data-Engel95 function

1995 British Family Expenditure Survey

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. data

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)