In bquast/RDDtools: Toolbox for Regression Discontinuity Design ('RDD')

knitr::opts_chunk$set(collapse = T, comment = "#>")

RDDtools works in an object-oriented way: the user has to define once the characteristic of the data, creating a rdd_data object, on which different anaylsis tools can be applied.

Data Preparation and Visualisation

Load the package, and load the built-in dataset from [Lee 2008]:

library(rddtools)
data(house)

Declare the data to be a rdd_data object:

house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0)

You can now directly summarise and visualise this data:

summary(house_rdd)
plot(house_rdd)

Parametric Estimation

Estimate parametrically, by fitting a 4th order polynomial.

reg_para <- rdd_reg_lm(rdd_object=house_rdd, order=4)
reg_para

plot(reg_para)

Non-parametric Estimation

Run a simple local regression, using the [Imbens and Kalyanaraman 2012] bandwidth.

bw_ik <- rdd_bw_ik(house_rdd)
reg_nonpara <- rdd_reg_np(rdd_object=house_rdd, bw=bw_ik)
print(reg_nonpara)

Regression Sensitivity tests:

One can easily check the sensitivity of the estimate to different bandwidths:

plotSensi(reg_nonpara, from=0.05, to=1, by=0.1)

Or run the Placebo test, estimating the RDD effect based on fake cutpoints:

plotPlacebo(reg_nonpara)

Design Sensitivity tests:

Design sensitivity tests check whether the discontinuity found can actually be attributed ot other causes. Two types of tests are available:

Discontinuity comes from manipulation: test whether there is possible manipulation around the cutoff, McCrary 2008 test: dens_test()
Discontinuity comes from other variables: should test whether discontinuity arises with covariates. Currently, only simple tests of equality of covariates around the threshold are available:

Discontinuity comes from manipulation: McCrary test

use simply the function dens_test(), on either the raw data, or the regression output:

dens_test(reg_nonpara)

Discontinuity comes from covariates: covariates balance tests

Two tests available: + equal means of covariates: covarTest_mean() + equal density of covariates: covarTest_dens()

We need here to simulate some data, given that the Lee (2008) dataset contains no covariates. We here simulate three variables, with the second having a different mean on the left and the right.

set.seed(123)
n_Lee <- nrow(house)
Z <- data.frame(z1 = rnorm(n_Lee, sd=2), 
                z2 = rnorm(n_Lee, mean = ifelse(house<0, 5, 8)), 
                z3 = sample(letters, size = n_Lee, replace = TRUE))
house_rdd_Z <- rdd_data(y = house$y, x = house$x, covar = Z, cutpoint = 0)