Affiliation: University of Montreal
Title: "Comparative Statics in Discrete Choice" (joint with Arthur Adam, Toulouse School of Economics).
Abstract: We use the "discard model" (Luce, 1960; Marley, 1965) as the jumping-off point to study a natural comparative static in discrete choice: the effect of adding (or removing) one product on the probability of choosing the remaining products. Since the discard model does not satisfy the Regularity axiom, it accommodates a rich variety of substitution patterns (e.g., complementarity, attraction, choice overload, and compromise) that are directly ruled out by other models of discrete choice.
We first provide an axiomatic characterization to identify the testable implications of the model. We then provide robust "qualitative" comparative statics à la Samuelson (1947) -- to identify what directional changes in choice probabilities can always be explained by the model and, conversely, what directional changes can never be explained. Finally, we propose a Slutsky-like decomposition where the income effect reflects the changes in choice probabilities explained by the multinomial logit (Luce, 1959; McFadden, 1974).