Researchers often use specifications that correctly estimate the average treatment effect under the assumption of constant effects. When treatment effects are heterogeneous, however, such specifications generally fail to recover this average effect. Augmenting these specifications with interaction terms between demeaned covariates and treatment eliminates this bias, but often leads to imprecise estimates and becomes infeasible under limited overlap. We propose a generalized ridge regression estimator, $\texttt{regulaTE}$, that penalizes the coefficients on the interaction terms to achieve an optimal trade-off between worst-case bias and variance in estimating the average effect under limited treatment effect heterogeneity. Building on this estimator, we construct confidence intervals that remain valid under limited overlap and can also be used to assess sensitivity to violations of the constant effects assumption. We illustrate the method in empirical applications under unconfoundedness and staggered adoption, providing a practical approach to inference under limited overlap.

翻译：研究者常采用在恒定效应假设下能正确估计平均处理效应的模型设定。然而，当处理效应存在异质性时，此类设定通常无法准确还原该平均效应。通过引入去中心化协变量与处理变量的交互项来扩展这些设定可以消除此偏差，但往往导致估计精度不足，且在有限重叠条件下变得不可行。我们提出一种广义岭回归估计量 $\texttt{regulaTE}$，该估计量通过对交互项系数施加惩罚，在有限处理效应异质性条件下实现估计平均效应时最坏情况偏差与方差的最优权衡。基于此估计量，我们构建了在有限重叠条件下仍保持有效的置信区间，该区间亦可用于评估对恒定效应假设违背的敏感性。我们通过无混淆假设与交错实验设计下的实证应用展示该方法，为有限重叠条件下的统计推断提供了一种实用途径。