Nonparametric identification of dynamic models with unobserved state variables - Yingyao Hu; Matthew Shum (Centre for Microdata Methods and Practice (cemmap), 2008)
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.
Keywords: 330; Markovscher Prozess; Ökonometrie