A "Quantum" Approach to Rational Inattention

32 Pages Posted: 17 Mar 2010

See all articles by Gilles Saint-Paul

Gilles Saint-Paul

University of Toulouse I - GREMAQ-IDEI; Centre for Economic Policy Research (CEPR); CESifo (Center for Economic Studies and Ifo Institute); IZA Institute of Labor Economics

Date Written: March 2010

Abstract

In this paper, I propose a model of rational inattention where the choice variable is a deterministic function of the exogenous variables, and still only a finite amount of information is being used. This holds provided the choice variable is discrete rather than continuous; that is, the mapping from the realization of the exogenous variables to the endogenous ones is piece-wise constant. Thus, limited information is now a source of lumpiness in behavior, rather than a source of noise. A central result is that the mutual information between the exogenous variable and the endogenous one is simply equal to the entropy, in the usual discrete sense, of the endogenous variable. The approach is illustrated with two applications: a general linear-quadratic problem with a uniform distribution, and a simple static model of price-setting where individual price setters face aggregate monetary shocks and idiosyncratic productivity shocks.

Keywords: entropy, lumpy adjustment, monetary policy, mutual information, price-setting, rational inattention

JEL Classification: D8, E3

Suggested Citation

Saint-Paul, Gilles, A "Quantum" Approach to Rational Inattention (March 2010). CEPR Discussion Paper No. DP7739. Available at SSRN: https://ssrn.com/abstract=1573443

Gilles Saint-Paul (Contact Author)

University of Toulouse I - GREMAQ-IDEI ( email )

Manufacture des Tabacs
21 Allees de Brienne
Toulouse, 31000
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+33 5 6112 8544 (Phone)
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Centre for Economic Policy Research (CEPR)

London
United Kingdom

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

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