rdq.band {QTE.RD}

Uniform confidence bands for QTE

Description

rdq.band produces uniform confidence bands for QTEs with and without bias correction. This function is used by rd.qte to generate uniform bands.

Usage

rdq.band(y, x, d, x0, z0 = NULL, tau, bdw, cov, alpha, 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. For example, if a female dummy is included, z0 = 1 may indicate the female subgroup.

tau

a vector of quantiles of interest.

bdw

the bandwidth value(s). If 'bdw' is a scalar, it is interpreted as the bandwidth for the median. The bandwidths for the rest of the quantiles are computed automatically using the formula in Yu and Jones (1998). If it is a vector with the same dimension as 'tau', the function will use these values for the respective quantiles accordingly.

cov

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

alpha

a number between 0 and 1, the desired significance level.

print.qte

a logical flag specifying whether to print an outcome table.

Value

qte

QTE estimates without bias correction.

qte.cor

bias corrected QTE estimates.

uband

uniform confidence band for QTE without bias correction.

uband.robust

uniform confidence band for QTE with robust bias correction.

sig

standard errors for each quantile level for estimates without bias correction.

sig.r

standard errors for each quantile level for estimates with robust bias correction.

uband.p

uniform confidence band for the conditional quantile estimates on the right side of the cutoff, without bias correction.

uband.robust.p

uniform confidence band for the conditional quantile estimates on the right side of the cutoff, robust to the bias correction.

uband.m

uniform confidence band for the conditional quantile estimates on the left side of the cutoff, without bias correction.

uband.robust.m

uniform confidence band for the conditional quantile estimates on the left side of the cutoff, robust to the bias correction.

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

Keming Yu and M. C. Jones (1998), “Local Linear Quantile Regression,” Journal of the American Statistical Association, 93(441), 228–237; https://doi.org/10.2307/2669619

See Also

rd.qte()

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)
D = rdq.band(y=y,x=x,d=d,x0=0,z0=NULL,tau=tlevel,bdw=2,cov=0,alpha=0.1)

# (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)
D = rdq.band(y=y,x=cbind(x,z),d=d,x0=0,z0=c(0,1),tau=tlevel,bdw=2,cov=1,alpha=0.1)