Quantitative Economics: Nov, 2010, Volume 1, Issue 2

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

Andriy Norets

This paper explores the properties of expected value functions in dynamic dis-
crete choice models. The continuity with respect to state variables and parame-
ters, 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.
Keywords. Dynamic discrete choice models, continuity, differentiability.
JEL classification. C35, C61.

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