Power Calculations for RD Designs
rdpower() performs power calculations for RD designs.
rdpower( data = NULL, cutoff = 0, tau = NULL, alpha = 0.05, nsamples = NULL, sampsi = NULL, samph = NULL, all = FALSE, bias = NULL, variance = NULL, plot = FALSE, graph.range = NULL, covs = NULL, covs_drop = TRUE, deriv = 0, p = 1, q = NULL, h = NULL, b = NULL, rho = NULL, kernel = "triangular", bwselect = "mserd", vce = "nn", cluster = NULL, scalepar = 1, scaleregul = 1, fuzzy = NULL, level = 95, weights = NULL, masspoints = "adjust", bwcheck = NULL, bwrestrict = TRUE, stdvars = FALSE )
data: a matrix (Y,R) containing the outcome variable and the running variable (as column vectors).cutoff: the RD cutoff (default is 0).tau: specifies the treatment effect under the alternative at which the power function is evaluated. The default is half the standard deviation of the outcome for the untreated group.alpha: specifies the significance level for the power function. Default is 0.05.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 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.bias: set bias to the left and right of the cutoff. If not specified, the biases are estimated using rdrobust.variance: set variance to the left and right of the cutoff. If not specified, the variances are estimated using rdrobust.plot: plots the power function using the conventional and robust bias corrected standard errors from rdrobust.graph.range: range of the plot.covs: option for rdrobust(): specifies additional covariates to be used for estimation and inference.covs_drop: option for rdrobust(): if TRUE, it checks for collinear additional covariates and drops them. Default is TRUE.deriv: option for rdrobust(): specifies the order of the derivative of the regression functions to be estimated.p: option for rdrobust(): specifies the order of the local-polynomial used to construct the point-estimator.q: option for rdrobust(): specifies the order of the local-polynomial used to construct the bias-correction.h: option for rdrobust(): specifies the values of the main bandwidth to be used on the left and on the right of the cutoff, respectively.b: option for rdrobust(): specifies the values of the bias bandwidth to be used on the left and on the right of the cutoff, respectively.rho: option for rdrobust(): specifies the value of rho so that the bias bandwidth b equals b=h/rho.kernel: option for rdrobust(): kernel function used to construct the local-polynomial estimators.bwselect: option for rdrobust(): specifies the bandwidth selection procedure to be used.vce: option for rdrobust(): specifies the procedure used to compute the variance-covariance matrix estimator.cluster: option for rdrobust(): indicates the cluster ID variable used for the cluster-robust variance estimation with degrees-of-freedom weights.scalepar: option for rdrobust(): specifies scaling factor for RD parameter of interest.scaleregul: option for rdrobust(): specifies scaling factor for the regularization terms of bandwidth selectors.fuzzy: option for rdrobust(): specifies the treatment status variable used to implement fuzzy RD estimation.level: option for rdrobust(): sets the confidence level for confidence intervals.weights: option for rdrobust(): is the variable used for optional weighting of the estimation procedure. The unit-specific weights multiply the kernel function.masspoints: option for rdrobust(): checks and controls for repeated observations in tue running variable.bwcheck: option for rdrobust(): if a positive integer is provided, the preliminary bandwidth used in the calculations is enlarged so that at least bwcheck unique observations are used.bwrestrict: option for rdrobust(): if TRUE, computed bandwidths are restricted to lie withing the range of x. Default is bwrestrict=TRUE.stdvars: option for rdrobust(): if TRUE, x and y are standardized before computing the bandwidths. Default is stdvars=TRUE.power.rbc: power against tau using robust bias corrected standard error
se.rbc: robust bias corrected standard error
sampsi.r: number of observations inside the window to the right of the cutoff
sampsi.l: number of observations inside the window to the left of the cutoff
samph.r: bandwidth to the right of the cutoff
samph.l: bandwidth to the left of the cutoff
alpha: significance level used in power function
tau: treatment effect under alternative hypothesis
bias.r: bias to the right of the cutoff
bias.l: bias to the left of the cutoff
Vr.rb: Robust bias corrected variance to the right of the cutoff
Vl.rb: Robust bias corrected variance to the left of the cutoff
N.r: Total sample size to the right of the cutoff
N.l: Total sample size to the left of the cutoff
power.conv: power against tau using conventional inference
se.conv: conventional standard error
# Toy dataset X <- array(rnorm(2000),dim=c(1000,2)) R <- X[,1] + X[,2] + rnorm(1000) Y <- 1 + R -.5*R^2 + .3*R^3 + (R>=0) + rnorm(1000) # Power against tau = 1 tmp <- rdpower(data=cbind(Y,R),tau=1) # Power against tau = 1 including covariates tmp <- rdpower(data=cbind(Y,R),tau=1,covs=X)
Cattaneo, M. D., R. Titiunik and G. Vazquez-Bare. (2019). Power Calculations for Regression Discontinuity Designs. Stata Journal, 19(1): 210-245.
Matias Cattaneo, Princeton University. cattaneo@princeton.edu
Rocio Titiunik, Princeton University. titiunik@princeton.edu
Gonzalo Vazquez-Bare, UC Santa Barbara. gvazquez@econ.ucsb.edu
Useful links