Abstract

This thesis focuses on endogenous approaches to studying macroeconomic dynamics and evaluates this tradition from different perspectives. It traces the origins and development of non-linear, endogenous theories of business cycles from its early beginnings up to its present frontiers. It argues that these theories emerged out of an attempt to reconcile the then existing corpus of (essentially static) economic theory with empirically observed fluctuations. It offers a re-reading of Harrod's `The Trade Cycle' and demonstrates that the accelerator in his theory to be non-linear and consequently claims that Harrod's text contains essential elements that constitute an endogenous theory. On the mathematical front, it examines the role of existence and uniqueness theorems (in particular, the Poincare--Bendixson Theorem in planar endogenous models of economic dynamics. Their underpinnings, their use and influence on the mathematical models of aggregate macroeconomic fluctuations are critically evaluated. In this context, it considers Goodwin(1951)'s nonlinear model of business cycles and shows how existence and uniqueness of limit cycles can be established even for the case of an asymmetric, nonlinear, accelerator with only one nonlinearity. This is achieved using a result by de Figueiredo(1960). It argues that an excessive reliance on proving 'existence' and 'uniqueness' hampered the enlargement of scope of nonlinear, endogenous theories. It outlines the non-constructive aspects of these theorems and discusses the issue of computability for limit cycles in these planar models. Furthermore, some methodological issues related to computational economic dynamics are analyzed. From an algorithmic point of view, it contends that there are inherent undecidabilities associated with many important properties of these dynamic models. These include characterizing attractors, determining their number, the domains of attraction and the possibility of exhibiting chaos, all of which have been important for dynamic economic theories. It makes a case for resorting to algorithmic economic dynamics in the future in order to overcome some of the limitations faced by the endogenous tradition.