Alternative Simulation-Based Estimators of Logit Models with Random Effects

Logit models with random effects are now widely used in applied Statistics and Econometrics. They usually lead to intractable likelihood functions, as they involve integrals without closed form solution. Numerical integration can be used to compute the likelihood and software is available (Hedeker and Gibbons, 1996). Difficulties can be encountered when the number of random effect parameters is not very small. With a detailed Monte Carlo experimentation, we show in this paper that the simulation-based estimators are almost as efficient as maximum likelihood. They are Simulated Maximum Likelihood (Gouri´eroux and Monfort, 1991), Indirect Inference (Gouri´eroux, Monfort and Renault, 1993) using an auxiliary approximated likelihood estimator, and Indirect Inference using an auxiliary linear probability model. The advantage of the latter is its great simplicity and computational speed.