Two-Step Estimation of Discrete/Continuous Econometric Models with Interdependent Multinomial Choices

This paper considers theoretical and practical aspects associated with the two-step estimation of discrete/continuous econometric models when the choice dimension concerns interdependent choices. A two-step procedure is favoured over a full-information one to avoid the specification errors that could arise from misspecifying the joint distribution of the mixed discrete and continuous random variables involved. A second advantage is simplicity. This is especially true when the choices are described with a multinomial probit (MNP) setting. For the estimation of the second step, we suggest adding selectivity correction terms to a conventional regression-based formulation. Because of the interdependencies among the choices, the correction terms depend on multivariate normal integrals that cannot be easily evaluated numerically in situations with many choices. As a solution we replace them with efficient simulators. The later are needed both for choice probabilities and for the conditional moments involved in the correction terms. The technique suggested may be viewed as an extension to the multinomial setting with interdependent alternatives of the well-known Heckman selectivity correction. As an application, we model the Quebec residential electricity demand accounting for interrelations between decisions on electricity-related durable holdings and usage.(This abstract was borrowed from another version of this item.)