Symbolic Algebra Programming for Analyzing the Long Run Dynamics of Economic Models: An Investigation of Overlapping Generations Models

Economists have long used overlapping generations models to explore important empirical and theoretical issues in public finance, development, international trade, savings and monetary policy. Recently, some researchers have criticized the way these and other models characterize the long run tendency of the economy. If the equations which codify the assumptions in the models can display bizarre behavior, the models could give misleading forecasts of the behavior of the economy. By studying the mathematical equations which economists use to codify and apply these models, I am investigating the relationship between the empirically determined parameters and the corresponding long run properties of the models. This paper shows how symbolic algebra programs can facilitate the analysis of the dynamics of these non-linear equation systems. I have used the symbolic algebra capabilities of Mathematica to develop a collection of programs for analyzing the asymptotic behavior of economic models. These symbolic programming algorithms implement a set of algorithms originally designed for numerical processing. The paper shows how to use these tools to derive formulae for characterizing the long run dynamics of overlapping generations models. The powerful symbolic and algebraic manipulation tools make it possible to analytically explore the subtle transitions between generic classes of long run behavior for these models. The paper develops formulae for characterizing the asymptotic behavior of the model for plausible ranges of the parameters. These results provide insights about features of these models which are useful for both theoretical and empirical economists.

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