IDEAS home Printed from https://ideas.repec.org/a/eee/eecrev/v52y2008i8p1353-1377.html
   My bibliography  Save this article

The second Engel law: Is it a paradox?

Author

Listed:
  • Perali, Federico

Abstract

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.

Suggested Citation

  • Perali, Federico, 2008. "The second Engel law: Is it a paradox?," European Economic Review, Elsevier, vol. 52(8), pages 1353-1377, November.
  • Handle: RePEc:eee:eecrev:v:52:y:2008:i:8:p:1353-1377
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0014-2921(08)00015-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. François Gardes & Christophe Starzec, 2000. "Economies of scale and food consumption: A reappraisal of the Deaton-Paxson paradox," Post-Print halshs-03721665, HAL.
    2. Yatchew, A., 1999. "An elementary nonparametric differencing test of equality of regression functions," Economics Letters, Elsevier, vol. 62(3), pages 271-278, March.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Pollak, Robert A & Wales, Terence J, 1981. "Demographic Variables in Demand Analysis," Econometrica, Econometric Society, vol. 49(6), pages 1533-1551, November.
    5. 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.
    6. 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.
    7. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
    8. repec:ebl:ecbull:v:4:y:2002:i:9:p:1-7 is not listed on IDEAS
    9. Anthony B. Atkinson & François Bourguignon, 1987. "Income Distribution and Differences in Needs," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Arrow and the Foundations of the Theory of Economic Policy, chapter 12, pages 350-370, Palgrave Macmillan.
    10. Nelson, Julie A, 1988. "Household Economies of Scale in Consumption: Theory and Evidence," Econometrica, Econometric Society, vol. 56(6), pages 1301-1314, November.
    11. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
    12. Margaret Grosh & Paul Glewwe, 2000. "Designing Household Survey Questionnaires for Developing Countries," World Bank Publications - Books, The World Bank Group, number 25338.
    13. 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.
    14. John Gibson, 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.
    15. François Gardes & Christophe Starzec, 2000. "Economies of scale and food consumption: A reappraisal of the Deaton-Paxson paradox," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03721665, HAL.
    16. Arthur Lewbel, 1985. "A Unified Approach to Incorporating Demographic or Other Effects into Demand Systems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 1-18.
    17. 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.
    18. 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.
    19. 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.
    20. Pashardes, Panos, 1995. "Equivalence scales in a rank-3 demand system," Journal of Public Economics, Elsevier, vol. 58(1), pages 143-158, September.
    21. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
    22. 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.
    23. 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.
    24. 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.
    25. Lewbel, Arthur, 1989. "Household equivalence scales and welfare comparisons," Journal of Public Economics, Elsevier, vol. 39(3), pages 377-391, August.
    26. repec:bla:obuest:v:64:y:2002:i:4:p:341-59 is not listed on IDEAS
    27. Federico Perali, 2002. "Some curiosites about the Engel method to estimate equivalence scales," Economics Bulletin, AccessEcon, vol. 4(9), pages 1-7.
    28. Gardes, F. & Starzec, C., 2000. "Economies of Scale and Food Consumption : a Reappraisal of the Deaton-Paxson Paradox," Papiers d'Economie Mathématique et Applications 2000.08, Université Panthéon-Sorbonne (Paris 1).
    29. 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, July.
    30. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Echeverría, Lucía & Molina, José Alberto, 2022. "Exploring household heterogeneities of the Deaton-Paxson puzzle: Evidence for Argentina," Nülan. Deposited Documents 3622, Universidad Nacional de Mar del Plata, Facultad de Ciencias Económicas y Sociales, Centro de Documentación.
    2. Chiara Elena Dalla & Menon Martina & Perali Federico, 2019. "An Integrated Database to Measure Living Standards," Journal of Official Statistics, Sciendo, vol. 35(3), pages 531-576, September.
    3. José Faro, 2013. "Cobb-Douglas preferences under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 273-285, October.
    4. Martina Menon & Elisa Pagani & Federico Perali, 2016. "A class of individual expenditure functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 291-305, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Trevon D. Logan, 2011. "Economies Of Scale In The Household: Puzzles And Patterns From The American Past," Economic Inquiry, Western Economic Association International, vol. 49(4), pages 1008-1028, October.
    2. Jayasinghe, Maneka & Chai, Andreas & Ratnasiri, Shyama & Smith, Christine, 2017. "The power of the vegetable patch: How home-grown food helps large rural households achieve economies of scale & escape poverty," Food Policy, Elsevier, vol. 73(C), pages 62-74.
    3. Echeverría, Lucía & Molina, José Alberto, 2022. "Exploring household heterogeneities of the Deaton-Paxson puzzle: Evidence for Argentina," Nülan. Deposited Documents 3622, Universidad Nacional de Mar del Plata, Facultad de Ciencias Económicas y Sociales, Centro de Documentación.
    4. Gibson, John, 2003. "Does Measurement Error Explain a Paradox About Household Size and Food Demand? Evidence from Variation in Household Survey Methods," 2003 Annual meeting, July 27-30, Montreal, Canada 22198, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Carlos Arias & Vincenzo Atella & Raffaella Castagnini & Federico Perali, 2003. "Estimation of the Sharing Rule between Adults and Children and Related Equivalence Scales within a Collective Consumption Framework," CHILD Working Papers wp07_03, CHILD - Centre for Household, Income, Labour and Demographic economics - ITALY.
    6. Karbasi, A. & Mohammadzadeh, S.H., 2018. "Estimating Household Expenditure Economies of Scale in Iran," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277152, International Association of Agricultural Economists.
    7. Thomas F. Crossley & Yuqian Lu, 2018. "Returns to scale in food preparation and the Deaton–Paxson puzzle," Review of Economics of the Household, Springer, vol. 16(1), pages 5-19, March.
    8. Timothy J. Halliday, 2010. "Mismeasured Household Size and its Implications for the Identification of Economies of Scale," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(2), pages 246-262, April.
    9. John Gibson & Bonggeun Kim, 2018. "Economies of scale, bulk discounts, and liquidity constraints: comparing unit value and transaction level evidence in a poor country," Review of Economics of the Household, Springer, vol. 16(1), pages 21-39, March.
    10. Fabrizio Balli, 2012. "Are Traditional Equivalence Scales Still Useful? A Review and A Possible Answer," Department of Economics University of Siena 656, Department of Economics, University of Siena.
    11. Garcia-Diaz Rocio, 2012. "Demand-Based Cost-of-Children Estimates and Child Poverty," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-32, January.
    12. Donald Vitaliano, 2015. "A note on the ‘food paradox’: some contradictory evidence," Review of Economics of the Household, Springer, vol. 13(4), pages 1043-1053, December.
    13. Devajyoti Deka, 2014. "The Living, Moving and Travel Behaviour of the Growing American Solo: Implications for Cities," Urban Studies, Urban Studies Journal Limited, vol. 51(4), pages 634-654, March.
    14. Shari Eli & Nicholas Li, 2015. "Caloric Requirements and Food Consumption Patterns of the Poor," NBER Working Papers 21697, National Bureau of Economic Research, Inc.
    15. Federico Perali, 2007. "Can PIGLOG preferences identify equivalence scales?," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 54(2), pages 248-260, June.
    16. Trevon D. Logan, 2008. "Are Engel Curve Estimates of CPI Bias Biased?," NBER Working Papers 13870, National Bureau of Economic Research, Inc.
    17. Martina Menon & Federico Perali, 2012. "The Sharing Rule: Where Is It?," Working Papers 16/2012, University of Verona, Department of Economics.
    18. Fiedler, John L. & Mwangi, Dena M., 2016. "Improving household consumption and expenditure surveys’ food consumption metrics: Developing a strategic approach to the unfinished agenda:," IFPRI discussion papers 1570, International Food Policy Research Institute (IFPRI).
    19. Antonella Caiumi & Federico Perali, 2015. "Who bears the full cost of children? Evidence from a collective demand system," Empirical Economics, Springer, vol. 49(1), pages 33-64, August.
    20. Srikanta Chatterjee & Claudio Michelini & Ranjan Ray, 1994. "Expenditure Patterns and Aggregate Consumer Behaviour: Some Experiments with Australian and New Zealand Data," The Economic Record, The Economic Society of Australia, vol. 70(210), pages 278-291, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:eecrev:v:52:y:2008:i:8:p:1353-1377. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eer .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.