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What are the advantages and disadvantages of different bandwidth selection methods for RDD?

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Regression discontinuity design (RDD) is a popular method for estimating causal effects of interventions or policies that are assigned based on a threshold or cutoff point. For example, you might want to evaluate the impact of a scholarship program on students' academic outcomes, where the scholarship is awarded to those who score above a certain level on a standardized test. In this case, the test score is the running variable or the assignment variable, and the scholarship is the treatment or the intervention.

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Gerard Kinneen

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1 Why bandwidth matters

One of the key challenges in RDD is to choose an appropriate bandwidth or window around the cutoff point, where you compare the outcomes of the treatment and control groups. The bandwidth determines the sample size and the degree of similarity between the groups. If the bandwidth is too large, you might include observations that are very different from the cutoff point, and thus introduce bias or confounding factors. If the bandwidth is too small, you might lose statistical power or precision, and thus increase the variance or uncertainty of your estimates.

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Gerard Kinneen

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In my experience, choosing the bandwidth in a regression discontinuity design (RDD) involves trade-offs. A smaller bandwidth provides a more precise estimate around the threshold, but it may lead to noise, while a larger bandwidth reduces noise but might smooth out the treatment effect. It's crucial to carefully consider the characteristics of the data and the research question when selecting the appropriate bandwidth method for RDD.

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2 Common bandwidth selection methods

When selecting the optimal bandwidth in RDD, there are several methods to consider. The Imbens and Kalyanaraman (IK) method minimizes the mean squared error (MSE) of the local linear regression estimator, taking into account both the bias and the variance. The Calonico, Cattaneo, and Titiunik (CCT) method also minimizes the MSE, but with a bias correction and robust standard errors. Cross-validation (CV) selects the bandwidth that minimizes the prediction error of the local linear regression model, using a hold-out sample or a k-fold partition. Alternatively, you can use the rule-of-thumb (ROT) method, which is a simple formula based on the sample size and the variance of the running variable, without any optimization.

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John Michael Riveros Gavilanes

Economist | Data Analyst | Specialist in Projects of Development | Econometrician | M. Sc. Economics
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An application can be easily done in R thanks to the packages developed by Calonico, Cattaneo, Farrell and Titiunik. The name of the package to develop these can be found in the package "rdrobust". This package allows estimating the bandwidth under several variants that are applied in the literature. For example, at the moment you use this function, you can select the argument "bwselect = mserd" to find an optimal bandwidth based on the Mean Square Error (MSE). You can do this specifically for below or after the cutoff point "bwselect = msetwo". Similarly, you can define "bwselect = cerrd" to find the optimal bandwidth under the Coverage Error Rate (CER).

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3 Advantages and disadvantages of each method

When selecting a bandwidth for analysis, each method has its own advantages and disadvantages depending on the context. The IK method is easy to implement and widely used, but it can be sensitive to outliers and extreme values and does not account for heteroskedasticity or non-normality of the errors. The CCT method is more robust and reliable, but it is computationally intensive and complex, requiring a large sample size to perform well. The CV method is flexible and adaptive, yet unstable and inconsistent, not providing any theoretical justification or confidence intervals. The ROT method is simple and intuitive, but can be arbitrary and suboptimal, not reflecting any features of the data or model.

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4 How to choose the best method for your data

When selecting a bandwidth for your data, there is no one-size-fits-all answer as it depends on various factors such as the shape and distribution of the running variable, the functional form and smoothness of the regression function, and the presence and magnitude of heterogeneity or discontinuity in the treatment effect. However, some general guidelines are to compare different methods and check the sensitivity and robustness of your results to different bandwidth choices. Additionally, use graphical and diagnostic tools to visualize and assess the fit and quality of your local linear regression model. Furthermore, consider the substantive and practical implications of your bandwidth choice, such as its relevance and credibility for causal inference.

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What are the advantages and disadvantages of different bandwidth selection methods for RDD?

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1 Why bandwidth matters

2 Common bandwidth selection methods

3 Advantages and disadvantages of each method

4 How to choose the best method for your data

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