Substitution Patterns of the Random Coefficients Logit

Previous research suggests that the random coefficients logit is a highly flexible model that overcomes the problems of the homogeneous logit by allowing for differences in tastes across individuals. The purpose of this paper is to show that this is not true. We prove that the random coefficients logit imposes restrictions on individual choice behavior that limit the types of substitution patterns that can be found through empirical analysis, and we raise fundamental questions about when the model can be used to recover individuals' preferences from their observed choices. Part of the misunderstanding about the random coefficients logit can be attributed to the lack of cross-level inference in previous research. To overcome this deficiency, we design several Monte Carlo experiments to show what the model predicts at both the individual and the population levels. These experiments show that the random coefficients logit leads a researcher to very different conclusions about individuals' tastes depending on how alternatives are presented in the choice set. In turn, these biased parameter estimates affect counterfactual predictions. In one experiment, the market share predictions for a given alternative in a given choice set range between 17% and 83% depending on how the alternatives are displayed both in the data used for estimation and in the counterfactual scenario under consideration. This occurs even though the market shares observed in the data are always about 50% regardless of the display.