Identification and Estimation of Non-stationary Hidden Markov Models

This paper provides a novel constructive identification proof for non-stationary Hidden Markov models. The identification result establishes that only two periods of time are required if one wants to identify transition probabilities between those two periods. This is achieved by using three conditionally independent noisy measures of the hidden state. The paper also provides a novel estimator for nonstationary hidden Markov models based on the identification proof. Montecarlo experiments show that this estimator is faster to compute than maximum likelihood, and almost as precise for large enough samples. Moreover, I show how my identification proof and my estimator can be used in two different relevant applications: Identification and estimation of Conditional Choice Probabilities, initial conditions and laws of motion in dynamic discrete choice models when there is an unobservable state; and identification and estimation of the production function of cognitive skills in a child development context when skills and investment are unobserved.