Engel95 {crs} | R Documentation |
1995 British Family Expenditure Survey
Description
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 - we compute nonparametric instrumental regression of an
## Engel curve for food expenditure shares using Landweber-Fridman
## iteration of Fredholm integral equations of the first kind.
## We consider an equation with an endogenous predictor ('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 predictor) for plotting purposes
## (i.e. so we can plot a curve for the fitted values versus logexp)
Engel95 <- Engel95[order(Engel95$logexp),]
attach(Engel95)
model.iv <- crsiv(y=food,z=logexp,w=logwages,method="Landweber-Fridman")
phihat <- model.iv$phi
## Compute the non-IV regression (i.e. regress y on z)
ghat <- crs(food~logexp)
## For the plots, we 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). This is often helpful as estimates in the tails of
## the support are less reliable (i.e. more variable) so we are
## interested in examining the relationship 'where the action is'.
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 Regression Splines",
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),
bty="n")
## End(Not run)