Identification and Efficiency Bounds for the Average Match Function Under Conditionally Exogenous Matching

33 Pages Posted: 21 Mar 2016 Last revised: 20 May 2023

See all articles by Bryan S. Graham

Bryan S. Graham

University of California, Berkeley - Department of Economics; National Bureau of Economic Research (NBER)

Guido W. Imbens

Stanford Graduate School of Business

Geert Ridder

University of Southern California

Multiple version iconThere are 2 versions of this paper

Date Written: March 2016

Abstract

Consider two heterogenous populations of agents who, when matched, jointly produce an output, `Y`. For example, teachers and classrooms of students together produce achievement, parents raise children, whose life outcomes vary in adulthood, assembly plant managers and workers produce a certain number of cars per month, and lieutenants and their platoons vary in unit effectiveness. Let `W\in\mathbb{W}={ w_1,\ldots,w_j} and X\in\mathbb{X}={ x_1,\ldots,x_k}` denote agent types in the two populations. Consider the following matching mechanism: take a random draw from the `W=w_j` subgroup of the first population and match her with an independent random draw from the `X=x_k` subgroup of the second population. Let `beta(w_j,x_k)`, the average match function (AMF), denote the expected output associated with this match. We show that (i) the AMF is identified when matching is conditionally exogenous, (ii) conditionally exogenous matching is compatible with a pairwise stable aggregate matching equilibrium under specific informational assumptions, and (iii) we calculate the AMF's semiparametric efficiency bound.

Suggested Citation

Graham, Bryan S. and Imbens, Guido W. and Ridder, Geert, Identification and Efficiency Bounds for the Average Match Function Under Conditionally Exogenous Matching (March 2016). NBER Working Paper No. w22098, Available at SSRN: https://ssrn.com/abstract=2752303

Bryan S. Graham (Contact Author)

University of California, Berkeley - Department of Economics ( email )

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Guido W. Imbens

Stanford Graduate School of Business ( email )

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Geert Ridder

University of Southern California ( email )

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