Hospital efficiency under competing panel data models

Motivated by an application to a longitudinal dataset regarding hospitals in Lombardy we propose a model to measure hospital efficiency which incorporates observed covariates and time-varying latent hospital effects. The distribution of the latter may be continuous-valued or discrete-valued. In the first case it is a mixture of auto-regressive AR(1) processes with specific mean values and correlation coefficients and common variances. In the second case it is based on a first order homogeneous Markov chain with a fixed number of states. Maximum likelihood estimation of the model parameters is performed by using the expectation-maximization algorithm and the Newton-Raphson algorithm. The effect of the different formulations is evaluated in terms of the estimated efficiency scores