Nonparametric identification of dynamic models with unobserved state variables

We consider the identification of a Markov process { W t , X t ∗ } 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 X t ∗ 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 f W t , X t ∗ ∣ W t − 1 , X t − 1 ∗ 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 f W t , X t ∗ ∣ W t − 1 , X t − 1 ∗ is a crucial input in methodologies for estimating Markovian dynamic models based on the “conditional-choice-probability (CCP)” approach pioneered by Hotz and Miller.