rdq.bandwidth {QTE.RD}

Bandwidth estimation

Description

rdq.bandwidth implements two bandwidth selection rules and obtains the cross-validation (CV) bandwidth and the MSE optimal bandwidth.

Usage

rdq.bandwidth(y, x, d, x0, z0=NULL, cov, cv, val,hp=NULL,pm.each=1,
     bdy=1,p.order=1,xl=0.5,print.qte=1)

Arguments

y

a numeric vector, the outcome variable.

x

a vector (or a matrix) of covariates, the first column is the running variable.

d

a numeric vector, the treatment status.

x0

the cutoff point.

z0

the value of the covariates at which to evaluate the effects.

cov

either 0 or 1. Set cov=1 when covariates are present in the model; otherwise set cov=0.

cv

either 0 or 1. When cv=1, both the CV and MSE optimal bandwidths are produced. When cv=0, the MSE optimal bandwidth is produced.

val

a set of candidate values for the CV bandwidth.

hp

a pilot bandwidth to estimate nuisance parameters for the MSE optimal bandwidth. It will be used only if cv=0. If cv=1, the CV bandwidth will be used as the pilot bandwidth to compute the MSE optimal bandwidth.

pm.each

either 0 or 1. When pm.each=1, the CV bandwidths for each side of the cutoff will be obtained separately.

bdy

either 0 or 1. When bdy=1, the CV bandwidth uses the boundary point procdure.

p.order

either 1 or 2. When p.order=1, a local linear regression is used, and when p.order=2, a local quadratic regression is used.

xl

if xl=0.5, the CV bandwidth use the 50% of observations closest to x_0.

print.qte

a logical flag specifying whether to print an outcome table.

Value

A list with elements:

cv

the selected CV bandwidth at the median.

opt.p

the MSE optimal bandwidth at the median from the right side of x_0.

opt.m

the MSE optimal bandwidth at the median from the left side of x_0.

References

Zhongjun Qu, Jungmo Yoon, Pierre Perron (2024), "Inference on Conditional Quantile Processes in Partially Linear Models with Applications to the Impact of Unemployment Benefits," The Review of Economics and Statistics; https://doi.org/10.1162/rest_a_01168

Zhongjun Qu and Jungmo Yoon (2019), "Uniform Inference on Quantile Effects under Sharp Regression Discontinuity Designs," Journal of Business and Economic Statistics, 37(4), 625–647; https://doi.org/10.1080/07350015.2017.1407323

Examples

# Without covariate
n = 500
x = runif(n,min=-4,max=4)
d = (x > 0)
y = x + 0.3*(x^2) - 0.1*(x^3) + 1.5*d + rnorm(n)
tlevel = seq(0.1,0.9,by=0.1)
rdq.bandwidth(y=y,x=x,d=d,x0=0,z0=NULL,cov=0,cv=1,val=(1:4))
rdq.bandwidth(y=y,x=x,d=d,x0=0,z0=NULL,cov=0,cv=0,val=(1:4),hp=2)

# (continued) With covariates
z = sample(c(0,1),n,replace=TRUE)
y = x + 0.3*(x^2) - 0.1*(x^3) + 1.5*d + d*z + rnorm(n)
rdq.bandwidth(y=y,x=cbind(x,z),d=d,x0=0,z0=c(0,1),cov=1,cv=1,val=(1:4),bdy=1,p.order=1)