rd.qte {QTE.RD}

QTE and its uniform confidence band.

Description

rd.qte is the main function of the QTE.RD package. If cov=1, it estimates QTE for each subgroup defined by covariates. If cov=0, it estimate QTE without covariates. If bias=1, it corrects the bias in QTE estimates and obtains the robust confidence band and if bias=0, no bias correction is implemented. If cband=1, it provides a (1-alpha)100% uniform confidence bands, and if cband=0, it presents point estimates without confidence band.

Usage

rd.qte(y, x, d, x0, z0=NULL, tau, bdw, cov, bias, cband, alpha=NULL, 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 z 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. See the function rdq.bandwidth for how to select this bandwidth. The bandwidths for the rest of the quantiles are computed automatically using the formula of 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.

bias

either 0 or 1. If bias=1, the QTE estimate is bias corrected and the robust confidence band in Qu, Yoon, and Perron (2024) is produced. If bias=0, no bias correction is implemented.

cband

either 0 or 1. If cband=1, a uniform band is obtained; if cband=0, a point estimate is reported without confidence band.

alpha

a number between 0 and 1, the desired significance level. For example, when alpha=0.1, one will get a 90% uniform band.

print.qte

a logical flag specifying whether to print an outcome table.

Value

A list with elements:

qte

QTE estimates.

uband

uniform confidence band for QTE. If bias=1, the band is robust capturing the effect of the bias correction. If If bias=0, no bias correction is implemented.

sigma

standard errors for each quantile level. If bias=1, its value captures the effect of the bias correction. If bias=0, no bias correction is implemented.

qp.est

conditional quantile estimates on the right side of x_{0} (or for the D=1 group).

qm.est

conditional quantile estimates on the left side of x_{0} (or for the D=0 group).

uband.p

uniform confidence band for conditional quantiles on the right side of x_{0}.

uband.m

uniform confidence band for conditional quantiles on 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

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

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)
A = rd.qte(y=y,x=x,d=d,x0=0,z0=NULL,tau=tlevel,bdw=2,cov=0,bias=1,cband=1,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)
A = rd.qte(y=y,x=cbind(x,z),d=d,x0=0,z0=c(0,1),tau=tlevel,bdw=2,cov=1,bias=1,cband=1,alpha=0.1)