Discrete choice estimator properties for finite population and simulation sample sizes

Econometric models based on simulations are used extensively in transportation. Simulation methods provide only an approximation of the objective function and produce estimators that suffer from bias and loss in efficiency. Two types of bias are known to exist in simulation-based estimators: simulation bias, as a result of the nonlinear transformation in the log likelihood (LL) function, and optimization bias, caused by the maximization operator, which depends on the variance of the simulated LL with respect to the random draws and the population sample. In this paper, the properties of the estimators are studied with resampling techniques in various simulation configurations. In the experiments, optimization bias dominates simulation bias, and in the presence of panel data the use of some randomized quasi-Monte Carlo techniques aiming at reducing simulation variance only marginally affects the estimated parameters for a given sample size. Results also confirm that the population resampling, though numerically costly, is a simple and effective procedure to deliver a better understanding of parameter properties.