Addressing Endogeneity in Discrete Choice Models: Assessing Control-Function and Latent- Variable Methods

Endogenity or non-orthogonality in discrete choice models occurs when the systematic part of the utility is correlated with the error term. Under this misspecification, the model's estimators are inconsistent. This problem is virtually unavoidable, for example, in discrete choice models of residential choice where endogeneity occurs at the level of each observation mainly because of the omission of attributes. In such a case, the principal technique to treat for endogeneity is the control-function method. This method consists in the construction of a function that accounts for the endogenous part of the error term which is then included as an additional variable in the model. Alternatively, the latent-variable method can also be viewed as a procedure to address the endogeneity problem in discrete choice models. In this case, the omitted quality attribute which is causing the endogeneity can be considered as a latent-variable and modeled, in a structural equation, as a function of observed variables and potentially enhanced through indicators. The main objective of this paper is to analyze similarities and differences among control-function and latent-variable techniques and the exploration of ways by means of which both methods would enhance each other in addressing endogeneity in discrete choice models. This objective is achieved by analyzing the properties of both methods and by testing their performance in the correction of the endogeniety problem in a Monte Carlo experiment. The paper concludes with the analysis of potential future lines of research in this area.