In applied microeconometric panel data analyses, time-constant random effects and first-order Markov chains are the most prevalent structures to account for intertemporal correlations in limited dependent variable models. An example from health economics shows that the addition of a simple autoregressive error terms leads to a more plausible and parsimonious model which also captures the dynamic features better. The computational problems encountered in the estimation of such models - and a broader class formulated in the framework of nonlinear state space models - hampers their widespread use. This paper discusses the application of different nonlinear filtering approaches developed in the time-series literature to these models and suggests that a straightforward algorithm based on sequential Gaussian quadrature can be expected to perform well in this setting. This conjecture is impressively confirmed by an extensive analysis of the example application.
LDV models panel data state space numerical integration health