Optimal Learning in Uncertain Environments

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This project examines the dynamics of decision-making under uncertainty, when reducing the degree of uncertainty by accumulation of information about the economic environment entails paying a cost. The general framework is one in which economic agents face a tradeoff between immediate expected gain and investing in information which might lead to increased future gains. The project brings the tools of Bayesian econometrics to bear in studying the accumulation of information by an optimizing agent in a stochastic economy with unknown aspects which can be learned, but where learning entails a cost. The tradeoff between current reward and accumulation of information of uncertain value is examined. Two important economic examples are studied: 1) a profit-maximizing monopolist facing uncertain demand, and 2) a controlled regression problem. This setting is also extended to include random environments in which information collection is an ongoing activity. Analytical and numerical methods for studying these types of problems are developed, and application to more general estimation of dynamic programming models is advanced. %%% Among the most important and difficult economic problems to model are those which deal with the making of decisions in the presence of uncertainty. These questions face most people in the economic marketplace, and include investing for the future, setting prices and output, making major purchases like automobiles and houses, and the purchase of insurance. In each of these circumstances uncertainty about the economic environment in which one is moving plays a key role, and that uncertainty can be reduced by acquiring more information. However, information is not costless, and the economic agent must make an implicit tradeoff between a current level of satisfaction or profit, or investing in the acquisition of more information, the value of which is uncertain. The project builds an analytical econometric framework which is based on Bayesian statistical methodology, and which incorporates learning and the cost of knowledge accumulation. The Bayesian approach differs from the usual statistical paradigm in being able to allow for the beliefs of the economic agents about the system in which they work. As knowledge and information are gained, those beliefs change, and in turn the dynamics of the decision-making process is altered. This research models the changing expectations and their effects on economic decisions, develops numerical techniques for estimation, and indicates how such models can be applied to empirical analysis.