Efficient Peer Effects Estimators with Group Effects
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含群组效应的高效同伴效应估计量
- 研究问题
- 在线性群组互动模型中，如何利用随机群组效应的假设和群组规模变化，识别同伴效应并缓解反射问题？
- 方法与思路
- 作者将既有矩条件写成线性随机群组效应模型，构造包含 QMLE 及既有估计量的 GMM 类，并考察协变量扩展。
- 材料陈述的贡献
- 摘要称，该框架在群组规模变化充分时可识别，容纳有限种规模或类型，并证明估计量的一致性与渐近正态性。
- 阅读关注点
- 应核对随机群组效应的限制、规模变化何谓充分、群组层面协变量的处理，以及不同估计量间效率比较的条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未获核实；摘要仅概述所需假设，不能判断任意群组形成机制下的识别有效性。
原文摘要
We study linear peer effects models where peers interact in groups, individual's outcomes are linear in the group mean outcome and characteristics, and group effects are random. Our specification is motivated by the moment conditions imposed in Graham 2008. We show that these moment conditions can be cast in terms of a linear random group effects model and lead to a class of GMM estimators that are generally identified as long as there is sufficient variation in group size. We also show that our class of GMM estimators contains a Quasi Maximum Likelihood estimator (QMLE) for the random group effects model, as well as the Wald estimator of Graham 2008 and the within estimator of Lee 2007 as special cases. Our identification results extend insights in Graham 2008 that show how assumptions about random group effects as well as variation in group size can be used to overcome the reflection problem in identifying peer effects. Our QMLE and GMM estimators accommodate additional covariates and are valid in situations with a large but finite number of different group sizes or types. Because our estimators are general moment based procedures, using instruments other than binary group indicators in estimation is straight forward. Our QMLE estimator accommodates group level covariates in the spirit of Mundlak and Chamberlain and offers an alternative to fixed effects specifications. Monte-Carlo simulations show that the bias of the QMLE estimator decreases with the number of groups and the variation in group size, and increases with group size. We also prove the consistency and asymptotic normality of the estimator under reasonable assumptions.