Equilibrium stability in open economy models

This paper derives analytical results for the relationship between the slope of the excess demand function and the dynamic properties around a deterministic steady state in a two country model. In models that admit multiple steady states, the sign of the slope of the excess demand function is positive for some steady states and negative for others. To obtain stationarity of the net foreign asset position under incomplete financial markets I introduce the stationary inducing devices analyzed in Schmitt-Grohé and Uribe (2003) and Ghironi (2006). For portfolio costs, a debt-elastic interest rate, or an overlapping generations framework the equilibrium dynamics around a steady state are unbounded if the excess demand function for the foreign traded good is increasing in the good’s own price. Otherwise the dynamics are bounded and locally unique. By contrast, with Uzawa-type preferences, the equilibrium dynamics around a steady state are shown to be bounded and locally unique irrespective of the sign of the slope of the excess demand function.