rdq.band: Uniform confidence bands for QTE

In QTE.RD: Quantile Treatment Effects under the Regression Discontinuity Design

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, alpha = 0.1)

Arguments

y	a numeric vector, the outcome variable.
x	a vector (or a matrix) of covariates, When no covariates are included, x is simply a vector of the running variable and z0 can be left unspecified. When covariates are included, x should be a matrix with the running variable in the first column and the covariates in the remaining columns.
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.
alpha	a numeric value between 0 and 1 specifying the significance level. For example, setting alpha = 0.1 yields a 90% uniform confidence band. Multiple significance levels can be specified, e.g., alpha = c(0.1, 0.05).

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; \Sexpr[results=rd]{tools:::Rd_expr_doi("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; \Sexpr[results=rd]{tools:::Rd_expr_doi("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; \Sexpr[results=rd]{tools:::Rd_expr_doi("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,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,alpha=0.1)

QTE.RD documentation built on Aug. 30, 2025, 9:06 a.m.