IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v154y2014icp310-348.html
   My bibliography  Save this article

Incomplete market dynamics and cross-sectional distributions

Author

Listed:
  • Toda, Alexis Akira

Abstract

The size distributions of many economic variables seem to obey the double power law, that is, the power law holds in both the upper and the lower tails. I explain this emergence of the double power law—which has important economic, econometric, and social implications—using a tractable dynamic stochastic general equilibrium model with heterogeneous agents subject to aggregate and idiosyncratic investment risks. I establish theoretical properties such as existence, uniqueness, and constrained efficiency of equilibrium, and provide a numerical algorithm that is guaranteed to converge. The model is widely applicable: it allows for arbitrary homothetic CRRA recursive preferences, an arbitrary Markov process governing aggregate shocks, and an arbitrary number of technologies and assets with arbitrary portfolio constraints.

Suggested Citation

  • Toda, Alexis Akira, 2014. "Incomplete market dynamics and cross-sectional distributions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 310-348.
  • Handle: RePEc:eee:jetheo:v:154:y:2014:i:c:p:310-348
    DOI: 10.1016/j.jet.2014.09.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053114001367
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, January.
    2. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2006. "Idiosyncratic production risk, growth and the business cycle," Journal of Monetary Economics, Elsevier, vol. 53(6), pages 1095-1115, September.
    3. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Urban Structure and Growth," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 597-624.
    4. Grossman, S J & Melino, Angelo & Shiller, Robert J, 1987. "Estimating the Continuous-Time Consumption-Based Asset-Pricing Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(3), pages 315-327, July.
    5. Hanno Lustig & Stijn Van Nieuwerburgh, 2008. "The Returns on Human Capital: Good News on Wall Street is Bad News on Main Street," Review of Financial Studies, Society for Financial Studies, vol. 21(5), pages 2097-2137, September.
    6. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, Oxford University Press, vol. 122(3), pages 1103-1144.
    7. Tom Krebs, 2003. "Human Capital Risk and Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 118(2), pages 709-744.
    8. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    9. Thomas Piketty & Emmanuel Saez, 2003. "Income Inequality in the United States, 1913–1998," The Quarterly Journal of Economics, Oxford University Press, vol. 118(1), pages 1-41.
    10. Ozaki, Hiroyuki & Streufert, Peter A., 1996. "Dynamic programming for non-additive stochastic objectives," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 391-442.
    11. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
    12. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
    13. Tom Krebs, 2006. "Recursive equilibrium in endogenous growth models with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 505-523, November.
    14. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    15. Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.
    16. Vasia Panousi, 2010. "Capital taxation with entrepreneurial risk," Finance and Economics Discussion Series 2010-56, Board of Governors of the Federal Reserve System (U.S.).
    17. Svensson, Lars E. O., 1989. "Portfolio choice with non-expected utility in continuous time," Economics Letters, Elsevier, vol. 30(4), pages 313-317, October.
    18. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    19. Streufert, Peter A., 1992. "An abstract topological approach to dynamic programming," Journal of Mathematical Economics, Elsevier, vol. 21(1), pages 59-88.
    20. Kieran Walsh, 2014. "Portfolio Choice and Partial Default in Emerging Markets: a quantitative analysis," 2014 Meeting Papers 789, Society for Economic Dynamics.
    21. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
    22. Angeletos, George-Marios & Panousi, Vasia, 2009. "Revisiting the supply side effects of government spending," Journal of Monetary Economics, Elsevier, vol. 56(2), pages 137-153, March.
    23. Ma, Chenghu, 1993. "Market Equilibrium with Heterogenous Recursive-Utility-Maximizing Agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 243-266, April.
    24. Makoto Nirei & Wataru Souma, 2007. "A Two Factor Model Of Income Distribution Dynamics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(3), pages 440-459, September.
    25. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    26. Peter A. Streufert, 1990. "Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 79-97.
    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. Alexis Akira Toda & Kieran James Walsh, 2017. "Fat tails and spurious estimation of consumption‐based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1156-1177, September.
    2. Toda, Alexis Akira, 2017. "A Note On The Size Distribution Of Consumption: More Double Pareto Than Lognormal," Macroeconomic Dynamics, Cambridge University Press, vol. 21(06), pages 1508-1518, September.
    3. Kieran Walsh, 2014. "Portfolio Choice and Partial Default in Emerging Markets: a quantitative analysis," 2014 Meeting Papers 789, Society for Economic Dynamics.
    4. Braun, R. Anton & Nakajima, Tomoyuki, 2016. "Uninsured risk, stagnation, and fiscal policy," FRB Atlanta Working Paper 2016-4, Federal Reserve Bank of Atlanta, revised 01 Mar 2016.
    5. Miyoshi, Yoshiyuki & Toda, Alexis Akira, 2017. "Growth effects of annuities and government transfers in perpetual youth models," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 1-6.
    6. Fischer, Thomas, 2017. "Thomas Piketty and the rate of time preference," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 111-133.
    7. repec:red:issued:16-223 is not listed on IDEAS
    8. repec:eee:dyncon:v:84:y:2017:i:c:p:77-90 is not listed on IDEAS
    9. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    10. Alexis Akira Toda, 2015. "Asset Prices and Efficiency in a Krebs Economy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(4), pages 957-978, October.
    11. Andrea L. Eisfeldt & Hanno Lustig & Lei Zhang, 2017. "Complex Asset Markets," NBER Working Papers 23476, National Bureau of Economic Research, Inc.
    12. Kasa, Kenneth & Lei, Xiaowen, 2018. "Risk, uncertainty, and the dynamics of inequality," Journal of Monetary Economics, Elsevier, vol. 94(C), pages 60-78.
    13. Gregory Phelan & Alexis Akira Toda, 2015. "On the Robustness of Theoretical Asset Pricing Models," Department of Economics Working Papers 2015-10, Department of Economics, Williams College.
    14. Dan Cao & Wenlan Luo, 2017. "Persistent Heterogeneous Returns and Top End Wealth Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 301-326, October.
    15. repec:aea:aejmac:v:9:y:2017:i:3:p:36-71 is not listed on IDEAS
    16. Staley, Mark, 2018. "The Knowledge-Diffusion Bottleneck in Economic Growth and Development," MPRA Paper 87255, University Library of Munich, Germany.
    17. Shuhei Aoki & Makoto Nirei, 2014. "Zipf’s Law, Pareto’s Law, and the Evolution of Top Incomes in the U.S," UTokyo Price Project Working Paper Series 023, University of Tokyo, Graduate School of Economics.
    18. Shuhei Aoki & Makoto Nirei, 2016. "Pareto Distribution of Income in Neoclassical Growth Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 20, pages 25-42, April.

    More about this item

    Keywords

    Applied general equilibrium analysis; Emergence; Inequality; Power law; Robustness;

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    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:eee:jetheo:v:154:y:2014:i:c:p:310-348. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.