Nonparametric identification of dynamic models with unobserved state variables

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