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rddtools

Matthieu Stigler

2022-01-10

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)
#> ### rdd_data object ###
#> 
#> Cutpoint: 0
#> Type: Sharp 
#> Sample size: 
#>  -Full : 6558 
#>  -Left : 2740 
#>  -Right: 3818
#> Covariates: no
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
#> ### RDD regression: parametric ###
#>  Polynomial order:  4 
#>  Slopes:  separate 
#>  Number of obs: 6558 (left: 2740, right: 3818)
#> 
#>  Coefficient:
#>   Estimate Std. Error t value  Pr(>|t|)    
#> D 0.076590   0.013239  5.7851 7.582e-09 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

plot(reg_para)
#> [1] "Mass points detected in the running variable."

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)
#> ### RDD regression: nonparametric local linear###
#>  Bandwidth:  0.2938561 
#>  Number of obs: 3200 (left: 1594, right: 1606)
#> 
#>  Coefficient:
#>   Estimate Std. Error z value  Pr(>|z|)    
#> D 0.079924   0.009465  8.4443 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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)

#> 
#>  McCrary Test for no discontinuity of density around cutpoint
#> 
#> data:  reg_nonpara
#> z-val = 1.2952, p-value = 0.1952
#> alternative hypothesis: Density is discontinuous around cutpoint
#> sample estimates:
#> Discontinuity 
#>     0.1035008

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)

Tests correctly reject equality of the second, and correctly do not reject equality for the first and third.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.