# Data and Examples from Greene (2003) 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 [https://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm](https://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 ```r ##################################### ## 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) ```

Greene2003 function