Stochastic equilibrium, the Phillips curve and Keynesian economics

Abstract

I uncover serious problems with the benchmark New Keynesian Phillips curve linearized around its non-stochastic zero inflation steady state when the underlying model features a subset of prices that stay rigid over multiple periods, as in the popular Calvo model. I am able to demonstrate that the dynamics of approximations taken at the non-stochastic steady state are non-hyperbolic. This means that approximations taken at this point do not represent a valid description of the dynamics of the underlying model at any other point in the state space. This allows me to overturn results such as the ’Divine Coincidence’ that equates welfare under price rigidity with the level prevailing under price dispersion. I introduce a dynamic stochastic concept of equilibrium that can be applied to New Keynesian models and offers a natural point to take approximations to analyze business cycle dynamics. It is methodologically interesting as it is a notion of general equilibrium that does not correspond to partial equilibrium. Keywords: Macroeconomics, Mathematical Economics, Random Dynamical Systems, General Equilibrium, Monetary Policy JEL Classification: C6, D5, E1, E3, E5 2010 Mathematics Subject Classification: 37Axx, 37Bxx, 37Cxx, 37Dxx, 37Gxx, 37Hxx