Critical assessment of five methods to correct for endogeneity in discrete-choice models

Endogeneity often arises in discrete-choice models, precluding the consistent estimation of the model parameters, but it is habitually neglected in practical applications. The purpose of this article is to contribute in closing that gap by assessing five methods to address endogeneity in this context: the use of Proxys (PR); the two steps Control-Function (CF) method; the simultaneous estimation of the CF method via Maximum-Likelihood (ML); the Multiple Indicator Solution (MIS); and the integration of Latent-Variables (LV). The assessment is first made qualitatively, in terms of the formulation, normalization and data needs of each method. Then, the evaluation is made quantitatively, by means of a Monte Carlo experiment to study the finite sample properties under a unified data generation process, and to analyze the impact of common flaws. The methods studied differ notably in the range of problems that they can address; their underlying assumptions; the difficulty of gathering proper auxiliary variables needed to apply them; and their practicality, both in terms of the need for coding and their computational burden. The analysis developed in this article shows that PR is formally inappropriate for many cases, but it is easy to apply, and often corrects in the right direction. CF is also easy to apply with canned software, but requires instrumental variables which may be hard to collect in various contexts. Since CF is estimated in two stages, it may also compromise efficiency and difficult the estimation of standard errors. ML guarantees efficiency and direct estimation of the standard errors, but at the cost of larger computational burden required for the estimation of a multifold integral, with potential difficulties in identification, and retaining the difficulty of gathering proper instrumental variables. The MIS method appears relatively easy to apply and requiring indicators that may be easier to obtain in various cases. Finally, the LV approach appears as the more versatile method, but at a high cost in computational burden, problems of identification and limitations in the capability of writing proper structural equations for the latent variable.