Claudia Noack

The confidence intervals (CIs) commonly reported in empirical fuzzy regression discontinuity studies are justified by theoretical arguments which assume that the running variable is continuously distributed with positive density around the cutoff, and that the jump in treatment probabilities at the cutoff is “large”. In this paper, we provide new confidence sets (CSs) that do not rely on such assumptions. Their construction is analogous to that of Anderson-Rubin CSs in the literature on instrumental variable models. Our CSs are based on local linear regression, and are bias-aware, in the sense that they explicitly take the possible smoothing bias into account. They are valid under a wide range of empirically relevant conditions in which existing CIs generally fail. These conditions include discrete running variables, donut designs, and weak identification. But our CS also perform favorably relative to existing CIs in the canonical setting with a continuous running variable, and can thus be used in all fuzzy regression discontinuity applications.

This paper presents a method to assess the sensitivity of treatment effect estimates to potential violations of the monotonicity assumption. I propose a model in which the degree to which monotonicity is violated is measured by two sensitivity parameters: One determines the population size of defiers and the other treatment effect heterogeneity between compliers and defiers. I identify the breakdown frontier, which is the set of sensitivity parameters that imply the weakest assumptions, which are necessary to draw a particular empirical conclusion, e.g. the average treatment effect is positive. Evaluating the plausibility of these parameters allows researchers to assess the credibility of this conclusion. I show how to conduct inference on these parameter estimates, where confidence sets are obtained through a bootstrap method. The performance of the breakdown frontier estimator is evaluated in a Monte Carlo study and illustrated in an empirical example.

Empirical regression discontinuity (RD) studies often use covariates to increase the precision of their estimates. In this paper, we propose a novel class of estimators that use such covariate information more efficiently than existing methods and can accommodate many covariates. It involves running a standard RD analysis in which a function of the covariates has been subtracted from the original outcome variable. We characterize the function that leads to the estimator with the smallest asymptotic variance, and consider feasible versions of such estimators in which this function is estimated, for example, through modern machine learning techniques.

We study the econometric properties of so-called donut regression discontinuity (RD) designs, a robustness exercise which involves repeating estimation and inference without the data points in some area around the treatment threshold. This approach is often motivated by concerns that possible systematic sorting of units, or similar data issues, in some neighborhood of the treatment threshold might distort estimation and inference of RD treatment effects. We show that donut RD estimators can have substantially larger bias and variance than contentional RD estimators, and that the corresponding confidence intervals can be substantially longer. We also provide a formal testing framework for comparing donut and conventional RD estimation results.

Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and derive high-level conditions under which the standard local linear RD estimator is asymptotically normal. We verify that our high-level assumptions hold across a wide range of empirical designs, including settings of growing cluster sizes. We further show that clustered standard errors that are currently used in practice can be either inconsistent or overly conservative in finite samples. To address these issues, we propose a novel nearest-neighbor-type variance estimator and illustrate its properties in a diverse set of empirical applications.