Continuity and differentiability of expected value functions in dynamic discrete choice models

• 成果类型: Article
• 署名作者: Norets, Andriy
• 署名单位: Princeton University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE41
• 发表日期: 2010
• 页码: 305-322
• 关键词: Dynamic discrete choice models; continuity; differentiability

摘要

This paper explores the properties of expected value functions in dynamic discrete choice models. The continuity with respect to state variables and parameters, and the differentiability with respect to state variables are established under fairly general conditions. The differentiability with respect to parameters is proved when some state variables do not affect the state transition probabilities and, thus, the expected value functions. It is shown that such variables are needed so as to apply the implicit function theorem used in the proof. The results are of particular relevance to estimable dynamic discrete choice models.