Delay differential neoclassical growth model

• Published in: Journal of economic behavior & organization 2011-05, Vol.78 (3), p.272-289
• Main Authors: Matsumoto, Akio, Szidarovszky, Ferenc
• Format: Article
• Language: English
• Subjects: Accumulation; Behavioural economics; Capital; Capital depreciation; Capital formation; Complex dynamics; Continuously distributed time delay; Delay; Density; Development; Dynamical systems; Dynamics; Economics; Fixed time delay; Fluctuations; Growth models; Growth rate; Neoclassical growth model; Neoclassical growth model Continuously distributed time delay Fixed time delay Complex dynamics Period-doubling bifurcation; Period-doubling bifurcation; Production functions; Studies
• ISSN: 0167-2681; 1879-1751
• DOI: 10.1016/j.jebo.2011.01.014

► Delays and non-linearity can be sources of continuous-time chaos. ► The fixed delay can generate complex dynamic involving chaos via period-doubling bifurcation. ► The continuously distributed delay model can approximate continuous-chaos generated by the fixed delay model when the shape parameter of the density function is large enough. This paper develops a continuous-time neoclassical growth model with time delay. Despite of its simple structure, the resulting dynamic system shows emergence of erratic fluctuations in the capital accumulation process when the production function is unimodal and the delay in production is explicitly considered. It complements the seminal paper of Day (1982) in which a discrete-time neoclassical growth model displayed chaotic behavior for some configurations of the propensity to save, the growth rate of labor and the capital depreciation rate. Our analysis has at least two implications. First, nonlinearities and delay matter for a birth of aperiodic fluctuations of national product in the continuous-time model. Second, comparing the effects caused by two different time delays, fixed and continuously distributed time delays, reveals that the continuous-time model with the former can generate complex fluctuations while the one with the latter generates simple fluctuations when the shape parameter of the density function is small and complex fluctuations when large.