The estimation of the costs of children based on random equivalence scales

• Authors: Kot Stanisław Maciej

Title variants

PL

Oszacowanie kosztów utrzymania dzieci na podstawie losowych skal ekwiwalentności

• Languages of publication: EN

Abstracts

EN

This paper measures the cost of children using the random equivalence scale (RES). From the general population perspective, the deterministic microeconomic equivalence scales appear as continuous random variables. The stude derived the distribution of RES, assuming the lognormal distribution of income. The truncated distribution of RES can account for possible economies of scale in income or expenditure. The positional measures of the truncated distribution of RES may serve as single equivalence scales. A society’s attitude towards inequality may help chose such scales. RES for Poland 2015 was estimated using microdata from the Household Budget Survey. Polish households exhibited a remarkable level of economies of scale in that year and the equivalence scales declined with expenditure. It was observed that the cost of bringing up a child is not constant; generally, it decreases with increasing household size.

PL

W artykule koszt utrzymania dziecka jest mierzony za pomocą losowej skali ekwiwalentności (RES). Z perspektywy populacji generalnej deterministyczne mikroekonomiczne skale ekwiwalentności ukazują się jako ciągłe zmienne losowe. W niniejszej pracy uzyskano rozkład RES na podstawie lognormalnego rozkładu dochodów. Ucięty rozkład RES umożliwia uwzględnienie korzyści wielkości dochodów lub wydatków. Za pojedyncze skale ekwiwalentności mogą służyć miary położenia w uciętym rozkładzie RES. W wyborze konkretnej skali pomocna może być postawa społeczeństwa wobec nierówności. W pracy oszacowano RES dla Polski w 2015 r. na podstawie mikrodanych z Sondażu Budżetów Gospodarstw Domowych. W owym roku polskie gospodarstwa domowe wykazywały znaczące korzyści wielkości wydatków. Ponadto skale ekwiwalentności malały wraz ze wzrostem wydatków. Zaobserwowano, że koszt utrzymania kolejnego dziecka nie jest stały – malał on wraz ze wzrostem wielkości gospodarstwa domowego.

Keywords

EN

equivalence scale; lognormal distribution; economies of scale; inequality aversion

PL

skale ekwiwalentności; rozkład lognormalny; korzyści skali; awersja do nierówności

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Śląski Przegląd Statystyczny
• Year: 2020
• Issue: 18 (24)

Contributors

author

Kot Stanisław Maciej

• Gdansk University of Technology, Poland

References

• Aitchison, J., and Brown, J. A. (1957). The lognormal distribution with special reference to its uses in economics. Cambridge: Cambridge University Press.
• Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, (2), 244-63.
• Bebu, I., and Mathew, T. (2009). Confidence intervals for limited moments and truncated moments in normal and lognormal models. Statistics & Probability Letters, 79, 375-380.
• Bellemare, C., Melenberg, B., and Van Soest, A. (2002). Semi-parametric models for satisfaction with income. Portuguese Economic Journal, (1), 181-203.
• Biewen, M., and Juhasz, A. (2017). Direct estimation of equivalence scales and more evidence on independence of base. Oxford Bulletin of Economics and Statistics, (79), 875-905.
• Blackorby, C., and Donaldson, D. (1993). Adult-equivalence scales and the economic implementation of interpersonal comparisons of wellbeing. Choice and Welfare, (10), 335-361.
• Blundell, R., and Lewbel, A. (1991). The information content of equivalence scales. Journal of Econometrics, (50), 49-68.
• Bollinger, C. R., Nicoletti, C., and Pudney, S. (2012). Two Can Live as Cheaply as One ... but three’s a Crowd. ISER Discussion Paper No. 2012-10. Institute for Social and Economic Research, University of Essex.
• Buhmann, B., Rainwater, L., Schmaus, G., and Smeeding, T. M. (1988). Equivalence scales, wellbeing, inequality, and poverty: sensitivity estimates across ten countries using the Luxembourg Income Study (LIS) database. Review of Income and Wealth, (34), 115-142.
• Cameron, A. C., and Trivedi, P. K. (2010). Microeconometrics Using Stata. College Station, TX: Stata Press.
• Chiappori, P. A. (2016). Equivalence versus indifference scales. Economic Journal, (126), 523-545.
• Deaton, A., and Muellbauer, J. (1980). Economics and consumer behavior. Cambridge: Cambridge University Press.
• Donaldson, D., and Pendakur, K. (2003). Equivalent-expenditure functions and expenditure dependent equivalence scales. Journal of Public Economics, (88), 175-208.
• Donaldson, D., and Pendakur, K. (2006). The identification of fixed costs from consumer behavior. Journal of Business Economic Statistics, (24), 255-265.
• Ebert, U., and Moyes, P. (2003). Equivalence scales reconsidered. Econometrica, (71) 319-343.
• Fisz, M. (1963). Probability theory and mathematical statistics. New York: Wiley.
• Hagenaars, A., de Vos, K., and Zaidi, A. (1994). Poverty statistics in the late 1980s: Research based on micro-data. Luxembourg: Eurostat.
• Jackson, C. A. (1968). Revised equivalence scale for estimating equivalent incomes or budget costs by family Type.”Bulletin No. 1570-1572 US Department of Labor. Bureau of Labor Statistics.
• Jawitz, J. W. (2004). Moments of truncated continuous univariate distributions. Advances in Water Resources, (27), 269-281.
• Johnson, N. L., Kotz, S., and Balakrishnan, N. (1994). Continuous Univariate Distributions. New York: Wiley.
• Jones, A., and O’Donnell, O. (1995). Equivalence scales and the costs of disability. Journal of Public Economics, (56), 273-289.
• Kapteyn, A., and Van Praag, B. (1978). A new approach to the construction of family equivalence scales. European Economic Review, (7), 313-335.
• Kleiber, C., and Kotz, S. (2003). Statistical size distributions in economics and actuarial sciences. Hoboken, New Jersey: Wiley.
• Koulovatianos, C., Schröder, C., and Schmidt, U. (2005). On the income dependence of equivalence scales. Journal of Public Economics, (89), 967-996.
• Lambert, P. J. (2001). The distribution and redistribution of income. Manchester-New York: Manchester University Press.
• Lewbel, A. (1999). Consumer demand systems and household equivalence scales. In M. H.
• Pesaran, P. Schmidt, (Eds.). Handbook of Applied Econometrics. Volume II:
• Microeconomics. Oxford: Blackwell Publishers Ltd.
• Majumder, A., and Chakrabarty, M. (2008). Estimating equivalence scales through engel curve analysis. Discussion Paper ERU, no. 05-2008.
• Melenberg, B., and van Soest, A. (1995). Semiparametric estimation of equivalence scales using subjective information. Tilburg University.
• OECD. (1982). The OECD list of social indicators. Paris: OECD.
• OECD. (2008). Growing unequal? Income distribution and poverty in OECD countries. Paris: OECD.
• Pollak, R., and Wales, T. (1979). Welfare comparisons and equivalence scales. American Economic Review, (69), 216- 221.
• Pollak, R., and Wales, T. (1992). Demand system specification and estimation. London: Oxford University Press.
• Pollastri, A., and Zambruno, G. (2010). Distribution of the ratio of two independent Dagum random variables. Operation Research and Decisions, (3-4), 95-102.
• Schwarze, J. (2003). Using panel data on income satisfaction to estimate equivalence scale elasticity. Review of Income and Wealth, (49), 359-372.
• Slesnick, D. (1998). Empirical approaches to the measurement of welfare. Journal of Economic Literature, (36), 2108-2165.
• Szulc, A. (2009). A matching estimator of household equivalence scales. Economic Letters, (103), 81-83.
• Thomopoulos, N. T. (2017). Statistical distributions. Applications and parameter estimates. Cham: Switzerland: Springer International Publishing.
• Tinbergen, J. (1991). On the measurement of welfare. Journal of Econometrics, (50), 7-13.
• Van Praag, B. M. (1968). Individual welfare functions and consumer behavior. Amsterdam: North-Holland Publishing Company.
• Van Praag, B. M. (1991). Ordinal and cardinal utility: an integration of the two dimensions of the welfare concept. Journal of Econometrics, (50), 69-89.