rdcqr

Regression discontinuity (RD) design is a popular quasi-experiment method to identify the local average treatment effect. rdcqr applies the local composite quantile regression method to estimate the treatment effect in both sharp and fuzzy RD designs. The package can be used to perform the following analysis.

• Estimation of local treatment effect for both sharp and fuzzy RD designs, with and without bias correction. Results based on asympotitic and fixed-n approximations are both available.

• Hypothesis testing on the treatment effect. Adjusted standard errors are computed to incorporate the additional variability due to bias-correction.

• A modified t test that eliminates the asymptotic size distortion due to weak identification in a fuzzy RD.

In addition, the package also offers functions to perform sharp RD analysis with covariates and to estimate the treatment effect in a sharp kink RD.

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("xhuang20/rdcqr")

Examples

Use the data on elections to the U.S. House of Representatives in Lee (2008) as an example.

library(rdcqr)
data(lee)
x = lee$margin
y = lee$voteshare

# Example 1 
# Use residuals from a local linear regression to compute the standard errors.
rdcqr(y, x, llr.residuals = TRUE)

# Example 2
# Use residuals from a local composite regression to compute the standard errors.
rdcqr(y, x, llr.residuals = FALSE)

# Example 3
# Use additional covariates in a sharp RD.
n   = length(x)
p   = 1                              # Select a polynomial order.
q   = 7                              # Select the number of quantile positions.
tau = (1:q) / (q + 1)                # quantile positions
h   = 0.3                            # Try a bandwidth.
treat = as.numeric(x >= 0)           # Create the treatment dummy variable.
z   = matrix(rnorm(2*n), nrow = n)   # Simulate an ad hoc covariate matrix.
xcv = cbind(treat, treat*x, z)       # Make sure the "treat" variable is the first column.
est = cqrMMxcv(x0     = 0,           # The cutoff.
               x_vec  = x,        
               y      = y,  
               xcv    = xcv,  
               kernID = 0,           # Use the triangular kernel.
               tau    = tau,
               h      = h,
               p      = p)
tau_hat = est$beta1[p+1]             # This gives the sharp RD estimate.

# Example 4
# Estimate sharp kink RD treatment effect.
p = 2      # Use a quadratic polynomial to estimate the first derivative.
est_n = cqrMMcpp(x0     = 0,
                 x_vec  = x[x < 0],
                 y      = y[x < 0],
                 kernID = 0,
                 tau    = tau,
                 h      = h,
                 p      = p)
est_p = cqrMMcpp(x0     = 0,
                 x_vec  = x[x >= 0],
                 y      = y[x >= 0],
                 kernID = 0,
                 tau    = tau,
                 h      = h,
                 p      = p)
kink_hat = est_p$beta1[1] - est_n$beta1[1] # This gives the sharp kink RD estimate.