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Detecting a change in wealth concentration without the knowledge of the wealth distribution

Abstract

Consumption is commonly used as a proxy for permanent income. We go a step further by establishing the link between the distribution of consumption and that of permanent income in terms of dominance orderings. We introduce two new dominance orderings, the Generalized Top Lorenz test and the related affluence ordering. If consumption is a concave function of permanent income, we get an indirect and robust method to detect a change in permanent income concentration when the full stream of income receipts along the life cycle is unknown and only consumption data are available. Our application on US data for the period 1980–2002 points out the difficult start in life of people belonging to the “Baby loser generation” (people born in the sixties) with respect to the previous and following cohort.

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References

  1. 1.

    Atkinson, A.B.: On the measurement of inequality. J. Econ. Theory 2, 244–263 (1970)

    Article  Google Scholar 

  2. 2.

    Atkinson, A.B, Saez, E., Piketty, T.: Top incomes in the long run of history revised January 2010. J. Econ. Lit. (2010, forthcoming)

  3. 3.

    Attanasio, O.T., Browning, M.: Consumption over the life cycle and over business cycle. Am. Econ. Rev. 85, 1118–1137 (1995)

    Google Scholar 

  4. 4.

    Attanasio, O., Battistin, E., Leicester, A.: From micro to macro, from poor to rich: consumption and income in the UK and the US. Working paper, University College London (2006)

  5. 5.

    Bavier, R.: Reconciliation of income and consumption data in poverty measurement. J. Policy Anal. Manage. 27, 40–62 (2008)

    Article  Google Scholar 

  6. 6.

    Browning, M., Lusardi, A.: Household saving: micro theories and micro facts. J. Econ. Lit. 34, 1797–1855 (2006)

    Google Scholar 

  7. 7.

    Carroll, D., Kimball, M.: On the concavity of the consumption function. Econometrica 64(4), 981–992 (1996)

    Article  Google Scholar 

  8. 8.

    Chauvel, L.: Un nouvel âge de la société am éricaine? Dynamiques et perspectives de la structure sociale aux É tats-Unis (1950–2000). Revue de l’OFCE 76, 7–51 (2001)

    Google Scholar 

  9. 9.

    Chauvel, L.: Social generations, life chances and welfare states. Working Paper for Transforming the Democratic Balance Among State, Market and Society: Comparative Perspective on France and the Developed Democracies, 17–18 May 2002. Minda de Gunzburg Center for European Studies, Harvard University (2002)

  10. 10.

    Dalaker, J., Naifeh, M.: U.S. Bureau of the Census, Current Population Reports, Series P60-201. Poverty in the United States: 1997. U.S. Government Printing Office, Washington, D.C. (1998)

    Google Scholar 

  11. 11.

    Davidson, R., Duclos, J.-Y.: Statistical inference for stochastic dominance and for the measurement of poverty and inequality. Econometrica 68(6), 1435–1464 (2000)

    Article  Google Scholar 

  12. 12.

    Deaton, A.: The Analysis of Household Surveys: a Microeconomic Approach to Development Policy, by Angus S. Deaton Softcover. World Bank Publications (1997)

  13. 13.

    Dynan, K.E., Skinner, J., Zeldes, S.P.: Do the rich save more? J. Polit. Econ. 112, 397–444 (2004)

    Article  Google Scholar 

  14. 14.

    Easterlin, R.A.: Birth and Fortune, 2nd edn. Basic Books, New York (1987)

    Google Scholar 

  15. 15.

    Foster, J.E., Shorrocks, A.F.: Poverty orderings. Econometrica 56, 173–177 (1988)

    Article  Google Scholar 

  16. 16.

    Friedman, M.A.: A Theory of the Consumption Function. NBER, Princeton University Press (1957)

    Google Scholar 

  17. 17.

    Garner, T., Janini, G., Passero, W., Paszkiewicz, L., Vandemia, M.: The consumer expenditure survey in comparison: focus on personal consumption expenditures. Paper Presented at the Federal Economic Statistics Advisory Committee Meeting, Bureau of Labor Statistics, Washington, DC (2003)

  18. 18.

    Kanbur, R., Mukherjee, D.: Poverty, relative to the ability to eradicate it: an index of poverty reduction failure. Econ. Lett. 97, 52–57 (2007)

    Article  Google Scholar 

  19. 19.

    Krueger, D., Perri, F.: Does income inequality lead to consumption inequality? Evidence and theory. CFS Working Paper Series 200515 (2005)

  20. 20.

    Krueger, D., Perri, F.: Does income inequality lead to consumption inequality? Evidence and theory. Rev. Econ. Stud. 73, 163–193 (2006)

    Article  Google Scholar 

  21. 21.

    Lusardi, A., Beeler, J.: Saving between cohorts: the role of planning. In: Mandrian, B., Mitchell, O., Soldo, B. (eds.) Redefining Retirement: How Will Boomers Fare? Oxford University Press (2007)

  22. 22.

    Marshall, A.W., Olkin, I.: Inequalities: Theory of Majorization and its Applications. Academic Press, New York (1979)

    Google Scholar 

  23. 23.

    Medeiros, M.: The rich and the poor: the construction of an affluence line fromthe Poverty line. Soc. Indic. Res. 78(1), 1–18 (2006)

    Article  Google Scholar 

  24. 24.

    Meyer, B.D., Sullivan, J.X.: Measuring the well-being of the poor using income and consumption. J. Hum. Resour. 38, 1180–1220 (2003)

    Article  Google Scholar 

  25. 25.

    Meyer, B.D., Sullivan, J.X.: Changes in the consumption, income, and well-being of single mother headed families. Am. Econ. Rev. 98, 2221–2241 (2008)

    Article  Google Scholar 

  26. 26.

    Moyes, P.: Some classes of functions that preserve the inequality and welfare orderings of income distributions. J. Econ. Theory 49, 347–359 (1989)

    Article  Google Scholar 

  27. 27.

    Paulin, G., Riordon, P.: Making it on their own: the baby boom meets generation X. Mon. Labor Rev. 121, 10–21 (1998)

    Google Scholar 

  28. 28.

    Paulin, G.: Expenditure patterns of young single adults: two recent generations compared. Mon. Labor Rev. 123, 19–50 (2008)

    Google Scholar 

  29. 29.

    Peichl, A., Schaefer, T., Scheicher, C.: Measuring richness and poverty a micro data application to Europe and Germany. Rev. Income Wealth 56, 597–619 (2010)

    Article  Google Scholar 

  30. 30.

    Peluso, E., Trannoy, A.: Does less inequality among household mean less inequality among individuals? J. Econ. Theory 133, 568–578 (2007)

    Article  Google Scholar 

  31. 31.

    Piketty T., Postel-Vinay, G., Rosenthal, J.L.: Wealth concentration in a developing economy: Paris and France, 1807–1994. Am. Econ. Rev. 96(1), 236–256 (2006)

    Article  Google Scholar 

  32. 32.

    Sahn, D.E., Stifel, D.C.: Poverty comparisons over time and across countries in africa. World Dev. 28, 2123–2155 (2000)

    Article  Google Scholar 

  33. 33.

    Sen, P.K.: The harmonic gini coefficient and affluence indexes. Math. Soc. Sci. 16, 65–76 (1988)

    Article  Google Scholar 

  34. 34.

    Shaked, M., Shanthikumar, J.G.: Stochastic Orders. Springer (2006)

  35. 35.

    Shorrocks, A.F.: Ranking income distribution. Economica 50, 3–17 (1983)

    Article  Google Scholar 

  36. 36.

    Shorrocks, A.F., Foster, J.E.: Transfer sensitive inequality measures. Rev. Econ. Stud. 54, 485–497 (1987)

    Article  Google Scholar 

  37. 37.

    Sierminska, E., Brandolini, A., Smeeding, T.: The Luxembourg wealth study: a cross-country comparable database for household wealth research. J. Econ. Inequality 4(3), 375–383 (2006)

    Article  Google Scholar 

  38. 38.

    Slesnick, D.T.: Aggregate consumption and saving in the Postwar United States. Rev. Econ. Stat. 74(4), 585–597 (1992)

    Article  Google Scholar 

  39. 39.

    Slesnick, D.T.: Are our data relevant to the theory? The case Of aggregate consumption. J. Bus. Econ. Stat. 16(1), 52–61 (1998)

    Article  Google Scholar 

  40. 40.

    Slesnick, D.T.: Consumption and Social Welfare: Living Standards and their Distribution in the United States. Cambridge University Press, Cambridge (2001)

    Google Scholar 

  41. 41.

    Triplett, J.E.: Measuring consumption: the post-1973 slowdown and the research issues. Federal Research Bank of St. Louis Review, May/June 79(3), 9–42 (1997)

    Google Scholar 

  42. 42.

    Wolff, E.N.: Changing inequality of wealth. Am. Econ. Rev. 82, 552–558 (1992)

    Google Scholar 

  43. 43.

    Wolff, E.N.: Recent trends in the size distribution of household wealth. J. Econ. Perspect. 12, 131–150 (1998)

    Article  Google Scholar 

  44. 44.

    Wolff, E.N.: Recent trends in household Wealth in the United States: rising debt and the middle-class squeeze. Working Paper 12, 131–150 (2007)

    Google Scholar 

  45. 45.

    Wolff, E.N., Zacharias, A.: Household wealth and the measurement of economic well-being in the United States. J. Econ. Inequality 7(2), 83–115 (2009)

    Article  Google Scholar 

  46. 46.

    Zeldes, S.P.: Optimal consumption with stochastic income: Deviations from certainty equivalence. Q. J. Econ. 104, 275–298 (1989)

    Article  Google Scholar 

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Correspondence to Alessandra Michelangeli.

Additional information

Preliminary versions of this paper have been presented at the Ecineq Conference (Berlin 2007) LGVC (Marseille 2009), PET Conference (Galway 2009), and the Cornell/LSE Conference on Inequality: New Directions. We thank participants and in particular Rolf Aaberge, Anthony Atkinson, Frank Cowell, Ravi Kanbur, Nicolas Pistolesi and two referees for useful comments. We also thank Fabrizio Perri for the availability of his data. Alessandra Michelangeli thanks MIUR (Prin 2007) for financial support. The usual disclaimer applies.

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Michelangeli, A., Peluso, E. & Trannoy, A. Detecting a change in wealth concentration without the knowledge of the wealth distribution. J Econ Inequal 9, 373–391 (2011). https://doi.org/10.1007/s10888-010-9160-1

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Keywords

  • Concavity
  • Wealth
  • Affluence orderings
  • Consumption

JEL Classification

  • D31
  • D63
  • D91