rdrbounds {rdlocrand}

Rosenbaum bounds for RD designs under local randomization

Description

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).

Usage

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.

Value

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.

Author(s)

Matias Cattaneo, Princeton University. [e-mail]

Rocio Titiunik, Princeton University. [e-mail]

Gonzalo Vazquez-Bare, UC Santa Barbara. [e-mail]

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.

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)