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The measurement of household cost functions

Revealed preference versus subjective measures

Abstract

Since the work of Pollak and Wales (1979), it is well-known that demand data are insufficient to identify a household cost function. Hence additional information is required. For that purpose I propose to employ direct measurement of feelings of well-being, elicited in surveys.

In the paper I formally establish the connection between subjective measures and the cost function underlying the AID system. The subjective measures fully identify cost functions and the expenditure data do this partly. This makes it possible to test the null hypothesis that both types of data are consistent with one another, i.e. that they measure the same thing. I use two separate data sets to set up a test of this equivalence. The outcomes are somewhat mixed and indicate the need for further specification search. Finally, I discuss some implications of the outcomes.

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References

  • Aigner DJ, Hsiao C, Kapteyn A, Wansbeek TJ (1984) Latent variables in econometrics. Handbook of econometrics, vol II. North-Holland, Amsterdam, pp 1321–1393

    Google Scholar 

  • Alessie RJM, Kapteyn A (1991) Habit formation, interdependent preferences and demographic effects in the almost ideal demand system. Econ J 101:404–419

    Google Scholar 

  • Alessie RJM, Kapteyn A, Melenberg B (1992) Subjective definitions of poverty and the measurement of reference groups. Working paper Tilburg University

  • Angrist JD, Krueger AB (1992) The effect of age at school entry on educational attainment. An application of instrumental variables with moments from two samples. J Am Statist Assoc 87:328–336

    Google Scholar 

  • Antonides G, Kapteyn A, Wansbeek TJ (1980) Reliability and validity assessment of ten methods for the measurement of individual welfare functions of income. Working paper Tilburg University

  • Arellano M, Meghir C (1988) Female labour supply and on-the-job search. An empirical model estimated using complementary data sets. Rev Econ Studies 59:537–559

    Google Scholar 

  • Banks J, Blundell R, Lewbel A (1994) Quadratic engel curves, indirect tax reform and welfare measurement. Department of Economics, University College London, Discussion Paper 94–04

  • Bekker PA (1994) Alternative approximations to the distribution of instrumental variable estimators. Econometrica 62:657–685

    Google Scholar 

  • Blackorby C, Donaldson D (1988) Adult-equivalence scales and the economic implementation of interpersonal comparisons of well-being. Discussion Paper 88–27, University of British Columbia

  • Blackorby C, Donaldson D (1993) Costs of children. Hand-out for presentation at the 1993 AEA meetings, Anaheim, California

    Google Scholar 

  • Blundell R, Lewbel A (1991) The information content of equivalence scales. J Economet 50:49–68

    Google Scholar 

  • Bound J, Jaeger DA, Baker RM (1993) The cure can be worse than the disease. A cautionary tale regarding instrumental variables. University of Michigan, working paper

  • Browning M (1992) Children and household economic behavior. J Econ Liter 30:1434–1475

    Google Scholar 

  • Browning M (1993) More than one angel can dance on the head of a pin. Notes on adult equivalence scales. Paper presented at the 1993 AEA meetings, Anaheim, California

    Google Scholar 

  • Buyze J (1982) The estimation of welfare levels of a cardinal utility function. Eur Econ Rev 17:325–332

    Google Scholar 

  • Colasanto D, Kapteyn A, van der Gaag J (1984) Two subjective definitions of poverty. Results from the Wisconsin basic needs study. J Human Resources 28:127–138

    Google Scholar 

  • Danziger S, van der Gaag J, Taussig M, Smolensky E (1984) The direct measurement of welfare levels. How much does it cost to make ends meet? Rev Econ Statist 66:500–505

    Google Scholar 

  • Davidson R, MacKinnon JG (1993) Estimation and inference in econometrics. Oxford University Press, Oxford

    Google Scholar 

  • Deaton AS, Muellbauer J (1980) An almost ideal demand system. Am Econ Rev 70:312–326

    Google Scholar 

  • De Vos K, Garner T (1986) An evaluation of subjective poverty definitions. Comparing results from the US and the Netherlands. Rev Income Wealth 37:267–285

    Google Scholar 

  • Dubnoff S (1979) Experiments in the use of survey data for the measurement of income minima. Working paper, Center for Survey Research, University of Massachusetts, Boston

    Google Scholar 

  • Fisher FM (1987) Household equivalence scales and interpersonal comparisons. Rev Econ Studies 54:519–524

    Google Scholar 

  • Hagenaars AJM (1986) The perception of poverty. North-Holland, Amsterdam

    Google Scholar 

  • Hartog J (1988) Poverty and the measurement of individual welfare. J Human Resources 23:241–266

    Google Scholar 

  • Kapteyn A (1977) A theory of preference formation. Unpublished PhD thesis, Leyden University. Leiden

    Google Scholar 

  • Kapteyn A (1985) Utility and economics. De Economist 133:1–20

    Google Scholar 

  • Kapteyn A, van Herwaarden FG (1980) Interdependent welfare functions and optimal income distribution. J Publ Econ 14:375–397

    Google Scholar 

  • Kapteyn A, van Praag BMS (1976) A new approach to the construction of family equivalence scales. Eur Econ Rev 7:313–335

    Google Scholar 

  • Kapteyn A, Wansbeek TJ (1982) Empirical evidence on preference formation. J Econ Psychol 2:137–149

    Google Scholar 

  • Kapteyn A, Kooreman P, Willemse R (1988) Some methodological issues in the implementation of subjective poverty definitions. J Human Resources 23:222–242

    Google Scholar 

  • Kapteyn A, van de Geer SA, van de Stadt H (1985) The impact of changes in income and family composition on subjective measures of well-being. In: David M, Smeeding T (eds) Horizontal equity, uncertainty, and economic well-being. University of Chicago Press, Chicago, pp 35–64

    Google Scholar 

  • Kapteyn A, Wansbeek TJ, Buyze J (1980) The dynamics of preference formation. J Econ Behavior Organ 1:123–157

    Google Scholar 

  • Lewbel A (1989) Household equivalence scales and welfare comparisons. J Publ Econ 39:377–391

    Google Scholar 

  • Lusardi A (1993) Euler equations in micro data. Merging data from two samples. Center Discussion Paper 9304

  • Muellbauer J (1975) Aggregation, income distribution and consumer demand. Rev Econ Studies 42:525–543

    Google Scholar 

  • Nelson JA (1993) Household equivalence scales. Theory versus policy? J Labor Econ 11:471–493

    Google Scholar 

  • Pashardes P (1992) Equivalence scales in a rank-3 demand system. Working Paper ITS

  • Pollak RA, Wales TJ (1979) Welfare comparisons and equivalence scales. Am Econ Rev 69:216–221

    Google Scholar 

  • Staiger D, Stock JH (1993) Asymptotics for instrumental variables regressions with weakly correlated instruments. Harvard University and NBER, working paper

  • Van Herwaarden FG, Kapteyn A (1981) Empirical comparison of the shape of welfare functions. Eur Econ Rev 15:261–286

    Google Scholar 

  • Van Praag BMS (1968) Individual welfare functions and consumer behavior. North-Holland, Amsterdam

    Google Scholar 

  • Van Praag BMS (1971) The welfare function of income in Belgium. An empirical investigation. Eur Econ Rev 2:337–369

    Google Scholar 

  • Van Praag BMS (1991) Ordinal and cardinal utility. An integration of the two dimensions of the welfare concept. J Economet 50:69–89

    Google Scholar 

  • Van Praag BMS, Kapteyn A (1973) Further evidence on the individual welfare function of income. An empirical investigation. Eur Econ Rev 4:32–62

    Google Scholar 

  • Van Praag BMS, van der Sar NL (1988) Household cost functions and equivalence scales. J Human Resources 23:193–210

    Google Scholar 

  • Van de Stadt H, Kapteyn A, van de Geer SA (1985) The relativity of utility. Evidence from panel data. Rev Econ Statist 67:179–187

    Google Scholar 

  • Vaughan DR (1984) Using subjective assessments of income to estimate family equivalence scales. A report on work in progress. Proceedings of the Social Statistics Section, American Statistical Association 1984

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Additional information

Presidential address delivered at the seventh annual meeting of the European Society for Population Economics, June 2–5, Budapest, Hungary. A first version was presented at the meetings of the Allied Social Sciences Associations, Anaheim, California, January 5–7, 1993. The author thanks Rob Alessie for help with the data, and the Netherlands Central Bureau of Statistics for their permission to use the data. Both Rob Alessie and an anonymous referee made very helpful comments on an earlier version.

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Kapteyn, A. The measurement of household cost functions. J Popul Econ 7, 333–350 (1994). https://doi.org/10.1007/BF00161471

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Keywords

  • Null Hypothesis
  • Cost Function
  • Direct Measurement
  • Subjective Measure
  • Expenditure Data