Maximum Simulated Likelihood and Expectation-Maximization Methods to Estimate Random Coefficients Logit with Panel Data

Abstract

The random coefficients logit model allows a more realistic representation of agents’ behavior. However, the estimation of that model may involve simulation, which may become impractical with many random coefficients because of the curse of dimensionality. In this paper, the traditional maximum simulated likelihood (MSL) method is compared with the alternative expectation-maximization (EM) method, which does not require simulation. Previous literature had shown that for cross-sectional data, MSL outperforms the EM method in the ability to recover the true parameters and estimation time and that EM has more difficulty in recovering the true scale of the coefficients. In this paper, the analysis is extended from cross-sectional data to the less volatile case of panel data to explore the effect on the relative performance of the methods with several realizations of the random coefficients. In a series of Monte Carlo experiments, evidence suggested four main conclusions: (a) efficiency increased when the true variance–covariance matrix became diagonal, (b) EM was more robust to the curse of dimensionality in regard to efficiency and estimation time, (c) EM did not recover the true scale with cross-sectional or with panel data, and (d) EM systematically attained more efficient estimators than the MSL method. The results imply that if the purpose of the estimation is only to determine the ratios of the model parameters (e.g., the value of time), the EM method should be preferred. For all other cases, MSL should be used.