"Small Data": Inference with Occasionally Observed States

Abstract

We study the estimation of dynamic economic models for which some of the state variables are observed only occasionally by the econometrician—a common problem in many fields, ranging from marketing to finance to industrial organization. If those occasional state observations are serially correlated, the likelihood function of the model becomes a high-dimensional integral over a nonstandard domain. We generalize the recursive likelihood function integration procedure (RLI; Reich, 2018) to incorporate the occasional observations, enabling likelihood-based inference in such estimation problems. In extensive Monte Carlo studies, we demonstrate the favorable properties of the proposed method for identifying all model parameters and compare it to alternative methods. 

Keywords: maximum likelihood estimation, occasional state observations, recursive likelihood function integration, interpolation, numerical quadrature, Markov models, dynamic discrete choice models, long-run risk models

JEL Classification: C13,C63,C49