Conditions for Asymptotic Stability in OLG and Growth Models

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Economists have long used overlapping generations and neoclassical growth models to explore important empirical and theoretical issues in public finance, development, international trade, savings and monetary policy. Recently, some researchers have attacked the way these models characterize the long run tendency of the economy. This project will study the mathematical equations which economists use to codify and apply these models and investigate the relationship between the empirically determined parameters and the corresponding long run properties of the models. Since the equations which codify the assumptions of the models can lead to bizarre behavior when these models are used in practice, the models could give misleading forecasts of the behavior of the economy. By applying state of the art computer programming techniques, formulae for characterizing the plausible ranges of parameters of interest will be developed. The concept of determinacy developed by Laitner and Anderson- Moore will be applied to identify fixed-point and limit cycles which possess stability properties that imply unique convergent trajectories from nearby points. The project will focus on discrete time models. Analytic expressions for specific utility and production functions will be developed when general formulae are unattainable. The asymptotic stability of these models will be investigated for empirically relevant ranges of model parameters in order to characterize the plausibility and relevance of the potentially complex asymptotic behavior when confronting real world data. The project will begin an investigation of the global convergence properties of these models with the objective of developing "higher order" turnpike theorems characterizing conditions guaranteeing convergence to limit cycles of a given periodicity.