Likelihood Approximation for Discrete Choice Models with Sparse Grids

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Discrete choice models are used to explain, analyze, and predict choices between discrete alternatives. The most widely used method for estimating the parameters is maximum likelihood, but the likelihood function can be analytically evaluated only for the most basic models. For more flexible versions like the multinomial probit or the mixed multinomial logit model, it involves multivariate integrals that do not have a closed-form solution. The most common approach is to approximate the likelihood function using Monte Carlo simulation, but a sufficiently accurate approximation can be computationally prohibitively costly. This restricts the practical use in empirical research.This project aims to develop alternatives to the common simulation-based estimation methods that promise a much faster convergence by efficiently using the given smoothness of the integrands. To this end we will adopt the method of sparse grids which has been used successfully in many different areas and tailor it to the specific problems at hand. Besides the efficient approximation of the likelihood function, we will also study the properties of the resulting estimators. Finally, we will implement the methods for specific empirical applications from health and competition economics that were significantly restricted by computational costs before.