Endogeneity in adaptive choice contexts

Abstract

Endogeneity arises in discrete choice models due to several factors and results in inconsistent estimates of the model parameters. In adaptive choice contexts such as choice-based recommender systems and adaptive stated preferences (ASP) surveys, endogeneity is expected because the attributes presented to an individual in a specific menu (or choice situation) depend on the previous choices of the same individual (as well as the alternative attributes in the previous menus). Nevertheless, the literature is indecisive on whether the parameter estimates in such cases are consistent or not. In this paper, we discuss cases where the estimates are consistent and those where they are not. We provide a theoretical explanation for this discrepancy and discuss the implications on the design of these systems and on model estimation. We conclude that endogeneity is not a concern when the likelihood function properly accounts for the data generation process. This can be achieved when the system is initialized exogenously and all the data are used in the estimation. In line with previous literature, Monte Carlo results suggest that, even when exogenous initialization is missing, empirical bias decreases with the number of choices per individual. We conclude by discussing the practical implications and extensions of this research.