Working Paper

Nonparametric identification of dynamic models with unobserved state variables


Yingyao Hu, Matthew Shum

Published Date

28 May 2008


Working Paper (CWP13/08)

We consider the identification of a Markov process {Wt, Xt*} for t=1,2,…,T when only {Wt} for t=1, 2,..,T is observed. In structural dynamic models, Wt denotes the sequence of choice variables and observed state variables of an optimizing agent, while Xt* denotes the sequence of serially correlated state variables. The Markov setting allows the distribution of the unobserved state variable Xt* to depend on Wt-1 and Xt-1*. We show that the joint distribution of (Wt, Xt*, Wt-1, Xt-1*) is identified from the observed distribution of (Wt+1, Wt, Wt-1, Wt-2, Wt-3) under reasonable assumptions. Identification of the joint distribution of (Wt, Xt*, Wt-1, Xt-1*) is a crucial input in methodologies for estimating dynamic models based on the “conditional-choice-probability (CCP)” approach pioneered by Hotz and Miller.