'Small Data': Efficient Inference with Occasionally Observed States

Abstract

We study the estimation of dynamic economic models if some of the state variables are observed only occasionally by the econometrician—a common problem in many fields, ranging from industrial organization over marketing to finance. If such occasional state observations are serially correlated, the likelihood function of the model becomes a potentially high-dimensional integral over a non-standard domain. We propose a method that generalizes the recursive likelihood function integration procedure (RLI; Reich, 2018) to numerically approximate this integral and demonstrate its statistical efficiency in several well-understood examples from finance and industrial organization. Further, we compare the performance of our approach to a recently suggested method of simulated moments in extensive Monte Carlo studies. In all our demonstrations, we can consistently and efficiently identify all model parameters, and we find that
the additional variance of our estimator when going from full to occasional state observations is small for the parameters of interest.

JEL Classification: CO1