Extrinsic uncertainty, ergodic chaos and monetary policy in two intertemporal economic models

Doctoral Thesis


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University of Cape Town

The thesis examines extrinsic uncertainty and ergodic chaos in two types of intertemporal economic models. The thesis is divided into four chapters. In the first chapter the existence of extrinsic uncertainty also known as sunspots is analysed within the framework of a single commodity two-period pure exchange over lapping generations model. Transversality techniques are utilised to show that extrinsically uncertain equilibria are locally generic in the space of endowments. An application of the methodology of the multijet transversality theorem demonstrates that equilibria are regular for a dense set of utility functions. The analysis of this paper extends and complements existence results concerning the robustness of stationary sunspot equilibria. In the second chapter, a multi-commodity version of the model of the first chapter is analysed. The equilibrium system is divided into the set of equations defined by (i) the stochastic budget constraints and by (ii) stochastic excess demand functions a geometric equilibrium is defined. A transversality technique shows that for almost every endowment vector the manifolds generated by (i) and (ii) do not intersect each other hence geometric stationary sunspot equilibria do not exist. This result is contrasted against the fact that regular non-stochastic monetary steady state equilibria generically exist. Furthermore, the existence of such equilibria is sufficient for the existence of an intrinsically uncertain equilibria. The results answer the question of the validity of the equilibrium concept of extrinsic uncertainty within a stationary environment.

Includes bibliographical references