'Small Data': Efficient Inference with Occasionally Observed States

We study the estimation of controlled Markov processes if the states are only occasionally observed by the econometrician. We propose an extension to the recursive likelihood integration method of Reich (2018), to which we incorporate such occasional state observations in a numerically efficient and accurate way. To evaluate the performance of the proposed method, we assess the computational feasibility as well as the statistical efficiency by applying it to a counter-factual scenario of the widely known bus engine replacement model of Rust (1987): We assume that the mileage state is observed only at replacement, but unobserved in between. We demonstrate that - despite reducing the amount of mileage observations to about only 2% of the original data set - the distribution of the cost parameter estimator under the occasional observation regime is almost indistinguishable from its distribution using all mileage observations; hence there is no (additional) bias and comparable variance.