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Maximum Entropy Estimation of Statistical Equilibrium in Economic Quantal Response Models

Author

Listed:
  • Ellis Scharfenaker

    (Department of Economics, University of Missouri Kansas City)

  • Duncan Foley

    (Department of Economics, New School for Social Research)

Abstract

Many problems in empirical economic analysis involve systems in which the quantal actions of a large number of participants determine the distribution of some social outcome. In many of these cases key model variables are un- observed. From the statistical perspective, when observed variables depend non-trivially on unobserved variables the joint distribution of the variables of interest is underdetermined and the model is ill-posed due to incomplete information. In this paper we examine the class of models defined by a joint distribution of discrete individual actions and an outcome variable, where one of the variables is unobserved, so that the joint distribution is underdetermined. We derive a general maximum entropy based method to infer the underdetermined joint distribution in this class of models. We apply this method to the classical Smithian theory of competition where firms' profit rates are observed but the entry and exit decisions that determine the distribution of profit rates is unobserved.

Suggested Citation

  • Ellis Scharfenaker & Duncan Foley, 2017. "Maximum Entropy Estimation of Statistical Equilibrium in Economic Quantal Response Models," Working Papers 1710, New School for Social Research, Department of Economics, revised May 2017.
    • Handle: RePEc:new:wpaper:1710
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    File URL: http://www.economicpolicyresearch.org/econ/2017/NSSR_WP_102017.pdf
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    References listed on IDEAS

    as
    1. Paulo dos Santos & Ellis Scharfenaker, 2016. "Informational Performance, Competitive Capital-Market Scaling, and the Frequency Distribution of Tobin’s Q," Working Papers 1607, New School for Social Research, Department of Economics.
    2. Ellis Scharfenaker & Gregor Semieniuk, 2017. "A Statistical Equilibrium Approach to the Distribution of Profit Rates," Metroeconomica, Wiley Blackwell, vol. 68(3), pages 465-499, July.
    3. Judge,George G. & Mittelhammer,Ron C., 2012. "An Information Theoretic Approach to Econometrics," Cambridge Books, Cambridge University Press, number 9780521869591, September.
    4. Alfarano, Simone & Milaković, Mishael & Irle, Albrecht & Kauschke, Jonas, 2012. "A statistical equilibrium model of competitive firms," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 136-149.
    5. George Judge, 2015. "Entropy Maximization as a Basis for Information Recovery in Dynamic Economic Behavioral Systems," Econometrics, MDPI, vol. 3(1), pages 1-10, February.
    6. Judge,George G. & Mittelhammer,Ron C., 2012. "An Information Theoretic Approach to Econometrics," Cambridge Books, Cambridge University Press, number 9780521689731, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ellis Scharfenaker, Markus P.A. Schneider, 2019. "Labor Market Segmentation and the Distribution of Income: New Evidence from Internal Census Bureau Data," Working Paper Series, Department of Economics, University of Utah 2019_08, University of Utah, Department of Economics.
    2. Emanuele Citera, 2021. "Stock Returns, Market Trends, and Information Theory: A Statistical Equilibrium Approach," Working Papers 2116, New School for Social Research, Department of Economics.
    3. Emanuele Citera & Francesco De Pretis, 2023. "An Information Theory Approach to the Stock and Cryptocurrency Market: A Statistical Equilibrium Perspective," Papers 2310.04907, arXiv.org.
    4. Ellis Scharfenaker, 2022. "Statistical Equilibrium Methods In Analytical Political Economy," Journal of Economic Surveys, Wiley Blackwell, vol. 36(2), pages 276-309, April.
    5. Jangho Yang, 2023. "Information‐theoretic model of induced technical change: Theory and empirics," Metroeconomica, Wiley Blackwell, vol. 74(1), pages 2-39, February.
    6. Ellis Scharfenaker, Duncan K. Foley, 2021. "Unfulfilled Expectations and Labor Market Interactions: A Statistical Equilibrium Theory of Unemployment," Working Paper Series, Department of Economics, University of Utah 2021_03, University of Utah, Department of Economics.

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    More about this item

    Keywords

    Quantal response; maximum entropy; Information-theoretic quantitative methods; incomplete information; link function; profit rate distribution;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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