Substitution Patterns of the Random Coefficients Logit

Abstract

The marketing literature often argues that the random coefficient logit model gives more realistic results than the homogeneous logit. The purpose of this paper is to show that the random coefficients logit improves upon, but does not completely solve the problems of the homogeneous logit. We show that both models lead to the following paradox: The assumptions of the utility function imply that individual decision makers have rational preferences. Yet, the derived choice probabilities imply that the individuals’ choices reflect context-dependent preferences instead. In addition, we show that the random coefficients logit is not as flexible as previous research suggests. Although it recovers more realistic substitution patterns in aggregate, it does not recover the patterns that are expected to occur in real life at either the individual or the aggregate levels.

Building on our analytical results, we design several Monte Carlo experiments to discuss the implications for inference and policy analysis. For example, in one experiment market share predictions range between 17% and 83% for a given alternative in a given choice set, depending on how the decision is framed in the data used for estimation and in the counterfactual scenario under consideration. This occurs even though the actual data shows that market shares remain about 50% regardless of how the decision is framed.