Bias estimation

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

y

a numeric vector, the outcome variable.

x

a vector (or a matrix) of covariates, the first column is the running variable.

dz

the number of covariates.

x0

the cutoff point.

z0

the value of the covariates at which to evaluate the effects.

taus

a vector of quantiles of interest.

h.tau

the bandwidth values (specified for each quantile level), for estimating conditional quantiles.

h.tau2

the bandwidth values for the local quadratic quantile regression, for estimating the bias terms.

fx

conditional density estimates.

cov

either 0 or 1. Set cov=1 if covariates are present in the model; otherwise set cov=0.

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; doi: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)