Identification With Additively Separable Heterogeneity

Abstract

This paper provides nonparametric identification results for a class of latent utility models with additively separable unobservable heterogeneity. These results apply to existing models of discrete choice, bundles, decisions under uncertainty, and matching. Under an independence assumption, such models admit a representative agent. As a result, we can identify how regressors alter the desirability of goods using only average demands. Moreover, average indirect utility (“welfare”) is identified without needing to specify or identify the distribution of unobservable heterogeneity.

Identification of Random Coefficient Latent Utility Models

“…Proof of Lemma 1. This follows line by line from the proof of Allen and Rehbeck [2019a], Theorem 1. The statement of that result included an additional Assumption 1, which was not used in the proof as long as the underlying choice is appropriately measurable.…”

“…Proof of Lemma 2. See Allen and Rehbeck [2019a], Lemma 1. The result may also be directly proven from Rockafellar [1970], Theorems 23.5 and 25.1.…”

“…McFadden and Fosgerau [2012] and Allen and Rehbeck [2019a] have studied related frameworks without random coefficients. We interpret Y p¨q as the quantity vector for K different goods.…”

“…Concavity in part (iii) is milder than it first appears, and delivers no additional restrictions on Y px, βq when the other assumptions are maintained. See the discussion in Allen and Rehbeck [2019a].…”

Injectivity and the Law of Demand

“…A corollary of this lemma is that if C is everywhere differentiable (and the other conditions are met), then Q is globally invertible. A version of this result has been used in Allen and Rehbeck [2019]; I include this result for completeness, to illustrate how additional structure allows us to further specialize the results, and because the quasilinear structure is widely used.…”