1.Discrete and Sticky Behavior From Shannon Information Constraints / 2.Information Constrained State Dependent Pricing / 3.Why are Prices Sticky?

東京大学大学院経済学研究科棟 6階 大会議室

1.Christopher Sims 氏 (Princeton University)
2.Michael Woodford 氏 (Columbia University)
3.Andrew Levin 氏 (Federal Reserve Board)

1) The literature applying information-theoretic ideas to economics has so far considered only Gaussian uncertainty. Ex post Gaussian uncertainty can be justified as optimal when the associated optimization problem is linear-quadratic, but the literature has often assumed Gaussian uncertainty even where it cannot be justified as optimal. This paper considers a simple two-period optimal saving problem with a Shannon capacity constraint and non-quadratic utility. It derives an optimal ex post probability density for wealth in two leading cases (log and linear utility) and lays out a general approach for handling other cases numerically. It displays and discusses numerical solutions for other utility functions, and considers the feasibility of extending this paper's approaches to general non-LQ dynamic programming problems. The introduction of the paper discusses approaches that have been taken in the existing literature to applying Shannon capacity to economic modeling, making criticisms and suggesting promising directions for further progress.

2) I present a generalization of the standard (full-information) model of state-dependent pricing in which decisions about when to review a firm's existing price must be made on the basis of imprecise awareness of current market conditions. The imperfect information is endogenized using a variant of the theory of rational inattention" proposed by Sims (1998, 2003, 2006). This results in a one-parameter family of models, indexed by the cost of information, which nests both the standard state-dependent pricing model and the Calvo model of price adjustment as limiting cases (corresponding to a zero information cost and an unboundedly large information cost respectively). For intermediate levels of the information cost, the model is equivalent to a "generalized Ss model" with a continuous "adjustment hazard" of the kind proposed by Caballero and Engel (1993a, 1993b), but provides an economic motivation for the hazard function and very specific predictions about its form. For moderate levels of the information cost, the Calvo model of price-setting is found to be a fairly accurate approximation to the exact equilibrium dynamics, except in the case of (infrequent) large shocks.

備考: Microworkshopと共催