rdrbounds function

Rosenbaum bounds for RD designs under local randomization

rdrbounds calculates lower and upper bounds for the randomization p-value under different degrees of departure from a local randomized experiment, as suggested by Rosenbaum (2002).

rdrbounds(
  Y,
  R,
  cutoff = 0,
  wlist,
  gamma,
  expgamma,
  bound = "both",
  statistic = "ranksum",
  p = 0,
  evalat = "cutoff",
  kernel = "uniform",
  fuzzy = NULL,
  nulltau = 0,
  prob,
  fmpval = FALSE,
  reps = 1000,
  seed = 666
)

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 window lengths to be evaluated. By default the program constructs 10 windows around the cutoff, the first one including 10 treated and control observations and adding 5 observations to each group in subsequent windows.
• gamma: the list of values of gamma to be evaluated.
• expgamma: the list of values of exp(gamma) to be evaluated. Default is c(1.5,2,2.5,3).
• bound: specifies which bounds the command calculates. Options are upper for upper bound, lower for lower bound and both for both upper and lower bounds. Default is both.
• 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.
• nulltau: the value of the treatment effect under the null hypothesis. Default is 0.
• prob: the probabilities of treatment for each unit when assignment mechanism is a Bernoulli trial. This option should be specified as a vector of length equal to the length of the outcome and running variables.
• fmpval: reports the p-value under fixed margins randomization, in addition to the p-value under Bernoulli trials.
• reps: number of replications. Default is 1000.
• seed: the seed to be used for the randomization tests.

Returns

• gamma: list of gamma values.

• expgamma: list of exp(gamma) values.

• wlist: window grid.

• p.values: p-values for each window (under gamma = 0).

• lower.bound: list of lower bound p-values for each window and gamma pair.

• upper.bound: list of upper bound p-values for each window and gamma pair.

Examples

# Toy dataset
R <- runif(100,-1,1)
Y <- 1 + R -.5*R^2 + .3*R^3 + (R>=0) + rnorm(100)
# Rosenbaum bounds
# Note: low number of replications and windows to speed up process.
# The user should increase these values.
rdrbounds(Y,R,expgamma=c(1.5,2),wlist=c(.3),reps=100)

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.

Rosenbaum, P. (2002). Observational Studies. Springer.

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