University of California Transportation Center

This paper focuses on estimating limited dependent variable models with incidentally truncated data and two selection mechanisms. While typical sample selection models have been widely estimated, extensions to multiple selection mechanisms have been sparse due to intractable likelihood functions or estimation algorithms with slow convergence. This paper extends the sampling algorithm from Chib et al. (2009) and proposes a computationally-ecient Markov chain Monte Carlo (MCMC) estimation algorithm with data augmentation. The algorithm only augments the posterior with a small subset of the total missing data caused by the selection mechanisms, which improves convergence of the MCMC chain and decreases computational load relative to standard algorithms. The resulting sampling densities are well-known despite not having the "complete" data. The methods are applied to estimate the e�ects of residential density on vehicle usage and holdings in California.