Stata package for bias correction and robust variance estimation in regression discontinuity design using the wild bootstrap (He and Bartalotti 2020).
This Stata command wraps rdrobust. To use it, replace rdrobust in your command lines with
rdboottest. It will run rdrobust, show results, and append bootstrap-based estimates of the bias-corrected coefficent, p value,
and confidence interval. It will add these results to e(), along with the sample marker and other results normally missing from rdrobust
return values.
When more mature, this package will be posted on SSC. For now, install it in Stata with
net install rdboottest, replace from(https://raw.github.com/droodman/rdboottest/vX.Y.Z)
where X.Y.Z represents the latest release version number.
Install and type help rdboottest in Stata.
As in He and Bartalotti (2020), this example jackknifes residuals used in the bootstrap and constructs an equal-tailed 95% confidence interval, in which 2.5% of the distribution lies beyond either end. It defaults to Rademacher weights.
. use https://github.com/rdpackages/rdrobust/raw/master/stata/rdrobust_senate
. rdboottest vote margin, seed(71438) jk ptype(equaltail)
Sharp RD estimates using local polynomial regression.
Cutoff c = 0 | Left of c Right of c Number of obs = 1297
-------------------+---------------------- BW type = mserd
Number of obs | 595 702 Kernel = Triangular
Eff. Number of obs | 360 323 VCE method = NN
Order est. (p) | 1 1
Order bias (q) | 2 2
BW est. (h) | 17.754 17.754
BW bias (b) | 28.028 28.028
rho (h/b) | 0.633 0.633
Outcome: vote. Running variable: margin.
--------------------------------------------------------------------------------
Method | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------------+------------------------------------------------------------
Conventional | 7.4141 1.4587 5.0826 0.000 4.5551 10.2732
Robust | - - 4.3110 0.000 4.0937 10.9193
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Wild bootstrap | 7.5839 0.000 4.13822 11.2495
--------------------------------------------------------------------------------
Bias-corrected. Bootstrap method of He and Bartalotti (2020)
Emulating Tables 1 and 2 of He and Bartalotti (2020), this table shows the bias, standard deviation, root-mean-squared error,
and empirical coverage (size) of three estimators. The three are conventional (CL) and robust bias-corrected (RBC), both as produced
by rdrobust with the bwselect(cerrd) option; and the wild bootstrap, using the same bandwidths.
+-------------------------------------------------------+
| ρ DGP estimator bias SD RMSE EC |
|-------------------------------------------------------|
| -.9 1 CL 0.015 0.050 0.052 0.934 |
| -.9 1 RBC 0.011 0.054 0.055 0.943 |
| -.9 1 WBS 0.013 0.053 0.055 0.939 |
| -.9 2 CL 0.065 0.074 0.098 0.659 |
| -.9 2 RBC 0.017 0.066 0.068 0.904 |
| -.9 2 WBS 0.019 0.064 0.067 0.955 |
| -.9 3 CL 0.002 0.052 0.052 0.948 |
| -.9 3 RBC 0.002 0.057 0.057 0.947 |
| -.9 3 WBS 0.004 0.055 0.056 0.954 |
| 0 1 CL 0.017 0.051 0.053 0.920 |
| 0 1 RBC 0.014 0.054 0.056 0.931 |
| 0 1 WBS 0.014 0.054 0.055 0.939 |
| 0 2 CL 0.072 0.071 0.101 0.697 |
| 0 2 RBC 0.024 0.063 0.067 0.926 |
| 0 2 WBS 0.023 0.062 0.066 0.969 |
| 0 3 CL 0.006 0.051 0.051 0.940 |
| 0 3 RBC 0.007 0.055 0.056 0.940 |
| 0 3 WBS 0.007 0.055 0.055 0.953 |
| .9 1 CL 0.018 0.051 0.055 0.945 |
| .9 1 RBC 0.015 0.055 0.058 0.955 |
| .9 1 WBS 0.013 0.054 0.055 0.949 |
| .9 2 CL 0.067 0.066 0.094 0.804 |
| .9 2 RBC 0.021 0.063 0.066 0.952 |
| .9 2 WBS 0.018 0.061 0.063 0.949 |
| .9 3 CL 0.006 0.051 0.051 0.947 |
| .9 3 RBC 0.007 0.055 0.056 0.950 |
| .9 3 WBS 0.005 0.054 0.054 0.939 |
+-------------------------------------------------------+
Notes: ρ = correlation between first and second-stage errors. DGP is a data-generating process defined in He and Bartalotti (2020). SD = standard deviation. RMSE = root-mean-square error. EC = empirical coverage, which is ideally 0.95. All bootstrap estimates use a triangular kernel, jackknifing, equal-tailed confidence intervals, and Rademacher weights. 1000 simulations are run for each case (each row).
+------------------------------------------------------+
| G DGP estimator bias SD RMSE EC |
|------------------------------------------------------|
| 5 1 CL 0.016 0.048 0.050 0.927 |
| 5 1 RBC 0.012 0.052 0.053 0.942 |
| 5 1 WBS 0.012 0.051 0.053 0.935 |
| 5 2 CL 0.077 0.070 0.104 0.662 |
| 5 2 RBC 0.024 0.063 0.068 0.902 |
| 5 2 WBS 0.022 0.063 0.066 0.937 |
| 5 3 CL 0.009 0.051 0.052 0.938 |
| 5 3 RBC 0.010 0.059 0.060 0.940 |
| 5 3 WBS 0.011 0.069 0.070 0.932 |
| 10 1 CL 0.019 0.049 0.053 0.893 |
| 10 1 RBC 0.015 0.054 0.056 0.914 |
| 10 1 WBS 0.015 0.053 0.055 0.901 |
| 10 2 CL 0.081 0.065 0.104 0.628 |
| 10 2 RBC 0.027 0.060 0.065 0.902 |
| 10 2 WBS 0.025 0.059 0.065 0.951 |
| 10 3 CL 0.006 0.047 0.048 0.936 |
| 10 3 RBC 0.007 0.052 0.053 0.943 |
| 10 3 WBS 0.007 0.052 0.052 0.932 |
| 25 1 CL 0.020 0.047 0.051 0.913 |
| 25 1 RBC 0.015 0.052 0.054 0.934 |
| 25 1 WBS 0.015 0.051 0.054 0.918 |
| 25 2 CL 0.084 0.069 0.109 0.613 |
| 25 2 RBC 0.024 0.062 0.067 0.904 |
| 25 2 WBS 0.023 0.061 0.066 0.917 |
| 25 3 CL 0.006 0.049 0.050 0.931 |
| 25 3 RBC 0.007 0.055 0.055 0.929 |
| 25 3 WBS 0.007 0.055 0.055 0.914 |
+------------------------------------------------------+
G = number of clusters. All simulations have ρ=0. Notes to previous table apply.