Simple calvo economies with heterogeneous pricing - Bertanha, Marinho Angelo (2009)
This paper was motivated by the main results of Carvalho and Schwartzman (2008), where heterogeneity emerges from di¤erent sectoral pricing rules, and sectoral moments of rigidity durations are su¢ cient to explain certain monetary e¤ects. Once we agree that heterogeneity is relevant for studying price-stickiness, how could we write a model with the smallest possible number of sectors, but still with a minimum of heterogeneity enough to produce any desired monetary e¤ect, or equivalently, any three moments of the price durations distribution? In order to answer this question, this paper is restricted to studying constant-hazard models and considers that the cumulative e¤ect and short-run dynamics of monetary shocks are good ways to summarize large heterogeneous economies. We show that two sectors are enough for summarizing the cumulative e¤ects of monetary shocks, where 3 sectors represent good approximations for the dynamics of these e¤ects. Numerical simulations for the short-run dynamics of any type of monetary shock in a sticky-information economy show that approximating a 500 sector economy using a 3 sector one produces approximation errors no larger than 3%. That is, if a monetary shock makes output fall 5%, the approximated economy will say the same impact lies between 4.85% and 5.15%. The same is true for the dynamics produced by shocks to the level of money supply in a sticky-prices economy. For shocks to the growth-rate of money supply, the maximum approximation error is 2.4%.