A benchmark for comparative dynamics and determinacy in overlapping- generations economies (Q808979)

The article investigates the determinacy of perfect-foresight equilibria in overlapping-generations economies, also with regard to the comparative dynamics of the underlying environment, by making use of nearly stationary price-paths. It does so by varying not only the future, but also the history of the dynamics when unanticipated policy shocks occur, i.e., times always runs from -\(\infty\) to \(+\infty\) (and perfect foresight is assumed to hold at all times). Following an approach of \textit{T. J. Kehoe} and \textit{D. K. Levine} [Econometrica 53, 433-453 (1985; Zbl 0563.90022); J. Math. Econ. 14, 69- 93 (1984; Zbl 0542.90016)], the paper first provides a benchmark OLG- model with respect to which regular stationary equilibria of a stationary economy are defined. Regularity is subsequently justified by its genericity. In a first attempt, the determinacy of `near stationary' equilibria is then proved, using only the elementary calculus of finite- dimensional Euclidean spaces. Thereafter, a review of calculus in infinite-dimensional spaces is given, including Fréchet differentials and the implicit mapping theorem. The determinacy problem is subsequently reconsidered from this perspective by way of a three-stage proof of its validity (and the meaningfulness of comparative dynamic exercises). The paper is related to an approach by \textit{J. Geanakoplos} and \textit{D. Brown} [``Comparative statics and local indeterminacy in overlapping generations economies: An application of the multiplicative ergodic theorem'', Cowles Foundation, 1985] in its two stage procedure (genericity step, validation step). It, however, differs in the details of techniques used as well as in scope from this latter work.