Abstract
The author explicitly specifies a New Keynesian style model embodying a financial constraint on the availability of equity and a financial market imperfection with regard to the existence of state-contingent assets based upon the published papers of Greenwald and Stiglitz (1988, 1990, and 1993). Using computer based numerical simulation, the author validates the three unproven Propositions found in the Greenwald and Stiglitz 1993 article with regard to the model's comparative static behaviour. Through the inclusion of a parameter for technology into the production function, the author shows that observations made by Greenwald and Stiglitz with regard to the effect of equity infusions is subject to qualification. Investigation of the model's inter-temporal behaviour reveals that the claims made by Greenwald and Stiglitz with regard to multiple periodicity are again subject to many qualifications. Linearization around the steady-state equilibrium as suggested by Greenwald and Stiglitz is shown to offer limited insight because of the implied non-linearity of the model's first order difference equation. Calibrated numerical simulation of the nonlinear difference equation reveals the potential for both single and multiple periodicity, period doubling bifurcations, and chaotic trajectories displaying sensitivity to initial conditions. In addition it was shown that the model's implied random attractor was key to understanding its inter-temporal behavior. In the Greenwald and Stiglitz articles the existence of derivative markets such as futures or options to manage risk are assumed away. The author, in order to investigate the effects of futures or options markets upon business cycles, modifies the explicitly specified model to include the use of state-contingent assets. Introducing the use of derivative financial products to manage risk, using numerical simulation, produces the surprising result that in the aggregate they may lead to slightly greater output instability. In addition to the model's structure, several intuitive reasons for these results are discussed in depth. The Greenwald and Stiglitz model also assumed that the cost of capital was not risk adjusted. The author modifies the explicitly specified model and using numerical simulation shows that like other unrealistic assumptions concerning dividend distribution, leads to alternative laws of motion. The research is concluded with discussion of possible policy and regulatory implications.