Greene2003 {AER} | R Documentation

## Data and Examples from Greene (2003)

### Description

This manual page collects a list of examples from the book. Some solutions might not be exact and the list is certainly not complete. If you have suggestions for improvement (preferably in the form of code), please contact the package maintainer.

### References

Greene, W.H. (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall. URL http://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm.

### See Also

`Affairs`, `BondYield`, `CreditCard`, `Electricity1955`, `Electricity1970`, `Equipment`, `Grunfeld`, `KleinI`, `Longley`, `ManufactCosts`, `MarkPound`, `Municipalities`, `ProgramEffectiveness`, `PSID1976`, `SIC33`, `ShipAccidents`, `StrikeDuration`, `TechChange`, `TravelMode`, `UKInflation`, `USConsump1950`, `USConsump1979`, `USGasG`, `USAirlines`, `USInvest`, `USMacroG`, `USMoney`

### Examples

    #####################################
    ## US consumption data (1970-1979) ##
    #####################################

    ## Example 1.1
    data("USConsump1979", package = "AER")
    plot(expenditure ~ income, data = as.data.frame(USConsump1979), pch = 19)
    fm <- lm(expenditure ~ income, data = as.data.frame(USConsump1979))
    summary(fm)
    abline(fm)

    #####################################
    ## US consumption data (1940-1950) ##
    #####################################

    ## data
    data("USConsump1950", package = "AER")
    usc <- as.data.frame(USConsump1950)
    usc$war <- factor(usc$war, labels = c("no", "yes"))

    ## Example 2.1
    plot(expenditure ~ income, data = usc, type = "n", xlim = c(225, 375), ylim = c(225, 350))
    with(usc, text(income, expenditure, time(USConsump1950)))

    ## single model
    fm <- lm(expenditure ~ income, data = usc)
    summary(fm)

    ## different intercepts for war yes/no
    fm2 <- lm(expenditure ~ income + war, data = usc)
    summary(fm2)

    ## compare
    anova(fm, fm2)

    ## visualize
    abline(fm, lty = 3)
    abline(coef(fm2)[1:2])
    abline(sum(coef(fm2)[c(1, 3)]), coef(fm2)[2], lty = 2)

    ## Example 3.2
    summary(fm)$r.squared
    summary(lm(expenditure ~ income, data = usc, subset = war == "no"))$r.squared
    summary(fm2)$r.squared

    ########################
    ## US investment data ##
    ########################

    data("USInvest", package = "AER")

    ## Chapter 3 in Greene (2003)
    ## transform (and round) data to match Table 3.1
    us <- as.data.frame(USInvest)
    us$invest <- round(0.1 * us$invest/us$price, digits = 3)
    us$gnp <- round(0.1 * us$gnp/us$price, digits = 3)
    us$inflation <- c(4.4, round(100 * diff(us$price)/us$price[-15], digits = 2))
    us$trend <- 1:15
    us <- us[, c(2, 6, 1, 4, 5)]

    ## p. 22-24
    coef(lm(invest ~ trend + gnp, data = us))
    coef(lm(invest ~ gnp, data = us))

    ## Example 3.1, Table 3.2
    cor(us)[1,-1]
    pcor <- solve(cor(us))
    dcor <- 1/sqrt(diag(pcor))
    pcor <- (-pcor * (dcor %o% dcor))[1,-1]

    ## Table 3.4
    fm  <- lm(invest ~ trend + gnp + interest + inflation, data = us)
    fm1 <- lm(invest ~ 1, data = us)
    anova(fm1, fm)

    ## Example 4.1
    set.seed(123)
    w <- rnorm(10000)
    x <- rnorm(10000)
    eps <- 0.5 * w
    y <- 0.5 + 0.5 * x + eps
    b <- rep(0, 500)
    for(i in 1:500) {
      ix <- sample(1:10000, 100)
      b[i] <- lm.fit(cbind(1, x[ix]), y[ix])$coef[2]
    }
    hist(b, breaks = 20, col = "lightgray")

    ###############################
    ## Longley's regression data ##
    ###############################

    ## package and data
    data("Longley", package = "AER")
    library("dynlm")

    ## Example 4.6
    fm1 <- dynlm(employment ~ time(employment) + price + gnp + armedforces,
      data = Longley)
    fm2 <- update(fm1, end = 1961)
    cbind(coef(fm2), coef(fm1))

    ## Figure 4.3
    plot(rstandard(fm2), type = "b", ylim = c(-3, 3))
    abline(h = c(-2, 2), lty = 2)

    #########################################
    ## US gasoline market data (1960-1995) ##
    #########################################

    ## data
    data("USGasG", package = "AER")

    ## Greene (2003)
    ## Example 2.3
    fm <- lm(log(gas/population) ~ log(price) + log(income) + log(newcar) + log(usedcar),
      data = as.data.frame(USGasG))
    summary(fm)

    ## Example 4.4
    ## estimates and standard errors (note different offset for intercept)
    coef(fm)
    sqrt(diag(vcov(fm)))
    ## confidence interval
    confint(fm, parm = "log(income)")
    ## test linear hypothesis
    linearHypothesis(fm, "log(income) = 1")

    ## Figure 7.5
    plot(price ~ gas, data = as.data.frame(USGasG), pch = 19,
      col = (time(USGasG) > 1973) + 1)
    legend("topleft", legend = c("after 1973", "up to 1973"), pch = 19, col = 2:1, bty = "n")

    ## Example 7.6
    ## re-used in Example 8.3
    ## linear time trend
    ltrend <- 1:nrow(USGasG)
    ## shock factor
    shock <- factor(time(USGasG) > 1973, levels = c(FALSE, TRUE), labels = c("before", "after"))

    ## 1960-1995
    fm1 <- lm(log(gas/population) ~ log(income) + log(price) + log(newcar) + log(usedcar) + ltrend,
      data = as.data.frame(USGasG))
    summary(fm1)
    ## pooled
    fm2 <- lm(
      log(gas/population) ~ shock + log(income) + log(price) + log(newcar) + log(usedcar) + ltrend,
      data = as.data.frame(USGasG))
    summary(fm2)
    ## segmented
    fm3 <- lm(
      log(gas/population) ~ shock/(log(income) + log(price) + log(newcar) + log(usedcar) + ltrend),
      data = as.data.frame(USGasG))
    summary(fm3)

    ## Chow test
    anova(fm3, fm1)
    library("strucchange")
    sctest(log(gas/population) ~ log(income) + log(price) + log(newcar) + log(usedcar) + ltrend,
      data = USGasG, point = c(1973, 1), type = "Chow")
    ## Recursive CUSUM test
    rcus <- efp(log(gas/population) ~ log(income) + log(price) + log(newcar) + log(usedcar) + ltrend,
       data = USGasG, type = "Rec-CUSUM")
    plot(rcus)
    sctest(rcus)
    ## Note: Greene's remark that the break is in 1984 (where the process crosses its boundary)
    ## is wrong. The break appears to be no later than 1976.

    ## Example 12.2
    library("dynlm")
    resplot <- function(obj, bound = TRUE) {
      res <- residuals(obj)
      sigma <- summary(obj)$sigma
      plot(res, ylab = "Residuals", xlab = "Year")
      grid()
      abline(h = 0)
      if(bound) abline(h = c(-2, 2) * sigma, col = "red")
      lines(res)
    }
    resplot(dynlm(log(gas/population) ~ log(price), data = USGasG))
    resplot(dynlm(log(gas/population) ~ log(price) + log(income), data = USGasG))
    resplot(dynlm(log(gas/population) ~ log(price) + log(income) + log(newcar) + log(usedcar) +
      log(transport) + log(nondurable) + log(durable) +log(service) + ltrend, data = USGasG))
    ## different shock variable than in 7.6
    shock <- factor(time(USGasG) > 1974, levels = c(FALSE, TRUE), labels = c("before", "after"))
    resplot(dynlm(log(gas/population) ~ shock/(log(price) + log(income) + log(newcar) + log(usedcar) +
      log(transport) + log(nondurable) + log(durable) + log(service) + ltrend), data = USGasG))
    ## NOTE: something seems to be wrong with the sigma estimates in the `full' models

    ## Table 12.4, OLS
    fm <- dynlm(log(gas/population) ~ log(price) + log(income) + log(newcar) + log(usedcar),
      data = USGasG)
    summary(fm)
    resplot(fm, bound = FALSE)
    dwtest(fm)

    ## ML
    g <- as.data.frame(USGasG)
    y <- log(g$gas/g$population)
    X <- as.matrix(cbind(log(g$price), log(g$income), log(g$newcar), log(g$usedcar)))
    arima(y, order = c(1, 0, 0), xreg = X)

    #######################################
    ## US macroeconomic data (1950-2000) ##
    #######################################
    ## data and trend
    data("USMacroG", package = "AER")
    ltrend <- 0:(nrow(USMacroG) - 1)

    ## Example 5.3
    ## OLS and IV regression
    library("dynlm")
    fm_ols <- dynlm(consumption ~ gdp, data = USMacroG)
    fm_iv <- dynlm(consumption ~ gdp | L(consumption) + L(gdp), data = USMacroG)

    ## Hausman statistic
    library("MASS")
    b_diff <- coef(fm_iv) - coef(fm_ols)
    v_diff <- summary(fm_iv)$cov.unscaled - summary(fm_ols)$cov.unscaled
    (t(b_diff) %*% ginv(v_diff) %*% b_diff) / summary(fm_ols)$sigma^2

    ## Wu statistic
    auxreg <- dynlm(gdp ~ L(consumption) + L(gdp), data = USMacroG)
    coeftest(dynlm(consumption ~ gdp + fitted(auxreg), data = USMacroG))[3,3]
    ## agrees with Greene (but not with errata)

    ## Example 6.1
    ## Table 6.1
    fm6.1 <- dynlm(log(invest) ~ tbill + inflation + log(gdp) + ltrend, data = USMacroG)
    fm6.3 <- dynlm(log(invest) ~ I(tbill - inflation) + log(gdp) + ltrend, data = USMacroG)
    summary(fm6.1)
    summary(fm6.3)
    deviance(fm6.1)
    deviance(fm6.3)
    vcov(fm6.1)[2,3]

    ## F test
    linearHypothesis(fm6.1, "tbill + inflation = 0")
    ## alternatively
    anova(fm6.1, fm6.3)
    ## t statistic
    sqrt(anova(fm6.1, fm6.3)[2,5])

    ## Example 6.3
    ## Distributed lag model:
    ## log(Ct) = b0 + b1 * log(Yt) + b2 * log(C(t-1)) + u
    us <- log(USMacroG[, c(2, 5)])
    fm_distlag <- dynlm(log(consumption) ~ log(dpi) + L(log(consumption)),
      data = USMacroG)
    summary(fm_distlag)

    ## estimate and test long-run MPC
    coef(fm_distlag)[2]/(1-coef(fm_distlag)[3])
    linearHypothesis(fm_distlag, "log(dpi) + L(log(consumption)) = 1")
    ## correct, see errata

    ## Example 6.4
    ## predict investiment in 2001(1)
    predict(fm6.1, interval = "prediction",
      newdata = data.frame(tbill = 4.48, inflation = 5.262, gdp = 9316.8, ltrend = 204))

    ## Example 7.7
    ## no GMM available in "strucchange"
    ## using OLS instead yields
    fs <- Fstats(log(m1/cpi) ~ log(gdp) + tbill, data = USMacroG,
      vcov = NeweyWest, from = c(1957, 3), to = c(1991, 3))
    plot(fs)
    ## which looks somewhat similar ...

    ## Example 8.2
    ## Ct = b0 + b1*Yt + b2*Y(t-1) + v
    fm1 <- dynlm(consumption ~ dpi + L(dpi), data = USMacroG)
    ## Ct = a0 + a1*Yt + a2*C(t-1) + u
    fm2 <- dynlm(consumption ~ dpi + L(consumption), data = USMacroG)

    ## Cox test in both directions:
    coxtest(fm1, fm2)
    ## ... and do the same for jtest() and encomptest().
    ## Notice that in this particular case two of them are coincident.
    jtest(fm1, fm2)
    encomptest(fm1, fm2)
    ## encomptest could also be performed `by hand' via
    fmE <- dynlm(consumption ~ dpi + L(dpi) + L(consumption), data = USMacroG)
    waldtest(fm1, fmE, fm2)

    ## Table 9.1
    fm_ols <- lm(consumption ~ dpi, data = as.data.frame(USMacroG))
    fm_nls <- nls(consumption ~ alpha + beta * dpi^gamma,
      start = list(alpha = coef(fm_ols)[1], beta = coef(fm_ols)[2], gamma = 1),
      control = nls.control(maxiter = 100), data = as.data.frame(USMacroG))
    summary(fm_ols)
    summary(fm_nls)
    deviance(fm_ols)
    deviance(fm_nls)
    vcov(fm_nls)

    ## Example 9.7
    ## F test
    fm_nls2 <- nls(consumption ~ alpha + beta * dpi,
      start = list(alpha = coef(fm_ols)[1], beta = coef(fm_ols)[2]),
      control = nls.control(maxiter = 100), data = as.data.frame(USMacroG))
    anova(fm_nls, fm_nls2)
    ## Wald test
    linearHypothesis(fm_nls, "gamma = 1")

    ## Example 9.8, Table 9.2
    usm <- USMacroG[, c("m1", "tbill", "gdp")]
    fm_lin <- lm(m1 ~ tbill + gdp, data = usm)
    fm_log <- lm(m1 ~ tbill + gdp, data = log(usm))
    ## PE auxiliary regressions
    aux_lin <- lm(m1 ~ tbill + gdp + I(fitted(fm_log) - log(fitted(fm_lin))), data = usm)
    aux_log <- lm(m1 ~ tbill + gdp + I(fitted(fm_lin) - exp(fitted(fm_log))), data = log(usm))
    coeftest(aux_lin)[4,]
    coeftest(aux_log)[4,]
    ## matches results from errata
    ## With lmtest >= 0.9-24:
    ## petest(fm_lin, fm_log)

    ## Example 12.1
    fm_m1 <- dynlm(log(m1) ~ log(gdp) + log(cpi), data = USMacroG)
    summary(fm_m1)

    ## Figure 12.1
    par(las = 1)
    plot(0, 0, type = "n", axes = FALSE,
         xlim = c(1950, 2002), ylim = c(-0.3, 0.225),
         xaxs = "i", yaxs = "i",
         xlab = "Quarter", ylab = "", main = "Least Squares Residuals")
    box()
    axis(1, at = c(1950, 1963, 1976, 1989, 2002))
    axis(2, seq(-0.3, 0.225, by = 0.075))
    grid(4, 7, col = grey(0.6))
    abline(0, 0)
    lines(residuals(fm_m1), lwd = 2)

    ## Example 12.3
    fm_pc <- dynlm(d(inflation) ~ unemp, data = USMacroG)
    summary(fm_pc)
    ## Figure 12.3
    plot(residuals(fm_pc))
    ## natural unemployment rate
    coef(fm_pc)[1]/coef(fm_pc)[2]
    ## autocorrelation
    res <- residuals(fm_pc)
    summary(dynlm(res ~ L(res)))

    ## Example 12.4
    coeftest(fm_m1)
    coeftest(fm_m1, vcov = NeweyWest(fm_m1, lag = 5))
    summary(fm_m1)$r.squared
    dwtest(fm_m1)
    as.vector(acf(residuals(fm_m1), plot = FALSE)$acf)[2]
    ## matches Tab. 12.1 errata and Greene 6e, apart from Newey-West SE

    #################################################
    ## Cost function of electricity producers 1870 ##
    #################################################

    ## Example 5.6: a generalized Cobb-Douglas cost function
    data("Electricity1970", package = "AER")
    fm <- lm(log(cost/fuel) ~ log(output) + I(log(output)^2/2) +
      log(capital/fuel) + log(labor/fuel), data=Electricity1970[1:123,])

    ####################################################
    ## SIC 33: Production for primary metals industry ##
    ####################################################

    ## data
    data("SIC33", package = "AER")

    ## Example 6.2
    ## Translog model
    fm_tl <- lm(
      output ~ labor + capital + I(0.5 * labor^2) + I(0.5 * capital^2) + I(labor * capital),
      data = log(SIC33))
    ## Cobb-Douglas model
    fm_cb <- lm(output ~ labor + capital, data = log(SIC33))

    ## Table 6.2 in Greene (2003)
    deviance(fm_tl)
    deviance(fm_cb)
    summary(fm_tl)
    summary(fm_cb)
    vcov(fm_tl)
    vcov(fm_cb)

    ## Cobb-Douglas vs. Translog model
    anova(fm_cb, fm_tl)
    ## hypothesis of constant returns
    linearHypothesis(fm_cb, "labor + capital = 1")

    ###############################
    ## Cost data for US airlines ##
    ###############################

    ## data
    data("USAirlines", package = "AER")

    ## Example 7.2
    fm_full <- lm(log(cost) ~ log(output) + I(log(output)^2) + log(price) + load + year + firm,
      data = USAirlines)
    fm_time <- lm(log(cost) ~ log(output) + I(log(output)^2) + log(price) + load + year,
      data = USAirlines)
    fm_firm <- lm(log(cost) ~ log(output) + I(log(output)^2) + log(price) + load + firm,
      data = USAirlines)
    fm_no <- lm(log(cost) ~ log(output) + I(log(output)^2) + log(price) + load, data = USAirlines)

    ## full fitted model
    coef(fm_full)[1:5]
    plot(1970:1984, c(coef(fm_full)[6:19], 0), type = "n",
         xlab = "Year", ylab = expression(delta(Year)),
         main = "Estimated Year Specific Effects")
    grid()
    points(1970:1984, c(coef(fm_full)[6:19], 0), pch = 19)

    ## Table 7.2
    anova(fm_full, fm_time)
    anova(fm_full, fm_firm)
    anova(fm_full, fm_no)

    ## alternatively, use plm()
    library("plm")
    usair <- pdata.frame(USAirlines, c("firm", "year"))
    fm_full2 <- plm(log(cost) ~ log(output) + I(log(output)^2) + log(price) + load,
      data = usair, model = "within", effect = "twoways")
    fm_time2 <- plm(log(cost) ~ log(output) + I(log(output)^2) + log(price) + load,
      data = usair, model = "within", effect = "time")
    fm_firm2 <- plm(log(cost) ~ log(output) + I(log(output)^2) + log(price) + load,
      data = usair, model = "within", effect = "individual")
    fm_no2 <- plm(log(cost) ~ log(output) + I(log(output)^2) + log(price) + load,
      data = usair, model = "pooling")
    pFtest(fm_full2, fm_time2)
    pFtest(fm_full2, fm_firm2)
    pFtest(fm_full2, fm_no2)

    ## Example 13.1, Table 13.1
    fm_no <- plm(log(cost) ~ log(output) + log(price) + load, data = usair, model = "pooling")
    fm_gm <- plm(log(cost) ~ log(output) + log(price) + load, data = usair, model = "between")
    fm_firm <- plm(log(cost) ~ log(output) + log(price) + load, data = usair, model = "within")
    fm_time <- plm(log(cost) ~ log(output) + log(price) + load, data = usair, model = "within",
      effect = "time")
    fm_ft <- plm(log(cost) ~ log(output) + log(price) + load, data = usair, model = "within",
      effect = "twoways")

    summary(fm_no)
    summary(fm_gm)
    summary(fm_firm)
    fixef(fm_firm)
    summary(fm_time)
    fixef(fm_time)
    summary(fm_ft)
    fixef(fm_ft, effect = "individual")
    fixef(fm_ft, effect = "time")

    ## Table 13.2
    fm_rfirm <- plm(log(cost) ~ log(output) + log(price) + load, data = usair, model = "random")
    fm_rft <- plm(log(cost) ~ log(output) + log(price) + load, data = usair, model = "random",
      effect = "twoways")
    summary(fm_rfirm)
    summary(fm_rft)

    #################################################
    ## Cost function of electricity producers 1955 ##
    #################################################

    ## Nerlove data
    data("Electricity1955", package = "AER")
    Electricity <- Electricity1955[1:145,]

    ## Example 7.3
    ## Cobb-Douglas cost function
    fm_all <- lm(log(cost/fuel) ~ log(output) + log(labor/fuel) + log(capital/fuel),
      data = Electricity)
    summary(fm_all)

    ## hypothesis of constant returns to scale
    linearHypothesis(fm_all, "log(output) = 1")

    ## Figure 7.4
    plot(residuals(fm_all) ~ log(output), data = Electricity)
    ## scaling seems to be different in Greene (2003) with logQ > 10?

    ## grouped functions
    Electricity$group <- with(Electricity, cut(log(output), quantile(log(output), 0:5/5),
      include.lowest = TRUE, labels = 1:5))
    fm_group <- lm(
      log(cost/fuel) ~ group/(log(output) + log(labor/fuel) + log(capital/fuel)) - 1,
      data = Electricity)

    ## Table 7.3 (close, but not quite)
    round(rbind(coef(fm_all)[-1], matrix(coef(fm_group), nrow = 5)[,-1]), digits = 3)

    ## Table 7.4
    ## log quadratic cost function
    fm_all2 <- lm(
      log(cost/fuel) ~ log(output) + I(log(output)^2) + log(labor/fuel) + log(capital/fuel),
      data = Electricity)
    summary(fm_all2)

    ##########################
    ## Technological change ##
    ##########################

    ## Exercise 7.1
    data("TechChange", package = "AER")
    fm1 <- lm(I(output/technology) ~ log(clr), data = TechChange)
    fm2 <- lm(I(output/technology) ~ I(1/clr), data = TechChange)
    fm3 <- lm(log(output/technology) ~ log(clr), data = TechChange)
    fm4 <- lm(log(output/technology) ~ I(1/clr), data = TechChange)

    ## Exercise 7.2 (a) and (c)
    plot(I(output/technology) ~ clr, data = TechChange)
    sctest(I(output/technology) ~ log(clr), data = TechChange,
      type = "Chow", point = c(1942, 1))

    ##################################
    ## Expenditure and default data ##
    ##################################

    ## full data set (F21.4)
    data("CreditCard", package = "AER")

    ## extract data set F9.1
    ccard <- CreditCard[1:100,]
    ccard$income <- round(ccard$income, digits = 2)
    ccard$expenditure <- round(ccard$expenditure, digits = 2)
    ccard$age <- round(ccard$age + .01)
    ## suspicious:
    CreditCard$age[CreditCard$age < 1]
    ## the first of these is also in TableF9.1 with 36 instead of 0.5:
    ccard$age[79] <- 36

    ## Example 11.1
    ccard <- ccard[order(ccard$income),]
    ccard0 <- subset(ccard, expenditure > 0)
    cc_ols <- lm(expenditure ~ age + owner + income + I(income^2), data = ccard0)

    ## Figure 11.1
    plot(residuals(cc_ols) ~ income, data = ccard0, pch = 19)

    ## Table 11.1
    mean(ccard$age)
    prop.table(table(ccard$owner))
    mean(ccard$income)

    summary(cc_ols)
    sqrt(diag(vcovHC(cc_ols, type = "HC0")))
    sqrt(diag(vcovHC(cc_ols, type = "HC2")))
    sqrt(diag(vcovHC(cc_ols, type = "HC1")))

    bptest(cc_ols, ~ (age + income + I(income^2) + owner)^2 + I(age^2) + I(income^4),
      data = ccard0)
    gqtest(cc_ols)
    bptest(cc_ols, ~ income + I(income^2), data = ccard0, studentize = FALSE)
    bptest(cc_ols, ~ income + I(income^2), data = ccard0)

    ## Table 11.2, WLS and FGLS
    cc_wls1 <- lm(expenditure ~ age + owner + income + I(income^2), weights = 1/income,
      data = ccard0)
    cc_wls2 <- lm(expenditure ~ age + owner + income + I(income^2), weights = 1/income^2,
      data = ccard0)

    auxreg1 <- lm(log(residuals(cc_ols)^2) ~ log(income), data = ccard0)
    cc_fgls1 <- lm(expenditure ~ age + owner + income + I(income^2),
      weights = 1/exp(fitted(auxreg1)), data = ccard0)

    auxreg2 <- lm(log(residuals(cc_ols)^2) ~ income + I(income^2), data = ccard0)
    cc_fgls2 <- lm(expenditure ~ age + owner + income + I(income^2),
      weights = 1/exp(fitted(auxreg2)), data = ccard0)

    alphai <- coef(lm(log(residuals(cc_ols)^2) ~ log(income), data = ccard0))[2]
    alpha <- 0
    while(abs((alphai - alpha)/alpha) > 1e-7) {
      alpha <- alphai
      cc_fgls3 <- lm(expenditure ~ age + owner + income + I(income^2), weights = 1/income^alpha,
        data = ccard0)
      alphai <- coef(lm(log(residuals(cc_fgls3)^2) ~ log(income), data = ccard0))[2]
    }
    alpha ## 1.7623 for Greene
    cc_fgls3 <- lm(expenditure ~ age + owner + income + I(income^2), weights = 1/income^alpha,
      data = ccard0)

    llik <- function(alpha)
      -logLik(lm(expenditure ~ age + owner + income + I(income^2), weights = 1/income^alpha,
        data = ccard0))
    plot(0:100/20, -sapply(0:100/20, llik), type = "l", xlab = "alpha", ylab = "logLik")
    alpha <- optimize(llik, interval = c(0, 5))$minimum
    cc_fgls4 <- lm(expenditure ~ age + owner + income + I(income^2), weights = 1/income^alpha,
      data = ccard0)

    ## Table 11.2
    cc_fit <- list(cc_ols, cc_wls1, cc_wls2, cc_fgls2, cc_fgls1, cc_fgls3, cc_fgls4)
    t(sapply(cc_fit, coef))
    t(sapply(cc_fit, function(obj) sqrt(diag(vcov(obj)))))

    ## Table 21.21, Poisson and logit models
    cc_pois <- glm(reports ~ age + income + expenditure, data = CreditCard, family = poisson)
    summary(cc_pois)
    logLik(cc_pois)
    xhat <- colMeans(CreditCard[, c("age", "income", "expenditure")])
    xhat <- as.data.frame(t(xhat))
    lambda <- predict(cc_pois, newdata = xhat, type = "response")
    ppois(0, lambda) * nrow(CreditCard)

    cc_logit <- glm(factor(reports > 0) ~ age + income + owner,
      data = CreditCard, family = binomial)
    summary(cc_logit)
    logLik(cc_logit)

    ## Table 21.21, "split population model"
    library("pscl")
    cc_zip <- zeroinfl(reports ~ age + income + expenditure | age + income + owner,
      data = CreditCard)
    summary(cc_zip)
    sum(predict(cc_zip, type = "prob")[,1])

    ###################################
    ## DEM/GBP exchange rate returns ##
    ###################################

    ## data as given by Greene (2003)
    data("MarkPound")
    mp <- round(MarkPound, digits = 6)

    ## Figure 11.3 in Greene (2003)
    plot(mp)

    ## Example 11.8 in Greene (2003), Table 11.5
    library("tseries")
    mp_garch <- garch(mp, grad = "numerical")
    summary(mp_garch)
    logLik(mp_garch)
    ## Greene (2003) also includes a constant and uses different
    ## standard errors (presumably computed from Hessian), here
    ## OPG standard errors are used. garchFit() in "fGarch"
    ## implements the approach used by Greene (2003).

    ## compare Errata to Greene (2003)
    library("dynlm")
    res <- residuals(dynlm(mp ~ 1))^2
    mp_ols <- dynlm(res ~ L(res, 1:10))
    summary(mp_ols)
    logLik(mp_ols)
    summary(mp_ols)$r.squared * length(residuals(mp_ols))

    ################################
    ## Grunfeld's investment data ##
    ################################

    ## subset of data with mistakes
    data("Grunfeld", package = "AER")
    ggr <- subset(Grunfeld, firm %in% c("General Motors", "US Steel",
      "General Electric", "Chrysler", "Westinghouse"))
    ggr[c(26, 38), 1] <- c(261.6, 645.2)
    ggr[32, 3] <- 232.6

    ## Tab. 13.4
    fm_pool <- lm(invest ~ value + capital, data = ggr)
    summary(fm_pool)
    logLik(fm_pool)
    ## White correction
    sqrt(diag(vcovHC(fm_pool, type = "HC0")))

    ## heteroskedastic FGLS
    auxreg1 <- lm(residuals(fm_pool)^2 ~ firm - 1, data = ggr)
    fm_pfgls <- lm(invest ~ value + capital, data = ggr, weights = 1/fitted(auxreg1))
    summary(fm_pfgls)

    ## ML, computed as iterated FGLS
    sigmasi <- fitted(lm(residuals(fm_pfgls)^2 ~ firm - 1 , data = ggr))
    sigmas <- 0
    while(any(abs((sigmasi - sigmas)/sigmas) > 1e-7)) {
       sigmas <- sigmasi
       fm_pfgls_i <- lm(invest ~ value + capital, data = ggr, weights = 1/sigmas)
       sigmasi <- fitted(lm(residuals(fm_pfgls_i)^2 ~ firm - 1 , data = ggr))
       }
    fm_pmlh <- lm(invest ~ value + capital, data = ggr, weights = 1/sigmas)
    summary(fm_pmlh)
    logLik(fm_pmlh)

    ## Tab. 13.5
    auxreg2 <- lm(residuals(fm_pfgls)^2 ~ firm - 1, data = ggr)
    auxreg3 <- lm(residuals(fm_pmlh)^2 ~ firm - 1, data = ggr)
    rbind(
      "OLS" = coef(auxreg1),
      "Het. FGLS" = coef(auxreg2),
      "Het. ML" = coef(auxreg3))

    ## Chapter 14: explicitly treat as panel data
    library("plm")
    pggr <- pdata.frame(ggr, c("firm", "year"))

    ## Tab. 14.1
    library("systemfit")
    fm_sur <- systemfit(invest ~ value + capital, data = pggr, method = "SUR",
      methodResidCov = "noDfCor")
    fm_psur <- systemfit(invest ~ value + capital, data = pggr, method = "SUR", pooled = TRUE,
      methodResidCov = "noDfCor", residCovWeighted = TRUE)

    ## Tab 14.2
    fm_ols <- systemfit(invest ~ value + capital, data = pggr, method = "OLS")
    fm_pols <- systemfit(invest ~ value + capital, data = pggr, method = "OLS", pooled = TRUE)
    ## or "by hand"
    fm_gm <- lm(invest ~ value + capital, data = ggr, subset = firm == "General Motors")
    mean(residuals(fm_gm)^2)   ## Greene uses MLE
    ## etc.
    fm_pool <- lm(invest ~ value + capital, data = ggr)

    ## Tab. 14.3 (and Tab 13.4, cross-section ML)
    ## (not run due to long computation time)
    ## Not run:
    fm_ml <- systemfit(invest ~ value + capital, data = pggr, method = "SUR",
      methodResidCov = "noDfCor", maxiter = 1000, tol = 1e-10)
    fm_pml <- systemfit(invest ~ value + capital, data = pggr, method = "SUR", pooled = TRUE,
      methodResidCov = "noDfCor", residCovWeighted = TRUE, maxiter = 1000, tol = 1e-10)

    ## End(Not run)

    ## Fig. 14.2
    plot(unlist(residuals(fm_sur)[, c(3, 1, 2, 5, 4)]),
      type = "l", ylab = "SUR residuals", ylim = c(-400, 400), xaxs = "i", yaxs = "i")
    abline(v = c(20,40,60,80), h = 0, lty = 2)

    ###################
    ## Klein model I ##
    ###################

    ## data
    data("KleinI", package = "AER")

    ## Tab. 15.3, OLS
    library("dynlm")
    fm_cons <- dynlm(consumption ~ cprofits + L(cprofits) + I(pwage + gwage), data = KleinI)
    fm_inv <- dynlm(invest ~ cprofits + L(cprofits) + capital, data = KleinI)
    fm_pwage <- dynlm(pwage ~ gnp + L(gnp) + I(time(gnp) - 1931), data = KleinI)
    summary(fm_cons)
    summary(fm_inv)
    summary(fm_pwage)
    ## Notes:
    ##  - capital refers to previous year's capital stock -> no lag needed!
    ##  - trend used by Greene (p. 381, "time trend measured as years from 1931")
    ##    Maddala uses years since 1919

    ## preparation of data frame for systemfit
    KI <- ts.intersect(KleinI, lag(KleinI, k = -1), dframe = TRUE)
    names(KI) <- c(colnames(KleinI), paste("L", colnames(KleinI), sep = ""))
    KI$trend <- (1921:1941) - 1931

    library("systemfit")
    system <- list(
      consumption = consumption ~ cprofits + Lcprofits + I(pwage + gwage),
      invest = invest ~ cprofits + Lcprofits + capital,
      pwage = pwage ~ gnp + Lgnp + trend)

    ## Tab. 15.3 OLS again
    fm_ols <- systemfit(system, method = "OLS", data = KI)
    summary(fm_ols)

    ## Tab. 15.3 2SLS, 3SLS, I3SLS
    inst <- ~ Lcprofits + capital + Lgnp + gexpenditure + taxes + trend + gwage
    fm_2sls <- systemfit(system, method = "2SLS", inst = inst,
      methodResidCov = "noDfCor", data = KI)

    fm_3sls <- systemfit(system, method = "3SLS", inst = inst,
      methodResidCov = "noDfCor", data = KI)

    fm_i3sls <- systemfit(system, method = "3SLS", inst = inst,
      methodResidCov = "noDfCor", maxiter = 100, data = KI)

    ############################################
    ## Transportation equipment manufacturing ##
    ############################################

    ## data
    data("Equipment", package = "AER")

    ## Example 17.5
    ## Cobb-Douglas
    fm_cd <- lm(log(valueadded/firms) ~ log(capital/firms) + log(labor/firms),
      data = Equipment)

    ## generalized Cobb-Douglas with Zellner-Revankar trafo
    GCobbDouglas <- function(theta)
     lm(I(log(valueadded/firms) + theta * valueadded/firms) ~ log(capital/firms) + log(labor/firms),
         data = Equipment)

    ## yields classical Cobb-Douglas for theta = 0
    fm_cd0 <- GCobbDouglas(0)

    ## ML estimation of generalized model
    ## choose starting values from classical model
    par0 <- as.vector(c(coef(fm_cd0), 0, mean(residuals(fm_cd0)^2)))

    ## set up likelihood function
    nlogL <- function(par) {
      beta <- par[1:3]
      theta <- par[4]
      sigma2 <- par[5]

      Y <- with(Equipment, valueadded/firms)
      K <- with(Equipment, capital/firms)
      L <- with(Equipment, labor/firms)

      rhs <- beta[1] + beta[2] * log(K) + beta[3] * log(L)
      lhs <- log(Y) + theta * Y

      rval <- sum(log(1 + theta * Y) - log(Y) +
        dnorm(lhs, mean = rhs, sd = sqrt(sigma2), log = TRUE))
      return(-rval)
    }

    ## optimization
    opt <- optim(par0, nlogL, hessian = TRUE)

    ## Table 17.2
    opt$par
    sqrt(diag(solve(opt$hessian)))[1:4]
    -opt$value

    ## re-fit ML model
    fm_ml <- GCobbDouglas(opt$par[4])
    deviance(fm_ml)
    sqrt(diag(vcov(fm_ml)))

    ## fit NLS model
    rss <- function(theta) deviance(GCobbDouglas(theta))
    optim(0, rss)
    opt2 <- optimize(rss, c(-1, 1))
    fm_nls <- GCobbDouglas(opt2$minimum)
    -nlogL(c(coef(fm_nls), opt2$minimum, mean(residuals(fm_nls)^2)))

    ############################
    ## Municipal expenditures ##
    ############################

    ## Table 18.2
    data("Municipalities", package = "AER")
    summary(Municipalities)

    ###########################
    ## Program effectiveness ##
    ###########################

    ## Table 21.1, col. "Probit"
    data("ProgramEffectiveness", package = "AER")
    fm_probit <- glm(grade ~ average + testscore + participation,
      data = ProgramEffectiveness, family = binomial(link = "probit"))
    summary(fm_probit)

    ####################################
    ## Labor force participation data ##
    ####################################

    ## data and transformations
    data("PSID1976", package = "AER")
    PSID1976$kids <- with(PSID1976, factor((youngkids + oldkids) > 0,
      levels = c(FALSE, TRUE), labels = c("no", "yes")))
    PSID1976$nwincome <- with(PSID1976, (fincome - hours * wage)/1000)

    ## Example 4.1, Table 4.2
    ## (reproduced in Example 7.1, Table 7.1)
    gr_lm <- lm(log(hours * wage) ~ age + I(age^2) + education + kids,
      data = PSID1976, subset = participation == "yes")
    summary(gr_lm)
    vcov(gr_lm)

    ## Example 4.5
    summary(gr_lm)
    ## or equivalently
    gr_lm1 <- lm(log(hours * wage) ~ 1, data = PSID1976, subset = participation == "yes")
    anova(gr_lm1, gr_lm)

    ## Example 21.4, p. 681, and Tab. 21.3, p. 682
    gr_probit1 <- glm(participation ~ age + I(age^2) + I(fincome/10000) + education + kids,
      data = PSID1976, family = binomial(link = "probit") )
    gr_probit2 <- glm(participation ~ age + I(age^2) + I(fincome/10000) + education,
      data = PSID1976, family = binomial(link = "probit"))
    gr_probit3 <- glm(participation ~ kids/(age + I(age^2) + I(fincome/10000) + education),
      data = PSID1976, family = binomial(link = "probit"))
    ## LR test of all coefficients
    lrtest(gr_probit1)
    ## Chow-type test
    lrtest(gr_probit2, gr_probit3)
    ## equivalently:
    anova(gr_probit2, gr_probit3, test = "Chisq")
    ## Table 21.3
    summary(gr_probit1)

    ## Example 22.8, Table 22.7, p. 786
    library("sampleSelection")
    gr_2step <- selection(participation ~ age + I(age^2) + fincome + education + kids,
      wage ~ experience + I(experience^2) + education + city,
      data = PSID1976, method = "2step")
    gr_ml <- selection(participation ~ age + I(age^2) + fincome + education + kids,
      wage ~ experience + I(experience^2) + education + city,
      data = PSID1976, method = "ml")
    gr_ols <- lm(wage ~ experience + I(experience^2) + education + city,
      data = PSID1976, subset = participation == "yes")
    ## NOTE: ML estimates agree with Greene, 5e errata.
    ## Standard errors are based on the Hessian (here), while Greene has BHHH/OPG.

    ####################
    ## Ship accidents ##
    ####################

    ## subset data
    data("ShipAccidents", package = "AER")
    sa <- subset(ShipAccidents, service > 0)

    ## Table 21.20
    sa_full <- glm(incidents ~ type + construction + operation, family = poisson,
      data = sa, offset = log(service))
    summary(sa_full)

    sa_notype <- glm(incidents ~ construction + operation, family = poisson,
      data = sa, offset = log(service))
    summary(sa_notype)

    sa_noperiod <- glm(incidents ~ type + operation, family = poisson,
      data = sa, offset = log(service))
    summary(sa_noperiod)

    ## model comparison
    anova(sa_full, sa_notype, test = "Chisq")
    anova(sa_full, sa_noperiod, test = "Chisq")

    ## test for overdispersion
    dispersiontest(sa_full)
    dispersiontest(sa_full, trafo = 2)

    ######################################
    ## Fair's extramarital affairs data ##
    ######################################

    ## data
    data("Affairs", package = "AER")

    ## Tab. 22.3 and 22.4
    fm_ols <- lm(affairs ~ age + yearsmarried + religiousness + occupation + rating,
      data = Affairs)
    fm_probit <- glm(I(affairs > 0) ~ age + yearsmarried + religiousness + occupation + rating,
      data = Affairs, family = binomial(link = "probit"))

    fm_tobit <- tobit(affairs ~ age + yearsmarried + religiousness + occupation + rating,
      data = Affairs)
    fm_tobit2 <- tobit(affairs ~ age + yearsmarried + religiousness + occupation + rating,
      right = 4, data = Affairs)

    fm_pois <- glm(affairs ~ age + yearsmarried + religiousness + occupation + rating,
      data = Affairs, family = poisson)

    library("MASS")
    fm_nb <- glm.nb(affairs ~ age + yearsmarried + religiousness + occupation + rating,
      data = Affairs)

    ## Tab. 22.6
    library("pscl")
    fm_zip <- zeroinfl(affairs ~ age + yearsmarried + religiousness + occupation + rating | age +
      yearsmarried + religiousness + occupation + rating, data = Affairs)

    ######################
    ## Strike durations ##
    ######################

    ## data and package
    data("StrikeDuration", package = "AER")
    library("MASS")

    ## Table 22.10
    fit_exp <- fitdistr(StrikeDuration$duration, "exponential")
    fit_wei <- fitdistr(StrikeDuration$duration, "weibull")
    fit_wei$estimate[2]^(-1)
    fit_lnorm <- fitdistr(StrikeDuration$duration, "lognormal")
    1/fit_lnorm$estimate[2]
    exp(-fit_lnorm$estimate[1])
    ## Weibull and lognormal distribution have
    ## different parameterizations, see Greene p. 794

    ## Example 22.10
    library("survival")
    fm_wei <- survreg(Surv(duration) ~ uoutput, dist = "weibull", data = StrikeDuration)
    summary(fm_wei)

[Package AER version 1.2-6 Index]