¹ Canadian Non-Farm Family Expenditures, 1947–48, DBS Reference Paper no. 42 (Ottawa, 06 1953)Google Scholar; City Family Expenditure, 1953, DBS Reference Paper no. 64 (Ottawa, 1956)Google Scholar; City Family Expenditure, 1955, DBS 62–510 (Ottawa, 1957)Google Scholar; City Family Expenditure, 1957, DBS 62–517 (Ottawa, 1961)Google Scholar; Urban Family Expenditure, 1959, DBS 62–521, (Ottawa, 03 1963).Google Scholar These publications are hereafter referred to by the year of the survey. The expenditure survey for 1962 is presently being prepared for publication.

² H. S. Houthakker used the 1947–48 data in his article, “An International Comparison of Household Expenditure Patterns, Commemorating the Centenary of Engel's Law,” Econometrica, XXVIII (10 1957), 532–51.Google Scholar W. M. MacLeod has fitted a variety of equations to the 1947–48 data in “A Note on the 1947–48 Family Budget Survey,” this Journal, XXVII (05 1961), 243–7.Google Scholar The 1959 data were used by R. D. Millican, “A Factor Analysis of Canadian Urban Family Expenditures,” ibid., XXX (May 1964), 241–5.

³ Friedman, Milton, A Theory of the Consumption Function (Princeton, 1957), 26–31.Google Scholar

⁴ “This method, which relies on the respondent's memory or on existing household accounts, is the one which has been generally preferred on this continent. Surveys in the United Kingdom and other European countries have favoured the account-book method in which families keep records of their purchases for a specified period. Each method has its own advantages and disadvantages. Although the interview method makes a considerable demand on the respondent's co-operation and memory as well as on the enumerator's patience and skill, respondents who would refuse to keep records or fail to complete them can sometimes be persuaded to give information to the enumerator by interview. The results may be affected by failure to recall or estimate expenditures accurately, but these inaccuracies are considered to be offsetting to a large extent, whereas in the account-book type of survey, memory failure is apt to be in one direction, i.e. forgetting to record a purchase entirely. The keeping of records also, in itself, may exert a conditioning effect on the data, not omy in limiting the survey to certain types of respondents, but in modifying the purchasing patterns of respondents for the period of record keeping. Canadian experience in the account-book method has been limited to surveys of food expenditure where a diary record of food expenditure in detail is kept for a two-week period in each month. A comparison of food expenditure averages obtained by the two methods is of interest. In 1957, the annual average of total family food expenditure estimated from the weekly surveys was $1,181 per family as compared with $1,178 per family obtained by annual recall.” 1957, 7–8.

⁵ These response rates are much lower than for the comprehensive United States survey for 1950, there “80 per cent of the eligible consumer units furnished complete and usable reports of income, expenditures, and savings.” Lamale, Helen Humes, Methodology of the Survey of Consumer Expenditures in 1950 (Philadelphia, 1959), 94.Google Scholar The drawing of consumer units from an alternate sample in cases of vacancy, non-contact, or complete refusal accounted for 17.1 per cent of the usable schedules.

⁶ 1947-48, 7. The size and characteristics of the spending units obtained for the survey are as they existed for the survey year and not at the time of interview.

⁷ 1959, 6.

⁸ This procedure makes no allowance for the market value of the owner's equity. Margaret G. Reid studied housing expenditure-income ratios and related characteristics by tenure for the BLS Consumption Survey of 1950 and concluded “(a) that housing expenditure greatly understates the consumption of owners compared to that of tenants because housing expenditure omits the housing represented by the equity of owners; (b) that the degree of the understatement varies among owners; (c) that the understatement tends to increase with lapse of time since purchase, and (d) that it is likely to be greatest among owners with an aged head.” Housing and Income (Chicago, 1962), 52.Google Scholar

⁹ 1957, 8.

¹⁰ Ibid.

¹¹ 1953, 38–39. See also Friend, Irwin and Schor, Stanley, “Who Saves,” Review of Economics and Statistics, 05 1959 Google Scholar; Modigliani, Franco and Ando, Albert, “The ‘Permanent Income’ and the ‘Life Cycle’ Hypothesis of Saving Behaviour: Comparison and Tests,” in Friend, and Jones, , eds., Consumption and Savings, II (Philadelphia, 1960), 49–172.Google Scholar

¹² For some such comparisons dealing with the BLS survey data for 1950, see Lamale, Methodology of the Survey of Consumer Expenditures in 1950.

¹³ The concepts and methods used in these two DBS surveys are discussed, and the income distributions obtained from the surveys for 1959 are compared, in “Discussion of Concepts and Methods in DBS Surveys of Family Expenditures and Incomes” (mimeographed) bv G. Oja and J. R. Podoluk.

¹⁴ MacLeod, “Note on the 1947–48 Family Budget Survey,” used income before tax as his independent variable. Since the income tax structure in Canada is progressive, the effect of MacLeod's choice of independent variable is to impart a downward bias to his estimates of income elasticity.

¹⁵ It was assumed that single individuals, at a given income, would pay more than a twoadult family, who would pay more than a medium-sized family, who in turn would pay more than a large-sized family. The average taxes shown as being paid by all family types in each income group were moved to lower or higher income groups or remained unchanged, for each of these family types in line with this reasoning, and then proportionately increased or decreased where necessary, to achieve consistency with published figures. The tax figures thus obtained satisfied two tests. When combined using the appropriate weights they closely reproduced the average tax paid in each income group for all family types, and the average tax paid by each family type over all income groups.

¹⁶ The seven income groups were: under $2,500; $2,500 to $3,499; $3,500 to $4,499; $4,500 to $5,499; $5,500 to $6,499; $6,500 to $7,999; $8,000 and over. The six family sizes were: one, single adults; two, families with one adult and one or more children, or two adults and no children; three, families with two adults and one child or three adults and no children; four, families with two adults and two children, or three adults and one child, or four adults and no children; five, families with two, three, four, or five adults, and three, two or more, one or more, and no children, respectively; six, families with two adults and four or more children, five adults with one or more children, or six adults with or with-out children.

¹⁷ Prais, S. J. and Houthakker, H. S., The Analysis of Family Budgets (Cambridge, 1955), 17.Google Scholar

¹⁸ “The most important of [the] noneconomic variables is probably family size, or more generally, family composition.” Houthakker, H. S., “An Economist's Approach to the Study of Spending” in Foote, Nelson N., ed., Household Decision-Making (New York, 1961), 136.Google Scholar Millican, “A Factor Analysis of Canadian Urban Family Expenditures,” concludes from his factor analysis of the 1959 expenditure survey that “at least three factors are present—income, age, and family size. The last one shows a split into three separate factors, indicating that it is not only the size of family which affects consumption, but also its composition—that is, young adults and children as compared with older families.” (245.)

¹⁹ For papers and discussions expressing discontent with cross-sectional predictors, see Foote, ed., Household Decision-Making.

²⁰ Crockett, Jean and Friend, Irwin, “A Complete Set of Consumer Demand Relationships,” in Friend, and Jones, , ed., Consumption and Savings, I, 1–92.Google Scholar

²¹ Our approach differs from that of both Houthakker and MacLeod. Houthakker used total expenditure rather than income as his independent variable, while MacLeod employed income before taxes. Further, MacLeod fitted income regression equations for each family size separately instead of using multiple regression to try and estimate the separate effects of the two variables on consumption.

²² The Analysis of Family Budgets, 88–90.

²³ “A Complete Set of Consumer Demand Relationships,” 28.

²⁴ Friedman, , A Theory of the Consumption Function, 207 Google Scholar, briefly sketched a method for dealing with the bias caused by the presence of transitory income when spending units are grouped by income. But the validity of this procedure depends on the postulates of the permanent income hypothesis, viz., the unit-elasticity of total consumption with respect to income, and the non-correlation of the transitory components of income and consumption as well as the further assumption that permanent income is taken to mean the same thing for different categories of consumption. Reid (Housing and Income) in her analysis of housing demand, used grouping devices such as census tracts to isolate groups whose average current income would reflect only normal income, and then obtained the regression of housing on income for these groups. This procedure cannot be followed here because of data limitations.

²⁵ Durbin, J., “Errors in Variables,” Revue de l'institut International de Statistique, XXII (1954), 23–32.CrossRefGoogle Scholar

²⁶ Liviatan, Nissan, “Errors in Variables and Engel Curves Analysis,” Econometrica, XXIX (07 1961), 336–62.CrossRefGoogle Scholar

²⁷ See Durbin, , “Errors in Variables,” 24 Google Scholar, for an expression of the probability limit of E(a).

²⁸ “A Theory of the Consumption Function,” 26–30.

²⁹ Durbin, , “Errors in Variables,” 24.Google Scholar

³⁰ It is extended to multiple regression in Durbin, Ibid. Durbin abo provides formulas for the variance of the difference between the least squares and instrumental variables estimates. They depend in part on the correlation between the independent and instrumental variables, but because of our inability to estimate this correlation from the grouped data available for this study they were not calculated.

³¹ Liviatan, , “Errors in Variables and Engel Curve Analysis,” 359.Google Scholar

³² Sargan, J. D., “The Estimation of Economic Relationships Using Instrumental Variables,” Econometrica, XXVI (07 1958), 393–415.CrossRefGoogle Scholar

³³ Prais, S. J. and Aitchison, J., “The Grouping of Observations in Regression Analysis,” Revue de l'Institut International de Statistique, XXII (1954), 1–22.CrossRefGoogle Scholar

³⁴ Allen, R. G. D. and Bowley, A. L., Family Expenditure (London, 1935).Google Scholar

³⁵ Tests of significance for the differences between the estimates were not carried out because of the inability to obtain estimates of the variances of the difference between the least squares and instrumental variable estimates (see above n. 30). In the light of our discussion of the reliability of the data in section I above, such tests would probably be unnecessary refinements.

³⁶ Housing and Income, 47.

³⁷ The results should be interpreted with caution because family type also changes with size and the estimates of the family size parameters may be aifected by the influence of the family type changes.

³⁸ This stability of the estimates of the parameters over time can be taken as an indication of the relevance of the economic theory of consumer behaviour. “… in the present state of the subject the most immediate test of the relevance of pure theory is the empirical constancy or stability of the parameters that it introduces. Because the economic theory of consumption puts such great stress on prices and incomes as determining factors, the requirement of constancy applies in particular to price and income elasticities, parameters whose dimensionless nature makes them particularly suitable for purposes of comparison. Even though the theory might be logically valid without such constancy, it clearly can have no predictive or explanatory value unless the parameters possess some degree of stability over time or between persons and communities.” Houthhakker, , in Household Decision-Making, 133.Google Scholar

³⁹ For a brief review see Ferber, R., “Research on Household Behavior,” American Economic Review, LII (03 1962), 19–63.Google Scholar

⁴⁰ See Modigliani and Ando, “The ‘Permanent Income’ and the ‘Life Cycle’ Hypothesis,” and references contained therein.

⁴¹ This way of setting out the hypotheses is contained in ibid., 75–6.

⁴² Friedman, , A Theory of the Consumption Function, 31–32.Google Scholar

⁴³ “The ‘Permanent Income’ and the ‘Life Cycle’ Hypothesis,” 96–111. Similar tests were used by Eisner, Robert, “The Permanent Income Hypothesis: Comment,” American Economic Review, XLVIII, 972–90Google Scholar, and by Reid, Housing and Income, to obtain estimates of the income elasticity of housing. For a critical review of these tests, see Crockett, Jean, “Biases in Estimating Income—Expenditure Regressions From Cross Section Data,” in Friend, and Jones, , eds., Consumption and Saving, 213–22.Google Scholar

⁴⁴ “The ‘Permanent Income’ and the ‘Life Cycle’ Hypothesis,” 104.

⁴⁵ Our results (and those of Modigliani and Ando) were obtained by using the logarithms of the arithmetic means for each cell, while the theory developed by Modigliani and Ando was in terms of the mean logarithms of consumption and income in each cell, or, equivalently, the logarithm of the geometric means of consumption and income. However, they proved that if it is assumed that the “within cell” variances of the logarithms of consumption and income are the same in all cells, then the propositions that they derived for the mean of the logarithms in each cell are also valid for the logarithms of the cell arithmetic means.

⁴⁶ One additional test of the permanent income hypothesis, suggested by Friedman, was carried out with the Canadian data. He stated: “Just as, on our hypothesis, the elasticity of consumption with respect to measured income can be viewed as a measure of P_y , the fraction of the variance of income contributed by the permanent component of income, so the elasticity of income with respect to measured consumption can be viewed as a measure of P_c , the fraction of variance of consumption contributed by the permanent component of consumption. Just as this interpretation requires that the measured income elasticity of consumption be less than unity and would be contradicted by observed elasticities greater than unity, so it requires that the measured consumption elasticity of income be less than unity and would be contradicted by observed elasticities greater than unity.” (A Theory of the Consumption Function, 201 ). Average consumption and average incomes for families classified according to expenditure were available for 1959, and the elasticity of income with respect to consumption was estimated. We obtained a value of the consumption elasticity of income of 0.962 (with a standard error of 0.022). This confirms Friedman's prediction that this value would be less than one.