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("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`

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.

# 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") # }