THE DYNAMICAL SYSTEMS APPROACH TO MACROECONOMICS

Abstract

<p>The aim of this thesis is to provide mathematical tools for an alternative to the mainstream study of macroeconomics with a focus on debt-driven dynamics.</p> <p>We start with a survey of the literature on formalizations of Minsky's Financial Instability Hypothesis in the context of stock-flow consistent models.</p> <p>We then study a family of macro-economical models that date back to the Goodwin model. In particular, we propose a stochastic extension where noise is introduced in the productivity. Besides proving existence and uniqueness of solutions, we show that orbits must loop around a specific point indefinitely.</p> <p>Subsequently, we analyze the Keen model, where private debt is introduced. We demonstrate that there are two key equilibrium points, intuitively denoted good and bad equilibria. Analytical stability analysis is followed by numerical study of the basin of attraction of the good equilibrium.</p> <p>Assuming low interest rate levels, we derive an approximate solution through perturbation techniques, which can be solved analytically. The zero order solution, in particular, is shown to converge to a limit cycle. The first order solution, on the other hand, is shown to explode, rendering its use dubious for long term assessments.</p> <p>Alternatively, we propose an extension of the Keen model that addresses the immediate completion time of investment projects. Using distributed time delays, we verify the existence of the key equilibrium points, good and bad, followed by their stability analysis. Through bifurcation theory, we verify the existence of limit cycles for certain mean completion times, which are absent in the original Keen model.</p> <p>Finally, we examine the Keen model under government intervention, where we introduce a general form for the government policy. Besides performing stability analysis, we prove several results concerning the persistence of both profits and employment. In economical terms, we demonstrate that when the government is responsive enough, total economic meltdowns are avoidable.</p>