Modelling Time and Macroeconomic Dynamics

Abstract

In this paper, we analyze the importance of the frequency of decision making for macroeconomic dynamics. We explain how the frequency of decision making (period length) and the unit of time measurement (calibration frequency) differ and study the implications of this difference for macroeconomic modelling. We construct a generic dynamic general equilibrium model that nests a wide range of macroeconomic models and which leaves the period length as an undetermined parameter. We provide a series of examples (variations of the Cass-Koopmans and the New Keynesian models) that fit into this framework and use these to do comparative dynamics with respect to the period length. In particular, we analyze local stability and how this is affected by changes in the period length. We find that in models with endogenous capital accumulation, as the period gets longer, indeterminacy occurs less often. Moreover, as economic agents become less patient and as capital depreciates more, indeterminacy also occurs less often. We also show that, in the case of the New Keynesian model, standard continuous and discrete time versions have entirely different local stability properties due to a discontinuity at zero period length.

Keywords: depreciation, discounting, local indeterminacy, Macroeconomic dynamics, period length

JEL Classification: C62, E22, O41