IDEAS home Printed from https://ideas.repec.org/p/hal/wpspec/hal-03476095.html
   My bibliography  Save this paper

Managing Inequality over Business Cycles: Optimal Policies with Heterogeneous Agents and Aggregate Shocks

Author

Listed:
  • François Le Grand

    (EM - EMLyon Business School)

  • Xavier Ragot

    (OFCE - Observatoire français des conjonctures économiques (Sciences Po) - Sciences Po - Sciences Po, ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

Abstract

We present a truncation theory of idiosyncratic histories for heterogeneous agent models. This method allows us to derive optimal Ramsey policies in heterogeneous agent models with aggregate shocks, in general frameworks. We use this method to characterize the optimal level of unemployment insurance over the business cycle in a production economy, with occasionally binding credit constraints.

Suggested Citation

  • François Le Grand & Xavier Ragot, 2020. "Managing Inequality over Business Cycles: Optimal Policies with Heterogeneous Agents and Aggregate Shocks," SciencePo Working papers hal-03476095, HAL.
  • Handle: RePEc:hal:wpspec:hal-03476095
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03476095
    as

    Download full text from publisher

    File URL: https://sciencespo.hal.science/hal-03476095/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Den Haan, Wouter J., 2010. "Assessing the accuracy of the aggregate law of motion in models with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 79-99, January.
    2. Edouard Challe & Julien Matheron & Xavier Ragot & Juan F. Rubio‐Ramirez, 2017. "Precautionary saving and aggregate demand," Quantitative Economics, Econometric Society, vol. 8(2), pages 435-478, July.
    3. Boppart, Timo & Krusell, Per & Mitman, Kurt, 2018. "Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative," Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 68-92.
    4. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-240, April.
    5. repec:hal:wpspec:info:hdl:2441/6bl2553ksc9vlq1fltjs9h1cht is not listed on IDEAS
    6. Sushant Acharya & Edouard Challe & Keshav Dogra, 2023. "Optimal Monetary Policy According to HANK," American Economic Review, American Economic Association, vol. 113(7), pages 1741-1782, July.
    7. Florin Bilbiie & Xavier Ragot, 2021. "Optimal Monetary Policy and Liquidity with Heterogeneous Households," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 41, pages 71-95, July.
    8. Julio Dávila & Jay H. Hong & Per Krusell & José‐Víctor Ríos‐Rull, 2012. "Constrained Efficiency in the Neoclassical Growth Model With Uninsurable Idiosyncratic Shocks," Econometrica, Econometric Society, vol. 80(6), pages 2431-2467, November.
    9. Edouard Challe & Xavier Ragot, 2016. "Precautionary Saving Over the Business Cycle," Economic Journal, Royal Economic Society, vol. 126(590), pages 135-164, February.
    10. YiLi Chien & Harold Cole & Hanno Lustig, 2012. "Is the Volatility of the Market Price of Risk Due to Intermittent Portfolio Rebalancing?," American Economic Review, American Economic Association, vol. 102(6), pages 2859-2896, October.
    11. Edouard Challe, 2017. "Uninsured Unemployment Risk and Optimal Monetary Policy," Working Papers 2017-54, Center for Research in Economics and Statistics.
    12. Bewley, Truman, 1983. "A Difficulty with the Optimum Quantity of Money," Econometrica, Econometric Society, vol. 51(5), pages 1485-1504, September.
    13. Bilbiie, Florin O., 2008. "Limited asset markets participation, monetary policy and (inverted) aggregate demand logic," Journal of Economic Theory, Elsevier, vol. 140(1), pages 162-196, May.
    14. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
    15. Elisa Faraglia & Albert Marcet & Rigas Oikonomou & Andrew Scott, 2019. "Government Debt Management: The Long and the Short of It," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(6), pages 2554-2604.
    16. Alisdair McKay & Ricardo Reis, 2021. "Optimal Automatic Stabilizers [Consumption versus Expenditure]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(5), pages 2375-2406.
    17. Sebastian Dyrda & Marcelo Pedroni, 2015. "Optimal Fiscal Policy in a Model with Uninsurable Idiosyncratic Shocks," Working Papers tecipa-550, University of Toronto, Department of Economics.
    18. Jonathan Heathcote, 2005. "Fiscal Policy with Heterogeneous Agents and Incomplete Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 161-188.
    19. Aiyagari, S. Rao & McGrattan, Ellen R., 1998. "The optimum quantity of debt," Journal of Monetary Economics, Elsevier, vol. 42(3), pages 447-469, October.
    20. Yili Chien & Harold Cole & Hanno Lustig, 2011. "A Multiplier Approach to Understanding the Macro Implications of Household Finance," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 199-234.
    21. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2017. "Optimal Tax Progressivity: An Analytical Framework," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1693-1754.
    22. Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2021. "Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models," Econometrica, Econometric Society, vol. 89(5), pages 2375-2408, September.
    23. Eichenbaum, Martin & Parker, Jonathan A. (ed.), . "NBER Macroeconomics Annual 2017," National Bureau of Economic Research Books, University of Chicago Press, number 9780226577838, July.
    24. Per Krusell & Toshihiko Mukoyama & Ayşegül Şahin, 2010. "Labour-Market Matching with Precautionary Savings and Aggregate Fluctuations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1477-1507.
    25. Nicola Pavoni & Christopher Sleet & Matthias Messner, 2018. "The Dual Approach to Recursive Optimization: Theory and Examples," Econometrica, Econometric Society, vol. 86(1), pages 133-172, January.
    26. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    27. Iván Werning, 2015. "Incomplete Markets and Aggregate Demand," NBER Working Papers 21448, National Bureau of Economic Research, Inc.
    28. Aiyagari, S Rao, 1995. "Optimal Capital Income Taxation with Incomplete Markets, Borrowing Constraints, and Constant Discounting," Journal of Political Economy, University of Chicago Press, vol. 103(6), pages 1158-1175, December.
    29. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    30. Thomas Winberry, 2018. "A method for solving and estimating heterogeneous agent macro models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1123-1151, November.
    31. Harold Cole & Felix Kubler, 2012. "Recursive Contracts, Lotteries and Weakly Concave Pareto Sets," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(4), pages 479-500, October.
    32. Raj Chetty, 2009. "Sufficient Statistics for Welfare Analysis: A Bridge Between Structural and Reduced-Form Methods," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 451-488, May.
    33. Krueger, Dirk & Ludwig, Alexander, 2016. "On the optimal provision of social insurance: Progressive taxation versus education subsidies in general equilibrium," Journal of Monetary Economics, Elsevier, vol. 77(C), pages 72-98.
    34. Pascal Michaillat & Emmanuel Saez, 2022. "An economical business-cycle model [Breaking through the zero lower bound]," Oxford Economic Papers, Oxford University Press, vol. 74(2), pages 382-411.
    35. Krusell, Per & Mukoyama, Toshihiko & Smith Jr., Anthony A., 2011. "Asset prices in a Huggett economy," Journal of Economic Theory, Elsevier, vol. 146(3), pages 812-844, May.
    36. Jonas Kolsrud & Camille Landais & Peter Nilsson & Johannes Spinnewijn, 2018. "The Optimal Timing of Unemployment Benefits: Theory and Evidence from Sweden," American Economic Review, American Economic Association, vol. 108(4-5), pages 985-1033, April.
    37. François Le Grand & Xavier Ragot, 2017. "Optimal Fiscal Policy with Heterogeneous Agents and Aggregate Shocks," Working Papers hal-03458683, HAL.
    38. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    39. SeHyoun Ahn & Greg Kaplan & Benjamin Moll & Thomas Winberry & Christian Wolf, 2018. "When Inequality Matters for Macro and Macro Matters for Inequality," NBER Macroeconomics Annual, University of Chicago Press, vol. 32(1), pages 1-75.
    40. Edouard Challe, 2020. "Uninsured Unemployment Risk and Optimal Monetary Policy in a Zero-Liquidity Economy," American Economic Journal: Macroeconomics, American Economic Association, vol. 12(2), pages 241-283, April.
    41. Raj Chetty & Amy Finkelstein, 2012. "Social Insurance: Connecting Theory to Data," NBER Working Papers 18433, National Bureau of Economic Research, Inc.
    42. Christian Bayer & Ralph Luetticke & Lien Pham‐Dao & Volker Tjaden, 2019. "Precautionary Savings, Illiquid Assets, and the Aggregate Consequences of Shocks to Household Income Risk," Econometrica, Econometric Society, vol. 87(1), pages 255-290, January.
    43. David G. Luenberger & Yinyu Ye, 2016. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 4, number 978-3-319-18842-3, December.
    44. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
    45. repec:hal:pseose:halshs-01313771 is not listed on IDEAS
    46. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    47. Yikai Wang & Hans Holter & Marcus Hagedorn, 2015. "The Optimum Quantity of Capital and Debt," 2015 Meeting Papers 1220, Society for Economic Dynamics.
    48. Villemot, Sébastien, 2011. "Solving rational expectations models at first order: what Dynare does," Dynare Working Papers 2, CEPREMAP.
    49. Raj Chetty & Adam Guren & Day Manoli & Andrea Weber, 2011. "Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins," American Economic Review, American Economic Association, vol. 101(3), pages 471-475, May.
    50. Robert Shimer, 2003. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies: Evidence and Theory," NBER Working Papers 9536, National Bureau of Economic Research, Inc.
    51. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    52. Ravn, Morten O. & Sterk, Vincent, 2017. "Job uncertainty and deep recessions," Journal of Monetary Economics, Elsevier, vol. 90(C), pages 125-141.
    53. Edward J. Green, 1994. "Individual Level Randomness in a Nonatomic Population," GE, Growth, Math methods 9402001, University Library of Munich, Germany.
    54. Mitman, Kurt & Rabinovich, Stanislav, 2015. "Optimal unemployment insurance in an equilibrium business-cycle model," Journal of Monetary Economics, Elsevier, vol. 71(C), pages 99-118.
    55. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    56. repec:hal:spmain:info:hdl:2441/6bl2553ksc9vlq1fltjs9h1cht is not listed on IDEAS
    57. Young, Eric R., 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm and non-stochastic simulations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 36-41, January.
    58. Ludwig Straub & Iván Werning, 2020. "Positive Long-Run Capital Taxation: Chamley-Judd Revisited," American Economic Review, American Economic Association, vol. 110(1), pages 86-119, January.
    59. V. V. Chari & Pedro Teles & Juan Nicolini, 2016. "More on the Optimal Taxation of Capital," 2016 Meeting Papers 1364, Society for Economic Dynamics.
    60. Lucas, Robert Jr., 1990. "Liquidity and interest rates," Journal of Economic Theory, Elsevier, vol. 50(2), pages 237-264, April.
    61. Lucas, Robert E, Jr, 1975. "An Equilibrium Model of the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 83(6), pages 1113-1144, December.
    62. repec:hal:spmain:info:hdl:2441/54k1p7hdq38odb1k39k1rdm8di is not listed on IDEAS
    63. Vincenzo Quadrini, 1999. "The Importance Of Entrepreneurship For Wealth Concentration And Mobility," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 45(1), pages 1-19, March.
    64. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    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. Stephane Auray & Aurelien Eyquem, 2024. "Optimal Unemployment Insurance in a THANK Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 53, pages 173-193, July.
    2. Chien, YiLi & Wen, Yi, 2021. "Time-inconsistent optimal quantity of debt," European Economic Review, Elsevier, vol. 140(C).
    3. Chen, Yunmin & Chien, YiLi & Wen, Yi & Yang, C.C., 2021. "Are unconditional lump-sum transfers a good idea?," Economics Letters, Elsevier, vol. 209(C).
    4. Le Grand, François & Ragot, Xavier, 2021. "Sovereign default and liquidity: The case for a world safe asset," Journal of International Economics, Elsevier, vol. 131(C).
    5. Mark Aguiar & Manuel Amador & Cristina Arellano, 2021. "Micro Risks and Pareto Improving Policies," Working Papers 2021-15, Princeton University. Economics Department..
    6. Mark Aguiar & Manuel Amador & Cristina Arellano, 2021. "Micro Risks and Pareto Improving Policies with Low Interest Rates," Staff Report 625, Federal Reserve Bank of Minneapolis.
    7. Julien Pascal, 2024. "Heterogeneity in macroeconomic models: A review of theory and computation," BCL working papers 185, Central Bank of Luxembourg.
    8. François Le Grand & Xavier Ragot, 2023. "Should we increase or decrease public debt? Optimal fiscal policy with heterogeneous agents," Working Papers halshs-03922359, HAL.
    9. Le Grand, François & Ragot, Xavier, 2023. "Optimal policies with heterogeneous agents: Truncation and transitions," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).
    10. François Le Grand & Xavier Ragot, 2022. "Refining the truncation method to solve heterogeneous-agent models," Post-Print hal-04384033, HAL.
    11. Grimaud, Alex, 2021. "Precautionary saving and un-anchored expectations," MPRA Paper 110651, University Library of Munich, Germany.
    12. Grimaud, Alex, 2021. "Precautionary saving and un-anchored expectations," MPRA Paper 108931, University Library of Munich, Germany.
    13. Beatriz González & Galo Nuño & Dominik Thaler & Silvia Albrizio, 2021. "Firm heterogeneity, capital misallocation and optimal monetary policy," Working Papers 2145, Banco de España.

    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. François Le Grand & Xavier Ragot, 2022. "Managing Inequality Over Business Cycles: Optimal Policies With Heterogeneous Agents And Aggregate Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 511-540, February.
    2. François Le Grand & Xavier Ragot, 2017. "Optimal Fiscal Policy with Heterogeneous Agents and Aggregate Shocks," Sciences Po Economics Discussion Papers 2017-03, Sciences Po Departement of Economics.
    3. repec:hal:spmain:info:hdl:2441/6bl2553ksc9vlq1fltjs9h1cht is not listed on IDEAS
    4. repec:hal:wpspec:info:hdl:2441/6bl2553ksc9vlq1fltjs9h1cht is not listed on IDEAS
    5. Krueger, D. & Mitman, K. & Perri, F., 2016. "Macroeconomics and Household Heterogeneity," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 843-921, Elsevier.
    6. Galo Nuño & Carlos Thomas, 2020. "Optimal Monetary Policy with Heterogeneous Agents," CESifo Working Paper Series 8670, CESifo.
    7. Chipeniuk, Karsten O. & Katz, Nets Hawk & Walker, Todd B., 2022. "Households, auctioneers, and aggregation," European Economic Review, Elsevier, vol. 141(C).
    8. François Le Grand & Xavier Ragot, 2023. "Should we increase or decrease public debt? Optimal fiscal policy with heterogeneous agents," SciencePo Working papers Main halshs-03922359, HAL.
    9. Grimaud, Alex, 2021. "Precautionary saving and un-anchored expectations," ECON WPS - Working Papers in Economic Theory and Policy 08/2021, TU Wien, Institute of Statistics and Mathematical Methods in Economics, Economics Research Unit.
    10. Kase, Hanno & Melosi, Leonardo & Rottner, Matthias, 2024. "Estimating Nonlinear Heterogeneous Agent Models with Neural Networks," The Warwick Economics Research Paper Series (TWERPS) 1499, University of Warwick, Department of Economics.
    11. Le Grand, François & Ragot, Xavier, 2023. "Optimal policies with heterogeneous agents: Truncation and transitions," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).
    12. Darracq Pariès, Matthieu & Notarpietro, Alessandro & Kilponen, Juha & Papadopoulou, Niki & Zimic, Srečko & Aldama, Pierre & Langenus, Geert & Alvarez, Luis Julian & Lemoine, Matthieu & Angelini, Elena, 2021. "Review of macroeconomic modelling in the Eurosystem: current practices and scope for improvement," Occasional Paper Series 267, European Central Bank.
    13. François Legrand & Xavier Ragot, 2016. "Optimal policy with heterogeneous agents and aggregate shocks : An application to optimal public debt dynamics," 2016 Meeting Papers 1272, Society for Economic Dynamics.
    14. Karsten O. Chipeniuk & Nets Hawk Katz & Todd Bruce Walker, 2022. "Households, Auctioneers, and Aggregation," CAEPR Working Papers 2022-005 Classification-E, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    15. Ralph Luetticke, 2021. "Transmission of Monetary Policy with Heterogeneity in Household Portfolios," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(2), pages 1-25, April.
    16. Schesch, Constantin, 2024. "Pseudospectral methods for continuous-time heterogeneous-agent models," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    17. Florin Bilbiie & Xavier Ragot, 2021. "Optimal Monetary Policy and Liquidity with Heterogeneous Households," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 41, pages 71-95, July.
    18. Nils M. Gornemann & Keith Kuester & Makoto Nakajima, 2021. "Doves for the Rich, Hawks for the Poor? Distributional Consequences of Systematic Monetary Policy," Opportunity and Inclusive Growth Institute Working Papers 50, Federal Reserve Bank of Minneapolis.
    19. Bayer, Christian & Born, Benjamin & Luetticke, Ralph, 2023. "The liquidity channel of fiscal policy," Journal of Monetary Economics, Elsevier, vol. 134(C), pages 86-117.
    20. Oliver Pfäuti & Fabian Seyrich, 2022. "A Behavioral Heterogeneous Agent New Keynesian Model," Discussion Papers of DIW Berlin 1995, DIW Berlin, German Institute for Economic Research.
    21. Francesco Ferlaino, 2024. "Does the financial accelerator accelerate inequalities?," Working Papers 538, University of Milano-Bicocca, Department of Economics.
    22. YiLi Chien & Yi Wen, 2022. "Optimal Ramsey Taxation in Heterogeneous Agent Economies with Quasi-Linear Preferences," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 46, pages 124-160, October.

    More about this item

    Keywords

    Incomplete markets; Optimal policies; Heterogeneous agent models;
    All these keywords.

    JEL classification:

    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

    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:hal:wpspec:hal-03476095. 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: Contact - Sciences Po Departement of Economics (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.