Open AccessContinuity and differentiability of expected value functions in dynamic discrete choice models
Author(s) -
Norets Andriy
Publication year - 2010
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe41
Subject(s) - differentiable function , state variable , mathematics , bellman equation , function (biology) , value (mathematics) , relevance (law) , discrete choice , variable (mathematics) , state (computer science) , mathematical economics , mathematical optimization , econometrics , mathematical analysis , statistics , algorithm , physics , evolutionary biology , biology , political science , law , thermodynamics
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.