Hybrid choice models vs. endogeneity of indicator variables: a Monte Carlo investigation

We investigate the problem of endogeneity in the context of hybrid choice (integrated choice and latent variable) models. We first provide a thorough analysis of potential causes of endogeneity and propose a working taxonomy. We demonstrate that although it is widely believed that the hybrid choice framework is devoid of the endogeneity problem, there is no theoretical reason to expect that this is the case. We then demonstrate empirically that the problem exists in the hybrid choice framework too. By conducting a Monte Carlo experiment, we display the extent of the bias resulting from measurement and endogeneity biases. Finally, we propose two novel solutions to address the problem: by explicitly accounting for correlation between structural and discrete choice component error terms (or with random parameters in a utility function), or by introducing additional latent variables. Using simulated data, we demonstrate that these approaches work as expected, that is, they result in unbiased estimates of all model parameters.