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Block-Recursive Equilibria in Heterogenous-Agent Models

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  • 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
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    as
    1. Edouard Challe & Xavier Ragot, 2016. "Precautionary Saving Over the Business Cycle," Economic Journal, Royal Economic Society, vol. 126(590), pages 135-164, February.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    7. 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.
    8. Shouyong Shi, 2009. "Directed Search for Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 77(2), pages 561-584, March.
    9. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(2), pages 284-306, April.
    10. Alessandro Citanna & Paolo Siconolfi, 2010. "Recursive Equilibrium in Stochastic Overlapping-Generations Economies," Post-Print hal-00537071, HAL.
    11. 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.
    12. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    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. Francisco M. Gonzalez & Shouyong Shi, 2010. "An Equilibrium Theory of Learning, Search, and Wages," Econometrica, Econometric Society, vol. 78(2), pages 509-537, March.
    19. Xavier Ragot, 2018. "Heterogeneous Agents in the Macroeconomy: Reduced-Heterogeneity Representations," Post-Print hal-03949569, HAL.
    20. 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.
    21. Ravn, Morten O. & Sterk, Vincent, 2017. "Job uncertainty and deep recessions," Journal of Monetary Economics, Elsevier, vol. 90(C), pages 125-141.
    22. 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.
    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. Citanna, Alessandro & Siconolfi, Paolo, 2012. "Recursive equilibrium in stochastic OLG economies: Incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 322-337.
    25. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
    26. 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.
    27. 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.
    28. 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.
    29. Alessandro Citanna & Paolo Siconolfi, 2010. "Recursive Equilibrium in Stochastic Overlapping-Generations Economies," Econometrica, Econometric Society, vol. 78(1), pages 309-347, January.
    30. 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.
    31. 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.
    32. Manuel Santos, "undated". "On Non-Existence of Markov Equilibria in Competitive-Market Economies," Working Papers 2133305, Department of Economics, W. P. Carey School of Business, Arizona State University.
    33. 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.
    34. Edouard Schaal, 2017. "Uncertainty and Unemployment," Econometrica, Econometric Society, vol. 85(6), pages 1675-1721, November.
    35. Johannes Brumm & Dominika Kryczka & Felix Kubler, 2017. "Recursive Equilibria in Dynamic Economies With Stochastic Production," Econometrica, Econometric Society, vol. 85, pages 1467-1499, September.
    36. 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.
    37. 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.
    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. 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.
    43. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    44. 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.
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    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

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