Continuous vs Discrete Time Modelling in Growth and Business Cycle Theory

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Facultad de CC Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE)
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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, towards the issue of equilibrium indeterminacy and endogenous cycles. In this paper, we introduce to some of those relevant issues in economic dynamics. First, we describe a baseline continuous vs discrete time modelling 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.
Anagnostopoulos, A. and C. Giannitsarou (2013), “Indeterminacy and Period Length under Balanced Budget Rules,” Macroeconomic Dynamics 17, 898-919. Asea, P. and P. Zak (1999), “Time-to-Build and Cycles,” Journal of Economic Dynamics and Control 23, 1155-1175. Bambi, M., F. Gozzi and O. Licandro (2014), “Endogenous growth and wave-like business fluctuations,” Journal of Economic Theory 154, 68-111. Bambi, M. and O. Licandro (2005), “(In)determinacy and Time–to–Build,” Economics Working Papers ECO2004/17, EUI. Benhabib, J. (2004), “Interest rate policy in continuous time with discrete delays,” Journal of Money, Credit and Banking, 36, 1-15. Benhabib, J. and R. Farmer (1994), “(In)determinacy and Increasing Returns,” Journal of Economic Theory, 63, 19-41. Boucekkine, R., O. Licandro, L.A. Puch and F. del Río (2005), “Vintage Capital and the Dynamics of the AK model,” Journal of Economic Theory, 120, 39-72. Burmeister, E., and S.J. Turnovsky (1977), “Price Expectations and Stability in a Short-Run Multi-Asset Macro Model,” American Economic Review, 67, 213-218. Carlstrom, C.T. and T.S. Fuerst (2005), “Investment and interest rate policy: a discrete time analysis,” Journal of Economic Theory, 123, 4-20. Collard, F., O. Licandro and L.A. Puch, (2008), “The short-run Dynamics of Optimal Growth Model with Delays,” Annals of Economics and Statistics, 90, 127-143. Debreu, G. (1959), Theory of Value. Cowles Foundation Monograph 17, New Haven, Yale University Press. Farmer, R. (1999), Macroeconomics of Self-fulfilling Prophecies. 2nd Edition, The MIT Press. Fernández, E., R. Pérez and J. Ruiz (2012), “The environmental Kuznets curve and equilibrium indeterminacy,” Economics Letters, 87, 285-290. Hansen, G. (1985), “Indivisible labor and the business cycle,” Journal of Monetary Economics, 16, 309-327. 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. Hintermaier, T. (2005), “A Sunspot Paradox,” Economics Letters, 87, 285-290. Inada, K. (1963), “On a Two-Sector Model of Economic Growth: Comments and a Generalization,” Review of Economic Studies, 30 (2), 119-127. Jovanovic, B. (1982), “Selection and the Evolution of Industry, ” Econometrica, 50, 649-670. Kolmanovskii, V. and A. Myshkis (1998), Introduction to the Theory and Applications of Functional Differential Equations. Kluwer Academic Publishers. Kydland, F. and E.C. Prescott (1982), “Time–to–Build and Aggregate Fluctuations,” Econometrica, 50, 1345-70. Licandro, O., and L.A. Puch (2006), “Is Discrete Time a Good Representation of Continuous Time?” Economics Working Papers ECO2006/28, EUI. Licandro, O., L.A. Puch and A.R. Sampayo (2008), “A vintage model of trade in secondhand markets and the lifetime of durable goods,” Mathematical Population Studies 15, 249-266. Novales, A., E. Fernández and J. Ruiz (2008), Economic growth: theory and numerical solution methods. Springer Science. Solow, R., (1956), “A contribution to the theory of economic growth,” Quarterly Journal of Economics 70, 65-94. Uzawa, H. (1963), “On a Two-Sector Model of Economic Growth II,” Review of Economic Studies, 30 (2), 105-118.