Swiss Journal of Economics and Statistics

, Volume 148, Issue 1, pp 1–35 | Cite as

Semiparametric base-independent equivalence scales and the cost of children in Switzerland

Open Access


How much additional income does a couple with two children need to be equally well-off as a childless couple? This question is important for public policy decisions on social benefits or child allowances. Since equivalence scales express the change in the cost required to attain a certain welfare level when the household size and composition varies, they answer this question. This paper provides semi-parametric estimates of consumption-based equivalence scales by applying the extended partially linear model to the Swiss Household Budget Survey 2000–2005. The results permit welfare comparisons across households and provide an indirect measure of the cost of children.


D12 C14 J12 


Semiparametric estimation Equivalence scales Engel curves 


  1. Barten, Anton P. (1964), “Family Composition, Prices, and Expenditure Patterns”, in Econometric Analysis for National Economic Planning: 16th Symposium of the Colston Society, P. Hart, L. Mills, and J. K. Whitaker, eds, London: Butterworth.Google Scholar
  2. Blackorby, Charles, and David Donaldson (1993), “Adult-Equivalence Scales and the Economic Implementation of Interpersonal Comparisons of Well-Being”, Social Choice and Welfare, 10(4), pp. 335–361.CrossRefGoogle Scholar
  3. Blundell, Richard, Alan Duncan, and Krishna Pendakur (1998), “Semiparametric Estimation and Consumer Demand”, Journal of Applied Econometrics, 13(5), pp. 435–461.CrossRefGoogle Scholar
  4. Blundell, Richard, and Arthur Lewbel (1991), “The Information Content of Equivalence Scales”,Journal of Econometrics, 50, pp. 49–68.CrossRefGoogle Scholar
  5. Blundell, Richard, Panos Pashardes, and Guglielmo Weber (1993), “What Do We Learn about Consumer Demand Patterns from Micro Data?”, The American Economic Review, 83(3), pp. 570–597.Google Scholar
  6. Bowman, Adrian W. (1984), “An Alternative Method of Cross-Validation for the Smoothing of Density Estimates”, Biometrika, 71(2), pp. 353–360.CrossRefGoogle Scholar
  7. Browning, Martin (1992), “Children and Household Economic Behavior”, Journal of Economic Literature, 30(3), pp. 1434–1475.Google Scholar
  8. Browning, Martin, and Costas Meghir (1991), “The Effects of Male and Female Labor Supply on Commodity Demands”, Econometrica, 59(4), pp. 925–951.CrossRefGoogle Scholar
  9. Deaton, Angus S., and John Muellbauer (1986), “On Measuring Child Costs: With Applications to Poor Countries”, Journal of Political Economy, 94(4), pp. 720–744.CrossRefGoogle Scholar
  10. Deaton, Angus S., Javier Ruiz-Castillo and Duncan Thomas (1989), “The Influence of Household Composition on Household Expenditure Patterns: Theory and Spanish Evidence”, Journal of Political Economy, 97(1), pp. 179–200.CrossRefGoogle Scholar
  11. Dickens, Richard, Vanessa Fry, and Panos Pashardes (1993), “Non-Linearities and Equivalence Scales”, Economic Journal, 103(417), pp. 359–368.CrossRefGoogle Scholar
  12. Donaldson, David, and Krishna Pendakur (2004), “Equivalent-Expenditure Functions and Expenditure-Dependent Equivalence Scales”, Journal of Public Economics, 88(1–2), pp. 175–208.CrossRefGoogle Scholar
  13. Dunbar, Geoffrey, Arthur Lewbel, and Krishna Pendakur (2010), “Children’s Resources in Collective Households: Identification, Estimation and an Application to Child Poverty in Malawi”, Boston College Working Papers in Economics, 758, Boston College Department of Economics.Google Scholar
  14. Engel, Ernst (1895), „Die Lebenskosten belgischer Arbeiter-Familien früher und jetzt“, International Statistical Institute Bulletin, 9, pp. 1–74.Google Scholar
  15. Gerfin, Michael, Thomas Oesch, Heidi Stutz and Silvia Strub (2009), Kinderkosten in der Schweiz, Bundesamt für Statistik, Bern.Google Scholar
  16. Gerfin, Michael, and Gabrielle Wanzenried (2001), Neue Schätzungen von Ausgaben-Äquivalenzskalen für die Schweiz, Bundesamt für Statistik, Bern.Google Scholar
  17. Gozalo, Pedro L. (1997), “Nonparametric Bootstrap Analysis with Applications to Demographic Effects in Demand Functions”, Journal of Econometrics, 81(2), pp. 357–393.CrossRefGoogle Scholar
  18. Härdle, Wolfgang K., and Enno Mammen (1993), “Comparing Nonparametric versus Parametric Regression Fits”, The Annals of Statistics, 21(4), pp. 1926–1947.CrossRefGoogle Scholar
  19. Hayfield, Tristen, and Jeffrey S. Racine (2008), “Nonparametric Econometrics: The np Package”, Journal of Statistical Software, 27(5), pp. 1–32.CrossRefGoogle Scholar
  20. Jenkins, Stephen P. (1991), “The Measurement of Income Inequality”, in Economic Inequality and Poverty, L. Osberg, ed., pp. 3–38, New York: Butterworth.Google Scholar
  21. Kapteyn, Arie, and Bernhard Van Praag (1978), “A New Approach to the Construction of Family Equivalence Scales”, European Economic Review, 7(4), pp. 313–335.CrossRefGoogle Scholar
  22. Lewbel, Arthur (1989), “Household Equivalence Scales and Welfare Comparisons”, Journal of Public Economics, 39(3), pp. 377–391.CrossRefGoogle Scholar
  23. Li, Qi, and Jeffrey Scott Racine (2006), Nonparametric Econometrics: Theory and Practice, Princeton University Press.Google Scholar
  24. Lise, Jeremy, and Shannon Seitz (2011), “Consumption Inequality and Intra-Household Allocations”, The Review of Economic Studies, 78, pp. 328–355.CrossRefGoogle Scholar
  25. Lyssiotou, Panayiota (1997), “Comparison of Alternative Tax and Transfer Treatment of Children using Adult Equivalence Scales”, Review of Income and Wealth, 43(1), pp. 105–117.CrossRefGoogle Scholar
  26. Mammen, Enno (1993), “Bootstrap and wild Bootstrap for High Dimensional Linear Models”, The Annals of Statistics, 21(1), pp. 255–285.CrossRefGoogle Scholar
  27. Muellbauer, John (1974), “Household Composition, Engel Curves and Welfare Comparisons between Households: A Duality Approach”, European Economic Review, 5(2), pp. 103–122.CrossRefGoogle Scholar
  28. Nadaraya, Èlizbar A. (1965), “On Non-Parametric Estimates of Density Functions and Regression Curves”, Theory of Probability and its Applications, 10(1), pp. 186–190.CrossRefGoogle Scholar
  29. Nelson, Julie A. (1989), “Separability, Scale and Intra-Family Distribution: Some Empirical Evidence”, Papers 346, California Davis — Institute of Governmental Affairs.Google Scholar
  30. Nelson, Julie A. (1993), “Household Equivalence Scales: Theory versus Policy?”, Journal of Labor Economics, 11(3), pp. 471–493.CrossRefGoogle Scholar
  31. Pashardes, Panos (1991), “Contemporaneous and Intertemporal Child Costs: Equivalent Expenditure vs. Equivalent Income Scales”,Journal of Public Economics, 45(2), pp. 191–213.CrossRefGoogle Scholar
  32. Pendakur, Krishna (1999), “Semiparametric Estimates and Tests of Base-Independent Equivalence Scales”,Journal of Econometrics, 88(1), pp. 1–40.CrossRefGoogle Scholar
  33. Phipps, Shelley A. (1998), “What is the Income ‘Cost of a Child’? Exact Equivalence Scales for Canadian Two-Parent Families”, The Review of Economics and Statistics, 80(1), pp. 157–164.CrossRefGoogle Scholar
  34. Pinkse, Joris, and Peter M. Robinson (1995), “Pooling Nonparametirc Estimates of Regression Functions with Similar Data”, in Advances in Econometrics and Quantitative Economics: Essays in Honor of Professor C.R. Rao, G. S. Maddala, T. N. Srinivasan and Peter Phillips, eds., pp. 172–195, Wiley-Blackwell.Google Scholar
  35. Rothbarth, Erwin (1943), “Note on a Method of Determining Equivalent Income for Families of Different Composition”, in War-Time Pattern of Saving and Spending, Charles Madge, ed., vol. Appendix 4, pp. 123–130, Cambridge: Cambridge University Press.Google Scholar
  36. Rudemo, Mats (1982), “Empirical Choice of Histograms and Kernel Density Estimators”, Scandinavian Journal of Statistics, 9(2), pp. 65–78.Google Scholar
  37. SKOS (2009), Richtlinien für die Ausgestaltung und Bemessung der Sozialhilfe, Bern: Schweizerische Konferenz für Sozialhilfe.Google Scholar
  38. Stone, Charles J. (1984), “An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates”, Annals of Statistics, 12(4), pp. 1285–1297.CrossRefGoogle Scholar
  39. Sun, Yiguo, Thanasis Stengos, and Dianqin Wang (2006), “Estimates of Semiparametric Equivalence Scales”, Journal of Applied Econometrics, 21(5), pp. 629–639.CrossRefGoogle Scholar
  40. Watson, Geoffrey S. (1964), “Smooth Regression Analysis”, Sankhya — The Indian Journal of Statistics, 26, pp. 359–372.Google Scholar
  41. Wilke, Ralf A. (2006), “Semi-Parametric Estimation of Consumption-Based Equivalence Scales: The Case of Germany”, Journal of Applied Econometrics, 21(6), pp. 781–802.CrossRefGoogle Scholar
  42. Yatchew, Adonis, Yiguo Sun, and Catherine Deri (2003), “Efficient Estimation of Semiparametric Equivalence Scales with Evidence from South Africa”, Journal of Business & Economic Statistics, 21(2), pp. 247–257.CrossRefGoogle Scholar

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© Swiss Society of Economics and Statistics 2012

Authors and Affiliations

  1. 1.Department of EconomicsNorwegian School of EconomicsBergenNorway

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