difference-in-differences

This paper addresses causal inference in two-period panel data under the “no pure control group” setting: all units receive a strictly positive, heterogeneous continuous treatment in period two, rendering conventional difference-in-differences (DID) inapplicable due to the absence of untreated (zero-dose) units. Building on the parallel trends assumption, we propose three methodological approaches: (1) a robust DID estimator that relaxes the mean independence assumption; (2) a local identification strategy using low-dose units as bandwidth-based controls; and (3) a novel framework integrating nonparametric identification bounds with parametric modeling of treatment effect heterogeneity. Relative to Pierce & Schott (2016) and Enikolopov et al. (2011), our methods correct systematic bias arising from the lack of zero-dose units, delivering consistent and robust estimation of treatment effects. The framework extends the applicability of DID to settings featuring continuous treatments and constrained control structures.

Accurate estimation and inference for the average treatment effect (ATE) in multi-covariate randomized controlled trials (RCTs) remain challenging, particularly under high-dimensional covariates and small sample sizes. Method: Building on the Neyman finite-population framework, we propose a bias-corrected regression-adjustment estimator with cross-fitting and introduce, for the first time, an HC3-type heteroskedasticity-robust standard error tailored to high-dimensional settings. We rigorously derive first- and second-order stochastic expansions of the random component of regression-adjustment estimators, identifying the source of higher-order bias in conventional inference; leveraging this insight, we design a cross-fitting procedure to eliminate bias and extend HC3 standard errors to stratified experimental designs. Results: Simulations and reanalysis of Angrist et al. (2009)’s education RCT demonstrate that our method substantially improves estimation accuracy, confidence interval coverage, and statistical power—especially in small-sample and high-dimensional scenarios.

This paper addresses three key challenges in difference-in-differences (DID) estimation under continuous treatment: (i) selection bias due to non-random treatment assignment, (ii) incomparability of treatment effects across varying intensities, and (iii) ambiguous causal interpretation of conventional two-way fixed-effects (TWFE) estimators. We propose a generalized parallel trends assumption and establish the first rigorous identification framework for continuous-treatment DID. We formally prove that TWFE estimators—even in a two-period setting—lack clear causal interpretation under continuous treatment. To overcome this, we develop a bias-corrected, group-weighted estimator grounded in treatment-effect decomposition and augmented with selection-bias sensitivity analysis. Empirically, our method substantially revises policy effect estimates derived from standard TWFE, mitigating systematic misattribution. The proposed approach provides a robust, interpretable tool for causal inference in settings involving graded or intensity-varying interventions.

The two-way fixed effects (TWFE) estimator is widely used for causal inference in political science but suffers from sensitivity to heterogeneous treatment effects (HTE) and the parallel trends (PT) assumption, undermining result reliability. This study conducts a systematic reanalysis of 49 influential political science papers employing TWFE, marking the first large-scale assessment in the discipline of six HTE-robust estimators’ stability, alongside comprehensive PT diagnostics, sensitivity analyses, and statistical power evaluation. Results show that while HTE-robust estimates are directionally consistent overall, they exhibit substantial variability; explicit PT violations are rare, yet over half the studies suffer severe statistical power deficits under joint HTE and PT constraints. The analysis reveals systematic robustness risks inherent in standard TWFE practice, providing an empirical benchmark and practical guidance for method selection and interpretation in applied political science research.

In large-scale aggregate-unit experiments (e.g., markets), conventional randomized treatment assignment often yields severe baseline imbalance due to extremely few treated units, leading to biased causal estimates. To address this, we systematically integrate the synthetic control method into experimental design, proposing a non-randomized treatment allocation mechanism: dynamically constructing a weighted synthetic control group based on pre-treatment covariates. We further develop配套 components—including counterfactual prediction, distance-driven unit matching, robust variance estimation, and a novel confidence interval construction procedure. Theoretically, our estimator is proven consistent and asymptotically normal. Empirically, it reduces estimation bias by 40–65% relative to standard randomization and substantially improves statistical power. Our core contribution is a new causal inference paradigm for small-N aggregate experiments—rigorous in inference, unbiased under mild assumptions, and highly interpretable.

研究通过蒙特卡洛模拟分析了准实验方法在观察性IS研究中的效能问题，揭示了面板损耗、交错采用偏差等因素对实验效力的影响，并提出AR(1)敏感计算器等解决方案。

This study addresses the bias arising from negative weights in staggered difference-in-differences (DiD) designs, which distorts the average of heterogeneous treatment effects—particularly when time-varying covariates are present. Within a model-agnostic framework, the paper nonparametrically defines group-time, group, period, and dynamic average treatment effects for the first time. To this end, the authors propose an augmented inverse variance-weighted (AIVW) estimator that integrates the augmented inverse probability weighting (AIPW) principle, achieving double robustness: consistent estimation of target parameters is maintained even if either the outcome or propensity score model is misspecified. The asymptotic variance is derived via influence functions, enabling valid causal inference with time-varying covariates. Simulations and an empirical application to China’s college admissions policy demonstrate that the estimator performs reliably in finite samples and effectively identifies the causal effects of parallel志愿 and immediate enrollment policies.

This study addresses the sensitivity of causal effect estimation to model misspecification in longitudinal cluster-randomized and quasi-experimental designs. Within an M-estimation framework, it demonstrates that fixed-effects models yield consistent and asymptotically normal estimates of nonparametrically defined treatment effects, provided the treatment effect structure is correctly specified—even when other model components are arbitrarily misspecified. The work establishes, for the first time, that fixed-effects models are valid for estimating superpopulation marginal effects and reveals their robustness to partial misspecification of the treatment effect structure across diverse longitudinal settings. Through theoretical analysis, simulations, and reanalyses of empirical data, the paper further shows that fixed-effects models outperform mixed-effects models in robustness and reliability when time-invariant confounding exists at the cluster or individual level.

This study addresses the inferential bias in the average treatment effect on the treated (ATT) arising from data-driven control group selection and covariance matrix estimation within difference-in-differences frameworks. To mitigate this, it proposes a selective inference framework that extends exact Gaussian procedures to settings with unknown covariance by employing plug-in estimators to correct for selection bias, applicable to both individual panel and repeated cross-sectional data. This work unifies inference under complex scenarios involving staggered adoption, treatment effect heterogeneity, and sample reuse. Furthermore, it establishes uniform conditional and marginal coverage guarantees, proves the asymptotic equivalence between plug-in estimators and known-covariance confidence intervals, and derives convergence rates for interval lengths, thereby ensuring the statistical validity of ATT confidence intervals.

This study addresses the challenge of causal inference when instrumental variables violate the exclusion restriction and unobserved confounding is present. The authors propose a multiplicative quasi-instrumental variable model that permits the instrument to directly affect the outcome through pathways other than the treatment. This approach relaxes the conventional exclusion assumption and achieves nonparametric identification of the average treatment effect even in the presence of treatment effect heterogeneity and violations of exclusion. Building on a modified Wald ratio, they develop an estimator that is multiply robust and semiparametrically efficient. The method’s validity and reliability are demonstrated through simulation studies and an empirical application examining the impact of China’s three-child policy on maternal labor force participation.