Identification and Efficiency Bounds for the Average Match Function Under Conditionally Exogenous Matching
研究了两个异质群体随机匹配时平均产出函数的识别问题，证明了在条件外生匹配下该函数可识别，并给出了半参数效率界，对分析师生匹配、亲子匹配等有参考价值。
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∈W={w1, …, wJ}$W\in \mathbb {W}=\lbrace w_{1}, \ldots, w_{J}\rbrace $ and X∈X={x1, …, xK}$X\in \mathbb {X}=\lbrace x_{1}, \ldots, x_{K}\rbrace $ denote agent types in the two populations. Consider the following matching mechanism: take a random draw from the W = wj subgroup of the first population and match her with an independent random draw from the X = xk subgroup of the second population. Let β(wj, xk), 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.