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Maximum Entropy Estimation of Statistical Equilibrium in Economic Quantal Response Models

Ellis Scharfenaker and Duncan Foley

No 1710, Working Papers from New School for Social Research, Department of Economics

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 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.

Keywords: Quantal response; maximum entropy; Information-theoretic quantitative methods; incomplete information; link function; profit rate distribution (search for similar items in EconPapers)
JEL-codes: C10 C18 C70 C79 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2017-03, Revised 2017-05
New Economics Papers: this item is included in nep-ecm and nep-hme
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