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A Practical Guide to Estimating Conditional Marginal Effects: Modern Approaches

条件边际效应估计的实用指南:现代方法

This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often suffer from unclarified estimands, limited overlap, and restrictive functional forms. This guide begins by clearly defining the estimand and presenting the main identification results. It then reviews and improves upon existing solutions, such…

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The Harmonic Synthetic Control Method

谐波合成控制方法

Synthetic control methods can produce misleading counterfactual predictions when outcome series contain unit-specific stochastic trends, a common feature of nonstationary macroeconomic data. Existing remedies, such as pre-filtering or differencing, reduce spurious matching but may discard shared nonstationary variation that helps estimate donor weights. We propose Harmonic Synthetic Control (HSC), which replaces this binary choice with a soft allocation mechanism. HSC…

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Degrees of Freedom and Information Criteria for the Synthetic Control Method

合成控制法的自由度与信息准则

We provide an analytical characterization of the model flexibility of the synthetic control method (SCM) in the familiar form of degrees of freedom. We obtain estimable information criteria, which may be used to circumvent cross-validation when selecting either the tuning parameter in penalized variants of SCM or the weighting matrix in the SCM with covariates. We assess the impact of car license rationing in Tianjin; while a natural match is available, both it and other…

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Cohort-Anchored Robust Inference for Event-Study with Staggered Adoption

交错处理事件研究中以处理队列为锚的稳健推断

This paper proposes a cohort-anchored framework for robust inference in event studies with staggered adoption, building on Rambachan and Roth (2023). Robust inference based on event-study coefficients aggregated across cohorts can be misleading due to the dynamic composition of treated cohorts, especially when pre-trends differ across cohorts. My approach avoids this problem by operating at the cohort-period level. To address the additional challenge posed by time-varying…

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A Response to Recent Critiques of Hainmueller, Mummolo and Xu (2019) on Estimating Conditional Relationships

回应关于估计条件关系的近期批评:对 Hainmueller、Mummolo 与 Xu(2019)的澄清

Simonsohn (2024a) and Simonsohn (2024b) critique Hainmueller, Mummolo and Xu (2019, HMX), arguing that failing to model nonlinear relationships between the treatment and moderator leads to biased marginal effect estimates and uncontrolled Type-I error rates. While these critiques highlight the issue of under-modeling nonlinearity in applied research, they are fundamentally flawed in several key ways. First, the causal estimand for interaction effects and the necessary…

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