This paper develops a general equilibrium model with Dixit-Stiglitz preferences, monopolistic competition and rational inattention on the side of both households and firms. We show how to solve a general equilibrium model with rational inattention. We use the model to study how rational inattention affects the impulse responses of macroeconomic variables to monetary policy shocks and technology shocks.

Bartosz Mackowiak

Mirko Wiederholt

English

Research Papers in Economics

Macroeconomic Dynamics under Rational Inattention∗
Bartosz Ma´ ckowiak
Humboldt University Berlin
Mirko Wiederholt
Humboldt University Berlin
February 2006
1E x t e n d e d a b s t r a c t
This paper develops a general equilibrium model with Dixit-Stiglitz preferences, monopo-
listic competition and rational inattention on the side of both households and ﬁrms. We
show how to solve a general equilibrium model with rational inattention. We use the model
to study how rational inattention aﬀects the impulse responses of macroeconomic variables
to monetary policy shocks and technology shocks.
The economy consists of a large number of households, a large number of ﬁrms and a
central bank. Firms supply diﬀerentiated goods and households supply diﬀerentiated types
of labor. Firm i supplies good i. Every period the ﬁrm sets the price of the good. The
ﬁrm commits to supply any quantity of the good at this price. The ﬁrm also chooses the
labor mix used in production. There are no adjustment costs, that is, the ﬁrm can change
the price and the labor mix every period at no cost. Household j supplies labor of type j.
Every period the household chooses how much to consume and which goods to consume.
Furthermore, the household sets the wage for its labor services. The household commits to
supply any quantity of labor services at this wage. There are no adjustment costs, that is,
the household can change the wage every period at no cost. We model the idea that ﬁrms
and households cannot attend perfectly to all available information. Following Sims (2003),
we model the inability to attend to all available information as a constraint on information
∗Email: bartosz@wiwi.hu-berlin.de and wiederholt@wiwi.hu-berlin.de.
1ﬂow. Each ﬁrm and each household decides what to pay attention to, subject to a constraint
on information ﬂow. Finally, every period the central bank sets the nominal interest rate
according to a feedback rule. The central bank commits to borrow or lend any quantity at
this interest rate.
We solve the model as follows. First, we study the attention problem of an individual
ﬁrm. We derive a loss function for the ﬁrm that expresses losses in proﬁts due to suboptimal
behavior as a function of deviations of actual behavior from optimal behavior. We solve the
ﬁrm’s attention problem by minimizing the loss function subject to the information ﬂow
constraint. The ﬁrm’s information ﬂow constraint bounds the information ﬂow between
actual behavior and optimal behavior. Second, we study the attention problem of an indi-
vidual household. We derive a loss function for the household that expresses losses in utility
due to suboptimal behavior as a function of deviations of actual behavior from optimal be-
havior. We solve the household’s attention problem by minimizing the loss function subject
to the information ﬂow constraint. The household’s information ﬂow constraint bounds the
information ﬂow between actual behavior and optimal behavior. Third, we compute the
rational expectations equilibrium.
We use the model to study how rational inattention aﬀects the impulse responses of
macroeconomic variables to monetary policy shocks and technology shocks.
References
[1] Sims, Christopher A. (2003): “Implications of Rational Inattention.” Journal of Mone-
tary Economics, 50, 665-690.
2

Macroeconomic Dynamics under Rational Inattention

http://repec.org/sce2006/up.27121.1141161429.pdf

Macroeconomic Dynamics under Rational Inattention

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