Skip to main content

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

Summary

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.

References

  • 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 

  • 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.

    Article  Google Scholar 

  • Blundell, Richard, Alan Duncan, and Krishna Pendakur (1998), “Semiparametric Estimation and Consumer Demand”, Journal of Applied Econometrics, 13(5), pp. 435–461.

    Article  Google Scholar 

  • Blundell, Richard, and Arthur Lewbel (1991), “The Information Content of Equivalence Scales”,Journal of Econometrics, 50, pp. 49–68.

    Article  Google Scholar 

  • 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 

  • Bowman, Adrian W. (1984), “An Alternative Method of Cross-Validation for the Smoothing of Density Estimates”, Biometrika, 71(2), pp. 353–360.

    Article  Google Scholar 

  • Browning, Martin (1992), “Children and Household Economic Behavior”, Journal of Economic Literature, 30(3), pp. 1434–1475.

    Google Scholar 

  • Browning, Martin, and Costas Meghir (1991), “The Effects of Male and Female Labor Supply on Commodity Demands”, Econometrica, 59(4), pp. 925–951.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Dickens, Richard, Vanessa Fry, and Panos Pashardes (1993), “Non-Linearities and Equivalence Scales”, Economic Journal, 103(417), pp. 359–368.

    Article  Google Scholar 

  • Donaldson, David, and Krishna Pendakur (2004), “Equivalent-Expenditure Functions and Expenditure-Dependent Equivalence Scales”, Journal of Public Economics, 88(1–2), pp. 175–208.

    Article  Google Scholar 

  • 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.

  • Engel, Ernst (1895), „Die Lebenskosten belgischer Arbeiter-Familien früher und jetzt“, International Statistical Institute Bulletin, 9, pp. 1–74.

    Google Scholar 

  • Gerfin, Michael, Thomas Oesch, Heidi Stutz and Silvia Strub (2009), Kinderkosten in der Schweiz, Bundesamt für Statistik, Bern.

    Google Scholar 

  • Gerfin, Michael, and Gabrielle Wanzenried (2001), Neue Schätzungen von Ausgaben-Äquivalenzskalen für die Schweiz, Bundesamt für Statistik, Bern.

    Google Scholar 

  • Gozalo, Pedro L. (1997), “Nonparametric Bootstrap Analysis with Applications to Demographic Effects in Demand Functions”, Journal of Econometrics, 81(2), pp. 357–393.

    Article  Google Scholar 

  • Härdle, Wolfgang K., and Enno Mammen (1993), “Comparing Nonparametric versus Parametric Regression Fits”, The Annals of Statistics, 21(4), pp. 1926–1947.

    Article  Google Scholar 

  • Hayfield, Tristen, and Jeffrey S. Racine (2008), “Nonparametric Econometrics: The np Package”, Journal of Statistical Software, 27(5), pp. 1–32.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Lewbel, Arthur (1989), “Household Equivalence Scales and Welfare Comparisons”, Journal of Public Economics, 39(3), pp. 377–391.

    Article  Google Scholar 

  • Li, Qi, and Jeffrey Scott Racine (2006), Nonparametric Econometrics: Theory and Practice, Princeton University Press.

  • Lise, Jeremy, and Shannon Seitz (2011), “Consumption Inequality and Intra-Household Allocations”, The Review of Economic Studies, 78, pp. 328–355.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Mammen, Enno (1993), “Bootstrap and wild Bootstrap for High Dimensional Linear Models”, The Annals of Statistics, 21(1), pp. 255–285.

    Article  Google Scholar 

  • Muellbauer, John (1974), “Household Composition, Engel Curves and Welfare Comparisons between Households: A Duality Approach”, European Economic Review, 5(2), pp. 103–122.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Nelson, Julie A. (1989), “Separability, Scale and Intra-Family Distribution: Some Empirical Evidence”, Papers 346, California Davis — Institute of Governmental Affairs.

  • Nelson, Julie A. (1993), “Household Equivalence Scales: Theory versus Policy?”, Journal of Labor Economics, 11(3), pp. 471–493.

    Article  Google Scholar 

  • Pashardes, Panos (1991), “Contemporaneous and Intertemporal Child Costs: Equivalent Expenditure vs. Equivalent Income Scales”,Journal of Public Economics, 45(2), pp. 191–213.

    Article  Google Scholar 

  • Pendakur, Krishna (1999), “Semiparametric Estimates and Tests of Base-Independent Equivalence Scales”,Journal of Econometrics, 88(1), pp. 1–40.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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 

  • Rudemo, Mats (1982), “Empirical Choice of Histograms and Kernel Density Estimators”, Scandinavian Journal of Statistics, 9(2), pp. 65–78.

    Google Scholar 

  • SKOS (2009), Richtlinien für die Ausgestaltung und Bemessung der Sozialhilfe, Bern: Schweizerische Konferenz für Sozialhilfe.

    Google Scholar 

  • Stone, Charles J. (1984), “An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates”, Annals of Statistics, 12(4), pp. 1285–1297.

    Article  Google Scholar 

  • Sun, Yiguo, Thanasis Stengos, and Dianqin Wang (2006), “Estimates of Semiparametric Equivalence Scales”, Journal of Applied Econometrics, 21(5), pp. 629–639.

    Article  Google Scholar 

  • Watson, Geoffrey S. (1964), “Smooth Regression Analysis”, Sankhya — The Indian Journal of Statistics, 26, pp. 359–372.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aline Bütikofer.

Additional information

The paper was written while the author was at the University of Bern, Switzerland. Without implication, I want to thank Michael Gerfin and two anonymous referees for their valuable comments. All errors are my own.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Bütikofer, A. Semiparametric base-independent equivalence scales and the cost of children in Switzerland. Swiss J Economics Statistics 148, 1–35 (2012). https://doi.org/10.1007/BF03399358

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03399358

JEL-Classification

  • D12
  • C14
  • J12

Keywords

  • Semiparametric estimation
  • Equivalence scales
  • Engel curves