Efficient peer effects estimators with group effects
含群组效应的高效同伴效应估计AI 解读 ↓
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含群组效应的高效同伴效应估计
- 研究问题
- 存在未观测群组效应和可能非随机分组时，如何利用群组规模或类型差异识别线性同伴效应，并构建估计方法？
- 方法与思路
- 作者把相关矩条件写成线性随机群组效应模型，构建包含 QMLE、Wald 和组内估计特例的 GMM 类，并纳入群组协变量。
- 材料陈述的贡献
- 摘要称该框架扩展了利用群组差异克服反射问题的识别策略，容纳更多协变量，并建立估计量的一致性与渐近正态性。
- 阅读关注点
- 应核对群组规模或类型的变异要求、随机效应和异方差假设，以及群组协变量控制相关性的范围与效率比较依据。
- 阅读边界
- 仅据所给出版社摘要，无法判断完整识别和效率条件；群组协变量控制不意味着任意非随机分组或未观测选择均已解决。
原文摘要
We study linear peer effect models where peers interact in groups and individual’s outcomes are linear in the group mean outcome and characteristics. We allow for unobserved random group effects as well as observed fixed group effects. The specification is in part 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 that they lead to a class of GMM estimators with parameters generally identified as long as there is sufficient variation in group size or group types. 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, variation in group size and certain forms of heteroscedasticity 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. This model feature significantly extends the applicability of Graham’s identification strategy to situations where group assignment may not be random but correlation of group level effects with peer effects can be controlled for with observable group level characteristics. 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.