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.

1 | ```
data("Engel95")
``` |

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`

Richard Blundell and Dennis Kristensen

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 | ```
## 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)
``` |

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