw materials.33 Third, an inventory-output ratio for domestic manufacturing industries34 is computed for the postwar years 1947-52, but not for the prewar years, since no adequate inventory data are available for the years 1928-38.

These variables are used in various regressions to explain the quantities of U.S. imports of raw materials in the prewar and postwar periods. Most of the regressions presented are for exploratory purposes. The regression considered the most satisfactory for the prewar period relates the quantity of U.S. raw material imports to the adjusted domestic manufacturing production index and a linear trend. The regression considered best for the postwar period uses as explanatory factors the adjusted domestic manufacturing production index and the inventory- output ratio of the preceding quarter. The correlation is not significantly improved by using the index of domestic output of competing raw materials as an additional explanatory variable.

In the equation for the postwar period, the regression coefficient for the inventory-output ratio term is found to be negative. This is interpreted as an indication that the changes in the manufacturers’ inventories of raw materials were involuntary. This point is elaborated both in the text and in an appendix to the article.

Standard errors of the regression coefficients have been computed and used to test the significance of the regression coefficients.

(25) G.D.A. MacDougall, “British and American Exports: A Study Suggested by the Theory of Comparative Costs,” Part I, The Economic Journal, Vol. LXI (December 1951), pp. 697-724; Part II, ibid., Vol. LXII (September 1952), pp. 487-521.

The author suggests a new approach to measuring substitution elasticities in international trade. Instead of the usual practice of correlating the movements, over a number of years, of relative quantities with the associated relative prices of a commodity or a group of commodities exported by two countries, he has correlated relative quantities with relative prices of a large number of different goods exported by two countries, all referring to the same year. He calls the elasticity thus measured the product elasticity of substitution, and asserts that this method of elasticity measurement, while open to special objections of its own, successfully avoids many of the difficulties involved in the use of time series. The author goes on to show that the total elasticity of substitution between the exports of the two countries can be derived by multiplying the product elasticity of substitution by an index of similarity of exports,35 assuming a uniform product elasticity of substitution for each commodity and a constant market demand for each.36

This approach is applied to the study of U.K. and U.S. exports during the interwar years. A correlation of the logarithms of relative quantities and relative dollar prices of manufactured exports from the two countries is made for 1913 and each of the years between 1922 and 1938, as well as for 1948. Similar calculations for 1929 are made for eight other pairs of the five major exporting countries of manufactures—United States, United Kingdom, Germany, Japan, and France. In all cases the correlation coefficients are rather small, but the estimated product elasticities are invariably large. No measure of the significance of the estimates is given. The author points out that allowance for the bias owing to errors of observations in the data would lead to an upward adjustment of the estimates. Based on the estimated product elasticity of substitution and the computed index of similarity, he has further derived the total elasticity of substitution between U.K. and U.S. exports for each of the years in the period 1928-38. After adjusting for bias in the estimate, he guesses that the total elasticity of substitution between the exports of the two countries might be near—3.

The elasticities obtained by this method, using data for a single year or an average of years, are described as long-term elasticities of substitution. To assess short-term elasticities of substitution, the author has made similar calculations using data for the changes between two years separated by a time interval in the relative quantities and relative prices of a large number of manufactured commodities exported from the United Kingdom and the United States. This is done for the changes between 1930 and 1932 and between 1932 and 1934, with the data expressed in index numbers on the basis of the respective values in the earlier years being equal to 1. The estimated elasticities in these cases are seen to be much lower than those obtained for the long-run elasticities. However, similar calculations for changes over longer periods—1928–31, 1929–37, and 1934–38—still fail to show higher elasticities. In any case, the correlation coefficients are very low and again no measure of significance is given.

(26) Vernon W. Malach, “Elasticity of Demand for Canadian Exports,” The Review of Economics and Statistics, Vol. XXXIX (February 1957), pp. 23-30.

The author uses the method suggested by Horner37 to estimate various elasticities relating to Canadian exports of wheat, newsprint, woodpulp, and iron ore. The method consists of deriving the various elasticities from estimated values of the basic elasticities of demand and supply of the commodity in the home and world markets. The elasticities derived in this article are the demand and supply elasticities of the Canadian exports of these commodities and the elasticities of export receipts with respect to the exchange rate for the respective commodities.

Among the basic elasticities, the only statistically derived ones are the income and price elasticities of demand for these commodities in the export market; the values of the others are all arbitrarily assumed. The demand for wheat in the United Kingdom in the period 1920-38 is assumed to represent the demand conditions in the entire export market for Canadian wheat. Similarly, the U.S. demands for newsprint, wood- pulp, and iron in 1919-39 are assumed to represent the world’s demands for these respective commodities. The price and income elasticities of demand for each of these commodities in the export market are estimated by a least-squares logarithmic equation relating the quantity of the commodity consumed to (1) the real income in the export market and (2) the ratio of a price index of the commodity to a general wholesale price index in the export market. Standard errors of the regression coefficients have been calculated to test the statistical significance of the estimated elasticities.38

A weighted average of the derived exchange elasticities of export receipts from the four commodities is calculated to represent the exchange elasticity of Canada’s total export receipts in foreign currency. The weights used are not explained, but are presumably the relative shares of the respective commodities in the total export receipts during some unspecified period.

The author is aware of the many pitfalls in estimating elasticities of demand and of the difficulties arising out of the particular assumptions he has introduced. Taking these into consideration, he believes that his estimated elasticities tend to be biased downward.

(27) R.L. Marris, “The Purchasing Power of British Exports,” Economica (new series), Vol. XXII (February 1955), pp. 13-28.

This study of the import purchasing power of U.K. exports is based on what the author calls an historical foreign transformation curve for the United Kingdom, derived from data for the prewar period 1920-38. He assumes an upward shift of this curve to fit the data for the postwar period 1948-54. The curve, a hyperbolic curve, is plotted on a chart with the U.K. import purchasing power (i.e., the value of U.K. exports divided by the import price) on the vertical scale and the actual volume of exports on the horizontal scale, both being measured in index numbers, 1930-38=100. The parameters in this hyperbolic function are derived from the coefficients in two linear regressions relating the U.K. volume of exports to its terms of trade (i.e., the import price divided by the export price); one is for the period 1920-29 and the other for the period 1930-38. The two regressions are shown to have practically identical coefficients. The rounded values of these coefficients are then used as parameters in the hyperbolic function of the foreign transformation curve.

Before testing this prewar relationship against the postwar data, the author has made some a priori adjustments to the postwar data in order to eliminate the effects of the abnormalities, such as excessive internal demand and shortage of raw materials, in the postwar conditions. The prewar relationship between the volume of exports and the terms of trade is then tested against these adjusted postwar data for 1948-54. The author finds that, if an upward shift in the demand of the postwar world for U.K. exports is assumed, the prewar relationship would fit the adjusted postwar data very well.39 The coefficients in the modified equation for the postwar period are then used as parameters in the hyperbolic equation for a foreign transformation curve in the postwar period.

On the basis of the U.K. position on this postwar foreign transformation curve, the author believes that the elasticity of the purchasing power of U.K. exports is very low; therefore, from the viewpoint of welfare, the policy he recommends is to reduce, instead of to increase, exports.

(28) 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.

This paper relates the authors’ experience of disappointment in applying both the commonly used least-squares regression method and the comparatively novel simultaneous equations approach to the estimation of price elasticities of demand in international trade. Their conclusion is that neither of these methods gives a result which is acceptable from the economic point of view.

They start with the least-squares method by considering a simple regression equation correlating the logarithm of the relative quantities of imports of a commodity from two sources with the logarithm of the corresponding relative prices (including import duties). The economic and statistical assumptions underlying this simple regression are examined with considerable thoroughness, and the difficulties with which the conditions may be fulfilled are carefully discussed. The results of 47 simple regression equations of this type are then presented. The regressions are based on statistics of the imports of the United Kingdom, the United States, Australia, Sweden, Canada, and India of some 25 commodities from various sources. The data used are mostly for the interwar period. But in a number of cases they refer to periods before World War I, as far back as 1870. It is seen that out of a total of 47 results, 36 of the regression coefficients are negative and 11 positive, and that 28 out of the 47 correlation coefficients are significant at the 5 per cent level.40

Into these simple regressions the authors then introduce successively a number of other variables designed to eliminate some systematic influences on relative quantities not explained by relative prices. Thus, a logarithm of the income in the importing country is added to each regression;41 next, a linear trend is introduced; then, finally, both the logarithm of income and the trend factor are included in the regression. The results of these experiments are seen to have varying degrees of success: there are 30 negative coefficients (out of 44 cases) from the first experiment, 38 (out of 47 cases) from the second, and 15 (out of 17 cases) from the third, for the logarithm of relative prices. The authors state that the use of the multicollinear test in these regressions would probably lead to rejection of a high proportion of them.

To deal with one of the objections mentioned against the least- squares method, viz., the possible existence of serial correlation in the residuals of the regression equation, the authors have computed another set of regressions of the year-to-year changes in the logarithm of relative quantities on the year-to-year changes in the logarithm of relative prices for the same 47 cases. Although no precise test of randomness has been attempted, they do give the d ratio, i.e., the ratio of mean square successive difference to variance adjusted for a number of observations, for the residuals from both sets of regression equations (viz., those using logarithms of the original figures and those using year-to-year changes in logarithms). These results, while showing some gain in randomness, fail to convince them that the use of successive difference is the perfect solution.

Leaving the least-squares method, they consider next the simultaneous equations approach. Four models are constructed. Model I investigates U.K. import demand for wheat from Australia and New Zealand, on the one hand, and from Argentina, on the other. Model II differs from Model I only in the coverage of the source of supply, taking Australia and New Zealand, on the one hand, and, instead of Argentina, all other suppliers, on the other. Model III studies the Swedish demand for imports from the United Kingdom and from Germany of a particular variety of steel plates. Model IV deals with the U.K. import demands for butter from Denmark, on the one hand, and from Australia and New Zealand, on the other. All four models are of the same simple pattern: two demand equations and two supply equations for the imports of the good from the sources of supply in question.

In general, the demand equations in each model relate the quantity demanded with (1) the unit value of the imports of the commodity from the particular source of supply, (2) the corresponding unit value for the opposite source of supply, (3) the general price level in the importing country, and (4) the level of money income in the importing country. In order to eliminate the effects of population growth, both the quantity of imports and money income are expressed on a per capita basis. In the case of Swedish import demand for steel plates, the domestic output of steel plates is also included as a predetermined variable; in the case of U.K. import demands for butter, the domestic retail price of margarine is also included in the demand equation.

The supply equations in all four models are regarded as being of a supplementary nature, intended to permit the coefficients of the demand equations to be identified. They generally relate the quantity of imports supplied to the unit value of imports and some other variable, such as output and carry-over, productivity, and wage rate, in the supplying country.

For each model (except the model for Swedish imports of steel plates), a few new variables, e.g., the size of stocks and price in the previous period, are alternately added to the model to determine their effects on the structural coefficients. Thus, for each basic model, there are a number of alternative models corresponding to some slightly different sets of predetermined variables.

The data used for the study of U.K. imports of wheat from various sources are for the period 1890-1914 (omitting drought years), and those for the other models are for the interwar period. All variables are in logarithms and are measured as deviations from their respective means.42

The results obtained from the simultaneous equations approach again show varying degrees of success. On the whole, the authors feel disappointed, for only rarely do all the estimated coefficients in any equation show the expected sign or magnitude, and from one case to another they are not consistently of the same sign. Furthermore, the results from applying the confidence region test to some of the price coefficients in the demand equations indicate that the estimated price elasticities are very unreliable. The confidence regions are either very large or even infinite.

In conclusion, after having carefully examined both the theoretical bases and the empirical results of the methods presented in their paper, the authors indicate great misgiving toward these methods, and they seriously doubt whether any reliable estimate of price elasticity could be obtained by using these methods.

(29) V.N. Murti and V.K. Sastri, “Elasticities of Demand for Certain Indian Imports and Exports,” The Indian Journal of Statistics, Vol. 11, Parts 3 and 4 (1951), pp. 309-36.

Elasticities of India’s demand for imports and of world demand for Indian exports are estimated in this paper by the least-squares method, based on data for the period 1927/28-1937/38. Demand elasticities are calculated for total imports and total exports and also for eight Indian import items43 and eight Indian export items.44

The regression equations are assumed to be linear, and the elasticities are all average elasticities. The demand equation for total imports relates the volume of imports to (1) an index of industrial production in India and (2) a ratio of an import price index adjusted for tariffs to a cost of living index. The demand equation for total exports relates the volume of exports to (1) an index of world real income,45 (2) a ratio of India’s export price index to a world price index,46 and (3) an industrial production index in India. The variables are all expressed in indices, 1927/28=100.

One feature of this paper is that it claims to be measuring short-run elasticities when the regression equation contains a trend variable, and long-run elasticities if there is no trend variable in the equation.

Standard errors of regression coefficients have been computed. Many of them are apparently too large relative to the size of the corresponding regression coefficients.

(30) Hans Neisser and Franco Modigliani, National Incomes and International Trade (Urbana, Illinois, 1953).

The framework of this study is a system of 36 structural equations connecting the volume of international trade with the incomes of the participating countries. The countries included in the study are divided into six groups: the United Kingdom, the United States, Germany, France, the remaining industrial countries,47 and the primary producing countries.48 The imports and exports of the six country groups are each divided into three commodity groups, viz., food, raw materials, and manufactures, so that there are 18 import functions and 18 export functions, each relating to a particular country group and commodity group.

In the 15 import functions relating to industrial country groups, the volume of imports is chiefly determined by real national income (or industrial output) in the importing country, while in the 3 import functions of the primary producing countries, the volume of imports is determined by the sum of exports and industrial output in the importing country, both expressed in terms of their purchasing power over imports. In the 18 export functions, the volume of exports in each commodity group is assumed to depend primarily on the aggregate imports by all countries of goods in that commodity group. Some of the equations in the system include additional explanatory variables, such as relative prices, food production, net capital exports, or time trends. Thus the 36 unknowns, i.e., the various import and export volumes, are solved in terms of national income, relative prices, etc., which are treated as exogenous variables.

The parameters in the structural equations are estimated by the single-equation least-squares method, based on data for 1925-37. The numerical solution of the system provides the basis of extensive inferences concerning the responses of trade to changes in each of the exogenous variables upon different assumptions. Studies are also made on the transmission of income changes from one country to another induced by fluctuations in the balance of payments, and on many other subjects.

From the regression equations, some elasticity estimates are made for several individual years as well as for the average of the whole period 1925-37.

The authors have applied certain statistical methods to ascertain the reliability of their estimates. Ample information about the techniques used, such as partial correlation coefficients between pairs of variables in a regression or correlation coefficients adjusted for the number of observations, as well as the results of these tests, are given in the study.

(31) R.J. Nicholson, “‘Product-Elasticities of Substitution’ in International Trade,” The Economic Journal, Vol. LXV (September 1955), pp. 441-46.

Several points are raised in this article as criticisms of the estimation by G.D.A. MacDougall49 of product elasticity of substitution. First, the author states that the concept itself lacks meaning, as it neither measures the elasticity of substitution of any particular commodity nor serves any purpose if viewed as an unweighted average of the substitution elasticities of all the goods in the mixed bag. Second, a basic assumption necessary in the estimation, viz., the existence of unique demand and supply substitution curves, is untenable, since relative quantities are affected not only by relative but also by absolute prices. Third, there is the question of identifiability, i.e., the difficulty of identifying demand and supply influences from a set of observed price and quantity data. Lastly, the author claims that his theoretical criticisms have been more or less empirically confirmed by the surprisingly high substitution elasticities he obtained by using MacDougall’s method in the field of foodstuffs.

In his experiment with MacDougall’s method of estimation, the author has correlated the logarithms of relative quantities with relative prices of certain exports (principally foodstuffs) in 1936, 1937, and 1948 from the United States and the United Kingdom in the food and drink categories. The author states that, despite the heterogeneity of the goods included in the regression, the product elasticities of substitution he obtained for food exports are inexplicably high, compared with those for manufactured exports. It should be noted that neither Nicholson nor MacDougall gives any measure of significance of his estimates, and the correlation coefficients which they do give are generally quite small.

The criticisms contained in the article are answered by MacDougall in a rejoinder in the same issue of The Economic Journal, pp. 447-49.

(32) J.J. Polak, “Contribution of the September 1949 Devaluations to the Solution of Europe’s Dollar Problem,” Staff Papers, Vol. II (1951-52), pp. 1-32.

At one point in this study, the author compares, for each of the six European countries which devalued substantially in September 1949, viz., the United Kingdom, France, Germany, the Netherlands, Norway, and Sweden, the percentage increase in the value of their respective exports to the United States between the first half of 1949 and the first half of 1950 with the percentage decrease in the dollar value of their respective currencies as a result of the devaluations. An apparent elasticity of supply of dollars is thus computed for each of the six countries on the assumption of a constant elasticity. For the value of exports, two sets of data have been used in each case: U.S. data on imports from the countries concerned and data on exports to the United States reported by the exporting countries. Percentage changes in their values from the first half of 1949 to the first half of 1950 are computed from both sets of data. The average of the two is used in the derivation of the apparent elasticity of supply of dollars.

The author asserts that this elasticity may be regarded as a summarization of the effects of all the relevant elasticities, such as the elasticity of foreign demand for the country’s exports or the elasticity of supply in the exporting country, on the dollar proceeds of the country’s export sales.50 The elasticity is referred to as apparent elasticity because it is estimated from a particular situation where devaluations were undertaken by a large number of countries and, furthermore, because no allowance for the effects on exports of income changes in the United States was made in the process of estimation.

(33) J.J. Polak, An International Economic System (Chicago, 1953; London, 1954).

This study presents an international economic system to show the interrelationships between international trade and national income of nations. The framework of the system is quite simple: for each nation, the volume of imports is assumed to depend upon real income and some autonomous factors, including relative prices; real income, in turn, is dependent upon the volume of exports and some further autonomous factors; the volume of exports is determined by the volume of world trade; and the volume of world trade is represented by the sum of the volumes of imports of all countries. Thus, in this system, the effects of an autonomous change in one country are transmitted through the system to affect the income and trade levels of all countries.

This theoretical structure is fitted to the data for 25 countries in the interwar period by means of the single-equation least-squares method. With respect to the export functions, it is found profitable, in many cases, to divide world trade into two parts—trade in primary products and trade in manufactures—and to use either of the two as an explanatory variable, depending upon the composition of the country’s exports. With respect to the import functions, where data on national income are lacking, imports are directly correlated with export receipts expressed in terms of their purchasing power for imports. Attempts to introduce relative prices into the export or import equations are successful in only a small number of cases. Other explanatory variables used include time trend, trend break, harvest, etc.

In general, in the export functions, variables are expressed as quantum indices with the averages for the whole period as 100, and those in the import equations are in national currencies in constant prices of the average for the period.

For each country, two interesting indicators, which require some explanation, are derived from the empirical equations. One is the marginal propensity to purchase from the country, which is the change in the volume of the country’s exports induced by a change in the volume of world trade. It is obtained from the export function by a transformation of the units of the variables from index numbers to values in constant prices and then by a correlation of the volume of world trade in primary products or in manufactures with the volume of total world trade. The other indicator is the international reflection ratio, defined as the ratio between a change in the volume of exports to the ensuing change in the volume of imports. It is derived by multiplying the marginal propensity to import by the income multiplier of exports obtained from the import and income equations, respectively.

Statistical tests are used to determine the significance of relative prices as an explanatory variable in each import or export equation. Where an import or export equation does not contain a relative-price term, it is understood that the variable has been tried in the equation and found to be not significant.

(34) Timothy D. Sweeney, “The Mexican Balance of Payments, 1947-50,” Staff Papers, Vol. III (1953-54), pp. 132-54.

The purpose of this article is to study the effects of the Mexican devaluations in the period July 1948 to June 1949 on the Mexican balance of payments. While mindful of the fact that other factors were also at work at the same time, the author attempts to make an approximate estimate of the extent of the changes in the balance of payments that could be attributed to the devaluations. With the given degrees of devaluation in this period (roughly from 4.86 pesos to 6.85 pesos per U.S. dollar in July 1948, then to 8.65 pesos in June 1949), these estimates thus imply estimates of the elasticities of the respective items in the balance of payments with respect to changes in the exchange rate.

The study is confined to the Mexican balance of payments with the United States. The items studied are foreign travel, investment income, Mexico’s exports to the United States, and Mexico’s imports from the United States. The periods selected for comparison in each case are the first half of 1948, the first half of 1949, and the first half of 1950, except that for investment income the estimate is based on the annual figure for 1947 alone.

The methods employed are admittedly crude. For foreign travel, Mexican tourist expenditure in the United States is regarded as inelastic with respect to changes in the exchange rate. Therefore, only U.S. tourist expenditure in Mexico is considered. This item increased from an annual rate of $114 million in the first half of 1948 to an annual rate of $128 million in the first half of 1949 and then to an annual rate of $142 million in the first half of 1950. These two successive increases of $14 million each are contrasted with the levels of U.S. tourist expenditure in Canada for about the same periods, which showed even a slight declining trend. They are therefore accepted as an approximation of the net effects of the devaluations on the Mexican travel account as a whole.

In considering the investment income account, the part covering Mexico’s interest payments to the United States is disregarded, since such payments were made in dollars and their dollar values were consequently not changed by the devaluations. There remains, therefore, only the peso payments to the United States resulting from U.S. direct investment in Mexico. The elasticity in this case is, of course, unity. Thus, the direct effects of the devaluations on the investment income account are simply the 1947 dividend payments of $42 million multiplied by the degrees of devaluation. The results are $12 million after the first devaluation and $18 million after the two devaluations.

For Mexican exports to the United States, only three major groups, viz., edible animals and animal products, nonmetallic minerals, and metals and manufactures,51 are examined. The changes in the first two export groups are attributed to causes other than the devaluations; therefore, only changes in the metals and manufactures group are considered. For this group, the changes in the value of exports resulting from price changes are eliminated by deflating the value of exports by an index of U.S. prices of copper, lead, and zinc. The result shows that the volume of exports of this group increased by 55 per cent (or $31 million at 1948 prices) after the first devaluation and by 22 per cent (or $13 million at 1948 prices) after the second devaluation. These increases are regarded as a rough approximation of the changes in Mexico’s total exports to the United States that were attributable to the devaluations.

Lastly, the changes in the volume of imports are examined. In order to separate the effect of the change in income on imports, the author arbitrarily assumes the income elasticity of imports to be unity. With real income in the first halves of 1948, 1949, and 1950 given,52 he obtains the estimated imports for the respective half years based on changed income and no devaluations. The differences between actual imports and these estimated imports are taken as an approximate measure of the effects of the devaluations. The effect on imports of the first devaluation is estimated at $23 million and of the two devaluations together at $88 million at 1948 prices.

(35) F.G. Thackeray, “Elasticity of Demand for U.K. Imports,” Bulletin of the Oxford University Institute of Statistics, Vol. 12 (April 1950), pp. 109-14.

This article describes the author’s failure in his attempts to estimate the U.K. elasticity of demand for imports.

First, he tried to modify some earlier estimates made by Tse Chun Chang.53 Chang’s estimates were derived from regressions of the logarithm of import volumes on the logarithms of U.K. home employment, import prices, and, in one case, export volumes. The data used are annual, covering the years 1924-38. Thackeray believed that real income should be a better explanatory variable than home employment in the equation. So he substituted it in Chang’s equations and found a wrong sign for the price elasticity in one case and for the income elasticity in another.

His second attempt was based on the belief that the period 1924-38 used by Chang is not a homogeneous one. So he calculated a new regression of import volumes on (1) real income and (2) a ratio of import prices to a price index of goods produced and consumed at home, using quarterly data for the period from the fourth quarter of 1932 to the first quarter of 1936. The data were adjusted for seasonal variations and expressed in logarithms. The result is quite unsatisfactory, a positive sign being obtained for the price elasticity (=0.23). The author states that this result is fully compatible (on the 10 per cent probability level) with a true elasticity anywhere between—0.3 and +0.7.

(36) J. Tinbergen, An Econometric Approach to Business Cycle Problems (Paris, 1937).

The author presents in this booklet a model of 22 equations to describe the functioning of the Netherlands economy. From the viewpoint of this collection, a number of equations relating to imports are of special interest.

One equation correlates the volume of imports of raw materials for investment goods with (1) the level of employment in the investment goods industry and (2) a linear trend.

Two competition equations indicate, for consumption goods and investment goods, respectively, the choice between importing raw materials or finished products as determined by the relative movements of import prices and of home prices of finished goods in the respective categories. These two equations, originally expressed as relationships between quantity ratios and price ratios, are reduced to a linear form by approximation.

A partial demand elasticity is estimated for imports of finished consumption goods and for imports of finished investment goods, with respect to their import prices. In each case, the elasticity is derived by considering the competition equation jointly with a demand equation, which expresses the quantity of total demand (for consumption goods and for investment goods, respectively) as a function of income.54 For each category of good, the quantity of total demand in the demand equation is assumed to equal the quantity of imported finished products plus the quantity of imported raw materials raised by a given factor. Since the competition equation and the demand equation are two independent linear equations explaining the levels of imports of finished products and of raw materials, one can obtain solutions for the imports of finished products and of raw materials in terms of the various explanatory variables, including import prices. The partial import demand elasticities are estimated from these linear solutions for the average of the entire period 1923-35.

The variables are measured as deviations from their respective means. No test of significance is given.

(37) J. Tinbergen, “Some Measurements of Elasticities of Substitution,” The Review of Economic Statistics, Vol. XXVIII (August 1946), pp. 109-16.

This article described some statistical measurements of substitution elasticities in international trade carried out in the Netherlands Central Statistical Office.

The estimated substitution elasticities are divided into three groups: (1) substitution between two countries’ exports of a particular commodity; (2) substitution between a country’s total exports and all other countries’ exports in the world market; and (3) substitution between a country’s imports and domestic production of a particular commodity.

In the first group, the exports of wheat and cotton from various major exporting countries are considered. For wheat, the substitution elasticities are obtained from simple regressions of quantity ratios on the corresponding price ratios. For cotton, however, the quantity ratio is found to lag behind the price ratio; the substitution elasticities are therefore obtained from multiple regressions of the quantity ratio on the ratio of current prices and on the price ratio for the previous year.

In the second group, the quantity ratios used are the ratios of each country’s quantum of exports to the quantum of world trade. The elasticities calculated from regressions of these quantity ratios on the corresponding price ratios are called quota elasticities.55 The exports of eight countries—Argentina, Australia, Germany, Hungary, Japan, the Union of South Africa, the United Kingdom, and the United States—relative to total world trade are thus studied in various regression equations.

In the third group, the cases studied are U.K. imports of potatoes and Swedish imports of cast iron, metal plates, and steel-plate and tin-plate goods.

It is found, in general, that the elasticities estimated for the well-organized staple markets are quite high, and those for exports as a whole, and still more for imports, are low.

In order to give some idea of the range of error, the author presents, in certain cases, elasticities calculated by using both the first and second regressions, i.e., considering alternately the quantity ratio and the price ratio as the dependent variable in the regression.

(38) J. Tinbergen, “Some Remarks on the Problem of Dollar Scarcity,” Econometric Society, Proceedings of the International Statistical Conferences, Vol. V (September 6-18,1947, Washington, D.C.), pp. 73-97.

The purpose of this paper is to examine the effectiveness of price adjustments as an instrument in solving long-term dollar scarcity problems. For this purpose, a static two-country (United States and the rest of the world) model is constructed, with two import demand equations, two export supply equations, and a balance of payments equation. Its solution shows that much depends upon the magnitudes of the two elasticities of demand for imports; therefore, a statistical measurement of these elasticities is undertaken.

For total U.S. imports, the author correlates the volume of imports with (1) real national income, (2) the difference between an index of import prices and a domestic wholesale price index reweighted according to the composition of imports, and (3) a linear trend. The data used are for 1924-41. The signs of the resulting regression coefficients are apparently correct, but the author states that a bunch map shows that the results are not reliable.

A more disaggregated approach is then tried by estimating the demand elasticities for U.S. imports of individual commodities. For imports directly competing with U.S. products, such as cheese, sugar, and woolen and cotton manufactures, he correlates the ratio of imports to domestic products with the relative prices and real national income. The resultant substitution elasticities are fairly high. For imports, such as bulbs, rubber, and tin, which do not compete with domestic products, he quotes the demand elasticities estimated by several others,56 which are seen to be much lower. These individual elasticities are then weighted by the values of imports in 1929 and combined into an average elasticity (=—0.9).

For the demand elasticity of the rest of the world for U.S. exports, he correlates the volume of U.S. exports with (1) real income of the rest of the world, (2) the difference between the U.S. export price index and the export price index of the rest of the world, and (3) an index of trade barriers assumed to be zero from 1924 to 1930, increasing regularly from 1930 to 1934, and remaining constant after 1934. The value obtained for the demand elasticity is then tested by estimates for some individual commodities, viz., wheat, cotton, and motorcars. From these results, he guesses the elasticity of demand for U.S. exports should be around—2.

The over-all conclusion of the article is very vague, as the complete solution of the assumed model depends on a number of quantities other than the demand elasticities. The author’s impression is that “a solution of the problem of dollar scarcity along the lines of price adaptation is not hopeless beforehand.”

(39) J. Tinbergen, “Quelques Estimations de l’Influence des Contingentements 1933-1938 sur l’Emploi aux Pays Bas,” Revue de l’Institut International de Statistique, Vol. 15 (1947), pp. 8-23.

This article presents an attempt to estimate the influence of the import quota system in the Netherlands in 1933-38 on domestic employment. A system of 15 equations is used to describe the structure of the economy. Four of the structural equations relate to the explanation of imports in four groups: imports of raw materials and of finished products for investment goods and for consumption goods.

The four import equations are of the same pattern, taking the value of imports in a particular group as a linear function of the volume of domestic production, import prices, and domestic prices, of either investment or consumption goods. The method used for empirical derivation of these equations, however, is not fully explained in the article.

The author states that the values computed from these equations fit the actual values of imports quite closely in the period 1923-33 and that, after the installation of the import quota system in 1933, the actual value of imports fell abruptly relative to what would have been expected from the 1923-33 relationships. The differences between the actual values of imports after 1933 and what would have been expected from the 1923-33 relationships are attributed to the import quota system.

(40) J. Tinbergen, “The Fluctuations of the Netherlands’ Imports, 1923-38,” Statistische en Econometrische Onderzoekingen, Jaargang 3 (June 1948), pp. 52-60 (in Dutch with a summary in English).

This article describes an attempt to explain the fluctuations in the volume of Netherlands imports in the period 1923-38 by the method of regression analysis. Imports of raw materials and imports of finished goods are considered separately.

Altogether, some 15 regression equations have been calculated, using the following explanatory variables: (1) real national product, represented by either real national income or by an industrial production index; (2) an index of price differences between domestically produced products and imported finished products; (3) in some cases, the volume of exports; (4) an index of the intensity of the Netherlands import quota system, indicated by the 1929 import value of all goods under the quota system in the year concerned; and (5) in some cases, a linear trend.

Most of the 15 regression equations are not considered to be satisfactory, as some of the explanatory variables used in the equations are shown by bunch maps to be strongly intercorrelated. Out of the 15, three are designated by the author to be the best ones.

(41) J. Tinbergen, “Long-Term Foreign Trade Elasticities,” Metroeconomica, Vol. I (December 1949), pp. 174-85.

The author suggests in this article that the low elasticities of demand in international trade frequently found in statistical estimations are but short-term elasticities, and that long-term demand elasticities may be expected to be considerably higher. He proposes several methods to estimate long-term elasticities.

One of the proposed methods is to use a multiple regression equation involving a distributed lag of the price effects. The empirical data used relate to the U.S. demand for imports of pig iron from the United Kingdom in the period 1879-1914. The quantity of U.S. pig iron imports from the United Kingdom expressed as a ratio to total U.S. consumption of pig iron is correlated with (1) a series of current and lagged (up to ten years) ratios of import price to the domestic price of pig iron and (2) an index representing cyclical factors, represented by pig iron production in the United States expressed as a ratio to its trend value. All the variables are expressed in logarithms. The estimated long-term elasticity is obtained by summing all the regression coefficients for the current and lagged price ratios. (No measure of significance is given.) It is seen to be only moderately higher than a short-term elasticity estimated from a similar regression equation but without the lagged price ratios.

Another method suggested is to use cross-section figures, i.e., to compare results for different importing countries observed at the same time instead of for the same country at different times. The empirical cases considered are the imports of pig iron by a number of countries (unspecified) from given pairs of exporting countries (viz., Germany vs. United Kingdom and United States vs. United Kingdom) during the same years (1913, 1929, and 1932). In each case, the relative quantities of the imports of a country from the two sources are correlated with the corresponding relative prices. In order to eliminate the possible political ties existing between the supplying and buying countries, another set of regressions is computed for the same cases, but excluding Australia, Canada, and the Union of South Africa from the group of importing countries. Together with these estimates, the corresponding elasticities estimated from the diagonal regressions, i.e., regressions considering the relative prices as the dependent variable, are presented in order to give an idea about the ranges of error.

A number of other methods of estimation are suggested, such as comparing the percentage shares of various markets with estimated transport costs.

(42) Herbert K. Zassenhaus, “Direct Effects of a United States Recession on Imports: Expectations and Events,” The Review of Economics and Statistics, Vol. XXXVII (August 1955), pp. 231-55.

This article seeks to obtain from the experience of the past a pattern for the effects of a U.S. recession on U.S. imports. It is found that, when allowances are made for the major known changes, the sensitivity of U.S. imports to recessions—both total imports and major components—has remained quite stable over the last 30 years. The author asserts that the effects of a U.S. recession on its imports should be reasonably predictable.

This pattern is based on the experience of the five recessions prior to 1953—those of 1923-24, 1926-27, 1929-32, 1937-38, and 1948-49. The results are then compared with events during the recession of 1953-54.

The index of U.S. manufacturing production is selected as the reference series for the recessions. Linear regressions are found between the percentage changes in manufacturing production during the five recessions and the corresponding percentage changes in both the volume and the value of imports (total imports as well as by broad commodity groups). Annual data are used for the comparison.57

The recession pattern of U.S. imports, however, is characterized mainly by two sets of ratios. The first set refers to the ratios, for total imports and for imports by individual commodity groups, of the average percentage change in imports for the five recessions before 1953 to the corresponding average percentage change in manufacturing production. The author calls these ratios, for convenience, a sort of production elasticity of imports. The second set consists of the ratios, for imports by individual commodity groups and by areas of origin, of the average percentage change in each import component to the average percentage change in total imports. These ratios are used to indicate the mean relative sensitivity of each import component to total imports.

Before computing the same ratios for the 1953-54 recession, the author takes into consideration certain developments which could have affected the applicability of the import pattern, established on the basis of the five previous recessions, to the conditions in the 1953-54 recession. Some of these developments are structural changes, such as increased U.S. demands for coffee and cocoa, newsprint, and petroleum products; others pertain to special conditions during the 1953-54 recession, such as the steep rise in the import prices of coffee and cocoa. Based on these considerations, some revisions are made of the mean relative sensitivity ratios for the individual areas of import origins. The corresponding ratios computed for the 1953-54 recession are seen to agree with these revised ratios quite closely. In computing the production elasticities of imports for the individual commodity groups in the 1953-54 recession, the author excludes the coffee and cocoa imports. The resultant elasticities for the 1953-54 recession differ considerably from the average elasticities obtained from the previous five recessions. The author states, however, that such differences are to be expected, in view of the relatively small recession in 1953-54 and some small price rise in the imports of finished manufactures.

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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.

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