¹ The paper is based on the author's unpublished PhD dissertation, “An Econometric Model of the Current Account of the Canadian Balance of Payments” (Department of Economics, University of Michigan, 1965).Google Scholar The author wishes to thank Professor Anthony Koo of the University of Michigan for his advice during this study and the University of Michigan for use of their computer facilities.

² The region of Western Europe represents the European OECD countries.

³ Rhomberg, Rudolf and Boissoneault, Lorette, “Effects of Income and Price Changes on the U.S. Balance of Payments,” I.M.F. Staff Papers, XI, 1 (03 1964), 59–124 CrossRefGoogle Scholar; and Rhomberg, Rudolf and Fortucci, Paola, “Projection of U.S. Current Account Balance for 1964 from a World Trade Model,” I.M.F. Staff Papers, XI, 3 (11 1964), 414–30.CrossRefGoogle Scholar

⁴ With the price of domestic substitutes in the numerator, and the price of imports in the denominator, the expected sign of the relative price variable is positive.

⁵ It is recognized that the GNP deflator represents the prices of a larger basket of goods and services than those which might be considered as domestic substitutes for imported goods, and that the export price index of a region with respect to all other regions in the world may not completely reflect the price of exports going to a particular region of the world. The use of these aggregative price indices was taken to be appropriate, however, given the extent of aggregation in the model.

⁶ The variable, r_j , is included in the denominator of the price variable in the import equations of Canada and Western Europe. As constructed, r_j is an exchange rate index that increases as the jth region's currency depreciates relative to the US dollar.

⁷ The signs in this identity are reversed to give the imports of the rest of the world a positive sign.

⁸ The US current account residual, B ₂, includes the net service transactions of the United States with the rest of the world. Specifically, B ₂ is equal to the net foreign balance contained in the US national accounts less the sum of the US trade balance, the US service balance with Canada, and the US service balance with Western Europe, the latter being considered exogenous and denoted by S ₃₂ ^*. The residual B ₃ for Western Europe is similarly constructed and includes Western Europe's net service transactions with the rest of the world. Separate equations were not used to treat US service transactions with Western Europe and the rest of the world because they would have expanded the model considerably. Separate equations were not used for Western Europe's service transactions with the rest of the world because data for such transactions were not available. In processing the model, variable M ₁₄ ^w was also considered exogenous in equation (3).

⁹ The assumption underlying this identity is that all of the countries in the rest of the world, mainly underdeveloped countries, will use their foreign exchange receipts to purchase imports. To the extent that some of these countries elect to accumulate reserves for use as a buffer stock, the predictive value of the identity with respect to imports may not be as high as desired.

¹⁰ The volume of exports of the rest of the world was used as a proxy for income movements in this region. Alternatively, the volume of exports may be thought of as a measure of the rest of the world's ability to pay for imported services.

¹¹ In the GNP identities for Canada and Western Europe, the foreign sectors are multiplied by the exchange rate index r_j (1954 = 1) because the data used for the foreign sector components were valued in terms of billions of US dollars at current prices and current exchange rates, while the data used for the domestic components were valued in terms of billions of US dollars at current prices and 1954 exchange rates. Adjusting the foreign sectors by r_j expresses all of the components of the identities in terms of 1954 exchange rates.

¹² Consumption expenditures are subtracted from GNP in these functions to overcome estimation bias resulting from two-way causation. While this procedure eliminates the direct feedback effect of an exogenous shift of consumption on GNP, it does not eliminate the indirect effect of an exogenous shift of consumption on GNP by way of the inventory equations.

¹³ For reasons of computational convenience, the data used in fitting the equations were converted, when necessary, into billions of US dollars. See also n. 11. A tabulation and source list of the data, while not contained in this paper, will be furnished by the author upon request.

¹⁴ The appropriate estimating technique for use in a simultaneous equation system is still a matter of dispute, particularly for a forecasting model employing a small number of observations. While it is recognized that the OLS method yields biased estimators, some observers believe that this undesirable property may be compensated to some extent by the OLS coefficients having a smaller variance around their (biased) expected values than the coefficients from some of the principal alternative techniques. For a discussion of the relative merits of alternative estimating techniques for a simultaneous equation system see Johnson, J., Econometric Methods (New York, 1963), chap. 10.Google Scholar

¹⁵ In equation (3), the exogenous variable B ₁ ^* denotes that a slight adjustment was made in the value of B ₁. Specifically, the value of B ₁ ^* was obtained by adding net inheritances and immigrants' funds to the value of B ₁ so that B ₁ ^* became identical to the value of official Canadian contributions. The adjustment was made because the model “explains” all of the items in the Canadian current account except mutual aid to NATO countries and official contributions, while the net foreign sector in Canada's national accounts excludes net inheritances and immigrants' funds and mutual aid to NATO countries.

¹⁶ Data for M ₁₂ and M ₁₃ were taken from Canadian sources, and data for M ₂₃ were taken from US sources. P ₃ was derived by dividing Western Europe's GNP in current prices and 1954 exchange rates by Western Europe's GNP in 1954 prices and 1954 exchange rates. The variable r ₃ was derived by dividing Western Europe's GNP in current prices and 1954 exchange rates by Western Europe's GNP in current prices and current exchange rates. The variable r ₁ was obtained from the average noon spot rates for the year expressed in Canadian cents per US dollar. P _x1 was derived by dividing the published Canadian export price index by the exchange rate index r ₁. The latter adjustment was made because the published index is based on the value of Canadian exports expressed largely in terms of Canadian dollars.

¹⁷ The dummy variable was given the value of 1 for the years 1948 and 1949, and 0.5 for the year 1950. An identical technique to allow for Canadian tariffs during these years was employed by Brown, T. M., “A Forecast Determination of National Product, Employment, and Price Level in Canada from an Econometric Model,” Models of Income Determination, NBER Studies in Income Determination 28 (Princeton 1964), 62.Google Scholar

¹⁸ The rationale and method of computing these extraordinary imports appears in Rhomberg, , Staff Papers (03 1964), 87, 93–4, and 122.Google Scholar

¹⁹ In fitting equation (4.1), the year 1952 was omitted because of the abnormal effects that the Korean war had on Canadian exports to the rest of the world in that year.

²⁰ Due to the non-availability of data for variables I ₃₁ and I ₁₃, the United Kingdom's investment position in Canada was used as a proxy variable for I ₃₁ in equation (7.2), and Canada's investment position in the United Kingdom was used as a proxy for I ₁₃ in equation (7.5). The sampling period for equation (7.5) was restricted to 1951–62 because of the lack of continuous data for the proxy variable I ₁₃ prior to 1951.

²¹ In equation (7.5) a dummy variable was added to reflect the substantial drop in Western Europe's payments to Canada in 1956–57 due to a temporary suspension by the United Kingdom in its servicing of an official Canadian loan. In equation (7.4), a dummy variable was used to reflect the sharp increase in US payments to Canada in 1951–52 for which no satisfactory explanation was found.

²² In this study, other service payments of Canada included inheritances and emigrants' funds, and “all other current payments,” which in turn included other government transactions, institutional remittances, miscellaneous payments, and business services. Excluded were payments for official contributions and mutual aid to NATO countries. Other service receipts of Canada included inheritances and immigrants' funds, gold production available for export, “and all other current receipts,” which in turn comprised the same type of items as those listed above in “all other current payments.”

²³ Staff Papers (03 1964), 90–105.Google Scholar

²⁴ The data for the lagged stock variable was obtained by summing the changes in inventory investment beginning in the year 1948. The effect of aggregate stock on inventory investment prior to that year is contained, therefore, in the constant term.

²⁵ The computations for the solution of the equation system were made in the early months of 1965 with the aid of a complete matrix inversion computer program. The values of the exogenous variables used in the model for the years 1962–65 are listed in the Appendix.

²⁶ The non-linear endogenous variable combinations which appeared as products, xy, were linearly approximated by xy ₋₁ + yx ₋₁ − x ₋₁ y ₋₁, and the variables which appeared as ratios, x/y, were linearly approximated by x ₋₁/y ₋₁ + x/y ₋₁ − x ₋₁ y/(y ₋₁)². The method of linearly approximating with respect to the value in the preceding period was considered more accurate for use in a forecasting model than linearly approximating around the means of the variables.

²⁷ The “actual” data used in computing the 1962–65 results, and appearing in Tables I, II, and III, were obtained from the latest sources available to the author early in 1965. Since that time, minor revisions have been made in the published data so that they may not agree precisely with the values listed in the tables.

²⁸ Canadian service payments probably were overestimated because no allowance was made in the model for the temporary restrictions placed on Canadian tourist purchases during the 1962 Canadian exchange crisis. Canadian exports may have been underestimated due to the failure of the model to capture the full effects of the mid-1962 devaluation of the Canadian dollar. It is recalled that the coefficients of the relative price ratios were statistically insignificant in equations (2.4) and (2.7) for the United States' and Western Europe's imports from Canada.

²⁹ This method yields the same results as the one wherein the equations in a model simply are differenced after they have been fitted to levels. See Suits, Daniel, The Theory and Application of Econometric Models (Center for Economic Research, Athens, 1963), 44.Google Scholar

³⁰ It was assumed that the value of extraordinary Canadian grain exports to the rest of the world would amount to (US) $.550 billion in 1965, compared to (US) $.744 billion in 1964. This assumption might prove to be somewhat on the low side since it was made prior to the August 1965 announcement that the USSR would purchase about (US) $.417 billion of Canadian wheat in 1965. However, a major proportion of these USSR purchases were implicitly allowed for in the 1965 assumption because in recent years the USSR has been the principal purchaser of Canadian grain exports going to the rest of the world.

³¹ Rhomberg, , Staff Papers (11 1964), 429.Google Scholar

³² The estimate for government expenditures and fixed investment in Canada was obtained from: Canada, House of Commons Debates, Official Report: The Budget, 26th Parliament, 3rd Session (Ottawa, 1965), 459 Google Scholar; and Canada, Department of Trade and Commerce, Private and Public Investment in Canada, Outlook 1965 (Ottawa, 1965), 20.Google Scholar The estimate for United States fixed investment was obtained from US Congress, Joint Economic Committee, Economic Indicators, 89th Congress, 1st Session, 03 1965, 8–9.Google Scholar The estimate for US government expenditures was that used by the Research Seminar in Quantitative Economics at the University of Michigan in its 1965 forecast for the US economy.