We develop a new approach for estimating average treatment effects in observational studies with unobserved group-level heterogeneity. We consider a general model with group-level unconfoundedness and provide conditions under which aggregate balancing statistics -- group-level averages of functions of treatments and covariates -- are sufficient to eliminate differences between groups. Building on these results, we reinterpret commonly used linear fixed-effect regression estimators by writing them in the Mundlak form as linear regression estimators without fixed effects but including group averages. We use this representation to develop Generalized Mundlak Estimators (GMEs) that capture group differences through group averages of (functions of) the unit-level variables and adjust for these group differences in flexible and robust ways in the spirit of the modern causal literature.

翻译：我们提出了一种在观测研究中估计平均处理效应的新方法，其中存在未观测到的组级异质性。我们考虑一个具有组级无混杂性的通用模型，并给出了条件下，聚合平衡统计量（处理变量和协变量函数的组级平均值）足以消除组间差异的条件。基于这些结果，我们通过将常用的线性固定效应回归估计量重新解释为Mundlak形式（即不含固定效应但包含组平均值的线性回归估计量），重新诠释了这些估计量。我们利用这一表示形式，开发了广义Mundlak估计量（GMEs），这些估计量通过单元级变量函数的组平均值捕捉组间差异，并以现代因果文献的精神，以灵活且稳健的方式调整这些组间差异。