Synopses & Reviews
Synopsis
Excerpt from Continuous Time Production Economies Under Incomplete Information I: A Separation Theorem
Section I describes the continuous time economy and the structure of the uncertainty. Section 11 states the inference problem and describes the logical steps of the reasoning which leads to its solution. I then consider the simple case of one technology and one state variable. The solution is closely related to standard economic results and provides a useful intuition. It is rigorously proved using the general results of section III. Section III states the non linear filtering results and the solution to the general inference problem. The mathematical problem was solved by Liptser and Shiryayev (1978) and the proofs are therefore not presented. This introduction to the use of non-linear filtering theory for economic analysis is brief but self-contained. The power of the technique and its applicability to a broad range of economic problems warrant its extensive development in that section. However, the reader is alerted that section III is not necessary for the understanding of the substantive economic argument.
Section IV contains the main result of separability and establishes the general equilibrium conditions. The results are contrasted with the conclusions of prior research.
Finally, the conclusion summarizes the implications for general equilibrium and further research currently underway. A later companion paper3 will develop these issues.
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