Theory of Stochastic Optimal Economic Growth

Stochastic optimal growth involves the study of the optimal intertemporal allocation of capital and consumption in an economy where production is subject to random disturbances. The theory traces its roots to the seminal work on deterministic optimal growth by Ramsey [106], Cass [21] and Koopmans [55]. Its influence has been enhanced by research that shows how the convex stochastic growth model can be decentralized to represent the behavior of consumers and firms in a dynamic competitive equilibrium of a productive economy ([102], [115], [15]). This makes the stochastic optimal growth model useful both as a normative exercise and in the development of positive theories of how the economy works. As a consequence, the theory has emerged as one of the central paradigms of dynamic economics. It is based on a simple, yet powerful model that encompasses fundamental questions that are basic to any theory of dynamic economic behavior: What are the characteristics and determinants of optimal policies? What are the economic incentives that govern the optimal intertemporal allocation of resources? What is the transient and long run behavior of variables in the model? Under different assumptions the model admits a rich set of answers to these questions. Historically, the main focal point of the theory has been issues of aggregate economic growth. At the same time its primary variable, capital, has a flexible interpretation that allows the model and its extensions to represent a wide variety of economic problems ranging from the study of business cycles ([59], [63]) and asset pricing ([14], [15]) to the allocation of renewable natural resources ([77], [82], [83]). Equally important, the model provides a strong theoretical foundation for applied analysis of these problems. The model can be solved numerically and has proved a testing ground for many numerical techniques used today in the analysis of dynamic economic problems. This chapter provides an overview of key results the theory of discounted stochastic optimal growth in discrete time.1 The paper begins with an analysis of