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

Description

Provides comprehensive methods for testing, estimating, and conducting uniform inference on quantile treatment effects (QTEs) in sharp regression discontinuity (RD) designs, incorporating covariates and implementing robust bias correction methods of Qu, Yoon, Perron (2024) doi:10.1162/rest_a_01168.

Details

The package QTE.RD includes four main functions:

• rd.qte estimates QTEs and provides uniform confidence bands, with or without covariates, and with or without robust bias correction.

• rdq.test conducts tests for three hypotheses, related to the significance of treatment effects, homogeneous treatment effects, and uniformly positive or negative treatment effects.

• rdq.bandwidth implements two bandwidth selection rules: the cross-validation bandwidth and the MSE optimal bandwidth.

• plot.qte generates figures summarizing the treatment effects along with their confidence bands.

Author(s)

• Zhongjun Qu qu@bu.edu

• Jungmo Yoon jmyoon@hanyang.ac.kr

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

Cross-validation bandwidth

Description

cv.bandwidth implements the cross-validation bandwidth selection rule. The function rdq.bandwidth calls this function to obtain the CV bandwidth.

Usage

cv.bandwidth(y, x, z, dz, x0, val, xl, order, bdy)

Arguments

Value

A list with elements:

h.cv

the selected CV bandwidth values at the median.

cand

values of the criterion function evaluated at each of candidate value.

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

See Also

rdq.bandwidth

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)
cv.bandwidth(y=y, x=x, z=NULL, dz=0, x0=0, val=c(1,2,3,4), xl=0.5, order=2, bdy=1)
cv.bandwidth(y=y, x=x, z=NULL, dz=0, x0=0, val=c(1,2,3,4), xl=0.5, order=1, bdy=1)

Epanechnikov kernel

Description

Epanechnikov kernel

Usage

depa(xx, loc = 0, scale = 1)

Arguments

Value

values.

Examples

depa(0)
depa(seq(-1,1,by=0.05))

Uniform confidence bands for QTE

Description

make.band constructs uniform confidence bands using the output of rdq.sim. The function rdq.band calls this function to generates uniform bands.

Usage

make.band(n.sam,Dc.p,Dc.m,Dr.p,Dr.m,dz,cov,taus,hh,Qy.p,Qy.m,
     bias.p,bias.m,alpha,n.sim)

Arguments

Value

A list with elements:

qte

QTE estimates without bias correction.

qte.r

QTE estimates with bias correction.

uband

uniform confidence band for QTE without bias correction.

uband.r

uniform confidence band for QTE with robust bias correction.

sig

standard errors for the bias-uncorrected QTE estimates.

sig.r

standard errors for the bias-corrected QTE estimates. The values reflect the impact of the bias correction on the estimation precision.

See Also

rdq.band

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=delta,cov=0)
fm = rdq.condf(x=x,Q=ab$qm.est,bcoe=ab$bcoe.m,taus=tlevel,taul=tlevel2,delta=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)
ba = make.band(n,Dc.p=sa$dcp,Dc.m=sa$dcm,Dr.p=sa$drp,Dr.m=sa$drm,dz=0,cov=0,
taus=tlevel,hh,Qy.p=as.matrix(ab$qp.est[sel,]),Qy.m=as.matrix(ab$qm.est[sel,]),
bias.p=bp$bias,bias.m=bm$bias,alpha=0.1,n.sim=200)

Uniform confidence bands for conditional quantile processes

Description

make.band.cq constructs uniform confidence bands for conditional quantile processes as functions of tau for each side of the cutoff. See make.band as well. The function rdq.band calls this function to generates uniform bands for conditional quantiles.

Usage

make.band.cq(n.sam,Dc.p,Dc.m,Dr.p,Dr.m,dz,cov,taus,hh,Qy.p,Qy.m,
     bias.p,bias.m,alpha,n.sim)

Arguments

Value

A list with elements:

qp

conditional quantile estimates at x_{0}^{+} (i.e., above the cutoff) without bias correction.

qp.r

bias corrected conditional quantile estimates at x_{0}^{+}.

qm

conditional quantile estimates at x_{0}^{-} (i.e., below the cutoff) without bias correction.

qm.r

bias corrected conditional quantile estimates at x_{0}^{-}.

ubandp

uniform confidence band for conditional quantiles at x_{0}^{+} without bias correction.

ubandp.r

uniform confidence band for conditional quantiles at x_{0}^{+} with robust bias correction.

ubandm

uniform confidence band for conditional quantiles at x_{0}^{-} without bias correction.

ubandm.r

uniform confidence band for conditional quantiles at x_{0}^{-} with robust bias correction.

sp

standard errors of the conditional quantile estimates without bias correction at x_{0}^{+}.

sp.r

standard errors of the conditional quantile estimates with robust bias correction at x_{0}^{+}.

sm

standard errors of the conditional quantile estimates without bias correction at x_{0}^{-}.

sm.r

standard errors of the conditional quantile estimates with robust bias correction at x_{0}^{-}.

See Also

make.band

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)
ba.cq = make.band.cq(n,Dc.p=sa$dcp,Dc.m=sa$dcm,Dr.p=sa$drp,Dr.m=sa$drm,dz=0,cov=0,
taus=tlevel,hh,Qy.p=as.matrix(ab$qp.est[sel,]),Qy.m=as.matrix(ab$qm.est[sel,]),
bias.p=bp$bias,bias.m=bm$bias,alpha=0.1,n.sim=200)

QTE plots

Description

plot.qte generates plots summarizing the QTE estimates and their uniform confidence bands, helping users visualize the results. It also makes plots for conditional quantile processes for each side of the cutoff.

Usage

## S3 method for class 'qte'
plot(x, ptype = 1, ytext = NULL, mtext = NULL, subtext = NULL, ...)

Arguments

Value

plot(s) of the QTE estimates and uniform confidence bands.

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)
plot(A)

y.text = "test scores"
m.text = "QTE and Uniform band"
plot(A,ytext=y.text,mtext=m.text)

A2 <- summary(A,alpha=0.1)
plot(A2)

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)
A2 <- summary(A,alpha=0.1)

y.text = "test scores"
m.text = c("D=0","D=1")
plot(A2,ytext=y.text,mtext=m.text)

# conditional quantile plots
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)
A2 <- summary(A,alpha=0.1)

y.text = "test scores"
m.text = "Conditional quantile functions"
sub.text = c("D=0 group","D=1 group")
plot(A2,ptype=2,ytext=y.text,mtext=m.text,subtext=sub.text)

Print a band.qte object

Description

Print a band.qte object

Usage

## S3 method for class 'band.qte'
print(x, ...)

Arguments

Print a bw.qte object

Description

Print a bw.qte object

Usage

## S3 method for class 'bw.qte'
print(x, ...)

Arguments

Print a qte object.

Description

Print a qte object.

Usage

## S3 method for class 'qte'
print(x, ...)

Arguments

Print a summary.qte object

Description

Print a summary.qte object

Usage

## S3 method for class 'summary.qte'
print(x, ...)

Arguments

Print a test.qte object

Description

Print a test.qte object

Usage

## S3 method for class 'test.qte'
print(x, ...)

Arguments

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.

Usage

rd.qte(y, x, d, x0, z0=NULL, tau, bdw, cov, bias)

Arguments

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 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).

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)

# (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)

Estimate the QTE under the RDD

Description

rdq estimates QTE under the RDD with or without covariates. This function is used by rd.qte to generate QTE estimates.

Usage

rdq(y, x, d, x0, z0 = NULL, tau, h.tau, cov)

Arguments

Value

A list with elements:

qte

QTE estimates.

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).

bcoe.p

quantile regression coefficients on the right side of x_{0}.

bcoe.m

quantile regression coefficients on the left side of x_{0}.

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)
hh = rep(2,length(tlevel))
rdq(y=y,x=x,d=d,x0=0,z0=NULL,tau=tlevel,h.tau=hh,cov=0)

# (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)
rdq(y=y,x=cbind(x,z),d=d,x0=0,z0=c(0,1),tau=tlevel,h.tau=hh,cov=1)

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, cov, alpha)

Arguments

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; 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

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,cov=0,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,cov=1,alpha=0.1)

Bandwidth estimation

Description

rdq.bandwidth implements two bandwidth selection rules and obtains the cross-validation (CV) bandwidth and the MSE optimal bandwidth.

Usage

rdq.bandwidth(y, x, d, x0, z0=NULL, cov, cv, val,hp=NULL,pm.each=1,
     bdy=1,p.order=1,xl=0.5)

Arguments

Value

A list with elements:

cv

the selected CV bandwidth at the median.

opt.p

the MSE optimal bandwidth at the median from the right side of x_0.

opt.m

the MSE optimal bandwidth at the median from 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

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)
rdq.bandwidth(y=y,x=x,d=d,x0=0,z0=NULL,cov=0,cv=1,val=(1:4))
rdq.bandwidth(y=y,x=x,d=d,x0=0,z0=NULL,cov=0,cv=0,val=(1:4),hp=2)

# (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)
rdq.bandwidth(y=y,x=cbind(x,z),d=d,x0=0,z0=c(0,1),cov=1,cv=1,val=(1:4),bdy=1,p.order=1)

Bias estimation

Description

rdq.bias estimates the bias terms using the local quadratic quantile regression.

Usage

rdq.bias(y, x, dz, x0, z0, taus, h.tau, h.tau2, fx, cov)

Arguments

Value

A list with elements:

bias

the bias estimates.

b.hat

the estimate of the B_{v}(x,z,\tau) term. See Qu, Yoon, and Perron (2024).

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

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))

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)
hh = rep(2,length(tlevel))
fe = rdq.condf(x,Q=ab$qp.est,bcoe=ab$bcoe.p,taus=tlevel,taul=tlevel2,delta=delta,cov=0)
be = rdq.bias(y[d==1],x[d==1],dz=0,x0=0,z0=NULL,taus=tlevel,hh,hh,fx=fe$ff[(d==1),],cov=0)

Conditional density estimation

Description

rdq.condf estimates conditional density functions by using the differencing method.

Usage

rdq.condf(x, Q, bcoe, taus, taul, delta, cov)

Arguments

Value

conditional density function estimates

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)
hh = rep(2,length(tlevel))

ab = rdq(y=y,x=x,d=d,x0=0,z0=NULL,tau=tlevel,h.tau=hh,cov=0)
delta = 0.186
fe = rdq.condf(x=x,Q=ab$qp.est,bcoe=ab$bcoe.p,taus=0.5,taul=tlevel,delta=delta,cov=0)

Simulation the asymptotic distributions

Description

rdq.sim produces iid draws from the asymptotic distribution of the conditional quantile process estimate.

Usage

rdq.sim(x, d, x0, z0, dz, cov, tt, hh, hh2, fxp, fxm, n.sim)

Arguments

Value

A list with elements:

dcp

realizations from the asymptotic distribution of the conditional quantile process, from the right side of x_0.

dcm

realizations from the asymptotic distribution of the conditional quantile process, from the left side of x_0.

drp

realizations from the asymptotic distribution of the bias corrected conditional quantile process, from the right side of x_0.

drm

realizations from the asymptotic distribution of the bias corrected conditional quantile process, from the left side of x_0.

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))

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)
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)

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)

Arguments

Value

A list with elements:

statistic

test statistics.

cr.va

critical values.

p.value

p 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))

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

Value

A list with elements:

test.stat

test statistics.

cr.value

critical values.

p.val

p 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)

Uniform confidence band for QTE.

Description

summary.qte returns uniform confidence bands and standard errors for QTE estimates.

Usage

## S3 method for class 'qte'
summary(object, alpha, ...)

Arguments

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 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

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)
A2 <- summary(A,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)
A2 <- summary(A,alpha=0.1)