Regression Discontinuity Designs Using Covariates Calonico, Sebastian; Cattaneo, Matias D.; Farrell, Max H. ...
The review of economics and statistics,
07/2019, Letnik:
101, Številka:
3
Journal Article
Recenzirano
We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive ...separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions and characterize the potential for estimation and inference improvements. We also present new covariate-adjusted mean-squared error expansions and robust bias-corrected inference procedures, with heteroskedasticity-consistent and cluster-robust standard errors. We provide an empirical illustration and an extensive simulation study. All methods are implemented in
and
software packages.
Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to ...tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice. This is achieved using a novel, yet simple, Studentization, which leads to a new way of constructing kernel-based bias-corrected confidence intervals. In addition, for practical cases, we derive coverage error optimal bandwidths and discuss easy-to-implement bandwidth selectors. For interior points, we show that the mean-squared error (MSE)-optimal bandwidth for the original point estimator (before bias correction) delivers the fastest coverage error decay rate after bias correction when second-order (equivalent) kernels are employed, but is otherwise suboptimal because it is too "large." Finally, for odd-degree local polynomial regression, we show that, as with point estimation, coverage error adapts to boundary points automatically when appropriate Studentization is used; however, the MSE-optimal bandwidth for the original point estimator is suboptimal. All the results are established using valid Edgeworth expansions and illustrated with simulated data. Our findings have important consequences for empirical work as they indicate that bias-corrected confidence intervals, coupled with appropriate standard errors, have smaller coverage error and are less sensitive to tuning parameter choices in practically relevant cases where additional smoothness is available. Supplementary materials for this article are available online.
Program evaluation methods are widely applied in economics to assess the effects of policy interventions and other treatments of interest. In this article, we describe the main methodological ...frameworks of the econometrics of program evaluation. In the process, we delineate some of the directions along which this literature is expanding, discuss recent developments, and highlight specific areas where new research may be particularly fruitful.
In this article, we introduce three commands to conduct robust data-driven statistical inference in regression-discontinuity (RD) designs. First, we present rdrobust, a command that implements the ...robust bias-corrected confidence intervals proposed in Calonico, Cattaneo, and Titiunik (2014d, Econometrica 82: 2295–2326) for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD, and fuzzy kink RD designs. This command also implements other conventional nonparametric RD treatment-effect point estimators and confidence intervals. Second, we describe the companion command rdbwselect, which implements several bandwidth selectors proposed in the RD literature. Following the results in Calonico, Cattaneo, and Titiunik (2014a, Working paper, University of Michigan), we also introduce rdplot, a command that implements several data-driven choices of the number of bins in evenly spaced and quantile-spaced partitions that are used to construct the RD plots usually encountered in empirical applications. A companion R package is described in Calonico, Cattaneo, and Titiunik (2014b, Working paper, University of Michigan).
This paper develops asymptotic approximations for kernel-based semiparametric estimators under assumptions accommodating slower-than-usual rates of convergence of their nonparametric ingredients. Our ...first main result is a distributional approximation for semiparametric estimators that differs from existing approximations by accounting for a bias. This bias is nonnegligible in general, and therefore poses a challenge for inference. Our second main result shows that some (but not all) nonparametric bootstrap distributional approximations provide an automatic method of correcting for the bias. Our general theory is illustrated by means of examples and its main finite sample implications are corroborated in a simulation study.
In this article, we introduce two community-contributed commands, rddensity and rdbwdensity, that implement automatic manipulation tests based on density discontinuity and are constructed using the ...results for local-polynomial density estimators in Cattaneo, Jansson, and Ma (2017b, Simple local polynomial density estimators, Working paper, University of Michigan). These new tests exhibit better size properties (and more power under additional assumptions) than other conventional approaches currently available in the literature. The first command, rddensity, implements manipulation tests based on a novel local-polynomial density estimation technique that avoids prebinning of the data (improving size properties) and allows for restrictions on other features of the model (improving power properties). The second command, rdbwdensity, implements several bandwidth selectors specifically tailored for the manipulation tests discussed herein. We also provide a companion R package with the same syntax and capabilities as rddensity and rdbwdensity.
Balance disorders and falls are frequently observed in subjects with multiple sclerosis (MS). Along with motor impairment, sensory disorders and integration deficits of sensory inputs lead to ...inadequate motor responses. The assessment of these sensory disorders in an every day tasks, such as upright stance, increases our knowledge of postural control in this pathology, thus promoting more effective treatments. The aim of the study was to describe sensory impairments and sensory strategies in different sensory conditions. A stabilometric assessment was carried out in a consecutive convenience sample of 53 subjects. The age of the sample was 52.7 (21.1) years; the onset of pathology was 27.20 (14.5) years before the assessment. Balance was assessed in six sensory conditions. The impact of pathology on balance control was shown by the high percentage of abnormal scores: 75% of subjects with MS showed abnormal scores even in the eyes open condition. The alteration of a single sensory input led to an increase of abnormal scores in up to 82% of subjects. Almost all subjects showed abnormal scores in the vestibular conditions where 22% of them fell. The pattern of the subjects’ performance in the six sensory conditions suggests that balance control may be more correlated to the number of reliable sensory inputs than the nature of the sensory input itself.
Summary
Modern empirical work in regression discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth ...yields an MSE-optimal RD treatment effect estimator, but is by construction invalid for inference. Robust bias-corrected (RBC) inference methods are valid when using the MSE-optimal bandwidth, but we show that they yield suboptimal confidence intervals in terms of coverage error. We establish valid coverage error expansions for RBC confidence interval estimators and use these results to propose new inference-optimal bandwidth choices for forming these intervals. We find that the standard MSE-optimal bandwidth for the RD point estimator is too large when the goal is to construct RBC confidence intervals with the smaller coverage error rate. We further optimize the constant terms behind the coverage error to derive new optimal choices for the auxiliary bandwidth required for RBC inference. Our expansions also establish that RBC inference yields higher-order refinements (relative to traditional undersmoothing) in the context of RD designs. Our main results cover sharp and sharp kink RD designs under conditional heteroskedasticity, and we discuss extensions to fuzzy and other RD designs, clustered sampling, and pre-intervention covariates adjustments. The theoretical findings are illustrated with a Monte Carlo experiment and an empirical application, and the main methodological results are available in R and Stata packages.
Simple Local Polynomial Density Estimators Cattaneo, Matias D.; Jansson, Michael; Ma, Xinwei
Journal of the American Statistical Association,
07/2020, Letnik:
115, Številka:
531
Journal Article
Recenzirano
This article introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not ...require prebinning or any other transformation of the data. We study the main asymptotic properties of the estimator, and use these results to provide principled estimation, inference, and bandwidth selection methods. As a substantive application of our results, we develop a novel discontinuity in density testing procedure, an important problem in regression discontinuity designs and other program evaluation settings. An illustrative empirical application is given. Two companion Stata and R software packages are provided.
In the regression-discontinuity (RD) design, units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff. In this design, local polynomial estimators ...are now routinely employed to construct confidence intervals for treatment effects. The performance of these confidence intervals in applications, however, may be seriously hampered by their sensitivity to the specific bandwidth employed. Available bandwidth selectors typically yield a "large" bandwidth, leading to data-driven confidence intervals that may be biased, with empirical coverage well below their nominal target. We propose new theory-based, more robust confidence interval estimators for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD, and fuzzy kink RD designs. Our proposed confidence intervals are constructed using a bias-corrected RD estimator together with a novel standard error estimator. For practical implementation, we discuss mean squared error optimal bandwidths, which are by construction not valid for conventional confidence intervals but are valid with our robust approach, and consistent standard error estimators based on our new variance formulas. In a special case of practical interest, our procedure amounts to running a quadratic instead of a linear local regression. More generally, our results give a formal justification to simple inference procedures based on increasing the order of the local polynomial estimator employed. We find in a simulation study that our confidence intervals exhibit close-to-correct empirical coverage and good empirical interval length on average, remarkably improving upon the alternatives available in the literature. All results are readily available in R and STATA using our companion software packages described in Calonico, Cattaneo, and Titiunik (2014d, 2014b).
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