Continuous versus Discrete Time Modeling in Growth and Business Cycle Theory

  • Omar Licandro
  • Luis A. PuchEmail author
  • Jesús Ruiz


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).


  1. Anagnostopoulos, A., & Giannitsarou, C. (2013). Indeterminacy and period length under balanced budget rules. Macroeconomic Dynamics, 17, 898–919. CrossRefGoogle Scholar
  2. Asea, P., & Zak, P. (1999). Time-to-build and cycles. Journal of Economic Dynamics and Control, 23, 1155–1175. MathSciNetCrossRefGoogle Scholar
  3. Bambi, M., Gozzi, F., & Licandro, O. (2014). Endogenous growth and wave-like business fluctuations. Journal of Economic Theory, 154, 68–111. MathSciNetCrossRefGoogle Scholar
  4. Bambi, M., & Licandro, O. (2005). (In)determinacy and Time-to-Build (Economics Working Papers ECO2004/17). European University Institute.Google Scholar
  5. Benhabib, J. (2004). Interest rate policy in continuous time with discrete delays. Journal of Money, Credit and Banking, 36, 1–15. CrossRefGoogle Scholar
  6. Benhabib, J., & Farmer, R. (1994). (In)determinacy and increasing returns. Journal of Economic Theory, 63, 19–41. CrossRefGoogle Scholar
  7. Boucekkine, R., Licandro, O., Puch, L. A., & Río, F. (2005). Vintage capital and the dynamics of the AK model. Journal of Economic Theory, 120, 39–72. MathSciNetCrossRefGoogle Scholar
  8. Burmeister, E., & Turnovsky, S. J. (1977). Price expectations and stability in a short-run multi-asset macro model. American Economic Review, 67, 213–218.Google Scholar
  9. Carlstrom, C. T., & Fuerst, T. S. (2005). Investment and interest rate policy: A discrete time analysis. Journal of Economic Theory, 123, 4–20. MathSciNetCrossRefGoogle Scholar
  10. Collard, F., Licandro, O., & Puch, L. A. (2008). The short-run dynamics of optimal growth model with delays. Annals of Economics and Statistics, 90, 127–143. Google Scholar
  11. Debreu, G. (1959). Theory of value: An axiomatic analysis of economic equilibrium. New Haven: Yale University Press.zbMATHGoogle Scholar
  12. Farmer, R. (1999). Macroeconomics of self-fulfilling prophecies (2nd ed.). Cambridge: The MIT Press.Google Scholar
  13. Fernández, E., Pérez, R., & Ruiz, J. (2012). The environmental Kuznets curve and equilibrium indeterminacy. Journal of Economic Dynamics and Control, 36(11), 1700–1717. MathSciNetCrossRefGoogle Scholar
  14. Hansen, G. (1985). Indivisible labor and the business cycle. Journal of Monetary Economics, 16, 309–327. CrossRefGoogle Scholar
  15. Hintermaier, T. (2003). On the minimum degree of returns to scale in sunspot models of the business cycle. Journal of Economic Theory, 110, 400–409. MathSciNetCrossRefGoogle Scholar
  16. Inada, K. (1963). On a two-sector model of economic growth: Comments and a generalization. Review of Economic Studies, 30(2), 119–127. CrossRefGoogle Scholar
  17. Jovanovic, B. (1982). Selection and the evolution of industry. Econometrica, 50, 649–670. MathSciNetCrossRefGoogle Scholar
  18. Kolmanovskii, V., & Myshkis, A. (1998). Introduction to the theory and applications of functional differential equations. Boston: Kluwer Academic Publishers.zbMATHGoogle Scholar
  19. Kydland, F., & Prescott, E. C. (1982). Time-to-build and aggregate fluctuations. Econometrica, 50, 1345–1370. CrossRefGoogle Scholar
  20. Licandro, O., & Puch, L. A. (2006). Is Discrete Time a Good Representation of Continuous Time? (Economics Working Papers ECO2006/28). European University Institute.Google Scholar
  21. Licandro, O., Puch, L. A., & Sampayo, A. R. (2008). A vintage model of trade in secondhand markets and the lifetime of durable goods. Mathematical Population Studies, 15, 249–266. MathSciNetCrossRefGoogle Scholar
  22. Novales, A., Fernández, E., & Ruiz, J. (2008). Economic growth: Theory and numerical solution methods. Berlin: Springer Science.zbMATHGoogle Scholar
  23. Solow, R. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70, 65–94. CrossRefGoogle Scholar
  24. Uzawa, H. (1963). On a two-sector model of economic growth II. Review of Economic Studies, 30(2), 105–118. CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of EconomicsUniversity of NottinghamNottinghamUK
  2. 2.Department of Economics and ICAEUniversidad Complutense de MadridMadridSpain

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