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Block-recursive equilibria in heterogeneous-agent models

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  • Kaas, Leo

Abstract

Equilibrium models with heterogeneous agents and aggregate uncertainty are difficult to analyze since policy functions and market prices usually depend on the cross-sectional distribution over agents' state variables which is a high-dimensional object. This paper considers a general model framework in which this curse of dimensionality does not arise because equilibrium prices are determined by market entry conditions and are independent of the cross-sectional distribution (block-recursive equilibrium). The paper first establishes existence and ergodic theorems which are useful for the theoretical analysis and numerical implementation of block-recursive equilibria. Then these results are applied to models of firm dynamics with competitive or frictional input markets and to incomplete-market economies with endogenous asset market participation.

Suggested Citation

  • Kaas, Leo, 2023. "Block-recursive equilibria in heterogeneous-agent models," Journal of Economic Theory, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:jetheo:v:212:y:2023:i:c:s0022053123000856
    DOI: 10.1016/j.jet.2023.105689
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    6. Edouard Challe & Xavier Ragot, 2016. "Precautionary Saving Over the Business Cycle," Economic Journal, Royal Economic Society, vol. 126(590), pages 135-164, February.
    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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