19 Simulation estimation methods for limited dependent variable models

Abstract

This chapter discusses estimation methods for limited dependent variable (LDV) models that employ Monte Carlo simulation techniques to overcome numerical intractabilities of such models. These difficulties arise because high dimensional integral expressions need to be calculated repeatedly. The simulation estimation methods offer dramatic computational advantages over classical methods, and make it possible to estimate LDV models that are computationlly intractable using classical estimation methods even on state-of-the-art supercomputers. The main simulation estimation methods for LDV models developed in the econometrics discussed in the chapter include (1) simulated maximum likelihood (SML), (2) method of simulated moments (MSM), (3) method of simulated scores (MSS), (4) simulated pseudo ML (SPML), and (5) smooth simulated maximum likelihood (SSML). Results have been presented about the asymptotic properties of such simulation-based estimators. Specific simulation algorithms to use in conjunction with these five estimation methods are also described in the chapter. The leading simulation estimation methods require the simulation of one or more of the following expressions: probabilities of the limited dependent variables, derivatives of such probabilities with respect to underlying parameters, and derivatives of the (natural) logarithm of the probabilities of the dependent variables.