Business Cycle Models with Embodied Technological Change and Poisson Shocks

• Main Author: Schlegel, Christoph
• Other Authors: Technische Universität Dresden, Wirtschaftswissenschaften
• Format: Doctoral Thesis
• Language: English
• Published: Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden 2004
• Subjects: Endogene Konjunkturzyklen; Funktional-Differentialgleichungen; Investitionsgebundener Technologischer Fortschritt; Poisson DGL; RBC Modelle in Stetiger Zeit; Delay Differential Equations; Embodied Technological Change; Endogenous Business Cycles; Poisson SDE; RBC Models in Continuous Time; ddc:330; rvk:QC 330; Differentialgleichung; Investition; Konjunkturzyklus
• Online Access: http://nbn-resolving.de/urn:nbn:de:swb:14-1099472232718-69586; http://nbn-resolving.de/urn:nbn:de:swb:14-1099472232718-69586; http://www.qucosa.de/fileadmin/data/qucosa/documents/1195/1099472232718-6958.pdf

The first part analyzes an Endogenous Business Cycle model with embodied technological change. Households take an optimal decision about their spending for consumption and financing of R&D. The probability of a technology invention occurring is an increasing function of aggregate R&D expenditure in the whole economy. New technologies bring higher productivity, but rather than applying to the whole capital stock, they require a new vintage of capital, which first has to be accumulated before the productivity gain can be realized. The model offers some valuable features: Firstly, the response of output following a technology shock is very gradual; there are no jumps. Secondly, R&D is an ongoing activity; there are no distinct phases of research and production. Thirdly, R&D expenditure is pro-cyclical and the real interest rate is counter-cyclical. Finally, long-run growth is without scale effects. The second part analyzes a RBC model in continuous time featuring deterministic incremental development of technology and stochastic fundamental inventions arriving according to a Poisson process. In a special case an analytical solution is presented. In the general case a delay differential equation (DDE) has to be solved. Standard numerical solution methods fail, because the steady state is path dependent. A new solution method is presented which is based on a modified method of steps for DDEs. It provides not only approximations but also upper and lower bounds for optimal consumption path and steady state. Furthermore, analytical expressions for the long-term equilibrium distributions of the stationary variables of the model are presented. The distributions can be described as extended Beta distributions. This is deduced from a methodical result about a delay extension of the Pearson system.