US Expenditures for Public Schools
Per capita expenditure on public schools and per capita income by state in 1979.
data(PublicSchools)
A data frame containing 51 observations of 2 variables.
per capita expenditure on public schools,
per capita income.
Table 14.1 in Greene (1993)
Cribari-Neto F. (2004). “Asymptotic Inference Under Heteroskedasticity of Unknown Form.” Computational Statistics \& Data Analysis, 45, 215-233.
Greene W.H. (1993). Econometric Analysis, 2nd edition. Macmillan Publishing Company, New York.
US Department of Commerce (1979). Statistical Abstract of the United States. US Government Printing Office, Washington, DC.
## Willam H. Greene, Econometric Analysis, 2nd Ed.
## Chapter 14
## load data set, p. 385, Table 14.1
data(PublicSchools)
## omit NA in Wisconsin and scale income
ps <- na.omit(PublicSchools)
ps$Income <- ps$Income * 0.0001
## fit quadratic regression, p. 385, Table 14.2
fmq <- lm(Expenditure ~ Income + I(Income^2), data = ps)
summary(fmq)
## compare standard and HC0 standard errors
## p. 391, Table 14.3
library(sandwich)
coef(fmq)
sqrt(diag(vcovHC(fmq, type = "const")))
sqrt(diag(vcovHC(fmq, type = "HC0")))
if(require(lmtest)) {
## compare t ratio
coeftest(fmq, vcov = vcovHC(fmq, type = "HC0"))
## White test, p. 393, Example 14.5
wt <- lm(residuals(fmq)^2 ~ poly(Income, 4), data = ps)
wt.stat <- summary(wt)$r.squared * nrow(ps)
c(wt.stat, pchisq(wt.stat, df = 3, lower = FALSE))
## Bresch-Pagan test, p. 395, Example 14.7
bptest(fmq, studentize = FALSE)
bptest(fmq)
## Francisco Cribari-Neto, Asymptotic Inference, CSDA 45
## quasi z-tests, p. 229, Table 8
## with Alaska
coeftest(fmq, df = Inf)[3,4]
coeftest(fmq, df = Inf, vcov = vcovHC(fmq, type = "HC0"))[3,4]
coeftest(fmq, df = Inf, vcov = vcovHC(fmq, type = "HC3"))[3,4]
coeftest(fmq, df = Inf, vcov = vcovHC(fmq, type = "HC4"))[3,4]
## without Alaska (observation 2)
fmq1 <- lm(Expenditure ~ Income + I(Income^2), data = ps[-2,])
coeftest(fmq1, df = Inf)[3,4]
coeftest(fmq1, df = Inf, vcov = vcovHC(fmq1, type = "HC0"))[3,4]
coeftest(fmq1, df = Inf, vcov = vcovHC(fmq1, type = "HC3"))[3,4]
coeftest(fmq1, df = Inf, vcov = vcovHC(fmq1, type = "HC4"))[3,4]
}
## visualization, p. 230, Figure 1
plot(Expenditure ~ Income, data = ps,
xlab = "per capita income",
ylab = "per capita spending on public schools")
inc <- seq(0.5, 1.2, by = 0.001)
lines(inc, predict(fmq, data.frame(Income = inc)), col = 4)
fml <- lm(Expenditure ~ Income, data = ps)
abline(fml)
text(ps[2,2], ps[2,1], rownames(ps)[2], pos = 2)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.