rdq.test {QTE.RD}

tests for QTE

Description

rdq.test provides testing results for hypotheses on the treatment effects concerning (i) treatment significance, (ii) homogeneity of effects over quantiles, and (iii) positive or negative dominance hypothesis.

Usage

rdq.test(y,x,d,x0,z0=NULL,tau,bdw,cov,bias,alpha,type,std.opt=1,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 indicates 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.

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.

alpha

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

type

a value in 1–4. Set type to 1 to test the null hypothesis of a zero treatment effect against the alternative hypothesis of significant treatment effects; set type to 2 to test the null hypothesis of homogeneous treatment against heterogeneous treatment effects; set type to 3 to test the null hypothesis of uniformly non-negative treatment effects against the presence of negative effects; and set type to 4 to test the null hypothesis of uniformly non-positive treatment effects against the presence of positive effects at some quantiles.

std.opt

either 0 or 1. If std.opt=1, the test statistic is standardized so that the variance is equalized across quantiles; if std.opt=0, the test is not standardized.

print.qte

a logical flag specifying whether to print an outcome table.

Value

A list with elements:

te.st

test statistics

cr.va

critical values.

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)
B = rdq.test(y=y,x=x,d=d,x0=0,z0=NULL,tau=tlevel,bdw=2,cov=0,bias=1,alpha=c(0.1,0.05),type=c(1,2,3))

# (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)
B = rdq.test(y=y,x=cbind(x,z),d=d,x0=0,z0=c(0,1),tau=tlevel,bdw=2,cov=1,bias=1,
alpha=c(0.1,0.05),type=c(3,4))