Information-Constrained State-Dependent Pricing∗

I present a generalization of the standard (full-information) model of statedependent 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 high enough levels of the information cost, the Calvo model of price-setting is found to be a reasonable approximation to the exact equilibrium dynamics, except in the case of (infrequent) large shocks. When the model is calibrated to match the frequency and size distribution of price changes observed in microeconomic data sets, prices are found to be much less flexible than in a full-information state-dependent pricing model, and only about 20 percent more flexible than under a Calvo model with the same average frequency of price adjustment. ∗I would like to thank Marco Bonomo, Ariel Burstein, Ricardo Caballero, Eduardo Engel, Ricardo Fernholz, Michael Golosov, Bob King, John Leahy, Bart Mackowiak, Filip Matejka, Giuseppe Moscarini, Emi Nakamura, Chris Sims, Tony Smith, Jon Steinsson and Alex Wolman for helpful discussions; Maxim Pinkovskiy and Luminita Stevens for outstanding research assistance; the NSF for research support through a grant to the NBER; and the Arthur Okun and Kumho Visiting Professorship, Yale University, for providing the time to begin work on this project. Models of state-dependent pricing [SDP], in which not only the size of price changes but also their timing is modeled as a profit-maximizing decision on the part of firms, have been the subject of an extensive literature. For the most part, the literature dealing with empirical models of inflation dynamics and the evaluation of alternative monetary policies have been based on models of a simpler sort, in which the size of price changes is modeled as an outcome of optimization, but the timing of price changes is taken as given, and hence neither explained nor assumed to be affected by policy. The popularity of models with exogenous timing [ET] for such purposes stems from their greater tractability, allowing greater realism and complexity on other dimensions. But there has always been general agreement that an analysis in which the timing of price changes is also endogenized would be superior in principle. This raises an obvious question: how much is endogeneity of the timing of price changes likely to change the conclusions that one obtains about aggregate dynamics? Results available in special cases have suggested that it may matter a great deal. In a dramatic early result, Caplin and Spulber (1987) constructed a tractable example of aggregate dynamics under SDP in which nominal disturbances have no effect whatsoever on aggregate output, despite the fact that individual prices remain constant for substantial intervals of time. Danziger (1999) obtains a similarly stark neutrality result, again for a special case allowing a closed-form solution, but this time with idiosyncratic as well as aggregate shocks. The Caplin-Spulber and Danziger examples are obviously extremely special; but Golosov and Lucas (2007) find, in numerical analysis of an SDP model calibrated to account for various facts about the probability distribution of individual price changes in U.S. data, that the predicted aggregate real effects of nominal disturbances are quite small, relative to what one might expect based on the average interval of time between price changes. And more recently, Caballero and Engel (2007) consider the real effects of variation in aggregate nominal expenditure in a fairly general class of “generalized Ss models,” and show that quite generally, variation in the “extensive margin” of price adjustment (i.e., variation in the number of prices that adjust, as opposed to variation in the amount by which each of these prices changes) implies a smaller real effect of nominal disturbances than would be predicted in an ET model (and hence variation only on the “intensive margin”); they argue that the degree of immediate adjustment of the overall level of See, for example, Burstein and Hellwig (2007), Dotsey and King (2005), Gertler and Leahy (2007), Golosov and Lucas (2007), Midrigan (2008), and Nakamura and Steinsson (2008a, 2008b) for some recent additions.