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Maximum Entropy Estimation of Statistical Equilibrium in Economic Quantal Response Models


  • Ellis Scharfenaker

    () (Department of Economics, University of Missouri Kansas City)

  • Duncan Foley

    () (Department of Economics, New School for Social Research)


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 de ned 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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    References listed on IDEAS

    1. George Judge, 2015. "Entropy Maximization as a Basis for Information Recovery in Dynamic Economic Behavioral Systems," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 1-10, February.
    2. Judge,George G. & Mittelhammer,Ron C., 2012. "An Information Theoretic Approach to Econometrics," Cambridge Books, Cambridge University Press, number 9780521869591, October.
    3. Ellis Scharfenaker & Gregor Semieniuk, 2015. "A Statistical Equilibrium Approach to the Distribution of Profit Rates," SCEPA working paper series. SCEPA's main areas of research are macroeconomic policy, inequality and poverty, and globalization. 2015-05, Schwartz Center for Economic Policy Analysis (SCEPA), The New School.
    4. 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.
    5. 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.
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    More about this item


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

    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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