Nonparametric identification of dynamic models with unobserved state variables

We consider the identification of a Markov process when only {W_t} is observed. In structural dynamic models, W_t includes the choice variables and observed state variables of an optimizing agent, while denotes time-varying serially correlated unobserved state variables (or agent-specific unobserved heterogeneity). In the non-stationary case, we show that the Markov law of motion is identified from five periods of data W_t+1,W_t,W_t−1,W_t−2,W_t−3. In the stationary case, only four observations W_t+1,W_t,W_t−1,W_t−2 are required. Identification of is a crucial input in methodologies for estimating Markovian dynamic models based on the “conditional-choice-probability (CCP)” approach pioneered by Hotz and Miller.