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Statistics/Data analysis

Title

rdmde Minimum Detectable Effect calculation for Regression Discontinuity

designs using robust bias−corrected local polynomial inference.

Syntax

rdmde depvar runvar [if] [in] [, c(#) alpha(#) beta(#) nsamples(# # # #) sampsi(#
#) samph(# #) all bias(# #) variance(# #) init_cond(#) covs(covars)
covs_drop(covsdropoption) deriv(#) p(#) q(#) h(# #) b(# #) rho(#)
fuzzy(fuzzyvar [sharpbw]) kernel(kernelfn) bwselect(bwmethod) vce(vcetype
[vceopt1 vceopt2]) weights(weightsvar) scalepar(#) scaleregul(#)
masspoints(masspointsoption) bwcheck(#) bwrestrict(bwropt) stdvars(stdopt) ]

Description

rdmde provides MDE calculations in Regression Discontinuity designs using

conventional and robust bias−corrected local polynomial methods. Companion
commands are: rdpow for power calculations and rdsampsi for sample size
calculations.

A detailed introduction to this command is given in Cattaneo, Titiunik and

Vazquez−Bare (2019).

Companion R functions are also available here.

This command employs the Stata (and R) package rdrobust for underlying
calculations. See Calonico, Cattaneo and Titiunik (2014) and Calonico,
Cattaneo, Farrell and Titiunik (2017) for more details.

Related Stata and R packages useful for inference in RD designs are described in
the following website:

https://rdpackages.github.io/

Options

rdmde options

c(#) specifies the RD cutoff for indepvar. Default is c(0).

alpha(#) specifies the significance level for the power function. Default is
alpha(.05).

beta(#) specifies the desired power. Default is beta(.8).

nsamples(# # # #) sets the total sample size to the left, sample size to the left
inside the bandwidth, total sample size to the right and sample size to the
right of the cutoff inside the bandwidth to calculate the variance when the
running variable is not specified. When this option is not specified, the
values are calculated using the running variable.

sampsi(# #) sets the sample size at each side of the cutoff for power calculation.
The first number is the sample size to the left of the cutoff and the second
number is the sample size to the right. Default values are the sample sizes
inside the chosen bandwidth.

samph(# #) sets the bandwidths at each side of the cutoff for power calculation.
The first number is the bandwidth to the left of the cutoff and the second
number is the bandwidth to the right. Default values are the bandwidths used
by rdrobust.

all displays the power using the conventional variance estimator, in addition to
the robust bias corrected one.
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bias(# #) allows the user to set bias to the left and right of the cutoff. If not
specified, the biases are estimated using rdrobust.

variance(# #) allows the user to set variance to the left and right of the cutoff.
If not specified, the variances are estimated using rdrobust.

init_cond(#) sets the initial condition for the Newton−Raphson algorithm that
finds the MDE. Default is 0.2 times the standard deviation of the outcome
below the cutoff.

rdrobust options

The following options are passed directly to rdrobust:

covs(covars) specifies additional covariates to be used for estimation and

inference.

covs_drop(covsdropoption) specifies options to assess collinearity in covariates

to be used for estimation and inference. Option on drops collinear additional
covariates (default choice). Option off only checks collinear additional
covariates but does not drop them.

deriv(#) specifies the order of the derivative of the regression functions to be

estimated. Default is deriv(0). Setting deriv(1) results in estimation of a
Kink RD design (up to scale).

p(#) specifies the order of the local polynomial used to construct the point
estimator. Default is p(1) (local linear regression).

q(#) specifies the order of the local polynomial used to construct the bias
correction. Default is q(2) (local quadratic regression).

h(# #) specifies the main bandwidth (h) used to construct the RD point estimator.
If not specified, bandwidth h is computed by the companion command rdbwselect.
If two bandwidths are specified, the first bandwidth is used for the data
below the cutoff and the second bandwidth is used for the data above the
cutoff.

b(# #) specifies the bias bandwidth (b) used to construct the bias−correction
estimator. If not specified, bandwidth b is computed by the companion command
rdbwselect. If two bandwidths are specified, the first bandwidth is used for
the data below the cutoff and the second bandwidth is used for the data above
the cutoff.

rho(#) specifies the value of rho, so that the bias bandwidth b equals b=h/rho.
Default is rho(1) if h is specified but b is not.

fuzzy(fuzzyvar [sharpbw]) specifies the treatment status variable used to

implement fuzzy RD estimation (or Fuzzy Kink RD if deriv(1) is also
specified). Default is Sharp RD design and hence this option is not used. If
the option sharpbw is set, the fuzzy RD estimation is performed using a
bandwidth selection procedure for the sharp RD model. This option is
automatically selected if there is perfect compliance at either side of the
threshold.

kernel(kernelfn) specifies the kernel function used to construct the

local−polynomial estimator(s). Options are: triangular, epanechnikov, and
uniform. Default is kernel(triangular).
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bwselect(bwmethod) specifies the bandwidth selection procedure to be used. By

default it computes both h and b, unless rho is specified, in which case it
only computes h and sets b=h/rho. Options are:
mserd one common MSE−optimal bandwidth selector for the RD treatment effect
estimator.
msetwo two different MSE−optimal bandwidth selectors (below and above the
cutoff) for the RD treatment effect estimator.
msesum one common MSE−optimal bandwidth selector for the sum of regression
estimates (as opposed to difference thereof).
msecomb1 for min(mserd,msesum).
msecomb2 for median(msetwo,mserd,msesum), for each side of the cutoff
separately.
cerrd one common CER−optimal bandwidth selector for the RD treatment effect
estimator.
certwo two different CER−optimal bandwidth selectors (below and above the
cutoff) for the RD treatment effect estimator.
cersum one common CER−optimal bandwidth selector for the sum of regression
estimates (as opposed to difference thereof).
cercomb1 for min(cerrd,cersum).
cercomb2 for median(certwo,cerrd,cersum), for each side of the cutoff
separately.
Note: MSE = Mean Square Error; CER = Coverage Error Rate.
Default is bwselect(mserd). For details on implementation, see rdbwselect and
references therein.

vce(vcetype [vceopt1 vceopt2]) specifies the procedure used to compute the

variance−covariance matrix estimator. Options are:
vce(nn [nnmatch]) for heteroskedasticity−robust nearest neighbor variance
estimator with nnmatch indicating the minimum number of neighbors to be
used.
vce(hc0) for heteroskedasticity−robust plug−in residuals variance estimator
without weights.
vce(hc1) for heteroskedasticity−robust plug−in residuals variance estimator
with hc1 weights.
vce(hc2) for heteroskedasticity−robust plug−in residuals variance estimator
with hc2 weights.
vce(hc3) for heteroskedasticity−robust plug−in residuals variance estimator
with hc3 weights.
vce(nncluster clustervar [nnmatch]) for cluster−robust nearest neighbor
variance estimation using with clustervar indicating the cluster ID
variable and nnmatch matches indicating the minimum number of neighbors to
be used.
vce(cluster clustervar) for cluster−robust plug−in residuals variance
estimation with degrees−of−freedom weights and clustervar indicating the
cluster ID variable.
Default is vce(nn 3).

weights(weightsvar) is the variable used for optional weighting of the estimation

procedure. The unit−specific weights multiply the kernel function.

scalepar(#) specifies scaling factor for RD parameter of interest. This option is

useful when the estimator of interest requires a known multiplicative factor
rescaling (e.g., Sharp Kink RD). Default is scalepar(1) (no rescaling).

scaleregul(#) specifies scaling factor for the regularization term added to the
denominator of the bandwidth selectors. Setting scaleregul(0) removes the
regularization term from the bandwidth selectors. Default is scaleregul(1).

masspoints(masspointsoption) checks and controls for repeated observations in the

running variable. Options are:
off ignores the presence of mass points.
check looks for and reports the number of unique observations at each side of
the cutoff.
adjust controls that the preliminary bandwidths used in the calculations
contain a minimal number of unique observations. By default it uses 10
observations, but it can be manually adjusted with the option bwcheck.
Default option is masspoints(adjust).

bwcheck(bwcheck) if a positive integer is provided, the preliminary bandwidth used

in the calculations is enlarged so that at least bwcheck unique observations
are used.
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bwrestrict(bwropt) if set on, computed bandwidths are restricted to lie within the
range of runvar. Default is on.

stdvars(stdopt) if set on, depvar and runvar are standardized before computing the
bandwidths. Default is off.

Example: Cattaneo, Frandsen and Titiunik (2015) Incumbency Data

Setup
. use rdpower_senate.dta

MDE calculation with default values

. rdmde demvoteshfor2 demmv

MDE calculation with user−specified bandwidths

. rdmde demvoteshfor2 demmv, samph(12 13)

MDE calculation with user−specified sample sizes

. rdmde demvoteshfor2 demmv, sampsi(350 320)

Power function plot with default options

. rdpow demvoteshfor2 demmv, tau(5) plot

Power function plot with user−specified range and step

. rdpow demvoteshfor2 demmv, tau(5) plot graph_range(−9 9) graph_step(2)

Power function plot with user−specified options

. rdpow demvoteshfor2 demmv, tau(5) plot graph_range(−9 9) graph_step(2)
graph_options(title(Power function) xline(0, lcolor(black) lpattern(dash))
xtitle(tau) ytitle(power) graphregion(fcolor(white)))

Saved results

rdpow saves the following in r():

Scalars
r(alpha) significance level used in power function
r(beta) desired power
r(mde) calculated MDE
r(N_h_l) sample size in bandwidth to the left used to calculate
variance
r(N_h_r) sample size in bandwidth to the right used to calculate
variance
r(N_l) sample size to the left used to calculate variance
r(N_r) sample size to the right used to calculate variance
r(samph_l) bandwidth to the left of the cutoff
r(samph_r) bandwidth to the right of the cutoff
r(sampsi_l) number of observations inside the window to the left of
the cutoff
r(sampsi_r) number of observations inside the window to the right of
the cutoff
r(se_rbc) robust bias corrected standard error
r(power_rbc) power against tau using robust bias corrected standard
error
r(se_conv) conventional standard error
r(power_conv) power against tau using conventional standard error
r(Vl_rb) robust variance to the left of the cutoff
r(Vr_rb) robust variance to the left of the cutoff
r(bias_l) bias to the left of the cutoff
r(bias_r) bias to the left of the cutoff
r(init_cond) initial condition of the Newton−Raphson algorithm

References

Calonico, S., M. D. Cattaneo, M. H. Farrell, and R. Titiunik. 2017. rdrobust:

Software for Regression Discontinuity Designs.
Stata Journal 17(2): 372−404.
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Calonico, S., M. D. Cattaneo, and R. Titiunik. 2014. Robust Data−Driven Inference

in the Regression−Discontinuity Design.
Stata Journal 14(4): 909−946.

Cattaneo, M. D., Frandsen, B., and R. Titiunik. 2015. Randomization Inference in

the Regression Discontinuity Design: An Application to Party Advantages in the
U.S. Senate.
Journal of Causal Inference 3(1): 1−24.

Cattaneo, M. D., R. Titiunik, and G. Vazquez−Bare. 2019. Power Calculations for

Regression Discontinuity Designs.
Stata Journal 19(1): 210−245.

Authors

Matias D. Cattaneo, Princeton University, Princeton, NJ. cattaneo@princeton.edu.

Rocio Titiunik, Princeton University, Princeton, NJ. titiunik@princeton.edu.

Gonzalo Vazquez−Bare, UC Santa Barbara, Santa Barbara, CA.

gvazquez@econ.ucsb.edu.