IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_9534.html
   My bibliography  Save this paper

Optimal Taxation with Multiple Incomes and Types

Author

Listed:
  • Kevin Spiritus
  • Etienne Lehmann
  • Sander Renes
  • Floris Zoutman

Abstract

We analyze the optimal nonlinear income tax schedule when taxpayers earn multiple incomes and differ along many unobserved dimensions. We derive the necessary conditions for the government’s optimum using both a tax perturbation and a mechanism design approach, and show that both methods produce the same results. Our main contribution is to propose a numerical method to find the optimal tax schedule. Applied to the optimal taxation of couples, we find that optimal isotax curves are very close to linear and parallel. The slope of isotax curves is strongly affected by the relative tax-elasticity of male and female income. We make several additional contributions, including a test for Pareto efficiency and a condition on primitives that ensures the government’s necessary conditions are sufficient and the solution to the problem is unique.

Suggested Citation

  • Kevin Spiritus & Etienne Lehmann & Sander Renes & Floris Zoutman, 2022. "Optimal Taxation with Multiple Incomes and Types," CESifo Working Paper Series 9534, CESifo.
    • Handle: RePEc:ces:ceswps:_9534
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp9534.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    2. Alessandro Gavazza, 2011. "Leasing and Secondary Markets: Theory and Evidence from Commercial Aircraft," Journal of Political Economy, University of Chicago Press, vol. 119(2), pages 325-377.
    3. Jacquet, Laurence & Lehmann, Etienne, 2021. "How to Tax Different Incomes?," IZA Discussion Papers 14739, Institute of Labor Economics (IZA).
    4. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    5. Raphael Calel, 2020. "Adopt or Innovate: Understanding Technological Responses to Cap-and-Trade," American Economic Journal: Economic Policy, American Economic Association, vol. 12(3), pages 170-201, August.
    6. Xepapadeas, Anastasios & de Zeeuw, Aart, 1999. "Environmental Policy and Competitiveness: The Porter Hypothesis and the Composition of Capital," Journal of Environmental Economics and Management, Elsevier, vol. 37(2), pages 165-182, March.
    7. Henrik Jacobsen Kleven & Claus Thustrup Kreiner & Emmanuel Saez, 2009. "The Optimal Income Taxation of Couples," Econometrica, Econometric Society, vol. 77(2), pages 537-560, March.
    8. François Bourguignon & Amedeo Spadaro, 2012. "Tax–benefit revealed social preferences," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(1), pages 75-108, March.
    9. Raouf Boucekkine & Natali Hritonenko & Yuri Yatsenko, "undated". "Optimal Firm Behavior under Environmental Constraints," Working Papers 2008_11, Business School - Economics, University of Glasgow.
    10. Petrick, Sebastian & Wagner, Ulrich J., 2014. "The impact of carbon trading on industry: Evidence from German manufacturing firms," Kiel Working Papers 1912, Kiel Institute for the World Economy (IfW Kiel).
    11. Gauthier, Stéphane & Laroque, Guy, 2009. "Separability and public finance," Journal of Public Economics, Elsevier, vol. 93(11-12), pages 1168-1174, December.
    12. Brueckner, Jan K. & Zhang, Anming, 2010. "Airline emission charges: Effects on airfares, service quality, and aircraft design," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 960-971, September.
    13. S. A. Montzka & E. J. Dlugokencky & J. H. Butler, 2011. "Non-CO2 greenhouse gases and climate change," Nature, Nature, vol. 476(7358), pages 43-50, August.
    14. Nejat Karabakal & Jack R. Lohmann & James C. Bean, 1994. "Parallel Replacement under Capital Rationing Constraints," Management Science, INFORMS, vol. 40(3), pages 305-319, March.
    15. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2005. "Environmental policy, the porter hypothesis and the composition of capital: Effects of learning and technological progress," Journal of Environmental Economics and Management, Elsevier, vol. 50(2), pages 434-446, September.
    16. Brueckner, Jan K. & Abreu, Chrystyane, 2020. "Does the fuel-conservation effect of higher fuel prices appear at both the aircraft-model and aggregate airline levels?," Economics Letters, Elsevier, vol. 197(C).
    17. Philippe Aghion & Antoine Dechezleprêtre & David Hémous & Ralf Martin & John Van Reenen, 2016. "Carbon Taxes, Path Dependency, and Directed Technical Change: Evidence from the Auto Industry," Journal of Political Economy, University of Chicago Press, vol. 124(1), pages 1-51.
    18. 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.
    19. Aart Gerritsen & Bas Jacobs & Alexandra V. Rusu & Kevin Spiritus, 2020. "Optimal Taxation of Capital Income with Heterogeneous Rates of Return," Tinbergen Institute Discussion Papers 20-038/VI, Tinbergen Institute.
    20. Raphael Calel & Antoine Dechezleprêtre, 2016. "Environmental Policy and Directed Technological Change: Evidence from the European Carbon Market," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 173-191, March.
    21. Meredith L. Fowlie, 2009. "Incomplete Environmental Regulation, Imperfect Competition, and Emissions Leakage," American Economic Journal: Economic Policy, American Economic Association, vol. 1(2), pages 72-112, August.
    22. Borghesi, Simone & Cainelli, Giulio & Mazzanti, Massimiliano, 2015. "Linking emission trading to environmental innovation: Evidence from the Italian manufacturing industry," Research Policy, Elsevier, vol. 44(3), pages 669-683.
    23. Felix J. Bierbrauer & Pierre C. Boyer & Emanuel Hansen, 2023. "Pareto‐Improving Tax Reforms and the Earned Income Tax Credit," Econometrica, Econometric Society, vol. 91(3), pages 1077-1103, May.
    24. Benmelech, Efraim & Bergman, Nittai K., 2011. "Vintage capital and creditor protection," Journal of Financial Economics, Elsevier, vol. 99(2), pages 308-332, February.
    25. Dechezleprêtre, Antoine & Gennaioli, Caterina & Martin, Ralf & Muûls, Mirabelle & Stoerk, Thomas, 2022. "Searching for carbon leaks in multinational companies," Journal of Environmental Economics and Management, Elsevier, vol. 112(C).
    26. Hendren, Nathaniel, 2020. "Measuring economic efficiency using inverse-optimum weights," Journal of Public Economics, Elsevier, vol. 187(C).
    27. Peter J. Hammond, 1979. "Straightforward Individual Incentive Compatibility in Large Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 263-282.
    28. Wayne B. Gray & Ronald J. Shadbegian, 1998. "Environmental Regulation, Investment Timing, and Technology Choice," Journal of Industrial Economics, Wiley Blackwell, vol. 46(2), pages 235-256, June.
    29. Fageda, Xavier & Teixidó, Jordi J., 2022. "Pricing carbon in the aviation sector: Evidence from the European emissions trading system," Journal of Environmental Economics and Management, Elsevier, vol. 111(C).
    30. John Haltiwanger & Russell Cooper & Laura Power, 1999. "Machine Replacement and the Business Cycle: Lumps and Bumps," American Economic Review, American Economic Association, vol. 89(4), pages 921-946, September.
    31. Scheuer, Florian & Werning, Iván, 2016. "Mirrlees meets Diamond-Mirrlees," CEPR Discussion Papers 11172, C.E.P.R. Discussion Papers.
    32. repec:adr:anecst:y:2014:i:113-114:p:12 is not listed on IDEAS
    33. Rahel Aichele & Gabriel Felbermayr, 2015. "Kyoto and Carbon Leakage: An Empirical Analysis of the Carbon Content of Bilateral Trade," The Review of Economics and Statistics, MIT Press, vol. 97(1), pages 104-115, March.
    34. 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.
    35. Popp, David & Newell, Richard, 2012. "Where does energy R&D come from? Examining crowding out from energy R&D," Energy Economics, Elsevier, vol. 34(4), pages 980-991.
    36. Jacobs, Bas & Jongen, Egbert L.W. & Zoutman, Floris T., 2017. "Revealed social preferences of Dutch political parties," Journal of Public Economics, Elsevier, vol. 156(C), pages 81-100.
    37. Normann Lorenz & Dominik Sachs, 2016. "Identifying Laffer Bounds: A Sufficient-Statistics Approach with an Application to Germany," Scandinavian Journal of Economics, Wiley Blackwell, vol. 118(4), pages 646-665, October.
    38. Olivier Bargain & Andreas Peichl, 2016. "Own-wage labor supply elasticities: variation across time and estimation methods," IZA Journal of Labor Economics, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 5(1), pages 1-31, December.
    39. Matthew E. Kahn & Jerry Nickelsburg, 2016. "An Economic Analysis of U.S Airline Fuel Economy Dynamics from 1991 to 2015," NBER Working Papers 22830, National Bureau of Economic Research, Inc.
    40. Atkinson, A. B. & Stiglitz, J. E., 1976. "The design of tax structure: Direct versus indirect taxation," Journal of Public Economics, Elsevier, vol. 6(1-2), pages 55-75.
    41. Hartman, Joseph C., 2004. "Multiple asset replacement analysis under variable utilization and stochastic demand," European Journal of Operational Research, Elsevier, vol. 159(1), pages 145-165, November.
    42. Austan Goolsbee, 1998. "The Business Cycle, Financial Performance, and the Retirement of Capital Goods," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(2), pages 474-496, April.
    43. aus dem Moore, Nils & Großkurth, Philipp & Themann, Michael, 2019. "Multinational corporations and the EU Emissions Trading System: The specter of asset erosion and creeping deindustrialization," Journal of Environmental Economics and Management, Elsevier, vol. 94(C), pages 1-26.
    44. Achim I. Czerny, 2015. "The Role of Capital Costs for Airline Responses to Emission Charges," Journal of Transport Economics and Policy, University of Bath, vol. 49(3), pages 475-495, July.
    45. Robert J. Barro & Charles J. Redlick, 2011. "Macroeconomic Effects From Government Purchases and Taxes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(1), pages 51-102.
    46. Adler, Nicole & Martini, Gianmaria & Volta, Nicola, 2013. "Measuring the environmental efficiency of the global aviation fleet," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 82-100.
    47. Gray, Wayne B & Shadbegian, Ronald J, 1998. "Environmental Regulation, Investment Timing, and Technology Choice," Journal of Industrial Economics, Wiley Blackwell, vol. 46(2), pages 235-256, June.
    48. Gavazza, Alessandro, 2010. "Asset liquidity and financial contracts: Evidence from aircraft leases," Journal of Financial Economics, Elsevier, vol. 95(1), pages 62-84, January.
    49. Sander Renes & Floris Zoutman, 2017. "As Easy as ABC? Multidimensional Screening in Public Finance," CESifo Working Paper Series 6301, CESifo.
    50. 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.
    51. Brueckner, Jan K. & Abreu, Chrystyane, 2017. "Airline fuel usage and carbon emissions: Determining factors," Journal of Air Transport Management, Elsevier, vol. 62(C), pages 10-17.
    52. Russell W. Cooper & John C. Haltiwanger, 2006. "On the Nature of Capital Adjustment Costs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(3), pages 611-633.
    53. Csereklyei, Zsuzsanna & Stern, David I., 2020. "Flying More Efficiently: Joint Impacts of Fuel Prices, Capital Costs and Fleet Size on Airline Fleet Fuel Economy," Ecological Economics, Elsevier, vol. 175(C).
    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. Jacquet, Laurence & Lehmann, Etienne, 2021. "How to Tax Different Incomes?," IZA Discussion Papers 14739, Institute of Labor Economics (IZA).
    2. Hellwig, Christian & Werquin, Nicolas, 2022. "A Fair Day's Pay for a Fair Day's Work: Optimal Tax Design as Redistributional Arbitrage," TSE Working Papers 22-1284, Toulouse School of Economics (TSE), revised Jan 2023.
    3. Aronsson, Thomas & Johansson-Stenman, Olof & Wendner, Ronald, 2021. "Charity, Status, and Optimal Taxation: Welfarist and Non-Welfarist Approaches," MPRA Paper 108337, University Library of Munich, Germany.
    4. Felix Bierbrauer & Pierre Boyer & Andreas Peichl & Daniel Weishaar, 2023. "The Taxation of Couples," Rationality and Competition Discussion Paper Series 405, CRC TRR 190 Rationality and Competition.
    5. Kevin Spiritus, 2022. "Optimal Commodity Taxation Under Non-linear Income Taxation," Tinbergen Institute Discussion Papers 22-018/VI, Tinbergen Institute.
    6. Robin Boadway & Kevin Spiritus, 2021. "Optimal Taxation of Normal and Excess Returns to Risky Assets," Tinbergen Institute Discussion Papers 21-025/VI, Tinbergen Institute.

    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. Laurence Jacquet & Etienne Lehmann, 2023. "Optimal tax problems with multidimensional heterogeneity: a mechanism design approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 135-164, January.
    2. Felix J. Bierbrauer & Pierre C. Boyer & Emanuel Hansen, 2023. "Pareto‐Improving Tax Reforms and the Earned Income Tax Credit," Econometrica, Econometric Society, vol. 91(3), pages 1077-1103, May.
    3. Hellwig, Christian & Werquin, Nicolas, 2022. "A Fair Day's Pay for a Fair Day's Work: Optimal Tax Design as Redistributional Arbitrage," TSE Working Papers 22-1284, Toulouse School of Economics (TSE), revised Jan 2023.
    4. Jacquet, Laurence & Lehmann, Etienne, 2021. "How to Tax Different Incomes?," IZA Discussion Papers 14739, Institute of Labor Economics (IZA).
    5. Bierbrauer Felix J., 2016. "Effizienz oder Gerechtigkeit?," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 17(1), pages 2-24, April.
    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. Jacobs, Bas & Jongen, Egbert L.W. & Zoutman, Floris T., 2017. "Revealed social preferences of Dutch political parties," Journal of Public Economics, Elsevier, vol. 156(C), pages 81-100.
    8. Boadway,Robin & Cuff,Katherine, 2022. "Tax Policy," Cambridge Books, Cambridge University Press, number 9781108949453.
    9. Koehne, Sebastian & Sachs, Dominik, 2022. "Pareto-improving reforms of tax deductions," European Economic Review, Elsevier, vol. 148(C).
    10. Antoine Ferey & Benjamin Lockwood & Dmitry Taubinsky, 2021. "Sufficient Statistics for Nonlinear Tax Systems with General Across-Income Heterogeneity," NBER Working Papers 29582, National Bureau of Economic Research, Inc.
    11. Spencer Bastani & Jacob Lundberg, 2017. "Political preferences for redistribution in Sweden," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(4), pages 345-367, December.
    12. Felix J. Bierbrauer & Pierre C. Boyer & Andreas Peichl, 2021. "Politically Feasible Reforms of Nonlinear Tax Systems," American Economic Review, American Economic Association, vol. 111(1), pages 153-191, January.
    13. Doligalski, Paweł & Rojas, Luis E., 2023. "Optimal redistribution with a shadow economy," Theoretical Economics, Econometric Society, vol. 18(2), May.
    14. Barbieri, Nicolò & Marzucchi, Alberto & Rizzo, Ugo, 2023. "Green technologies, interdependencies, and policy," Journal of Environmental Economics and Management, Elsevier, vol. 118(C).
    15. Felix Bierbrauer, 2016. "Effizienz oder Gerechtigkeit? Ungleiche Einkommen, ungleiche Vermögen und die Theorie der optimalen Besteuerung," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2016_03, Max Planck Institute for Research on Collective Goods.
    16. Ayaz, Mehmet & Fricke, Lea & Fuest, Clemens & Sachs, Dominik, 2023. "Who should bear the burden of COVID-19 related fiscal pressure? An optimal income taxation perspective," European Economic Review, Elsevier, vol. 153(C).
    17. Christian Moser & Pedro Olea de Souza e Silva, 2019. "Optimal Paternalistic Savings Policies," Opportunity and Inclusive Growth Institute Working Papers 17, Federal Reserve Bank of Minneapolis.
    18. Albert Jan Hummel, 2021. "Monopsony Power, Income Taxation and Welfare," CESifo Working Paper Series 9128, CESifo.
    19. Nicolo Barbieri & Alberto Marzucchi & Ugo Rizzo, 2021. "Green technologies, complementarities, and policy," SPRU Working Paper Series 2021-08, SPRU - Science Policy Research Unit, University of Sussex Business School.
    20. Albert Jan Hummel, 2021. "Monopsony power, income taxation and welfare," Tinbergen Institute Discussion Papers 21-051/VI, Tinbergen Institute.

    More about this item

    Keywords

    nonlinear optimal taxation; multidimensional screening; household income taxation;
    All these keywords.

    JEL classification:

    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies
    • H24 - Public Economics - - Taxation, Subsidies, and Revenue - - - Personal Income and Other Nonbusiness Taxes and Subsidies
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ces:ceswps:_9534. 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: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.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.