The second Engel law: Is it a paradox?
The second Engel law says that the Engel curve for food moves out as family size increases, thus showing a decrease in welfare. What is puzzling, though, is that this regularity does not hold for equivalent income functions expressed in per capita terms. Deaton and Paxon [1998. Economies of scale, household size, and the demand for food. Journal of Political Economy 106 (5), 897-930] show that holding per capita total household expenditure constant, per capita expenditure on food falls with the number of heads. Deaton and Paxson's empirical evidence from developed and less developed countries seems to invalidate the claim of the second Engel's law. The main objective of this paper is to understand such paradoxical relationship between food consumption and household size. Our nonparametric empirical evidence, drawn from the Colombian 1985 urban survey, shows that the food share is negatively related to total household per capita expenditure in line with Deaton and Paxson's claim, but equivalent incomes shift to the right as theory predicts. The regularity of our nonparametric results is an indication of a problem in the parametric specification of the Engel curve modified by family size. In fact, using also the surveys of Italy, Nepal, Djibouti, and Bangladesh we show that a theoretically plausible modified Engel curve is coherent with the claim of the second Engel law and explains Deaton and Paxson's paradox.
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- Yatchew, A., 1999. "An elementary nonparametric differencing test of equality of regression functions," Economics Letters, Elsevier, vol. 62(3), pages 271-278, March.
- Pollak, Robert A & Wales, Terence J, 1981. "Demographic Variables in Demand Analysis," Econometrica, Econometric Society, vol. 49(6), pages 1533-1551, November.
- Li Gan & Victoria Vernon, 2003. "Testing the Barten Model of Economies of Scale in Household Consumption: Toward Resolving a Paradox of Deaton and Paxson," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1361-1377, December.
- Angus Deaton & Christina Paxson, 1998.
"Economies of Scale, Household Size, and the Demand for Food,"
Journal of Political Economy,
University of Chicago Press, vol. 106(5), pages 897-930, October.
- Deaton, A. & Paxson, C., 1997. "Economies of Scale, Household Size, and the Demand for Food," Papers 178, Princeton, Woodrow Wilson School - Development Studies.
- Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
- repec:ebl:ecbull:v:4:y:2002:i:9:p:1-7 is not listed on IDEAS
- Nelson, Julie A, 1988. "Household Economies of Scale in Consumption: Theory and Evidence," Econometrica, Econometric Society, vol. 56(6), pages 1301-1314, November.
- Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
- Singh, Balvir, 1972. "On the Determination of Economies of Scale in Household Consumption," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(2), pages 257-270, June.
- Gibson, John, 2002. " Why Does the Engel Method Work? Food Demand, Economies of Size and Household Survey Methods," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(4), pages 341-359, September.
- John Gibson, 2002. "Why Does the Engel Method Work? Food Demand, Economies of Size and Household Survey Methods," Working Papers in Economics 02/02, University of Waikato, Department of Economics.
- Arthur Lewbel, 1985. "A Unified Approach to Incorporating Demographic or Other Effects into Demand Systems," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 1-18.
- Federico Perali & Jean-Paul Chavas, 2000. "Estimation of Censored Demand Equations from Large Cross-Section Data," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 82(4), pages 1022-1037.
- Shelley A. Phipps, 1998. "What Is The Income "Cost Of A Child"? Exact Equivalence Scales For Canadian Two-Parent Families," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 157-164, February.
- C. Andrea Bollino & Federico Perali & Nicola Rossi, 2000. "Linear household technologies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(3), pages 275-287.
- Pashardes, Panos, 1995. "Equivalence scales in a rank-3 demand system," Journal of Public Economics, Elsevier, vol. 58(1), pages 143-158, September.
- Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
- Lazear, Edward P & Michael, Robert T, 1980. "Family Size and the Distribution of Real Per Capita Income," American Economic Review, American Economic Association, vol. 70(1), pages 91-107, March.
- Angus Deaton & Christina Paxson, 2003. "Engel's What? A Response to Gan and Vernon," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1378-1381, December.
- Donaldson, David & Pendakur, Krishna, 2004. "Equivalent-expenditure functions and expenditure-dependent equivalence scales," Journal of Public Economics, Elsevier, vol. 88(1-2), pages 175-208, January.
- Lewbel, Arthur, 1989. "Household equivalence scales and welfare comparisons," Journal of Public Economics, Elsevier, vol. 39(3), pages 377-391, August.
- Gardes, F. & Starzec, C., 2000. "Economies of Scale and Food Consumption : a Reappraisal of the Deaton-Paxson Paradox," Papiers d'Economie MathÃ©matique et Applications 2000.08, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Awudu Abdulai, 2003. "Economies of Scale and the Demand for Food in Switzerland: Parametric and Non-Parametric Analysis," Journal of Agricultural Economics, Wiley Blackwell, vol. 54(2), pages 247-267.
- John Gibson & Bonggeun Kim, 2007. "Measurement Error in Recall Surveys and the Relationship between Household Size and Food Demand," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 89(2), pages 473-489. Full references (including those not matched with items on IDEAS)