Essays on the Random Parameters Logit Model

Abstract

This research uses quasi-Monte Carlo sampling experiments to examine the properties of pretest and positive-part Stein-like estimators in the random parameters logit (RPL) model based on the Lagrange Multiplier (LM), likelihood ratio (LR) and Wald tests. First, we explore the properties of quasi-random numbers, which are generated by the Halton sequence, in estimating the random parameters logit model. We show that increases in the number of Halton draws influence the efficiency of the RPL model estimators only slightly. The maximum simulated likelihood estimator is consistent and it is not necessary to increase the number of Halton draws when the sample size increases for this result to be evident. In the second essay, we study the power of the LM, LR and Wald tests for testing the random coefficients in the RPL model, using the conditional logit model as the restricted model, since we found that the LM-based pretest estimator provides the poor risk properties. We claimed that the power of LR and Wald tests decreases with increases in the mean of the coefficient distribution. The LM test has the weakest power for presence of the random coefficient in the RPL model. In the last essay, the pretest and shrinkage are showed to reduce the risk of the fully correlated RPL model estimators significantly. The percentage of correct predicted choices is increased by 2% using the positive-part Stein-like estimates compared to the results using the pretest and fully correlated RPL model estimates with using the marketing consumer choice data.