Inventories, markups, and real rigidities in menu cost models

Real rigidities that limit the responsiveness of real marginal cost to output are a key ingredient of sticky price models necessary to account for the dynamics of output and inflation. We argue here, in the spirit of Bils and Kahn (2000), that the behavior of marginal cost over the cycle is directly related to that of inventories, data on which is readily available.We study a menu cost economy in which firms hold inventories in order to avoid stockouts and to economize on fixed ordering costs. We find that, for low rates of depreciation similar to those in the data, inventories are highly sensitive to changes in the cost of holding and acquiring them over the cycle. This implies that the model requires an elasticity of real marginal cost to output approximately equal to the inverse of the elasticity of intertemporal substitution in order to account for the countercyclical inventory-tosales ratio in the data. Stronger real rigidities lower the cost of acquiring and holding inventories during booms and counterfactually predict a procyclical inventory-to-sales ratio.