The (Mis)Behaviour of the Aggregate Price Level

Abstract

This paper investigates the response of the price level to random monetary shocks through a model of the fixed cost of changing a nominal price. It shows that in an inflationary environment, an expansionary monetary shock is accommodated faster than a contractionary monetary shock. Furthermore, when the average rate of monetary expansion increases, the lag in response to a positive shock decreases. The study also proves that the relationship between the expected rate of inflation and the variance of real prices is positive only above a critical level of expected inflation. The most striking result in this area appears in the work of Caplin and Spulber (1987). They show that in the aggregate, when inflation is monotone, stickiness disappears even when all firms follow a strict {S, s} rule. In their model, since firms are uniformly distributed, discontinuous price adjustment at the firm level does not create stickiness at the aggregate level. Caballero and Engel (1992) extend this analysis to incorporate idiosyncratic shocks. They show that in the presence of (monotone) idiosyncratic shocks, the long-run stationary distribution of prices is the uniform distribution, but in the short run, when the distribution of prices is arbitrary, aggregate stickiness can result from firms' discontinuous price adjustments. In the present work, the focus shifts. I use a model where aggregate stickiness emerges naturally from firms' discontinuous price setting to investigate the effects of the rate of inflation on aggregate stickiness. This work shows that aggregate stickiness is negatively correlated with the rate of inflation: the higher the rate of inflation, the less sticky the response of the aggregate price level with respect to positive nominal shocks, and the closer the economy approaches the Caplin and Spulber model. Therefore, when modeling a dynamic inflation tax one must account not only for the decrease in the monetary base but also for the increase in the speed at which the aggregate price level 889