Comparing Four Models of Aggregate Fluctuations due to Self-Fulfilling Expectations

This paper studies four models which allow for aggregate fluctuations due to self-fulfilling expectations. It compares the minimum degree of increasing returns to scale necessary to make such equilibria possible and the ability of these models to explain the observed co-movements in macroeconomic time series at business cycle frequencies. The four models discussed are Gali (1994), Rotemberg and Woodford (1992), Benhabib and Farmer (1994) and Baxter and King (1991). These economies are modified, if necessary, to be presented in a unified framework and calibrated uniformly using King, Plosser, and Rebelo (1988) values. Beyond those parameters each model has up to three additional free parameters. For three models necessary and sufficient conditions for the existence of stationary sunspot equilibria are derived analytically, and for each model a numerical example is given to show for which values of these additional parameters stationary sunspot equilibria exist. I find that the two models with variable markups (i.e., Gali and Rotemberg and Woodford) require a lower degree of increasing returns to allow for endogenous fluctuations than do the two models of fixed markups. However, endogenous fluctuations in all four models occur only for markup values in the upper range of available empirical estimates. I also show that persistent output fluctuations are not a necessary property of these models of the business cycle when the only source of fluctuations are changes in people's expectations about the future path of the economy.