British cross-section data consisting of a random sample taken from
the British Family Expenditure Survey for 1995. The households consist
of married couples with an employed head-of-household between the ages
of 25 and 55 years. There are 1655 household-level observations in
total.
Usage
data("Engel95")
Format
A data frame with 10 columns, and 1655 rows.
food
expenditure share on food, of type numeric
catering
expenditure share on catering, of type numeric
alcohol
expenditure share on alcohol, of type numeric
fuel
expenditure share on fuel, of type numeric
motor
expenditure share on motor, of type numeric
fares
expenditure share on fares, of type numeric
leisure
expenditure share on leisure, of type numeric
logexp
logarithm of total expenditure, of type numeric
logwages
logarithm of total earnings, of type numeric
nkids
number of children, of type numeric
Source
Richard Blundell and Dennis Kristensen
References
Blundell, R. and X. Chen and D. Kristensen (2007),
“Semi-Nonparametric IV Estimation of Shape-Invariant Engel
Curves,” Econometrica, 75, 1613-1669.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics:
Theory and Practice, Princeton University Press.
Examples
## Not run:
## Example - compute nonparametric instrumental regression using
## Landweber-Fridman iteration of Fredholm integral equations of the
## first kind.
## We consider an equation with an endogenous regressor (`z') and an
## instrument (`w'). Let y = phi(z) + u where phi(z) is the function of
## interest. Here E(u|z) is not zero hence the conditional mean E(y|z)
## does not coincide with the function of interest, but if there exists
## an instrument w such that E(u|w) = 0, then we can recover the
## function of interest by solving an ill-posed inverse problem.
data(Engel95)
## Sort on logexp (the endogenous regressor) for plotting purposes
Engel95 <- Engel95[order(Engel95$logexp),]
attach(Engel95)
model.iv <- npregiv(y=food,z=logexp,w=logwages,method="Landweber-Fridman")
phihat <- model.iv$phi
## Compute the non-IV regression (i.e. regress y on z)
ghat <- npreg(food~logexp,regtype="ll")
## For the plots, restrict focal attention to the bulk of the data
## (i.e. for the plotting area trim out 1/4 of one percent from each
## tail of y and z)
trim <- 0.0025
plot(logexp,food,
ylab="Food Budget Share",
xlab="log(Total Expenditure)",
xlim=quantile(logexp,c(trim,1-trim)),
ylim=quantile(food,c(trim,1-trim)),
main="Nonparametric Instrumental Kernel Regression",
type="p",
cex=.5,
col="lightgrey")
lines(logexp,phihat,col="blue",lwd=2,lty=2)
lines(logexp,fitted(ghat),col="red",lwd=2,lty=4)
legend(quantile(logexp,trim),quantile(food,1-trim),
c(expression(paste("Nonparametric IV: ",hat(varphi)(logexp))),
"Nonparametric Regression: E(food | logexp)"),
lty=c(2,4),
col=c("blue","red"),
lwd=c(2,2))
## End(Not run)