1.     “A Quantile Regression Approach for Estimating Panel Data Models Using Instrumental Variables" with C. Lamarche, Economics Letters 104(3), 2009. R code

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# Quantile Regression IV Panel Data Functions

# Harding and Lamarche, Economics Letters 104 (2009), 133-135 

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# Functions

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rq.fit.fe <- function(X,y,w=1,taus=tau){

require(SparseM)

require(quantreg)

K <- length(w)

if(K != length(taus))

stop("length of w and taus must match")

X <- as.matrix(X)

p <- ncol(X)

n <- length(levels(as.factor(s)))

N <- length(y)

if( N != nrow(X))

 stop("dimensions of y,X must match")

D <- cbind(as(w,"matrix.diag.csr") %x% X)

y <- c(w %x% y)

a <- c((w*(1-taus)) %x% (t(X)%*%rep(1,N)))

rq.fit.sfn(D,y,rhs=a)}

#############################################

rq.fit.ivpanel <- function(d,exo,iv,y,s,tau){

# IV Quantile Regression with Fixed Effects

# s is an strata indicator

# d is the endogenous variable

# exo are the exogenous variables, no intercept.

# iv is the intrument

Z <- model.matrix(s~as.factor(s)-1)[,-1]

exo <- cbind(exo,Z)

X <- cbind(exo,1)

x <- cbind(d,X)

w <- cbind(iv,X)

ww <- t(w) %*% w

ww.inv <- ginv(as.matrix(ww))

wd <- t(w)%*%d

dhat <- w%*%ww.inv%*%wd

PSI <- cbind(dhat,X)

PSI1 <- cbind(d,X)

coef <- rq.fit.fe(PSI,y,tau=tau)$coef

resid <- y - PSI1%*%coef

mu1 <- mean(resid)

sigma1 <- var(resid)

c <- ((1-tau)*tau)/(dnorm(qnorm(tau,mu1,sqrt(sigma1)),mu1,sqrt(sigma1))^2)

PSIinv <- diag(length(coef))

PSIinv <- backsolve(qr(x)$qr[1:length(coef), 1:length(coef)], PSIinv)

PSIinv <- PSIinv %*% t(PSIinv)

vc1 <- c*PSIinv

std <- sqrt((length(y)/100)*diag(vc1))

alpha <- seq(coef[1]-2*std[1],coef[1]+2*std[1],by=std[1]/20)

z <- cbind(dhat,X)

betas <- matrix(NA,dim(z)[2],length(alpha))

g <- matrix(NA,length(alpha),1)

for (i in 1:length(alpha)){

ya <- y - alpha[i]*d

betas[,i] <- rq.fit.fe(z,ya,tau=tau)$coef

g[i,] <- max(svd(betas[1:dim(dhat)[2],i])$d)}

I <- which.min(g[,1])

param1 <- alpha[I]

est1 <- betas[(dim(dhat)[2]+1):dim(z)[2],I]

c(param1,est1)}

#############################################

rq.se.ivpanel <- function(bhat,d,exo,iv,y,s,tau){

n=length(y)

Z <- model.matrix(s~as.factor(s)-1)[,-1]

X <- cbind(exo,Z,1)

S0 <- cbind(iv,X)

D <- cbind(d,X)

k=dim(D)[2]

vc <- matrix(0,k,k)

S <- (1/n)*t(S0)%*%S0

resid <- y - D%*%bhat

h <- c(1.364 * ((2*sqrt(pi))^(-1/5))*sqrt(var(resid))*(n^(-1/5)))

J = (1/(n*h))*t(c(dnorm(resid/h)) %o% c(rep(1,dim(D)[2])) * D)%*%S0

vc = (1/n)*(tau-tau^2)*ginv(as.matrix(J))%*%S%*%ginv(as.matrix(J))

rbind(bhat,(sqrt(diag(vc))))}

##########################################################################

##########################################################################

# Libraries

library(quantreg)

library(MASS)

#############################################

# A simple example:

#

n <- 10                                      # number of cross sectional units

m <- 25                                      # number of time series units

rdu = 0.5                                    # correlation parameter

tau = 0.5                                    # quantile of interest

s <- rep(1:n,each=m)                         # strata 

Z <- model.matrix(s~as.factor(s)-1)[,-1]     # incidence matrix 

set.seed(25)

mu <- rep(rchisq(n,3), each=m)

epsilon <- rchisq(length(s),3)

XZ <- cbind(mu + epsilon,Z)

iv <- rep(rnorm(n), each=m) + rnorm(length(s))

ief <- rep(rnorm(n), each=m)

v <- rep(rnorm(n), each=m) + rnorm(length(s))

u <- v*rdu + rnorm(length(s))*sqrt(1-rdu^2)

d <- iv + v

y <- ief + u

rq.fit.ivpanel(d,XZ[,1],iv,y,s,tau=tau) -> bhat

round(bhat,3)

rq.se.ivpanel(bhat,d,XZ[,1],iv,y,s,tau=tau) -> bsehat

round(bsehat,3) -> bsehat

colnames(bsehat) <- c("endog", "exog", rep("ie",n-1), "int")

rownames(bsehat) <- c("beta", "se")

bsehat

http://s9/mw690/001Rt2X3gy6P9tFpQIU98&690quantile regression with Fixed Effects" TITLE="面板数据分位数回归固定效应方法（ quantile regression with Fixed Effects" />