1. These concerns are summarized in Hollis Chenery et al., Redistribution with Growth: An Approach to Policy (New York: Oxford University Press for the World Bank, 1974).

2. These criteria hold if the object is to identify groups all of which may be reached by government policy. If it is desired only to affect the poor, it does not matter if the nonpoor are quite heterogeneous and differ considerably in welfare.

3. See Rafael Prieto Durán, Estructura del gasto y distribución del ingreso familiar en cuatro ciudades colombianas, 1967–68 (Bogotá: Universidad de los Andes, 1971), and Adolfo Figueroa Arévalo, Estructura del consumo y distribución de ingresos en Lima metropolitana, 1968–69 (Lima: Pontificia Universidad Católica del Peru, 1974).

4. Philip Musgrove, Consumer Behavior in Latin America (Washington, D.C.: The Brookings Institution, 1978), chap. 2, “Household Incomes.”

5. Robert Ferber, “Income Distribution and Income Inequality in Selected Urban Areas of South America,” mimeographed. (Washington, D.C.: The Brookings Institution, August 1975). Published in translation as “Distribución de ingreso y desigualdad de ingresos en algunas areas urbanas,” Ensayos ECIEL 3 (August 1976).

6. See chaps. 3, 4, and 5 of Musgrove, Consumer Behavior; the studies by Prieto and Figueroa cited earlier; Howard J. Howe, “Estimation of the Linear and Quadratic Expenditure Systems: A Cross-Section Case for Colombia” (Ph.D. dissertation, University of Pennsylvania, 1974); and Howard J. Howe and Philip Musgrove “Analysis of ECIEL Household Budget Data for Bogotá, Caracas, Guayaquil, and Lima,” in Constantino Lluch, Alan Powell, and Ross Williams, Patterns in Household Demand and Saving (New York: Oxford University Press for the World Bank, 1977).

7. These are William R. Cline, “Income Distribution and Economic Development: A Survey, and Tests for Selected Latin American Cities”; Adolfo Figueroa and Richard Weisskoff, “Viewing Social Pyramids: Income Distribution in Latin America”; and Philip Musgrove, “Permanent Household Income and Consumption in Urban South America.” All three papers were presented to a conference sponsored by ECIEL and held under the auspices of the Institut für Iberoamerika Kunde, Hamburg, Germany, 1–3 October 1973. The paper by Weisskoff and Figueroa has been published as “Traversing the Social Pyramid,” LARR 11, no. 2 (1976):71–112, and that by Musgrove in the American Economic Review 69 (June 1979). All three have been published in Spanish in Ensayos ECIEL: Figueroa and Weisskoff in 1 (1974), Musgrove in 2 (1975), and Cline in 4 (1977).

8. These estimates are summarized and compared to family incomes, for Colombia, in Philip Musgrove, “Potential Earnings, Subsistence Needs, and Poverty in Urban Colombia,” Paper presented to the Conference on Distribution, Poverty, and Development, CEDE, Universidad de los Andes, Bogotá, Colombia, 2–4 June 1977. The most extensive estimates are from Howe, “Linear and Quadratic Expenditure Systems”; the others, and comparable estimates for Peru, are from Aquiles Arellano, “La pobreza en diez ciudades sudamericanas,” mimeographed (ECIEL, 1977).

9. This is the basis of the “Orshansky index” used to define poverty in the United States. See Molly Orshansky, “Counting the Poor: Another Look at the Poverty Profile,” Social Security Bulletin 28 (1965) and “How Poverty is Measured,” Monthly Labor Review 92 (1969).

10. Estimated by plotting log Z (food) against log N; the data are from Howe, “Linear and Quadratic Expenditure Systems,” table 7.20, p. 299.

11. This leads to systematic bias only when the variable(s) by which families are classified, in seeking to identify poverty, explicitly distinguish between adults and children, or among categories of expenditure.

12. “Permanent income” refers to the concept developed by Milton Friedman, A Theory of the Consumption Function (Princeton, N.J.: Princeton University Press for NBER, 1957). Permanent income is the household's concept of long-term income on which it bases its consumption decisions; differences between this and observed income in any interval are called “transitory.” Part of consumption is also transitory, but it is assumed to be unrelated to transitory income.

13. Musgrove, Consumer Behavior, table 2–18.

14. Another way to approach this question is to ask for which families it is most important to divide Z by N. Clearly the per capita adjustment has the greatest effect for values of N far from the modal value—that is, for very large or very small households. See Carmel Ullman Chiswick, “Income Distribution in Thailand: Measuring Poverty,” IBRD Research Project No. 671–36, Working Paper A–1, mimeographed (Washington, D.C.: World Bank, March 1976), pp. 10–13. For an extensive discussion of the superiority of per capita over total measures, see Simon Kuznets, “Demographic Aspects of the Size Distribution of Income: An Exploratory Essay,” Economic Development and Cultural Change 25 (Oct. 1976).

15. Since permanent consumption C_p is by definition an exact function of Y_p, there is no need to treat it separately.

16. Musgrove, “Permanent Household Income.” Y_p was estimated with three occupational variables and twelve combinations of age and education, and—in Colombia—dummy variables for city. More accuracy can be achieved by adding more explanatory variables, but the cost and difficulty rise very rapidly.

17. Some forms of income, notably capital other than imputed rent on owned dwellings, may be expected to be received mostly by rich households, but the absence of such income is too widespread to aid in separating the poor from those who are neither rich nor poor.

18. Ferber, “Income Distribution and Income Inequality,” tables 5.1–5.5.

19. Musgrove, Consumer Behavior, table 2–7. The figure for Colombia includes Barran-quilla and Cali together with Bogotá and Medellín.

20. Musgrove, Consumer Behavior, table 2–11. The share in Bogotá is unusually low. (Shares for Medellín and Lima are typical of those in other cities.)

21. Cline, “Income Distribution and Economic Development,” tables 2 and 4.

22. The individual mean percentage is the mean of the shares for individual households; it is not the ratio of mean income of one type to mean total income. Labor income shares are from Musgrove, Consumer Behavior, table 2–5, and imputed rent shares are from table 2–9.

23. Y_w refers to cash income plus the imputed value of domestic production. N_w refers only to members with paid employment, excluding unpaid family workers, and so is biased downward for some families.

24. N_u,/N is biased downward in the Colombian cities, by the exclusion of supple-mentary members (adults who work and pay something toward the family budget, while keeping much of their own budgets separate) from some households. No such bias exists in the estimates for Lima, which use the most inclusive concept of the household. In all cities, domestic servants are not counted in N_w; they are included in N for Lima but not for Bogotá or Medellín.

25. The relation of C/N to the overall employment rate N_u/N, the adult employment rate N_u./N_a (and the share of adults in the household N_a/N), is extended to seven other Andean cities—two each in Colombia, Ecuador and Venezuela, plus Santiago, Chile—in Philip Musgrove, “Household Size and Composition, Employment and Poverty in Urban Latin America,” Economic Development and Cultural Change (forthcoming).

26. In the ECIEL samples, a “rich” household is about three or four times as likely to be interviewed as a “poor” household, in Colombia, and twenty-one times as likely in Peru. All the calculations are weighted so as to represent the population without distortion.

27. It is widely believed in Lima that nearly all the city's poverty is to be found in the marginal squatter settlements. Thus, the surprising finding of this study is not that those neighborhoods are indeed poor, but that there are also many equally poor families living in the center of Lima. On this point see Figueroa, Estructura del consumo, pp. 28–31 and 91–92 (Figueroa's analysis is based on total income Y rather than C/N).

28. At least, these problems arise in large cities. Geographic location may still be an important classifying variable because of large urban-rural income differences, or differences between cities or between different rural areas. For evidence on the concentration of poverty in rural areas, see Weisskoff and Figueroa, “Traversing the Social Pyramid,” sections 3 and 4.

29. Musgrove, Consumer Behavior, tables 5-1, 5-5, 5-8, 5-12, 5-14, 5-15, 5-16, and 5-18.

30. Poor families tend to be concentrated more in houses than in apartments, because any free-standing single-unit dwelling, even a shack, is classified as a house. There is no strong association between houses and poverty, however.

31. See in particular, Musgrove, Consumer Behavior, chap. 2, part 3, and Weisskoff and Figueroa, “Traversing the Social Pyramid.” Family size N was also associated with Y in these analyses, but we exclude it here since our welfare indicator is a per capita measure. See also Ferber, “Income Distribution and Income Inequality,” tables 2.1 and 2.2.

32. See Vladimir Stoikov, “How Misleading are Income Distributions?,” Review of Income and Wealth, series 21, no. 2 (June 1975); Morton Paglin, “The Measurement and Trend of Inequality: A Basic Revision,” American Economic Review 65 (Sept. 1975); and Kuznets, “Demographic Aspects.”

33. To the extent that N_w is negatively correlated with C/N, more than 25 percent of working individuals will belong to households in the poorest quartile of consumption per head. This effect must be removed in judging whether a particular sector or occupational class is closely associated with poverty. If P₁ is the proportion of all employed people coming from first-quartile households, then the index of association with poverty for a given class i of occupation or sector is 25 Pi₁/P₁. A value of 25 (Pi₁ = P₁) means that the class is not more related to poverty than is the entire labor force. In Bogotá and Lima, P₁ is about 27 percent, while in Medellín it is only 24 percent.

34. Some “occupations” are found in only a single “sector,” so the two variables are not always distinguished. Any such case analyzed in table 17 is omitted from table 18. In other cases, “occupation” is more disaggregated than “sector,” as for commercial jobs, construction, and clerical workers.