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Multidimensioned Approaches to Welfare Analysis

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Handbook of Income Inequality Measurement

Part of the book series: Recent Economic Thought Series ((RETH,volume 71))

Abstract

A general survey of multidimensional approaches to the measurement and comparisons of welfare situations is provided. The survey covers some aspects of welfare representation, data availability and experience, axiomatic characterization of inequality measures, existing multidimensional indices, the stochastic dominance alternative for comparing welfare situations, and mobility. Applications to national and international data are described. The paper emphasizes implementability issues and statistical methods in the context of a comparative analysis of the philosophical and theoretical desirability of alternative approaches.

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References

  • Aigner, D. and A. Heins. 1967. “A Social Welfare View of the Measurement of Income Inequality.” Review of Income and Wealth 13: 13–25.

    Article  Google Scholar 

  • Anderson, G.J. 1996. “Nonparametric Tests of Stochastic Dominance in Income Distributions.” Econometrica 64(5): 1183–1193.

    Article  Google Scholar 

  • Arrow, K.J. 1971. “A Utilitarian Approach to the Concept of Equity in Public Expenditure.” Quarterly Journal of Economics 85: 409–415

    Article  Google Scholar 

  • Atkinson, A. 1970. “On the Measurement of Inequality.” Journal of Economic Theory II: 244–263.

    Article  Google Scholar 

  • Atkinson, A. and F. Bourguignon. 1982. “The Comparison of Multi-Dimensioned Distributions of Economic Status.” Review of Economic Studies 49: 183–201.

    Article  Google Scholar 

  • Atkinson, A. and F. Bourguignon. 1987. “Income Distribution and Differences in Needs.” In G.R. Feiwel, ed., Arrow and the Foundations of the Theory of Economic Policy. London: Macmillan.

    Google Scholar 

  • Atkinson, A. and F. Bourguignon. 1989. “The Design of Direct Taxation and Family Benefits.” Journal of Public Economics 41: 3–29.

    Article  Google Scholar 

  • Atkinson, A., F. Bourguignon, and C. Morrison. 1992. Empirical Studies of Earnings Mobility. Harwood Academic Publishers.

    Google Scholar 

  • Basu, K. 1980. Revealed Preference of Government. Cambridge: Cambridge University Press.

    Google Scholar 

  • Beach, C.M and R. Davidson. 1983. “Distribution-free Statistical Inference with Lorenz Curves and Income Shares.” Review of Economic Studies 50: 723–735.

    Article  Google Scholar 

  • Beach, C.M. and J. Richmond. 1985. “Joint Confidence Intervals for Income Shares and Lorenz Curves.” International Economic Review 26: 439–450.

    Article  Google Scholar 

  • Beach, C.M., R. Davidson and G.A. Slotsve. 1995. “Distribution-free Statistical Inference for Inequality Dominance with Crossing Lorenz Curves.” Unpublished paper N95A03, University of Aix-Marseille: GREQAM.

    Google Scholar 

  • Bishop, J.A., S. Chakraborti and P.D. Thistle. 1989 “Asymptotically Distribution Free Inference for Generalized Lorenz Curves.” Review of Economics and Statistics 71(4): 725–727.

    Google Scholar 

  • Bishop, J.A., J.P. Formby and W.J. Smith. 1991. “Lorenz Dominance and Welfare Changes in the US Distribution of Income, 1967-1986.” Review of Economics and Statistics 73: 134–139.

    Article  Google Scholar 

  • Bishop, J.A, J.P. Formby and P.D. Thistle. 1989. “Statistical Inference, Income Distributions, and Social Welfare.” Research on Economic Inequality 1: 49–82.

    Google Scholar 

  • Bishop, J.A., K.V. Chow and J.P. Formby. 1994. “Testing for Marginal Changes in Income Distributions with Lorenz and Concentration Curves.” International Economic Review 35(2): 479–488.

    Article  Google Scholar 

  • Blackorby, C. and D. Donaldson. 1978. “Measures of Relative Equality and Their Meaning in Terms of Social Welfare.” Journal of Economic Theory 18: 59–80.

    Article  Google Scholar 

  • Blundell, R. and A. Lewbel. 1991. “The Information Content of Equivalence Scales.” Journal of Econometrics (Annals issue edited by Maasoumi, cited below) 50(1/2): 49–68.

    Article  Google Scholar 

  • Bourguignon, F. 1979. “Decomposable Income Inequality Measures.” Econometrica 47: 901–920.

    Article  Google Scholar 

  • Bourguignon, F. 1989. “Family Size and Social Utility: Income Distribution Dominance Criteria.” Journal of Econometrics 42 (Annals): 67–80.

    Article  Google Scholar 

  • Coulter, F.A.E., F.A. Cowell and S.P. Jenkins. 1992. “Differences in Needs and Assessments of Income Distributions.” Bulletin of Economic Research 44(2): 77–124.

    Article  Google Scholar 

  • Cowell, F.A. 1989. “Sampling Variance and Decomposable Inequality Measures.” Journal of Econometrics 42(1): 27–42.

    Article  Google Scholar 

  • Cowell, F.A. and K. Kuga. 1981. “Inequality Measurement: An Axiomatic Approach.” European Economic Review 15: 287–305.

    Article  Google Scholar 

  • Cowell, F.A. and K. Kuga. 1990. “On the Relationship Between Inequality Measures and Social Welfare Functions.” Journal of Econometrics 43 (Annals): 91–102.

    Article  Google Scholar 

  • Dagum, C. 1990. “On the Relationship Between Income Inequality Measures and Social Welfare Functions.” Journal of Econometrics 43: 91–103.

    Article  Google Scholar 

  • Dagum, C. 1993. “The Social Welfare Bases of Gini and Other Income Inequality Measures.” Statistica 53: 3–30.

    Google Scholar 

  • Dardanoni, V. 1993. “Measuring Social Mobility.” Journal of Economic Theory 61: 372–394.

    Article  Google Scholar 

  • Dasgupta, P., A. Sen and D. Starrett. 1973. “Notes on the Measurement of Inequality.” Journal of Economic Theory 6: 180–187.

    Article  Google Scholar 

  • Davies, J.B. and M. Hoy. 1995. “Making Inequality Comparisons when Lorenz Curves Intersect.” American Economic Review 85: 980–986

    Google Scholar 

  • Durbin, J. 1973. Distribution Theory for Tests Based on the Sample Distribution Function. Philadelphia: SIAM.

    Book  Google Scholar 

  • Durbin, J. 1985. “The First Passage Density of a Continuous Gaussian Process to a General Boundary.” Journal of Applied Probability 22: 99–122.

    Article  Google Scholar 

  • Ebert, U. 1995. “Income Inequality and Differences in Household Size.” Mathematical Social Sciences 30: 37–55.

    Article  Google Scholar 

  • Ebert, U. 1997. “Social Welfare When Needs Differ: An Axiomatic Approach.” Economica 64(254): 233–244.

    Article  Google Scholar 

  • Gourieroux, C., A. Holly and A. Monfort. 1982. “Likelihood Ratio Test, Wald Test and Kuhn-Tucker Test in Linear Models with Inequality Constraints in the Regression Parameters.” Econometrica 50: 63–80.

    Article  Google Scholar 

  • Hirschberg, J.G., E. Maasoumi and D.J. Slottje. 1991. “Cluster Analysis for Measuring Welfare and Quality of Life Across Countries.” Journal of Econometrics 50(1/2) (Annals): 131–150.

    Article  Google Scholar 

  • Kaur, A., B.L.S. Prakasa Rao and H. Singh. 1994. “Testing for Second-Order Stochastic Dominance of Two Distributions.” Econometric Theory 10: 849–866.

    Article  Google Scholar 

  • Klecan, L., R. McFadden and D. McFadden. 1991. “A Robust Test for Stochastic Dominance.” Working paper, Department of Economics, MIT.

    Google Scholar 

  • Kodde, D.A. and F.C. Palm. 1986. “Wald Criteria for Jointly Testing Equality and Inequality Restrictions.” Econometrica 50: 1243–1248.

    Article  Google Scholar 

  • Kolm, S.C. 1969. “The Optimal Production of Social Justice.” In J. Margolis and H. Guitton, eds., Public Economics. London: Macmillan. Also presented at IEA conference on Public Economics, Biarritz, 1966.

    Google Scholar 

  • Kolm, S.C. 1976a. “Unequal Inequalities: I.” Journal of Economic Theory 12: 416–442.

    Article  Google Scholar 

  • Kolm, S.C. 1976b. “Unequal Inequalities: II.” Journal of Economic Theory 13: 82–111.

    Article  Google Scholar 

  • Kolm, S.C. 1977. “Multidimensional Egalitarianism.” Quarterly Journal of Economics 91:1–13.

    Article  Google Scholar 

  • Kudo, A. 1963. “A Multivariate Analogue of the One-sided Test.” Biometrica 50: 403–418.

    Google Scholar 

  • Lewbel, A. 1989. “Household Equivalence Scales and Welfare Comparisons.” Journal of Public Economics 39: 377–391.

    Article  Google Scholar 

  • Maasoumi, E. 1979. “An Entropy Index of Multivariable Inequality.” Department of Economics, University of Southern California: Mimeograph.

    Google Scholar 

  • Maasoumi, E. 1986a. “The Measurement and Decomposition of Multi-Dimensional Inequality.” Econometrica 54: 991–997.

    Article  Google Scholar 

  • Maasoumi, E. 1986b. “Unknown Regression Functions and Efficient Functional Forms: An Interpretation.” Advances in Econometrics 5: 301–309.

    Google Scholar 

  • Maasoumi, E. 1989a. “Composite Indices of Income and Other Developmental Indicators: A General Approach.” Research on Economic Inequality 1: 269–286.

    Google Scholar 

  • Maasoumi, E. 1989b. “Continuously Distributed Attributes and Measures of Multivariate Inequality.” Journal of Econometrics 42(1): 131–144.

    Article  Google Scholar 

  • Maasoumi, E. (ed.). 1991. Measurement of Welfare and Inequality, Annals of Econometrics, Journal of Econometrics 50(1/2).

    Google Scholar 

    Google Scholar 

  • Maasoumi, E. 1993. “A Compendium to Information Theory in Economics and Econometrics.” Econometric Reviews 12(3): 1–49.

    Google Scholar 

  • Maasoumi, E. 1998a. “Empirical Analyses of Welfare and Inequality.” In P. Schmidt and M.H. Pesaran, eds., Handbook of Applied Microeconometrics. Oxford: Basil Blackwell.

    Google Scholar 

  • Maasoumi, E. 1998b. “On Mobility.” In D. Giles and A. Ullah, eds., Handbook of Economic Statistics. New York: Marcel Dekker, Inc.

    Google Scholar 

  • Maasoumi, E. and J-H. Jeong. 1985. “The Trend and the Measurement of World Inequality over Extended Periods of Accounting.” Economics Letters 19: 295–301.

    Article  Google Scholar 

  • Maasoumi, E., J. Mills and S. Zandvakili. 1996. “Consensus Ranking of US Income Distributions: A Bootstrap Application of Tests for Stochastic Dominance.” Mimeograph, Department of Economics, Southern Methodist University, Texas.

    Google Scholar 

  • Maasoumi, E. and G. Nickelsburg. 1988. “Multivariate Measures of Well Being and an Analysis of Inequality in the Michigan Data.” Journal of Business and Economic Statistics 6(3): 327–334.

    Google Scholar 

  • Maasoumi, E. and S. Zandvakili. 1986. “A Class of Generalized Measures of Mobility with Applications.” Economics Letters 22: 97–102.

    Article  Google Scholar 

  • Maasoumi, E. and S. Zandvakili. 1989. “Mobility Profiles and Time Aggregates of Individual Incomes.” Research on Economic Inequality 1: 195–218.

    Google Scholar 

  • Maasoumi, E. and S. Zandvakili. 1990. “Generalized Entropy Measures of Mobility for Different Sexes and Income Levels.” Journal of Econometrics 43: 121–133.

    Article  Google Scholar 

  • McFadden, D. 1989. “Testing for Stochastic Dominance.” In T. Fomby and T.K. Seo, eds., Studies in the Economics of Uncertainty, Part II (in honor of J. Hadar). Springer-Verlag.

    Google Scholar 

  • Mills, J. and S. Zandvakili. 1996. “Bootstrapping Inequality Measures.” Working paper, Department of Economics, University of Cincinnati.

    Google Scholar 

  • Perlman, M.D. 1969. “One-sided Testing Problems in Multivariate Analysis.” Annals of Mathematical Statistics 40: 549–562.

    Article  Google Scholar 

  • Pollak, R. 1991. “Welfare Comparisons and Situation Comparisons.” Journal of Econometrics (Annals issue edited by Maasoumi, op. cited) 50(1/2): 31–48.

    Article  Google Scholar 

  • Pollak, R. and T. Wales. 1979. “Welfare Comparisons and Equivalence Scales.” American Economic Review 69:216–221.

    Google Scholar 

  • Ram, R. 1982. “Composite Indices of Physical Quality of Life, Basic Needs Fulfillment, and Income: A Principal Component Representation.” Journal of Development Economics 11: 227–247.

    Article  Google Scholar 

  • Robertson, T. and F.T. Wright. 1981. “Likelihood Ratio Tests for and Against Stochastic Ordering between Multinomial Populations.” Annals of Statistics 9: 1248–1257.

    Article  Google Scholar 

  • Ryu, H.K. “Maximum Entropy Estimation of Density and Regression Functions.” Journal of Econometrics 56: 397–440.

    Google Scholar 

  • Sen, A. 1970a. Collective Choice and Social Welfare. San Francisco, CA: Holden Day. Reprinted, North-Holland, 1979.

    Google Scholar 

  • Sen, A. 1970b. “Degrees of Cardinality and Aggregate Partial Orderings.” Econometrica 43: 393–409.

    Article  Google Scholar 

  • Sen, A. 1973. On Economic Inequality. Oxford, UK: Clarendon Press.

    Book  Google Scholar 

  • Sen, A. 1977. “On Weights and Measures: Informational Constraints in Social Welfare Analysis.” Econometrica 45: 1539–1572.

    Article  Google Scholar 

  • Shapiro, A. 1985. “Asymptotic Distribution of Test Statistics under Inequality Constraints.” Biometrica 72: 133–144.

    Article  Google Scholar 

  • Shapiro, A. 1988. “Towards a Unified Theory of Inequality Constrained Testing in Multivariate Analysis.” International Statistical Review 56: 49–62.

    Article  Google Scholar 

  • Shorrocks, A.F. 1978. “Income Inequality and Income Mobility.” Journal of Economic Theory 19: 376–393.

    Article  Google Scholar 

  • Shorrocks, A.F. 1980. “The Class of Additively Decomposable Inequality Measures.” Econometrica 48: 613–625.

    Article  Google Scholar 

  • Shorrocks, A.F. 1981. “Income Stability in the United States.” In N.A. Klevmarken and J.A. Lybeck, eds., The Statics and Dynamics of Income. Bristol, UK: Tieto, Ltd.

    Google Scholar 

  • Shorrocks, A.F. 1983. “Ranking Income Distribution.” Economica 50: 3–17.

    Article  Google Scholar 

  • Shorrocks, A.F. 1984. “Inequality Decomposition by Population Subgroups.” Econometrica 52: 1369–1385.

    Article  Google Scholar 

  • Shorrocks, A.F. 1995. “Inequality and Welfare Evaluation of Heterogeneous Income Distributions.” Unpublished paper, University of Essex, UK.

    Google Scholar 

  • Shorrocks, A.F. and J. Foster. 1987. “Transfer Sensitive Inequality Measures.” Review of Economic Studies 54: 485–497.

    Article  Google Scholar 

  • Slottje, D.J. 1989. “Econometric Issues in Analyzing Inequality. Part I: Estimation.” Journal of Econometrics (Special Annals Issue).

    Google Scholar 

  • Slottje, D.J. 1990. “Econometric issues in Analyzing Inequality. Part II: Modelling Methods.” Journal of Econometrics (Special Annals Issue).

    Google Scholar 

  • Tsui, K-Y. 1992. “Complete Indices of Well-Being: Axiomatic Foundations.” Mimeograph, Department of Economics, Chinese University of Hong Kong.

    Google Scholar 

  • Tsui, K-Y. 1995. “Multidimensional Generalizations of the Relative and Absolute Inequality Indices: The Atkinson-Kolm-Sen Approach.” Journal of Economic Theory 67: 251–265.

    Article  Google Scholar 

  • van Praag, B.M.S. 1991. “Ordinal and Cardinal Utility: An Integration of Two Dimensions of the Welfare Concept.” In E. Maasoumi (ed.), Measurement of Welfare and Inequality, Annals of Econometrics, Journal of Econometrics 50: 69–90.

    Google Scholar 

  • Whitmore, G.A. and M.C. Findley. 1978. Stochastic Dominance: An Approach to Decision Making Under Risk. Lexington, MA: Heath.

    Google Scholar 

  • Wolak, F.A. 1988. “Duality in Testing Multivariate Hypothesis.” Biometrica 75: 611–615.

    Article  Google Scholar 

  • Wolak, F.A. 1991. “The Local Nature of Hypothesis Testing Involving Inequality Constraints.” Econometrica 59: 981–995.

    Article  Google Scholar 

  • Xu, K. 1995. “Asymptotically Distribution-Free Statistical Test for Generalized Lorenz Curves: An Alternative Approach.” Department of Economics, Dalhousie University, Canada. Presented at the 7th World Congress of Econometric Society, Japan.

    Google Scholar 

  • Xu, K., G. Fisher and D. Wilson. 1995. “New Distribution-Free-Tests for Stochastic Dominance.” Working paper No. 95-02, Department of Economics, Dalhousie University, Canada.

    Google Scholar 

  • Atkinson, A. and F. Bourguignon. 1982. “The Comparison of Multi-dimensional Distribution of Economic Status.” Review of Economic Studies 49: 183–201.

    Article  Google Scholar 

  • Atkinson, A. and F. Bourguignon. 1987. “Income Distribution and Differences in Needs.” In G.R. Feiwel, ed., Arrow and the Foundations of the Theory of Economic Policy, London: Macmillan.

    Google Scholar 

  • Ebert, U. 1995. “Income Inequality and Differences in Household Size.” Mathematical Social Sciences 30: 37–55.

    Article  Google Scholar 

  • Maasoumi, E. 1986. “The Measurement and Decomposition of Multidimensional Inequality.” Econometrica 54: 991–997.

    Article  Google Scholar 

  • Shorrocks, A. 1995. “Inequality and Welfare Evaluation of Heterogeneous Income Distributions.” Mimeo, University of Essex.

    Google Scholar 

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Maasoumi, E. (1999). Multidimensioned Approaches to Welfare Analysis. In: Silber, J. (eds) Handbook of Income Inequality Measurement. Recent Economic Thought Series, vol 71. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4413-1_16

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  • DOI: https://doi.org/10.1007/978-94-011-4413-1_16

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