Chapter 40 Classical estimation methods for LDV models using simulation

This chapter discusses classical estimation methods for limited dependent variable (LDV) models that employ Monte Carlo simulation techniques to overcome computational problems in such models. These difficulties take the form of high-dimensional integrals that need to be calculated repeatedly. In the past, investigators were forced to restrict attention to special classes of LDV models that are computationally manageable. The simulation estimation methods we discuss here make it possible to estimate LDV models that are computationally intractable using classical estimation methods. The chapter first reviews the ways in which LDV models arise, describing the differences and similarities in censored and truncated data generating processes. Censoring and truncation give rise to the troublesome multivariate integrals. Following the LDV models, we described various simulation methods for evaluating such integrals. Naturally, censoring and truncation play roles in simulation as well. Finally, estimation methods that rely on simulation are described. The chapter also reviews three general approaches that combine estimation of LDV models and simulation: simulation of the log-likelihood function (MSL), simulation of moment functions (MSM), and simulation of the score (MSS). The MSS is a combination of ideas from MSL and MSM, treating the efficient score of the log-likelihood function as a moment function.