Two-stage differences in differences
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两阶段双重差分AI 解读 ↓
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A recent literature has shown that when adoption of a treatment is staggered and average treatment effects vary across groups and over time, difference-in-differences regression does not identify an easily interpretable measure of the typical effect of the treatment. In this paper, I extend this literature in two ways. First, I provide some simple underlying intuition for why difference-in-differences regression does not identify a group$\times$period average treatment effect. Second, I propose an alternative two-stage estimation framework, motivated by this intuition. In this framework, group and period effects are identified in a first stage from the sample of untreated observations, and average treatment effects are identified in a second stage by comparing treated and untreated outcomes, after removing these group and period effects. The two-stage approach is robust to treatment-effect heterogeneity under staggered adoption, and can be used to identify a host of different average treatment effect measures. It is also simple, intuitive, and easy to implement. I establish the theoretical properties of the two-stage approach and demonstrate its effectiveness and applicability using Monte-Carlo evidence and an example from the literature.
伪面板事件研究:可信应用的计量经济学基础
Event studies with panel data are widely used to estimate treatment effects. With repeated cross-sections, future treatment dates are unobserved for untreated individuals. Pseudo-panel event studies impute pre-treatment outcomes of the treated using matched untreated individuals. This paper establishes identification in such designs and characterizes bias when identification conditions fail. I show that the pseudo-panel regression is equivalent to weighted least squares with…
双重差分与合成控制的结合:双重稳健识别和估计
Difference-in-Differences (DiD) and Synthetic Control (SC) are widely used methods for causal inference in panel data, each with distinct strengths and limitations. We propose a novel method for short-panel causal inference that integrates the advantages of both approaches. Our method delivers a doubly robust identification strategy for the average treatment effect on the treated (ATT) under either of two non-nested assumptions: parallel trends or a group-level SC condition.…
含时变中介变量与滞后结果的双重差分模型
We study difference-in-differences (DiD) designs in which a binary treatment changes an endogenous time-varying (continuous, discrete, or mixed) mediator that in turn affects an outcome. We allow for the inclusion of lagged outcomes in the model. Under our model assumptions, we show that the usual DiD estimand mixes the average direct effect on the treated, the average indirect effect, and a trend bias term. A two-way fixed effects (TWFE) regression that controls for the…
测地线双重差分
Summary Difference-in-differences (DID) is a widely used quasi-experimental design for causal inference, traditionally applied to scalar or Euclidean outcomes, while extensions to outcomes residing in non-Euclidean spaces remain limited. Existing methods for such outcomes have primarily focused on univariate distributions, leveraging linear operations in the space of quantile functions, but these approaches cannot be directly extended to outcomes in general metric spaces. In…
含不良控制变量的双重差分
This paper considers difference-in-differences identification strategies when the parallel trends assumption holds after conditioning on covariates that may themselves be affected by the treatment (often referred to as "bad controls"). We show that common approaches such as simply dropping bad controls are often ill-advised and develop two alternative approaches that allow bad controls to function as genuine controls despite being affected by treatment. First, we derive…
面板双重差分估计的简单变换方法
In the case of panel data with staggered interventions, we propose a simple time-series transformation that can be combined with various treatment effect estimators. The transformation is at the unit level, and simply requires computing the average outcome prior to an intervention, subtracting it from a post-treatment outcome, and then carefully selecting the control units in each time period. We show that under no anticipation and parallel trends assumptions, the cohort…