run.test: 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)

Value

A list with elements:

test.stat: test statistics.
cr.value: critical values.
p.val: p values.

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.

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

Examples

Run this code

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 <- QTE.RD:::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 <- QTE.RD:::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)