rdsensitivity function

Sensitivity analysis for RD designs under local randomization

rdsensitivity analyze the sensitivity of randomization p-values and confidence intervals to different window lengths.

rdsensitivity(
  Y,
  R,
  cutoff = 0,
  wlist,
  wlist_left,
  tlist,
  statistic = "diffmeans",
  p = 0,
  evalat = "cutoff",
  kernel = "uniform",
  fuzzy = NULL,
  ci = NULL,
  ci_alpha = 0.05,
  reps = 1000,
  seed = 666,
  nodraw = FALSE,
  quietly = FALSE
)

Arguments

• Y: a vector containing the values of the outcome variable.
• R: a vector containing the values of the running variable.
• cutoff: the RD cutoff (default is 0).
• wlist: the list of windows to the right of the cutoff. By default the program constructs 10 windows around the cutoffwith 5 observations each.
• wlist_left: the list of windows to the left of the cutoff. If not specified, the windows are constructed symmetrically around the cutoff based on the values in wlist.
• tlist: the list of values of the treatment effect under the null to be evaluated. By default the program employs ten evenly spaced points within the asymptotic confidence interval for a constant treatment effect in the smallest window to be used.
• statistic: the statistic to be used in the balance tests. Allowed options are diffmeans (difference in means statistic), ksmirnov (Kolmogorov-Smirnov statistic) and ranksum (Wilcoxon-Mann-Whitney standardized statistic). Default option is diffmeans. The statistic ttest is equivalent to diffmeans and included for backward compatibility.
• p: the order of the polynomial for outcome adjustment model. Default is 0.
• evalat: specifies the point at which the adjusted variable is evaluated. Allowed options are cutoff and means. Default is cutoff.
• kernel: specifies the type of kernel to use as weighting scheme. Allowed kernel types are uniform (uniform kernel), triangular (triangular kernel) and epan (Epanechnikov kernel). Default is uniform.
• fuzzy: indicates that the RD design is fuzzy. fuzzy can be specified as a vector containing the values of the endogenous treatment variable, or as a list where the first element is the vector of endogenous treatment values and the second element is a string containing the name of the statistic to be used. Allowed statistics are ar (Anderson-Rubin statistic) and tsls (2SLS statistic). Default statistic is ar. The tsls statistic relies on large-sample approximation.
• ci: returns the confidence interval corresponding to the indicated window length. ci has to be a two-dimensional vector indicating the left and right limits of the window. Default alpha is .05 (95% level CI).
• ci_alpha: Specifies value of alpha for the confidence interval. Default alpha is .05 (95% level CI).
• reps: number of replications. Default is 1000.
• seed: the seed to be used for the randomization tests.
• nodraw: suppresses contour plot.
• quietly: suppresses the output table.

Returns

• tlist: treatment effects grid

• wlist: window grid

• results: table with corresponding p-values for each window and treatment effect pair.

• ci: confidence interval (if ci is specified).

Examples

# Toy dataset
R <- runif(100,-1,1)
Y <- 1 + R -.5*R^2 + .3*R^3 + (R>=0) + rnorm(100)
# Sensitivity analysis
# Note: low number of replications to speed up process.
# The user should increase the number of replications.
tmp <- rdsensitivity(Y,R,wlist=seq(.75,2,by=.25),tlist=seq(0,5,by=1),reps=500)

References

Cattaneo, M.D., R. Titiunik and G. Vazquez-Bare. (2016). Inference in Regression Discontinuity Designs under Local Randomization. Stata Journal 16(2): 331-367.

Author(s)

Matias Cattaneo, Princeton University. cattaneo@princeton.edu

Rocio Titiunik, Princeton University. titiunik@princeton.edu

Gonzalo Vazquez-Bare, UC Santa Barbara. gvazquez@econ.ucsb.edu