Quasi-Random Maximum Simulated Likelihood Estimation Methods

This research work proposes the use of a quasi-random sequence for the estimation of the econometric discrete choice models. The estimation of models which are not analytically-tractable has been achieved in the past using the pseudo-random maximum simulated likelihood method that evaluates the multi-dimensional integrals in the log-likelihood function by computing the integrand at a sequence of pseudo-random points and taking the average of the resulting integrand values. We suggest and implement an alternative quasi-random maximum simulated likelihood method which uses cleverly crafted non-random but more uniformly distributed sequences in place of the pseudo-random points in the estimation of the mixed logit model. Numerical experiments indicate that the quasi-random method provides considerably better accuracy with much fewer draws and computational time than does the pseudo-random method. This result has the potential to dramatically influence the use of the mixed logit model in practice; specifically, given the flexibility of the mixed logit model, the use of the quasi-random method of estimation should facilitate the application of behaviorally rich structures in discrete choice analysis. The implementation and testing of other, potentially more efficient, quasi-random methods is currently underway.