Optimal Learning in Uncertain Environments

这个项目研究了在全球化背景下的决策动态。 不确定性，当减少不确定性的程度， 经济环境信息的积累 需要付出代价。 总体框架是一个在 哪些经济主体面临着一个权衡， 预期收益和投资于可能 增加未来收益。 该项目带来了贝叶斯计量经济学的工具，以承担 通过优化代理研究信息的积累 在具有未知方面的随机经济中， 但学习是有代价的 电流之间的权衡 奖励和积累的不确定价值的信息进行检查。 研究了两个重要的经济学例子：1）利润最大化 垄断者面对不确定的需求，2）控制回归 问题. 此设置还扩展为包括随机 信息收集是一项持续活动的环境。 研究这类问题的分析和数值方法 并应用于更一般的动态估计 编程模式先进。 %%% 在最重要和最困难的经济问题建模中， 是那些处理决策的存在， 不确定性 这些问题面临着大多数人在经济 市场，包括投资未来，设定价格， 产出，主要购买汽车和房屋， 购买保险。 在每一种情况下的不确定性 一个人所处的经济环境是关键 作用，而不确定性可以通过获得更多的 信息. 然而，信息不是没有成本的， 代理必须在当前的 满意度或利润，或投资于收购更多 信息，其价值是不确定的。 该项目建立了一个分析计量经济学框架， 贝叶斯统计方法，其中包括学习 以及知识积累的成本。 贝叶斯方法与 从通常的统计范式，能够允许 经济主体对他们工作的系统的信念。 随着知识和信息的获得，这些信念发生了变化， 改变了决策过程的动态。这 研究模型不断变化的期望及其对 经济决策，开发用于估计的数值技术，以及 说明了如何将这些模型应用于实证分析。

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.