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Distributional Comparative Statics

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  • Martin Kaae Jensen

Abstract

Distributional comparative statics is the study of how individual decisions and equilibrium outcomes vary with changes in the distribution of economic parameters (income, wealth, productivity, distortions, information, etc.). This paper develops tools to address such issues. Central to the developments is a new condition called quasi-concave differences which implies concavity of the policy function in optimization problems. The results are used to show how Bayesian equilibria respond to increased individual uncertainty (less precise private signals); and to derive conditions for concavity of policy functions in general stochastic dynamic programming problems. The latter generalizes Carroll and Kimball (1996) to models with borrowing constraints in the spirit of Aiyagari (1994).

Suggested Citation

  • Martin Kaae Jensen, 2015. "Distributional Comparative Statics," Discussion Papers in Economics 15/14, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:15/14
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    References listed on IDEAS

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    1. Martin Kaae Jensen, 2018. "Distributional Comparative Statics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 581-610.
    2. 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.
    3. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May.
    4. 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.
    5. Charles N. Noussair & Stefan T. Trautmann & Gijs van de Kuilen, 2014. "Higher Order Risk Attitudes, Demographics, and Financial Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 325-355.
    6. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    8. Mark Huggett, 2004. "Precautionary Wealth Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 769-781.
    9. Cowan, Simon & Vickers, John & Aguirre Pérez, Iñaki, 2009. "Monopoly Price Discrimination and Demand Curvature," IKERLANAK 2009-39, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    10. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    11. Jean-Charles Rochet & Jean Tirole, 2003. "Platform Competition in Two-Sided Markets," Journal of the European Economic Association, MIT Press, vol. 1(4), pages 990-1029, June.
    12. Iñaki Aguirre & Simon Cowan & John Vickers, 2010. "Monopoly Price Discrimination and Demand Curvature," American Economic Review, American Economic Association, vol. 100(4), pages 1601-1615, September.
    13. Dorfman, Robert, 1979. "A Formula for the Gini Coefficient," The Review of Economics and Statistics, MIT Press, vol. 61(1), pages 146-149, February.
    14. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    15. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    16. Marco Scarsini & Alfred Muller, 2006. "Stochastic order relations and lattices of probability measures," Post-Print hal-00539119, HAL.
    17. John Kennan, 2001. "Uniqueness of Positive Fixed Points for Increasing Concave Functions on Rn: An Elementary Result," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 893-899, October.
    18. Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(4), pages 401-414.
    19. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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    Cited by:

    1. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R2, Cowles Foundation for Research in Economics, Yale University, revised Oct 2021.
    2. Anwesha Banerjee & Nicolas Gravel, 2020. "Contribution to a public good under subjective uncertainty," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(3), pages 473-500, June.
    3. Martin Kaae Jensen, 2018. "Distributional Comparative Statics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 581-610.
    4. David Staines, 2023. "Stochastic Equilibrium the Lucas Critique and Keynesian Economics," Papers 2312.16214, arXiv.org.
    5. Camacho, Carmen & Kamihigashi, Takashi & Sağlam, Çağrı, 2018. "Robust comparative statics for non-monotone shocks in large aggregative games," Journal of Economic Theory, Elsevier, vol. 174(C), pages 288-299.
    6. Acikgoz, Omer, 2015. "On the Existence and Uniqueness of Stationary Equilibrium in Bewley Economies with Production," MPRA Paper 71066, University Library of Munich, Germany, revised 30 Apr 2016.
    7. Açıkgöz, Ömer T., 2018. "On the existence and uniqueness of stationary equilibrium in Bewley economies with production," Journal of Economic Theory, Elsevier, vol. 173(C), pages 18-55.
    8. Mekonnen, Teddy & Leal Vizcaíno, René, 2022. "Bayesian comparative statics," Theoretical Economics, Econometric Society, vol. 17(1), January.
    9. Stachurski, John & Toda, Alexis Akira, 2019. "An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity," Journal of Economic Theory, Elsevier, vol. 182(C), pages 1-24.
    10. 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.
    11. Damir Stijepic, 2019. "The impact of the productivity dispersion across employers on the labor's income share," Economics Bulletin, AccessEcon, vol. 39(1), pages 73-83.
    12. Uttiya Paul & Tarun Sabarwal, 2023. "Directional monotone comparative statics in function spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 153-169, April.
    13. Carmen Camacho & Hye-Jin Cho, 2020. "Sorting in Credit Rationing: An Elementary Survey," PSE Working Papers halshs-03030433, HAL.
    14. Carmen Camacho & Hye-Jin Cho, 2020. "Sorting in Credit Rationing: An Elementary Survey," Working Papers halshs-03030433, HAL.
    15. Sanjith Gopalakrishnan & Daniel Granot & Frieda Granot & Greys Sošić & Hailong Cui, 2021. "Incentives and Emission Responsibility Allocation in Supply Chains," Management Science, INFORMS, vol. 67(7), pages 4172-4190, July.
    16. Adriani, Fabrizio & Sonderegger, Silvia, 2019. "A theory of esteem based peer pressure," Games and Economic Behavior, Elsevier, vol. 115(C), pages 314-335.
    17. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R3, Cowles Foundation for Research in Economics, Yale University, revised Jun 2022.

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    More about this item

    Keywords

    Distributional comparative statics; concave policy functions; income distribution; inequality; uncertainty; Bayesian games; dynamic stochastic general equilibrium models; arg max correspondence.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • I30 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General

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