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.
A data frame with 10 columns, and 1655 rows.
expenditure share on food, of type
expenditure share on catering, of type
expenditure share on alcohol, of type
expenditure share on fuel, of type
expenditure share on motor, of type
expenditure share on fares, of type
expenditure share on leisure, of type
logarithm of total expenditure, of type
logarithm of total earnings, of type
number of children, of type
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.
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## 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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