On the regularity of equilibria in dynamic economies

For discrete-time, infinite-horizon economies that are represented by a sequence of interrelated smooth equations, we provide sufficient conditions to guarantee regularity of equilibria on a full measure set of economies. Our approach exploits the sequential nature of a dynamic economy. An equilibrium is represented by a sequence of endogenous variables that solves a sequence of systems of smooth equations. At every point in time, standard smooth analysis techniques are used. The task then is to link periods, in order to obtain properties of equilibria. This link is represented by a correspondence, whose parallel in the macro/capital theoretic literature is the law of motion for state variables. Regularity conditions for the systems of equations and continuity properties of the law of motion drive most of the results. The set of tools proposed in this paper can also be used to analyze other properties of dynamic macroeconomic models, in particular, robustness of equilibria to smooth perturbations of utility and production functions.