This chapter discusses simulation estimation methods that overcome the computational intractability of classical estimation of limited dependent variable models with flexible correlation structures in the unobservable stochastic terms. These diﬀiculties arise because of the need to evaluate accurately very high dimensional integrals. The methods based on simulation do not require the exact evaluation of these integrals and hence are feasible using computers of even moderate power. I ﬁrst discuss a series of ideas that had been used in eﬀorts to circumvent these computational problems by employing standard numerical analysis approximation methods. I then show how simulation techniques solve the computational problems without the need to resort to either generally unsatisfactory numerical approximations. All currently know simulation algorithms are then compared in terms of theoretical properties and practical performance.
Hajivassiliou, Vassilis A., "Simulation Estimation Methods for Limited Dependent Variable Models" (1992). Cowles Foundation Discussion Papers. 1250.