IDEAS home Printed from https://ideas.repec.org/a/aea/aejpol/v14y2022i3p352-79.html
   My bibliography  Save this article

Gini and Optimal Income Taxation by Rank

Author

Listed:
  • Laurent Simula
  • Alain Trannoy

Abstract

We solve the nonlinear income tax program for rank-dependent social welfare functions, expressing the trade-off between size and inequality using the Gini and related families of positional indices. Absent bunching, ranks in the actual and optimal allocations are invariant. Exploiting this feature, we provide new, simple, and intuitive tax formulas for both the quasilinear and additive cases and new comparative static results. Our approach makes insights from optimal taxation more widely accessible. In some of our simulations the actual US tax policy is close to being optimal—except at the top, where optimal rates are much higher than in actuality.

Suggested Citation

  • Laurent Simula & Alain Trannoy, 2022. "Gini and Optimal Income Taxation by Rank," American Economic Journal: Economic Policy, American Economic Association, vol. 14(3), pages 352-379, August.
    • Handle: RePEc:aea:aejpol:v:14:y:2022:i:3:p:352-79
    DOI: 10.1257/pol.20200272
    as

    Download full text from publisher

    File URL: https://www.aeaweb.org/doi/10.1257/pol.20200272
    Download Restriction: no
    File URL: https://doi.org/10.3886/E141861V1
    Download Restriction: no
    File URL: https://www.aeaweb.org/doi/10.1257/pol.20200272.appx
    Download Restriction: no
    File URL: https://www.aeaweb.org/doi/10.1257/pol.20200272.ds
    Download Restriction: Access to full text is restricted to AEA members and institutional subscribers.
    File URL: https://libkey.io/10.1257/pol.20200272?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Laurent Simula, 2010. "Optimal nonlinear income tax and nonlinear pricing: optimality conditions and comparative static properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 199-220, July.
    2. Boadway, Robin & Jacquet, Laurence, 2008. "Optimal marginal and average income taxation under maximin," Journal of Economic Theory, Elsevier, vol. 143(1), pages 425-441, November.
    3. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    4. Emmanuel Saez & Joel Slemrod & Seth H. Giertz, 2012. "The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 50(1), pages 3-50, March.
    5. repec:hal:pseose:halshs-00944873 is not listed on IDEAS
    6. Etienne Lehmann & Laurent Simula & Alain Trannoy, 2014. "Tax me if you can! Optimal Nonlinear Income Tax Between Competing Governments," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1995-2030.
    7. Thomas Piketty & Emmanuel Saez, 2012. "Optimal Labor Income Taxation," NBER Working Papers 18521, National Bureau of Economic Research, Inc.
    8. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    9. Thomas Piketty & Emmanuel Saez, 2013. "Optimal Taxation of Labor Income," PSE-Ecole d'économie de Paris (Postprint) halshs-00944881, HAL.
    10. Thomas Piketty & Emmanuel Saez & Stefanie Stantcheva, 2014. "Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities," American Economic Journal: Economic Policy, American Economic Association, vol. 6(1), pages 230-271, February.
    11. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    12. Emmanuel Saez & Stefanie Stantcheva, 2016. "Generalized Social Marginal Welfare Weights for Optimal Tax Theory," American Economic Review, American Economic Association, vol. 106(1), pages 24-45, January.
    13. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    14. Weymark, John A, 1987. "Comparative Static Properties of Optimal Nonlinear Income Taxes," Econometrica, Econometric Society, vol. 55(5), pages 1165-1185, September.
    15. Alain Trannoy, 2019. "Talent, equality of opportunity and optimal non-linear income tax," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 17(1), pages 5-28, March.
    16. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    17. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
    18. Salanié, Bernard, 2011. "The Economics of Taxation," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262016346, April.
    19. Bastani, Spencer & Selin, Håkan, 2014. "Bunching and non-bunching at kink points of the Swedish tax schedule," Journal of Public Economics, Elsevier, vol. 109(C), pages 36-49.
    20. Raj Chetty & Nathaniel Hendren & Patrick Kline & Emmanuel Saez, 2014. "Where is the land of Opportunity? The Geography of Intergenerational Mobility in the United States," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1553-1623.
    21. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    22. Vincenzo Prete & Alessandro Sommacal & Claudio Zoli, 2016. "Optimal Non-Welfarist Income Taxation for Inequality and Polarization Reduction," Working Papers 23/2016, University of Verona, Department of Economics.
    23. Sen, Amartya, 1974. "Informational bases of alternative welfare approaches : Aggregation and income distribution," Journal of Public Economics, Elsevier, vol. 3(4), pages 387-403, November.
    24. Emmanuel Saez, 2010. "Do Taxpayers Bunch at Kink Points?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 180-212, August.
    25. Diamond, Peter A, 1998. "Optimal Income Taxation: An Example with a U-Shaped Pattern of Optimal Marginal Tax Rates," American Economic Review, American Economic Association, vol. 88(1), pages 83-95, March.
    26. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
    27. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February.
    28. Emmanuel Saez, 2001. "Using Elasticities to Derive Optimal Income Tax Rates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(1), pages 205-229.
    29. Bernard Salanié, 2005. "The Economics of Contracts: A Primer, 2nd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262195259, April.
    30. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Støstad, Morten Nyborg & Cowell, Frank, 2024. "Inequality as an externality: consequences for tax design," LSE Research Online Documents on Economics 123752, London School of Economics and Political Science, LSE Library.
    2. Morten Nyborg Støstad & Frank Cowell, 2021. "Inequality as an Externality: Consequences for Tax Design," PSE Working Papers halshs-03495989, HAL.
    3. Mikhail Lvovitch Dorofeev, 2021. "Does Income Inequality Create Excessive Threats to the Sustainable Development of Russia? Evidence from Intercountry Comparisons via Analysis of Inequality Heatmaps," Economies, MDPI, vol. 9(4), pages 1-17, November.
    4. Støstad, Morten Nyborg & Cowell, Frank, 2024. "Inequality as an externality: Consequences for tax design," Journal of Public Economics, Elsevier, vol. 235(C).
    5. Laurent Simula & Alain Trannoy, 2020. "Bunching and Rank-Dependent Optimal Income Taxation," CESifo Working Paper Series 8443, CESifo.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Laurent Simula & Alain Trannoy, 2020. "Bunching and Rank-Dependent Optimal Income Taxation," CESifo Working Paper Series 8443, CESifo.
    2. Laurent Simula & Alain Trannoy, 2023. "Bunching in rank-dependent optimal income tax schedules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 237-263, January.
    3. Morten Nyborg Støstad & Frank Cowell, 2021. "Inequality as an Externality: Consequences for Tax Design," PSE Working Papers halshs-03495989, HAL.
    4. Støstad, Morten Nyborg & Cowell, Frank, 2024. "Inequality as an externality: consequences for tax design," LSE Research Online Documents on Economics 123752, London School of Economics and Political Science, LSE Library.
    5. Rolf Aaberge & Ugo Colombino, 2014. "Labour Supply Models," Contributions to Economic Analysis, in: Handbook of Microsimulation Modelling, volume 127, pages 167-221, Emerald Group Publishing Limited.
    6. Laurence Jacquet & Etienne Lehmann, 2021. "Optimal Income Taxation with Composition Effects," Journal of the European Economic Association, European Economic Association, vol. 19(2), pages 1299-1341.
    7. Rolf Aaberge & Ugo Colombino, 2005. "Designing Optimal Taxes With a Microeconometric Model of Household Labour Supply," Public Economics 0510013, University Library of Munich, Germany.
    8. Rolf Aaberge, 2007. "Gini’s nuclear family," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 305-322, December.
    9. Carina Neisser, 2021. "The Elasticity of Taxable Income: A Meta-Regression Analysis [The top 1% in international and historical perspective]," The Economic Journal, Royal Economic Society, vol. 131(640), pages 3365-3391.
    10. Vincenzo Prete & Alessandro Sommacal & Claudio Zoli, 2016. "Optimal Non-Welfarist Income Taxation for Inequality and Polarization Reduction," Working Papers 23/2016, University of Verona, Department of Economics.
    11. Støstad, Morten Nyborg & Cowell, Frank, 2024. "Inequality as an externality: Consequences for tax design," Journal of Public Economics, Elsevier, vol. 235(C).
    12. Laurence Jacquet & Etienne Lehmann, 2015. "Optimal Income Taxation when Skills and Behavioral Elasticities are Heterogeneous," CESifo Working Paper Series 5265, CESifo.
    13. Saez, Emmanuel & Stantcheva, Stefanie, 2018. "A simpler theory of optimal capital taxation," Journal of Public Economics, Elsevier, vol. 162(C), pages 120-142.
    14. Rolf Aaberge & Tarjei Havnes & Magne Mogstad, 2021. "Ranking intersecting distribution functions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(6), pages 639-662, September.
    15. Aaberge, Rolf, 2001. "Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings," Journal of Economic Theory, Elsevier, vol. 101(1), pages 115-132, November.
    16. Margherita Fort & Nichole Schneeweis & Rudolf Winter-Ebmer, 2011. "More Schooling, More Children: Compulsory Schooling Reforms and Fertility in Europe," Economics working papers 2011-05, Department of Economics, Johannes Kepler University Linz, Austria.
    17. Satya Chakravarty, 2007. "A deprivation-based axiomatic characterization of the absolute Bonferroni index of inequality," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 339-351, December.
    18. Dai, Darong & Gao, Wenzheng & Tian, Guoqiang, 2020. "Relativity, mobility, and optimal nonlinear income taxation in an open economy," Journal of Economic Behavior & Organization, Elsevier, vol. 172(C), pages 57-82.
    19. Rolf Aaberge & Magne Mogstad, 2009. "On the Measurement of Long-Term Income Inequality and Income Mobility," ICER Working Papers 09-2009, ICER - International Centre for Economic Research.
    20. Rolf Aaberge & Magne Mogstad, 2011. "Robust inequality comparisons," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 353-371, September.

    More about this item

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • H24 - Public Economics - - Taxation, Subsidies, and Revenue - - - Personal Income and Other Nonbusiness Taxes and Subsidies
    • K34 - Law and Economics - - Other Substantive Areas of Law - - - Tax Law

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aea:aejpol:v:14:y:2022:i:3:p:352-79. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Michael P. Albert (email available below). General contact details of provider: https://edirc.repec.org/data/aeaaaea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.