Working Paper: NBER ID: w22098
Authors: Bryan S. Graham; Guido W. Imbens; Geert Ridder
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.\n\n
Keywords: No keywords provided
JEL Codes: No JEL codes provided
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Conditionally exogenous matching (C78) | Average Match Function (AMF) (C78) |
| Unobserved teacher quality does not predict classroom characteristics (D29) | Average Match Function (AMF) (C78) |
| Conditionally exogenous matching (C78) | Pairwise stability in matching equilibrium (C62) |
| Characterization of semiparametric efficiency bound (C51) | Average Match Function (AMF) (C78) |