I am indebted to the Social Science and Humanities Research Council of Canada for the research grant that permitted me to undertake the collection and analysis of the data set used in this study, to M. C. Urquhart who first drew my attention to this data set, to Thomas Stoker and Dale Jorgenson for technical advice and encouragement, to the participants at the 1985 World Cliometric Society Conference, to Gavin Wright and the participants at the 1985 annual meeting of the Economic History Association, and to the Editor and her assistant for helping me to clarify the presentation.

¹ See, for example, Jorgenson, Dale W., Lau, Lawrence J., and Stoker, Thomas, “The Transcendental Logarithmic Model of Aggregate Consumer Behavior,” in Basman, Robert L. and Rhodes, George F. Jr, eds., Advances in Econometrics (Greenwich, 1982), vol. 1, pp. 97–238. A significant feature of their study is the invariance of their empirical results to using either cross section data alone or pooled time series and cross section data. The present study will exploit this result.Google Scholar

² The literature that explores the relationship between these shares and growth is vast stretching back to Ernst Engel. For recent statistical evidence see Kuznets, Simon, Modern Economic Growth, Rate, Structure and Spread (New Haven, 1966), pp. 262–82;Google Scholar and Chenery, Hollis and Syrquin, M., Patterns of Development 1950–1970 (London, 1975), pp. 34–35.Google Scholar

³ The older view is represented by Easterbrook, W. T. and Aitken, H.G.J., Canadian Economic History (Toronto, 1958), pp. 395–405;Google Scholar and Rostow, W. W., The World Economy: History and Prospect (Austin, 1978),CrossRefGoogle Scholar chap. 36. The revisionists include Bertram, Gordon, “Economic Growth and Canadian Industry, 1870–1915: The Staple Model and the Take-Off Hypothesis,” Canadian Journal of Economics and Political Science, 29 (05 1963), pp. 162–84;CrossRefGoogle ScholarMcDougall, D. M., “Canadian Manufactured Commodity Output 1870–1915,” Canadian Journal of Economics, 4 (02 1971), pp. 21–36;CrossRefGoogle Scholar and Pomfret, Richard, “Capital Formation in Canada 1870–1900,” Explorations in Economic History, 18 (01 1981), pp. 84–96.CrossRefGoogle Scholar

⁴ See Urquhart, M. C., “New Estimates of Gross National Product, 1870–1926: Some Implications for Canadian Development,” in Engerman, Stanley L. and Gailman, Robert E., eds., Long-Term Factors in American Economic Growth, NBER Studies in Income and Wealth, vol. 51 (Chicago, forthcoming).Google Scholar

⁵ See Firestone, O. J., Canada's Economic Development 1867–1953 (London, 1958), chap. 4.Google Scholar

⁶ The evidence produced by the Royal Commission for Ontario and Quebec has been summarized and discussed by Kealey, Gregory, Canada Investigates Industrialism (Toronto, 1973);Google Scholar and Harvey, F., Revolution Industrielle et les Travailleurs (Montreal, 1978).Google Scholar For the work done by the Department of Labour, see Canada, Department of Labour, Report of the Board of Inquiry into the Cost of Living in Canada (Ottawa, 1915), 2 vols.Google Scholar

⁷ A short summary of these cost of living studies is provided by Davidson, John, “Statistics of Expenditure and Consumption in Canada,” Transactions of the Nova Scotia Institute of Science, 10 (1898–1899), pp. 1–32.Google Scholar

⁸ See Woodbury, Robert Morse, “Economic Consumption Scales and their Uses,” Journal of the American Statistical Association, 39 (12. 1944), pp. 455–68.CrossRefGoogle Scholar

⁹ The evidence consists of prices drawn from farmers' and wholesale market reports for 18 food items at 19 cities and towns across southern Ontario for the years 1864, 1873, and 1880.

¹⁰ For a sample of these studies see Houthakker, H. S., “An International Comparison of Household Expenditure Patterns, Commemorating the Centenary of Engel's Law,” Econometrica, 25 (10. 1957), pp. 532–51;CrossRefGoogle ScholarLeser, C. E. V., “Forms of Engel Functions,” Econometrica, 31 (10. 1963), pp. 694–703;CrossRefGoogle ScholarLewis, H. Gregg and Douglas, Paul, “Studies in Consumer Expenditures (1901,1918–1919, 1922–1924),” Journal of Business, 17 (Supplement 1947)Google Scholar and Williamson, Jeffrey G., “Consumer Behavior in the Nineteenth Century: Carroll D. Wright's Massachusetts Workers in 1875,” Explorations in Economic History, second series, 4 (Winter 1967), pp. 98–135.Google Scholar

¹¹ For example, the linear hypothesis implies constant marginal expenditure and an elasticity that rises or falls with income toward unity in the limit. The semi-log form makes expenditure and share elasticities inversely proportional to the level of consumption. The double-log form leads to constant elasticities and variable marginal expenditure.

¹² The satisfaction of this Engel aggregation condition allows the coefficients of the nth equation to be derived from the estimated parameters of the rest of the system. Barten, A. P., “Maximum Likelihood Estimation of a Complete System of Demand Equations,” European Economic Review, 1 (Fall 1969), pp. 7–73 has shown, however, that OLS applied to each equation will provide consistent estimators, and I follow this procedure.CrossRefGoogle Scholar

¹³ Within a translog functional form, this has been achieved by Jorgenson, et al., “The Transcendental Logarithmic Model of Aggregate Consumer Behavior.”

¹⁴ Because equation I omits a price term, the integrability restrictions that have to be imposed on the full demand model to incorporate exact aggregation are bypassed. For the effect on expenditure elasticity of including a price term and imposing these restrictions see Stoker, Thomas M., “Aggregation over Individuals and Demand Analysis: A Theoretical and Applied Study” (Ph.D. diss., Harvard University, 1979), chap. 3, especially pp. 60–63, 69.Google Scholar

¹⁵ The per capita version of many specifications performed best, perhaps as a solution to multicollinearity problems. Given that the data here are grouped, heteroskedasticity is treated by assuming the variance within each of the cross-section groups is proportional to the number of households represented by the group average as in Houthakker, “An International Comparison.”

¹⁶ For the Massachusetts workers, see Williamson, , “Consumer Behavior in the Nineteenth Century,” pp. 116–17,Google Scholar and for the later Canadian sample results, see Houthakker, , “An International Comparison,” p. 341.Google Scholar

¹⁷ Given grouped data in the form of averages, it is not possible to convert all attributes into dummy variables, resulting in a somewhat more restrictive form incorporating these attributes than would be implied by the assumption of exact aggregation alone. See Jorgenson, et al. , “Transcendental Logarithmic Model,” p. 208.Google Scholar

¹⁸ A range of evidence on fragmentary expenditure patterns covering workers in Ontario, Quebec, Nova Scotia, and New Brunswick from the 1860s down to 1900 tends to support the view that the attribute effects estimated from the Ontario worker sample represent a wider Canadian experience. A summary table of this evidence is available from the author on request.

¹⁹ See Jorgenson et al., “The Transcendental Logarithmic Model,” section 5.

²⁰ The rationale for this is described in Stoker, , “Aggregation over Individuals and Demand Analysis,” p. 136.Google Scholar

²¹ The reasonableness of this result supplies some warrant for the theory used but also reflects the quality of the data that can be made to reveal this much structure. The lack of success with other categories of consumption is partially caused by the greater amount of unknown sources of measurement error in these data. The food share data does advance the historical analysis to follow.

²² Using Urquhart, “New Estimates of Gross National Product,” gross national product at factor cost is reduced by gross fixed capital formation, government spending and net exports to yield personal consumption spending. Family formation data is taken from Firestone, O. J., Industry and Education (Ottawa, 1969).Google Scholar According to MacLean, M. C., “The Canadian Family,” Congres International de la Population, (Paris, 1937), vol. 4, pp. 66–82, family and household formation have been very similar over long periods of time.Google Scholar

²³ See Firestone, Canada's Economic Development, chap. 4.

²⁴ See Urquhart, “New Estimates of Gross National Product.”

²⁵ Changes in the relative price of nontraded goods are noted in Viner, Jacob, Canada's Balance of International Indebtedness, 1900–1913 (Toronto, 1975), chap. 10. In preliminary work revising Viner's indexes I show that nontraded goods excluded most food items and their prices rose relative to traded goods' prices after 1900.Google Scholar