IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_8737.html
   My bibliography  Save this paper

Block-Recursive Equilibria in Heterogenous-Agent Models

Author

Listed:
  • Leo Kaas

Abstract

Equilibrium models with heterogeneous agents and aggregate uncertainty are difficult to analyze since policy functions and market prices depend on the cross-sectional distribution over agents’ state variables which is generally a high-dimensional object. This paper develops and applies a general model framework in which this problem does not arise. If sufficiently many agents enter the economy in every aggregate state of the world, policy functions and prices depend only on the exogenous aggregate state but are independent of the distribution over idiosyncratic states. The first part of this paper proves existence results for such block-recursive equilibria and derives an ergodic property which is useful for their computation. The second part applies this equilibrium concept to models of firm dynamics with competitive or frictional input markets and to incomplete-market economies with endogenous asset market participation.

Suggested Citation

  • Leo Kaas, 2020. "Block-Recursive Equilibria in Heterogenous-Agent Models," CESifo Working Paper Series 8737, CESifo.
  • Handle: RePEc:ces:ceswps:_8737
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp8737.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    2. Menzio, Guido & Shi, Shouyong, 2010. "Block recursive equilibria for stochastic models of search on the job," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1453-1494, July.
    3. Edouard Challe & Xavier Ragot, 2016. "Precautionary Saving Over the Business Cycle," Economic Journal, Royal Economic Society, vol. 126(590), pages 135-164, February.
    4. Leo Kaas & Philipp Kircher, 2015. "Efficient Firm Dynamics in a Frictional Labor Market," American Economic Review, American Economic Association, vol. 105(10), pages 3030-3060, October.
    5. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(2), pages 284-306, April.
    6. Alessandro Citanna & Paolo Siconolfi, 2010. "Recursive Equilibrium in Stochastic Overlapping-Generations Economies," Post-Print hal-00537071, HAL.
    7. Aubhik Khan & Julia K. Thomas, 2013. "Credit Shocks and Aggregate Fluctuations in an Economy with Production Heterogeneity," Journal of Political Economy, University of Chicago Press, vol. 121(6), pages 1055-1107.
    8. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    9. Lee, Yoonsoo & Mukoyama, Toshihiko, 2018. "A model of entry, exit, and plant-level dynamics over the business cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 96(C), pages 1-25.
    10. Miao, Jianjun, 2006. "Competitive equilibria of economies with a continuum of consumers and aggregate shocks," Journal of Economic Theory, Elsevier, vol. 128(1), pages 274-298, May.
    11. Xavier Ragot, 2018. "Heterogeneous Agents in the Macroeconomy: Reduced-Heterogeneity Representations," Post-Print hal-03949569, HAL.
    12. Gian Luca Clementi & Berardino Palazzo, 2016. "Entry, Exit, Firm Dynamics, and Aggregate Fluctuations," American Economic Journal: Macroeconomics, American Economic Association, vol. 8(3), pages 1-41, July.
    13. Francisco M. Gonzalez & Shouyong Shi, 2010. "An Equilibrium Theory of Learning, Search, and Wages," Econometrica, Econometric Society, vol. 78(2), pages 509-537, March.
    14. Adrien Bilal & Niklas Engbom & Simon Mongey & Giovanni L. Violante, 2022. "Firm and Worker Dynamics in a Frictional Labor Market," Econometrica, Econometric Society, vol. 90(4), pages 1425-1462, July.
    15. Michael W. L. Elsby & Ryan Michaels, 2013. "Marginal Jobs, Heterogeneous Firms, and Unemployment Flows," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(1), pages 1-48, January.
    16. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
    17. Marcelo L. Veracierto, 2002. "Plant-Level Irreversible Investment and Equilibrium Business Cycles," American Economic Review, American Economic Association, vol. 92(1), pages 181-197, March.
    18. Guido Menzio & Shouyong Shi, 2011. "Efficient Search on the Job and the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 468-510.
    19. Petr Sedláček & Vincent Sterk, 2017. "The Growth Potential of Startups over the Business Cycle," American Economic Review, American Economic Association, vol. 107(10), pages 3182-3210, October.
    20. Daron Acemoglu & Martin Kaae Jensen, 2015. "Robust Comparative Statics in Large Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 123(3), pages 587-640.
    21. 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.
    22. Santos, Manuel S., 2002. "On Non-existence of Markov Equilibria in Competitive-Market Economies," Journal of Economic Theory, Elsevier, vol. 105(1), pages 73-98, July.
    23. Aubhik Khan & Julia K. Thomas, 2008. "Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics," Econometrica, Econometric Society, vol. 76(2), pages 395-436, March.
    24. 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.
    25. Roberto M. Samaniego, 2008. "Entry, Exit and Business Cycles in a General Equilibrium Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 529-541, July.
    26. Shouyong Shi, 2009. "Directed Search for Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 77(2), pages 561-584, March.
    27. Lars A. Stole & Jeffrey Zwiebel, 1996. "Intra-firm Bargaining under Non-binding Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 375-410.
    28. Grand, François Le & Ragot, Xavier, 2018. "A class of tractable incomplete-market models for studying asset returns and risk exposure," European Economic Review, Elsevier, vol. 103(C), pages 39-59.
    29. R?diger Bachmann & Ricardo J. Caballero & Eduardo M. R. A. Engel, 2013. "Aggregate Implications of Lumpy Investment: New Evidence and a DSGE Model," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(4), pages 29-67, October.
    30. Albrecht, James W. & Holmlund, Bertil & Lang, Harald, 1991. "Comparative statics in dynamic programming models with an application to job search," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 755-769, October.
    31. Ravn, Morten O. & Sterk, Vincent, 2017. "Job uncertainty and deep recessions," Journal of Monetary Economics, Elsevier, vol. 90(C), pages 125-141.
    32. Citanna, Alessandro & Siconolfi, Paolo, 2012. "Recursive equilibrium in stochastic OLG economies: Incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 322-337.
    33. Alessandro Citanna & Paolo Siconolfi, 2010. "Recursive Equilibrium in Stochastic Overlapping-Generations Economies," Econometrica, Econometric Society, vol. 78(1), pages 309-347, January.
    34. 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.
    35. Hopenhayn, Hugo & Rogerson, Richard, 1993. "Job Turnover and Policy Evaluation: A General Equilibrium Analysis," Journal of Political Economy, University of Chicago Press, vol. 101(5), pages 915-938, October.
    36. Edouard Schaal, 2017. "Uncertainty and Unemployment," Econometrica, Econometric Society, vol. 85(6), pages 1675-1721, November.
    37. Johannes Brumm & Dominika Kryczka & Felix Kubler, 2017. "Recursive Equilibria in Dynamic Economies With Stochastic Production," Econometrica, Econometric Society, vol. 85, pages 1467-1499, September.
    38. Shi, Shouyong, 2001. "Frictional Assignment. I. Efficiency," Journal of Economic Theory, Elsevier, vol. 98(2), pages 232-260, June.
    39. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    40. repec:hal:spmain:info:hdl:2441/54k1p7hdq38odb1k39k1rdm8di is not listed on IDEAS
    41. Felix Kubler & Herakles Polemarchakis, 2004. "Stationary Markov equilibria for overlapping generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 623-643, October.
    42. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    43. 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)

    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. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    2. Lee, Yoonsoo & Mukoyama, Toshihiko, 2018. "A model of entry, exit, and plant-level dynamics over the business cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 96(C), pages 1-25.
    3. Pavol Majher, 2015. "Firm entry and exit, investment irreversibility, and business cycle dynamics," Vienna Economics Papers 1513, University of Vienna, Department of Economics.
    4. Richard Audoly, 2023. "Firm Dynamics and Random Search over the Business Cycle," Staff Reports 1069, Federal Reserve Bank of New York.
    5. Pavol Majher, 2015. "Firm entry and exit, investment irreversibility, and business cycle dynamics," Vienna Economics Papers vie1513, University of Vienna, Department of Economics.
    6. Leo Kaas & Philipp Kircher, 2015. "Efficient Firm Dynamics in a Frictional Labor Market," American Economic Review, American Economic Association, vol. 105(10), pages 3030-3060, October.
    7. François Le Grand & Xavier Ragot, 2017. "Optimal Fiscal Policy with Heterogeneous Agents and Aggregate Shocks," Working Papers hal-03458683, HAL.
    8. Sedláček, Petr, 2020. "Lost generations of firms and aggregate labor market dynamics," Journal of Monetary Economics, Elsevier, vol. 111(C), pages 16-31.
    9. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(1), pages 83-110, February.
    10. repec:hal:spmain:info:hdl:2441/6bl2553ksc9vlq1fltjs9h1cht is not listed on IDEAS
    11. Pau Roldan & Sophia Gilbukh, 2017. "Firm Dynamics and Pricing under Customer Capital Accumulation," 2017 Meeting Papers 1235, Society for Economic Dynamics.
    12. repec:hal:wpspec:info:hdl:2441/6bl2553ksc9vlq1fltjs9h1cht is not listed on IDEAS
    13. Ia Vardishvili, 2020. "Entry Decision, the Option to Delay Entry, and Business Cycles," Auburn Economics Working Paper Series auwp2020-07, Department of Economics, Auburn University.
    14. repec:spo:wpecon:info:hdl:2441/6bl2553ksc9vlq1fltjs9h1cht is not listed on IDEAS
    15. Bernstein, Joshua & Richter, Alexander W. & Throckmorton, Nathaniel A., 2021. "Cyclical net entry and exit," European Economic Review, Elsevier, vol. 136(C).
    16. Manuel Santos & Jianjun Miao, 2005. "Numerical Solution of Dynamic Non-Optimal Economies," 2005 Meeting Papers 266, Society for Economic Dynamics.
    17. repec:spo:wpmain:info:hdl:2441/6bl2553ksc9vlq1fltjs9h1cht is not listed on IDEAS
    18. Andrea Colciago & Marco Membretti, 2024. "Barriers to Entry and the Labor Market," Working Papers 813, DNB.
    19. Menzio, Guido & Shi, Shouyong & Sun, Hongfei, 2013. "A monetary theory with non-degenerate distributions," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2266-2312.
    20. Vasco M. Carvalho & Basile Grassi, 2019. "Large Firm Dynamics and the Business Cycle," American Economic Review, American Economic Association, vol. 109(4), pages 1375-1425, April.
    21. 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.
    22. Kubler, Felix & Scheidegger, Simon, 2023. "Uniformly self-justified equilibria," Journal of Economic Theory, Elsevier, vol. 212(C).
    23. Nicholas Bloom & Max Floetotto & Nir Jaimovich & Itay Saporta†Eksten & Stephen J. Terry, 2018. "Really Uncertain Business Cycles," Econometrica, Econometric Society, vol. 86(3), pages 1031-1065, May.
    24. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.

    More about this item

    Keywords

    block-recursive equilibrium; dynamic general equilibrium; heterogeneous agents;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

    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:_8737. 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.