Continuous versus Discrete Time Modeling in Growth and Business Cycle Theory
Economists model time as continuous or discrete. For long, either alternative has brought about relevant economic issues, from the implementation of the basic Solow and Ramsey models of growth and the business cycle toward the issue of equilibrium indeterminacy and endogenous cycles. In this paper, we introduce some of those relevant issues in economic dynamics. First, we describe a baseline continuous versus discrete time modeling setting relevant for questions in growth and business cycle theory. Then we turn to the issue of local indeterminacy in a canonical model of economic growth with a pollution externality whose size is related to the model period. Finally, we propose a growth model with delays to show that a discrete time representation implicitly imposes a particular form of time-to-build to the continuous time representation. Our approach suggests that the recent literature on continuous time models with delays should help to bridge the gap between continuous and discrete time representations in economic dynamics.
We thank Mauro Bambi, Raouf Boucekkine, Fabrice Collard, Esther Fernández, Gustavo Marrero, and Alfonso Novales for insightful discussions. We also thank a reviewer and the editors for their suggestions. Finally, we thank the financial support from the Spanish Ministerio de Economía y Competitividad (grant ECO2014-56676) and the Bank of Spain (grant Excelencia 2016–17).
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