# data-Engel95: 1995 British Family Expenditure Survey In np: Nonparametric Kernel Smoothing Methods for Mixed Data Types

 Engel95 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 - 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)
```

np documentation built on Oct. 19, 2022, 1:08 a.m.