run.test {QTE.RD}

Run tests

Description

run.test performs hypothesis testing. The function rdq.test calls this function to run tests.

Usage

run.test(n.sam,dz,taus,hh,Dc.p,Dc.m,Dr.p,Dr.m,Qy.p,Qy.m,bias.p,bias.m,
     cov,bias,alpha,n.sim,test.type,std.opt)

Arguments

n.sam

the sample size.

dz

the number of covariates.

taus

a vector of quantiles of interest.

hh

the bandwidth values.

Dc.p

simulated values from D_{1,v}(x_{0}^{+},z,\tau).

Dc.m

simulated values from D_{1,v}(x_{0}^{-},z,\tau).

Dr.p

simulated values from D_{1,v}(x_{0}^{+},z,\tau) - D_{2,v}(x_{0}^{+},z,\tau).

Dr.m

simulated values from D_{1,v}(x_{0}^{-},z,\tau) - D_{2,v}(x_{0}^{-},z,\tau).

Qy.p

estimated conditional quantiles at (x_{0}^{+},z).

Qy.m

estimated conditional quantiles at (x_{0}^{-},z).

bias.p

estimated bias terms at (x_{0}^{+},z).

bias.m

estimated bias terms at (x_{0}^{-},z).

cov

either 0 or 1. Set cov=1 if 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.

n.sim

the number of simulation repetitions.

test.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.

Value

A list with elements:

test.stat

test statistics

cr.value

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

See Also

rdq.test()

Examples

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)
tlevel2 = c(0.05,tlevel,0.95)
hh = rep(2,length(tlevel))
hh2 = rep(2,length(tlevel2))
sel = tlevel2 %in% tlevel

ab = rdq(y=y,x=x,d=d,x0=0,z0=NULL,tau=tlevel2,h.tau=hh2,cov=0)
delta = c(0.05,0.09,0.14,0.17,0.19,0.17,0.14,0.09,0.05)
fp = rdq.condf(x=x,Q=ab$qp.est,bcoe=ab$bcoe.p,taus=tlevel,taul=tlevel2,delta,cov=0)
fm = rdq.condf(x=x,Q=ab$qm.est,bcoe=ab$bcoe.m,taus=tlevel,taul=tlevel2,delta,cov=0)
bp = rdq.bias(y[d==1],x[d==1],dz=0,x0=0,z0=NULL,taus=tlevel,hh,hh,fx=fp$ff[(d==1),],cov=0)
bm = rdq.bias(y[d==0],x[d==0],dz=0,x0=0,z0=NULL,taus=tlevel,hh,hh,fx=fm$ff[(d==0),],cov=0)

sa = rdq.sim(x=x,d=d,x0=0,z0=NULL,dz=0,cov=0,tt=tlevel,hh,hh,fxp=fp$ff,fxm=fm$ff,n.sim=200)
bt <- run.test(n,dz=0,taus=tlevel,hh,Dc.p=sa$dcp,Dc.m=sa$dcm,Dr.p=sa$drp,Dr.m=sa$drm,
Qy.p=as.matrix(ab$qp.est[sel,]),Qy.m=as.matrix(ab$qm.est[sel,]),bias.p=bp$bias,bias.m=bm$bias,
cov=0,bias=1,alpha=0.1,n.sim=200,test.type=1,std.opt=1)