Package 'AER'

Description

Infidelity data, known as Fair's Affairs. Cross-section data from a survey conducted by Psychology Today in 1969.

Usage

data("Affairs")

Format

A data frame containing 601 observations on 9 variables.

affairs

numeric. How often engaged in extramarital sexual intercourse during the past year? 0 = none, 1 = once, 2 = twice, 3 = 3 times, 7 = 4–10 times, 12 = monthly, 12 = weekly, 12 = daily.

gender

factor indicating gender.

age

numeric variable coding age in years: 17.5 = under 20, 22 = 20–24, 27 = 25–29, 32 = 30–34, 37 = 35–39, 42 = 40–44, 47 = 45–49, 52 = 50–54, 57 = 55 or over.

yearsmarried

numeric variable coding number of years married: 0.125 = 3 months or less, 0.417 = 4–6 months, 0.75 = 6 months–1 year, 1.5 = 1–2 years, 4 = 3–5 years, 7 = 6–8 years, 10 = 9–11 years, 15 = 12 or more years.

children

factor. Are there children in the marriage?

religiousness

numeric variable coding religiousness: 1 = anti, 2 = not at all, 3 = slightly, 4 = somewhat, 5 = very.

education

numeric variable coding level of education: 9 = grade school, 12 = high school graduate, 14 = some college, 16 = college graduate, 17 = some graduate work, 18 = master's degree, 20 = Ph.D., M.D., or other advanced degree.

occupation

numeric variable coding occupation according to Hollingshead classification (reverse numbering).

rating

numeric variable coding self rating of marriage: 1 = very unhappy, 2 = somewhat unhappy, 3 = average, 4 = happier than average, 5 = very happy.

Source

Online complements to Greene (2003). Table F22.2.

https://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm

References

Greene, W.H. (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall.

Fair, R.C. (1978). A Theory of Extramarital Affairs. Journal of Political Economy, 86, 45–61.

See Also

Greene2003

Examples

data("Affairs")

## Greene (2003)
## 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)

Description

Time series of consumer price index (CPI) in Argentina (index with 1969(4) = 1).

Usage

data("ArgentinaCPI")

Format

A quarterly univariate time series from 1970(1) to 1989(4).

Source

Online complements to Franses (1998).

References

De Ruyter van Steveninck, M.A. (1996). The Impact of Capital Imports; Argentina 1970–1989. Amsterdam: Thesis Publishers.

Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.

See Also

Franses1998

Examples

data("ArgentinaCPI")
plot(ArgentinaCPI)
plot(log(ArgentinaCPI))

library("dynlm")
## estimation sample 1970.3-1988.4 means
acpi <- window(ArgentinaCPI, start = c(1970,1), end = c(1988,4)) 

## eq. (3.90), p.54
acpi_ols <- dynlm(d(log(acpi)) ~ L(d(log(acpi))))
summary(acpi_ols)

## alternatively
ar(diff(log(acpi)), order.max = 1, method = "ols")

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

Baltagi, B.H. (2002). Econometrics, 3rd ed., Berlin: Springer-Verlag.

See Also

BenderlyZwick, CigarettesB, EuroEnergy, Grunfeld, Mortgage, NaturalGas, OECDGas, OrangeCounty, PSID1982, TradeCredit, USConsump1993, USCrudes, USGasB, USMacroB

Examples

################################
## Cigarette consumption data ##
################################

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

## Table 3.3
cig_lm <- lm(packs ~ price, data = CigarettesB)
summary(cig_lm)

## Figure 3.9
plot(residuals(cig_lm) ~ price, data = CigarettesB)
abline(h = 0, lty = 2)

## Figure 3.10
cig_pred <- with(CigarettesB,
  data.frame(price = seq(from = min(price), to = max(price), length = 30)))
cig_pred <- cbind(cig_pred, predict(cig_lm, newdata = cig_pred, interval = "confidence"))
plot(packs ~ price, data = CigarettesB)
lines(fit ~ price, data = cig_pred)
lines(lwr ~ price, data = cig_pred, lty = 2)
lines(upr ~ price, data = cig_pred, lty = 2)

## Chapter 5: diagnostic tests (p. 111-115)
cig_lm2 <- lm(packs ~ price + income, data = CigarettesB)
summary(cig_lm2)
## Glejser tests (p. 112)
ares <- abs(residuals(cig_lm2))
summary(lm(ares ~ income, data = CigarettesB))
summary(lm(ares ~ I(1/income), data = CigarettesB))
summary(lm(ares ~ I(1/sqrt(income)), data = CigarettesB))
summary(lm(ares ~ sqrt(income), data = CigarettesB))
## Goldfeld-Quandt test (p. 112)
gqtest(cig_lm2, order.by = ~ income, data = CigarettesB, fraction = 12, alternative = "less")
## NOTE: Baltagi computes the test statistic as mss1/mss2,
## i.e., tries to find decreasing variances. gqtest() always uses
## mss2/mss1 and has an "alternative" argument.

## Spearman rank correlation test (p. 113)
cor.test(~ ares + income, data = CigarettesB, method = "spearman")
## Breusch-Pagan test (p. 113)
bptest(cig_lm2, varformula = ~ income, data = CigarettesB, student = FALSE)
## White test (Table 5.1, p. 113)
bptest(cig_lm2, ~ income * price + I(income^2) + I(price^2), data = CigarettesB)
## White HC standard errors (Table 5.2, p. 114)
coeftest(cig_lm2, vcov = vcovHC(cig_lm2, type = "HC1"))
## Jarque-Bera test (Figure 5.2, p. 115)
hist(residuals(cig_lm2), breaks = 16, ylim = c(0, 10), col = "lightgray")
library("tseries")
jarque.bera.test(residuals(cig_lm2))

## Tables 8.1 and 8.2
influence.measures(cig_lm2)


#####################################
## US consumption data (1950-1993) ##
#####################################

## data
data("USConsump1993", package = "AER")
plot(USConsump1993, plot.type = "single", col = 1:2)

## Chapter 5 (p. 122-125)
fm <- lm(expenditure ~ income, data = USConsump1993)
summary(fm)
## Durbin-Watson test (p. 122)
dwtest(fm)
## Breusch-Godfrey test (Table 5.4, p. 124)
bgtest(fm)
## Newey-West standard errors (Table 5.5, p. 125)
coeftest(fm, vcov = NeweyWest(fm, lag = 3, prewhite = FALSE, adjust = TRUE)) 

## Chapter 8
library("strucchange")
## Recursive residuals
rr <- recresid(fm)
rr
## Recursive CUSUM test
rcus <- efp(expenditure ~ income, data = USConsump1993)
plot(rcus)
sctest(rcus)
## Harvey-Collier test
harvtest(fm)
## NOTE" Mistake in Baltagi (2002) who computes
## the t-statistic incorrectly as 0.0733 via
mean(rr)/sd(rr)/sqrt(length(rr))
## whereas it should be (as in harvtest)
mean(rr)/sd(rr) * sqrt(length(rr))

## Rainbow test
raintest(fm, center = 23)

## J test for non-nested models
library("dynlm")
fm1 <- dynlm(expenditure ~ income + L(income), data = USConsump1993)
fm2 <- dynlm(expenditure ~ income + L(expenditure), data = USConsump1993)
jtest(fm1, fm2)

## Chapter 11
## Table 11.1 Instrumental-variables regression
usc <- as.data.frame(USConsump1993)
usc$investment <- usc$income - usc$expenditure
fm_ols <- lm(expenditure ~ income, data = usc)
fm_iv <- ivreg(expenditure ~ income | investment, data = usc)
## Hausman test
cf_diff <- coef(fm_iv) - coef(fm_ols)
vc_diff <- vcov(fm_iv) - vcov(fm_ols)
x2_diff <- as.vector(t(cf_diff) %*% solve(vc_diff) %*% cf_diff)
pchisq(x2_diff, df = 2, lower.tail = FALSE)

## Chapter 14
## ACF and PACF for expenditures and first differences
exps <- USConsump1993[, "expenditure"]
(acf(exps))
(pacf(exps))
(acf(diff(exps)))
(pacf(diff(exps)))

## dynamic regressions, eq. (14.8)
fm <- dynlm(d(exps) ~ I(time(exps) - 1949) + L(exps))
summary(fm)


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

## select the first three companies (as panel data)
data("Grunfeld", package = "AER")
pgr <- subset(Grunfeld, firm %in% levels(Grunfeld$firm)[1:3])
library("plm")
pgr <- pdata.frame(pgr, c("firm", "year"))

## Ex. 10.9
library("systemfit")
gr_ols <- systemfit(invest ~ value + capital, method = "OLS", data = pgr)
gr_sur <- systemfit(invest ~ value + capital, method = "SUR", data = pgr)


#########################################
## Panel study on income dynamics 1982 ##
#########################################

## data
data("PSID1982", package = "AER")

## Table 4.1
earn_lm <- lm(log(wage) ~ . + I(experience^2), data = PSID1982)
summary(earn_lm)

## Table 13.1
union_lpm <- lm(I(as.numeric(union) - 1) ~ . - wage, data = PSID1982)
union_probit <- glm(union ~ . - wage, data = PSID1982, family = binomial(link = "probit"))
union_logit <- glm(union ~ . - wage, data = PSID1982, family = binomial)
## probit OK, logit and LPM rather different.

Description

Wages of employees of a US bank.

Usage

data("BankWages")

Format

A data frame containing 474 observations on 4 variables.

job

Ordered factor indicating job category, with levels "custodial", "admin" and "manage".

education

Education in years.

gender

Factor indicating gender.

minority

Factor. Is the employee member of a minority?

Source

Online complements to Heij, de Boer, Franses, Kloek, and van Dijk (2004).

https://global.oup.com/booksites/content/0199268010/datasets/ch6/xr614bwa.asc

References

Heij, C., de Boer, P.M.C., Franses, P.H., Kloek, T. and van Dijk, H.K. (2004). Econometric Methods with Applications in Business and Economics. Oxford: Oxford University Press.

Examples

data("BankWages")

## exploratory analysis of job ~ education
## (tables and spine plots, some education levels merged)
xtabs(~ education + job, data = BankWages)
edcat <- factor(BankWages$education)
levels(edcat)[3:10] <- rep(c("14-15", "16-18", "19-21"), c(2, 3, 3))
tab <- xtabs(~ edcat + job, data = BankWages)
prop.table(tab, 1)
spineplot(tab, off = 0)
plot(job ~ edcat, data = BankWages, off = 0)

## fit multinomial model for male employees
library("nnet")
fm_mnl <- multinom(job ~ education + minority, data = BankWages,
  subset = gender == "male", trace = FALSE)
summary(fm_mnl)
confint(fm_mnl)

## same with mlogit package
library("mlogit")
fm_mlogit <- mlogit(job ~ 1 | education + minority, data = BankWages,
  subset = gender == "male", shape = "wide", reflevel = "custodial")
summary(fm_mlogit)

Description

Time series data, 1952–1982.

Usage

data("BenderlyZwick")

Format

An annual multiple time series from 1952 to 1982 with 5 variables.

returns

real annual returns on stocks, measured using the Ibbotson-Sinquefeld data base.

growth

annual growth rate of output, measured by real GNP (from the given year to the next year).

inflation

inflation rate, measured as growth of price rate (from December of the previous year to December of the present year).

growth2

annual growth rate of real GNP as given by Baltagi.

inflation2

inflation rate as given by Baltagi

Source

The first three columns of the data are from Table 1 in Benderly and Zwick (1985). The remaining columns are taken from the online complements of Baltagi (2002). The first column is identical in both sources, the other two variables differ in their numeric values and additionally the growth series seems to be lagged differently. Baltagi (2002) states Lott and Ray (1992) as the source for his version of the data set.

References

Baltagi, B.H. (2002). Econometrics, 3rd ed. Berlin, Springer.

Benderly, J., and Zwick, B. (1985). Inflation, Real Balances, Output and Real Stock Returns. American Economic Review, 75, 1115–1123.

Lott, W.F., and Ray, S.C. (1992). Applied Econometrics: Problems with Data Sets. New York: The Dryden Press.

Zaman, A., Rousseeuw, P.J., and Orhan, M. (2001). Econometric Applications of High-Breakdown Robust Regression Techniques. Economics Letters, 71, 1–8.

See Also

Baltagi2002

Examples

data("BenderlyZwick")
plot(BenderlyZwick)

## Benderly and Zwick (1985), p. 1116
library("dynlm")
bz_ols <- dynlm(returns ~ growth + inflation,
  data = BenderlyZwick/100, start = 1956, end = 1981)
summary(bz_ols)

## Zaman, Rousseeuw and Orhan (2001)
## use larger period, without scaling
bz_ols2 <- dynlm(returns ~ growth + inflation,
  data = BenderlyZwick, start = 1954, end = 1981)
summary(bz_ols2)

Description

Monthly averages of the yield on a Moody's Aaa rated corporate bond (in percent/year).

Usage

data("BondYield")

Format

A monthly univariate time series from 1990(1) to 1994(12).

Source

Online complements to Greene (2003), Table F20.1.

https://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm

References

Greene, W.H. (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall.

See Also

Greene2003

Examples

data("BondYield")
plot(BondYield)

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

Cameron, A.C. and Trivedi, P.K. (1998). Regression Analysis of Count Data. Cambridge: Cambridge University Press.

See Also

DoctorVisits, NMES1988, RecreationDemand

Examples

library("MASS")
library("pscl")

###########################################
## Australian health service utilization ##
###########################################

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

## Poisson regression
dv_pois <- glm(visits ~ . + I(age^2), data = DoctorVisits, family = poisson)
dv_qpois <- glm(visits ~ . + I(age^2), data = DoctorVisits, family = quasipoisson)

## Table 3.3 
round(cbind(
  Coef = coef(dv_pois),
  MLH = sqrt(diag(vcov(dv_pois))),
  MLOP = sqrt(diag(vcovOPG(dv_pois))),
  NB1 = sqrt(diag(vcov(dv_qpois))),
  RS = sqrt(diag(sandwich(dv_pois)))
), digits = 3)

## Table 3.4
## NM2-ML
dv_nb <- glm.nb(visits ~ . + I(age^2), data = DoctorVisits)
summary(dv_nb)
## NB1-GLM = quasipoisson
summary(dv_qpois)

## overdispersion tests (page 79)
lrtest(dv_pois, dv_nb) ## p-value would need to be halved
dispersiontest(dv_pois, trafo = 1)
dispersiontest(dv_pois, trafo = 2)


##########################################
## Demand for medical care in NMES 1988 ##
##########################################

## select variables for analysis
data("NMES1988", package = "AER")
nmes <- NMES1988[,-(2:6)]

## dependent variable
## Table 6.1
table(cut(nmes$visits, c(0:13, 100)-0.5, labels = 0:13))

## NegBin regression
nmes_nb <- glm.nb(visits ~ ., data = nmes)

## NegBin hurdle
nmes_h <- hurdle(visits ~ ., data = nmes, dist = "negbin")

## from Table 6.3
lrtest(nmes_nb, nmes_h)

## from Table 6.4
AIC(nmes_nb)
AIC(nmes_nb, k = log(nrow(nmes)))
AIC(nmes_h)
AIC(nmes_h, k = log(nrow(nmes)))

## Table 6.8
coeftest(nmes_h, vcov = sandwich)
logLik(nmes_h)
1/nmes_h$theta


###################################################
## Recreational boating trips to Lake Somerville ##
###################################################

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

## Poisson model:
## Cameron and Trivedi (1998), Table 6.11
## Ozuna and Gomez (1995), Table 2, col. 3
fm_pois <- glm(trips ~ ., data = RecreationDemand, family = poisson)
summary(fm_pois)
logLik(fm_pois)
coeftest(fm_pois, vcov = sandwich)

## Negbin model:
## Cameron and Trivedi (1998), Table 6.11
## Ozuna and Gomez (1995), Table 2, col. 5
library("MASS")
fm_nb <- glm.nb(trips ~ ., data = RecreationDemand)
coeftest(fm_nb, vcov = vcovOPG)
logLik(fm_nb)

## ZIP model:
## Cameron and Trivedi (1998), Table 6.11
fm_zip <- zeroinfl(trips ~  . | quality + income, data = RecreationDemand)
summary(fm_zip)
logLik(fm_zip)

## Hurdle models
## Cameron and Trivedi (1998), Table 6.13
## poisson-poisson
sval <- list(count = c(2.15, 0.044, .467, -.097, .601, .002, -.036, .024), 
             zero = c(-1.88, 0.815, .403, .01, 2.95, 0.006, -.052, .046))
fm_hp0 <- hurdle(trips ~ ., data = RecreationDemand, dist = "poisson",
  zero = "poisson", start = sval, maxit = 0)
fm_hp1 <- hurdle(trips ~ ., data = RecreationDemand, dist = "poisson",
  zero = "poisson", start = sval)
fm_hp2 <- hurdle(trips ~ ., data = RecreationDemand, dist = "poisson",
  zero = "poisson")
sapply(list(fm_hp0, fm_hp1, fm_hp2), logLik)

## negbin-negbin
fm_hnb <- hurdle(trips ~ ., data = RecreationDemand, dist = "negbin", zero = "negbin")
summary(fm_hnb)
logLik(fm_hnb)

sval <- list(count = c(0.841, 0.172, .622, -.057, .576, .057, -.078, .012), 
             zero = c(-3.046, 4.638, -.025, .026, 16.203, 0.030, -.156, .117),
             theta = c(count = 1/1.7, zero = 1/5.609))
fm_hnb2 <- try(hurdle(trips ~ ., data = RecreationDemand,
  dist = "negbin", zero = "negbin", start = sval))
if(!inherits(fm_hnb2, "try-error")) {
summary(fm_hnb2)
logLik(fm_hnb2)
}

## geo-negbin
sval98 <- list(count = c(0.841, 0.172, .622, -.057, .576, .057, -.078, .012), 
             zero = c(-2.88, 1.44, .4, .03, 9.43, 0.01, -.08, .071),
             theta = c(count = 1/1.7))
sval96 <- list(count = c(0.841, 0.172, .622, -.057, .576, .057, -.078, .012), 
             zero = c(-2.882, 1.437, .406, .026, 11.936, 0.008, -.081, .071),
             theta = c(count = 1/1.7))
      
fm_hgnb <- hurdle(trips ~ ., data = RecreationDemand, dist = "negbin", zero = "geometric")
summary(fm_hgnb)
logLik(fm_hgnb)

## logLik with starting values from Gurmu + Trivedi 1996
fm_hgnb96 <- hurdle(trips ~ ., data = RecreationDemand, dist = "negbin", zero = "geometric",
                  start = sval96, maxit = 0)
logLik(fm_hgnb96)

## logit-negbin
fm_hgnb2 <- hurdle(trips ~ ., data = RecreationDemand, dist = "negbin")
summary(fm_hgnb2)
logLik(fm_hgnb2)

## Note: quasi-complete separation
with(RecreationDemand, table(trips > 0, userfee))

Description

Weekly observations on prices and other factors from 1880–1886, for a total of 326 weeks.

Usage

data("CartelStability")

Format

A data frame containing 328 observations on 5 variables.

price

weekly index of price of shipping a ton of grain by rail.

cartel

factor. Is a railroad cartel operative?

quantity

total tonnage of grain shipped in the week.

season

factor indicating season of year. To match the weekly data, the calendar has been divided into 13 periods, each approximately 4 weeks long.

ice

factor. Are the Great Lakes innavigable because of ice?

Source

Online complements to Stock and Watson (2007).

References

Porter, R. H. (1983). A Study of Cartel Stability: The Joint Executive Committee, 1880–1886. The Bell Journal of Economics, 14, 301–314.

Stock, J.H. and Watson, M.W. (2007). Introduction to Econometrics, 2nd ed. Boston: Addison Wesley.

See Also

StockWatson2007

Examples

data("CartelStability")
summary(CartelStability)

Description

The dataset contains data on test performance, school characteristics and student demographic backgrounds for school districts in California.

Usage

data("CASchools")

Format

A data frame containing 420 observations on 14 variables.

district

character. District code.

school

character. School name.

county

factor indicating county.

grades

factor indicating grade span of district.

students

Total enrollment.

teachers

Number of teachers.

calworks

Percent qualifying for CalWorks (income assistance).

lunch

Percent qualifying for reduced-price lunch.

computer

Number of computers.

expenditure

Expenditure per student.

income

District average income (in USD 1,000).

english

Percent of English learners.

read

Average reading score.

math

Average math score.

Details

The data used here are from all 420 K-6 and K-8 districts in California with data available for 1998 and 1999. Test scores are on the Stanford 9 standardized test administered to 5th grade students. School characteristics (averaged across the district) include enrollment, number of teachers (measured as “full-time equivalents”, number of computers per classroom, and expenditures per student. Demographic variables for the students are averaged across the district. The demographic variables include the percentage of students in the public assistance program CalWorks (formerly AFDC), the percentage of students that qualify for a reduced price lunch, and the percentage of students that are English learners (that is, students for whom English is a second language).

Source

Online complements to Stock and Watson (2007).

References

Stock, J. H. and Watson, M. W. (2007). Introduction to Econometrics, 2nd ed. Boston: Addison Wesley.

See Also

StockWatson2007, MASchools

Examples

## data and transformations
data("CASchools")
CASchools$stratio <- with(CASchools, students/teachers)
CASchools$score <- with(CASchools, (math + read)/2)

## Stock and Watson (2007)
## p. 152
fm1 <- lm(score ~ stratio, data = CASchools)
coeftest(fm1, vcov = sandwich)

## p. 159
fm2 <- lm(score ~ I(stratio < 20), data = CASchools)
## p. 199
fm3 <- lm(score ~ stratio + english, data = CASchools)
## p. 224
fm4 <- lm(score ~ stratio + expenditure + english, data = CASchools)

## Table 7.1, p. 242 (numbers refer to columns)
fmc3 <- lm(score ~ stratio + english + lunch, data = CASchools)
fmc4 <- lm(score ~ stratio + english + calworks, data = CASchools)
fmc5 <- lm(score ~ stratio + english + lunch + calworks, data = CASchools)

## More examples can be found in:
## help("StockWatson2007")

Description

Time series of real national income in China per section (index with 1952 = 100).

Usage

data("ChinaIncome")

Format

An annual multiple time series from 1952 to 1988 with 5 variables.

agriculture

Real national income in agriculture sector.

industry

Real national income in industry sector.

construction

Real national income in construction sector.

transport

Real national income in transport sector.

commerce

Real national income in commerce sector.

Source

Online complements to Franses (1998).

References

Chow, G.C. (1993). Capital Formation and Economic Growth in China. Quarterly Journal of Economics, 103, 809–842.

Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.

See Also

Franses1998

Examples

data("ChinaIncome")
plot(ChinaIncome)

Description

Cross-section data on cigarette consumption for 46 US States, for the year 1992.

Usage

data("CigarettesB")

Format

A data frame containing 46 observations on 3 variables.

packs

Logarithm of cigarette consumption (in packs) per person of smoking age (> 16 years).

price

Logarithm of real price of cigarette in each state.

income

Logarithm of real disposable income (per capita) in each state.

Source

The data are from Baltagi (2002).

References

Baltagi, B.H. (2002). Econometrics, 3rd ed. Berlin, Springer.

Baltagi, B.H. and Levin, D. (1992). Cigarette Taxation: Raising Revenues and Reducing Consumption. Structural Change and Economic Dynamics, 3, 321–335.

See Also

Baltagi2002, CigarettesSW

Examples

data("CigarettesB")

## Baltagi (2002)
## Table 3.3
cig_lm <- lm(packs ~ price, data = CigarettesB)
summary(cig_lm)

## Chapter 5: diagnostic tests (p. 111-115)
cig_lm2 <- lm(packs ~ price + income, data = CigarettesB)
summary(cig_lm2)
## Glejser tests (p. 112)
ares <- abs(residuals(cig_lm2))
summary(lm(ares ~ income, data = CigarettesB))
summary(lm(ares ~ I(1/income), data = CigarettesB))
summary(lm(ares ~ I(1/sqrt(income)), data = CigarettesB))
summary(lm(ares ~ sqrt(income), data = CigarettesB))
## Goldfeld-Quandt test (p. 112)
gqtest(cig_lm2, order.by = ~ income, data = CigarettesB, fraction = 12, alternative = "less")
## NOTE: Baltagi computes the test statistic as mss1/mss2,
## i.e., tries to find decreasing variances. gqtest() always uses
## mss2/mss1 and has an "alternative" argument.

## Spearman rank correlation test (p. 113)
cor.test(~ ares + income, data = CigarettesB, method = "spearman")
## Breusch-Pagan test (p. 113)
bptest(cig_lm2, varformula = ~ income, data = CigarettesB, student = FALSE)
## White test (Table 5.1, p. 113)
bptest(cig_lm2, ~ income * price + I(income^2) + I(price^2), data = CigarettesB)
## White HC standard errors (Table 5.2, p. 114)
coeftest(cig_lm2, vcov = vcovHC(cig_lm2, type = "HC1"))
## Jarque-Bera test (Figure 5.2, p. 115)
hist(residuals(cig_lm2), breaks = 16, ylim = c(0, 10), col = "lightgray")
library("tseries")
jarque.bera.test(residuals(cig_lm2))

## Tables 8.1 and 8.2
influence.measures(cig_lm2)

## More examples can be found in:
## help("Baltagi2002")

Description

Panel data on cigarette consumption for the 48 continental US States from 1985–1995.

Usage

data("CigarettesSW")

Format

A data frame containing 48 observations on 7 variables for 2 periods.

state

Factor indicating state.

year

Factor indicating year.

cpi

Consumer price index.

population

State population.

packs

Number of packs per capita.

income

State personal income (total, nominal).

tax

Average state, federal and average local excise taxes for fiscal year.

price

Average price during fiscal year, including sales tax.

taxs

Average excise taxes for fiscal year, including sales tax.

Source

Online complements to Stock and Watson (2007).

References

Stock, J.H. and Watson, M.W. (2007). Introduction to Econometrics, 2nd ed. Boston: Addison Wesley.

See Also

StockWatson2007, CigarettesB

Examples

## Stock and Watson (2007)
## data and transformations 
data("CigarettesSW")
CigarettesSW <- transform(CigarettesSW,
  rprice  = price/cpi,
  rincome = income/population/cpi,
  rtax    = tax/cpi,
  rtdiff  = (taxs - tax)/cpi
)
c1985 <- subset(CigarettesSW, year == "1985")
c1995 <- subset(CigarettesSW, year == "1995")

## convenience function: HC1 covariances
hc1 <- function(x) vcovHC(x, type = "HC1")

## Equations 12.9--12.11
fm_s1 <- lm(log(rprice) ~ rtdiff, data = c1995)
coeftest(fm_s1, vcov = hc1)
fm_s2 <- lm(log(packs) ~ fitted(fm_s1), data = c1995)
fm_ivreg <- ivreg(log(packs) ~ log(rprice) | rtdiff, data = c1995)
coeftest(fm_ivreg, vcov = hc1)

## Equation 12.15
fm_ivreg2 <- ivreg(log(packs) ~ log(rprice) + log(rincome) | log(rincome) + rtdiff, data = c1995)
coeftest(fm_ivreg2, vcov = hc1)
## Equation 12.16
fm_ivreg3 <- ivreg(log(packs) ~ log(rprice) + log(rincome) | log(rincome) + rtdiff + rtax,
  data = c1995)
coeftest(fm_ivreg3, vcov = hc1)

## More examples can be found in:
## help("StockWatson2007")

Description

Cross-section data from the High School and Beyond survey conducted by the Department of Education in 1980, with a follow-up in 1986. The survey included students from approximately 1,100 high schools.

Usage

data("CollegeDistance")

Format

A data frame containing 4,739 observations on 14 variables.

gender

factor indicating gender.

ethnicity

factor indicating ethnicity (African-American, Hispanic or other).

score

base year composite test score. These are achievement tests given to high school seniors in the sample.

fcollege

factor. Is the father a college graduate?

mcollege

factor. Is the mother a college graduate?

home

factor. Does the family own their home?

urban

factor. Is the school in an urban area?

unemp

county unemployment rate in 1980.

wage

state hourly wage in manufacturing in 1980.

distance

distance from 4-year college (in 10 miles).

tuition

average state 4-year college tuition (in 1000 USD).

education

number of years of education.

income

factor. Is the family income above USD 25,000 per year?

region

factor indicating region (West or other).

Details

Rouse (1995) computed years of education by assigning 12 years to all members of the senior class. Each additional year of secondary education counted as a one year. Students with vocational degrees were assigned 13 years, AA degrees were assigned 14 years, BA degrees were assigned 16 years, those with some graduate education were assigned 17 years, and those with a graduate degree were assigned 18 years.

Stock and Watson (2007) provide separate data files for the students from Western states and the remaining students. CollegeDistance includes both data sets, subsets are easily obtained (see also examples).

Source

Online complements to Stock and Watson (2007).

References

Rouse, C.E. (1995). Democratization or Diversion? The Effect of Community Colleges on Educational Attainment. Journal of Business & Economic Statistics, 12, 217–224.

Stock, J.H. and Watson, M.W. (2007). Introduction to Econometrics, 2nd ed. Boston: Addison Wesley.

See Also

StockWatson2007

Examples

## exclude students from Western states
data("CollegeDistance")
cd <- subset(CollegeDistance, region != "west")
summary(cd)

Description

Time series of distribution, market share and price of a fast-moving consumer good.

Usage

data("ConsumerGood")

Format

A weekly multiple time series from 1989(11) to 1991(9) with 3 variables.

distribution

Distribution.

share

Market share.

price

Price.

Source

Online complements to Franses (1998).

References

Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.

See Also

Franses1998

Examples

data("ConsumerGood")
plot(ConsumerGood)

Description

Cross-section data originating from the May 1985 Current Population Survey by the US Census Bureau (random sample drawn for Berndt 1991).

Usage

data("CPS1985")

Format

A data frame containing 534 observations on 11 variables.

wage

Wage (in dollars per hour).

education

Number of years of education.

experience

Number of years of potential work experience (age - education - 6).

age

Age in years.

ethnicity

Factor with levels "cauc", "hispanic", "other".

region

Factor. Does the individual live in the South?

gender

Factor indicating gender.

occupation

Factor with levels "worker" (tradesperson or assembly line worker), "technical" (technical or professional worker), "services" (service worker), "office" (office and clerical worker), "sales" (sales worker), "management" (management and administration).

sector

Factor with levels "manufacturing" (manufacturing or mining), "construction", "other".

union

Factor. Does the individual work on a union job?

married

Factor. Is the individual married?

Source

StatLib.

https://lib.stat.cmu.edu/datasets/CPS_85_Wages

References

Berndt, E.R. (1991). The Practice of Econometrics. New York: Addison-Wesley.

See Also

CPS1988, CPSSW

Examples

data("CPS1985")

## Berndt (1991)
## Exercise 2, p. 196
cps_2b <- lm(log(wage) ~ union + education, data = CPS1985)
cps_2c <- lm(log(wage) ~ -1 + union + education, data = CPS1985)

## Exercise 3, p. 198/199
cps_3a <- lm(log(wage) ~ education + experience + I(experience^2),
  data = CPS1985)
cps_3b <- lm(log(wage) ~ gender + education + experience + I(experience^2),
  data = CPS1985)
cps_3c <- lm(log(wage) ~ gender + married + education + experience + I(experience^2),
  data = CPS1985)
cps_3e <- lm(log(wage) ~ gender*married + education + experience + I(experience^2),
  data = CPS1985)

## Exercise 4, p. 199/200
cps_4a <- lm(log(wage) ~ gender + union + ethnicity + education + experience + I(experience^2),
  data = CPS1985)
cps_4c <- lm(log(wage) ~ gender + union + ethnicity + education * experience + I(experience^2),
  data = CPS1985)

## Exercise 6, p. 203
cps_6a <- lm(log(wage) ~ gender + union + ethnicity + education + experience + I(experience^2),
  data = CPS1985)
cps_6a_noeth <- lm(log(wage) ~ gender + union + education + experience + I(experience^2),
  data = CPS1985)
anova(cps_6a_noeth, cps_6a)

## Exercise 8, p. 208
cps_8a <- lm(log(wage) ~ gender + union + ethnicity + education + experience + I(experience^2),
  data = CPS1985)
summary(cps_8a)
coeftest(cps_8a, vcov = vcovHC(cps_8a, type = "HC0"))

Description

Cross-section data originating from the March 1988 Current Population Survey by the US Census Bureau.

Usage

data("CPS1988")

Format

A data frame containing 28,155 observations on 7 variables.

wage

Wage (in dollars per week).

education

Number of years of education.

experience

Number of years of potential work experience.

ethnicity

Factor with levels "cauc" and "afam" (African-American).

smsa

Factor. Does the individual reside in a Standard Metropolitan Statistical Area (SMSA)?

region

Factor with levels "northeast", "midwest", "south", "west".

parttime

Factor. Does the individual work part-time?

Details

A sample of men aged 18 to 70 with positive annual income greater than USD 50 in 1992, who are not self-employed nor working without pay. Wages are deflated by the deflator of Personal Consumption Expenditure for 1992.

A problem with CPS data is that it does not provide actual work experience. It is therefore customary to compute experience as age - education - 6 (as was done by Bierens and Ginther, 2001), this may be considered potential experience. As a result, some respondents have negative experience.

Source

Personal web page of Herman J. Bierens.

References

Bierens, H.J., and Ginther, D. (2001). Integrated Conditional Moment Testing of Quantile Regression Models. Empirical Economics, 26, 307–324.

Buchinsky, M. (1998). Recent Advances in Quantile Regression Models: A Practical Guide for Empirical Research. Journal of Human Resources, 33, 88–126.

See Also

CPS1985, CPSSW

Examples

## data and packages
library("quantreg")
data("CPS1988")
CPS1988$region <- relevel(CPS1988$region, ref = "south")

## Model equations: Mincer-type, quartic, Buchinsky-type
mincer <- log(wage) ~ ethnicity + education + experience + I(experience^2)
quart <- log(wage) ~ ethnicity + education + experience + I(experience^2) +
  I(experience^3) + I(experience^4)
buchinsky <- log(wage) ~ ethnicity * (education + experience + parttime) + 
  region*smsa + I(experience^2) + I(education^2) + I(education*experience)

## OLS and LAD fits (for LAD see Bierens and Ginter, Tables 1-3.A.)
mincer_ols <- lm(mincer, data = CPS1988)
quart_ols <- lm(quart, data = CPS1988)
buchinsky_ols <- lm(buchinsky, data = CPS1988)

quart_lad <- rq(quart, data = CPS1988)
mincer_lad <- rq(mincer, data = CPS1988)
buchinsky_lad <- rq(buchinsky, data = CPS1988)

Description

Stock and Watson (2007) provide several subsets created from March Current Population Surveys (CPS) with data on the relationship of earnings and education over several year.

Usage

data("CPSSW9204")
data("CPSSW9298")
data("CPSSW04")
data("CPSSW3")
data("CPSSW8")
data("CPSSWEducation")

Format

CPSSW9298: A data frame containing 13,501 observations on 5 variables. CPSSW9204: A data frame containing 15,588 observations on 5 variables. CPSSW04: A data frame containing 7,986 observations on 4 variables. CPSSW3: A data frame containing 20,999 observations on 3 variables. CPSSW8: A data frame containing 61,395 observations on 5 variables. CPSSWEducation: A data frame containing 2,950 observations on 4 variables.

year

factor indicating year.

earnings

average hourly earnings (sum of annual pretax wages, salaries, tips, and bonuses, divided by the number of hours worked annually).

education

number of years of education.

degree

factor indicating highest educational degree ("bachelor" or"highschool").

gender

factor indicating gender.

age

age in years.

region

factor indicating region of residence ("Northeast", "Midwest", "South", "West").

Details

Each month the Bureau of Labor Statistics in the US Department of Labor conducts the Current Population Survey (CPS), which provides data on labor force characteristics of the population, including the level of employment, unemployment, and earnings. Approximately 65,000 randomly selected US households are surveyed each month. The sample is chosen by randomly selecting addresses from a database. Details can be found in the Handbook of Labor Statistics and is described on the Bureau of Labor Statistics website (https://www.bls.gov/).

The survey conducted each March is more detailed than in other months and asks questions about earnings during the previous year. The data sets contain data for 2004 (from the March 2005 survey), and some also for earlier years (up to 1992).

If education is given, it is for full-time workers, defined as workers employed more than 35 hours per week for at least 48 weeks in the previous year. Data are provided for workers whose highest educational achievement is a high school diploma and a bachelor's degree.

Earnings for years earlier than 2004 were adjusted for inflation by putting them in 2004 USD using the Consumer Price Index (CPI). From 1992 to 2004, the price of the CPI market basket rose by 34.6%. To make earnings in 1992 and 2004 comparable, 1992 earnings are inflated by the amount of overall CPI price inflation, by multiplying 1992 earnings by 1.346 to put them into 2004 dollars.

CPSSW9204 provides the distribution of earnings in the US in 1992 and 2004 for college-educated full-time workers aged 25–34. CPSSW04 is a subset of CPSSW9204 and provides the distribution of earnings in the US in 2004 for college-educated full-time workers aged 25–34. CPSSWEducation is similar (but not a true subset) and contains the distribution of earnings in the US in 2004 for college-educated full-time workers aged 29–30. CPSSW8 contains a larger sample with workers aged 21–64, additionally providing information about the region of residence. CPSSW9298 is similar to CPSSW9204 providing data from 1992 and 1998 (with the 1992 subsets not being exactly identical). CPSSW3 provides trends (from 1992 to 2004) in hourly earnings in the US of working college graduates aged 25–34 (in 2004 USD).

Source

Online complements to Stock and Watson (2007).

References

Stock, J.H. and Watson, M.W. (2007). Introduction to Econometrics, 2nd ed. Boston: Addison Wesley.

See Also

StockWatson2007, CPS1985, CPS1988

Examples

data("CPSSW3")
with(CPSSW3, interaction.plot(year, gender, earnings))

## Stock and Watson, p. 165
data("CPSSWEducation")
plot(earnings ~ education, data = CPSSWEducation)
fm <- lm(earnings ~ education, data = CPSSWEducation)
coeftest(fm, vcov = sandwich)
abline(fm)

Description

Cross-section data on the credit history for a sample of applicants for a type of credit card.

Usage

data("CreditCard")

Format

A data frame containing 1,319 observations on 12 variables.

card

Factor. Was the application for a credit card accepted?

reports

Number of major derogatory reports.

age

Age in years plus twelfths of a year.

income

Yearly income (in USD 10,000).

share

Ratio of monthly credit card expenditure to yearly income.

expenditure

Average monthly credit card expenditure.

owner

Factor. Does the individual own their home?

selfemp

Factor. Is the individual self-employed?

dependents

Number of dependents.

months

Months living at current address.

majorcards

Number of major credit cards held.

active

Number of active credit accounts.

Details

According to Greene (2003, p. 952) dependents equals 1 + number of dependents, our calculations suggest that it equals number of dependents.

Greene (2003) provides this data set twice in Table F21.4 and F9.1, respectively. Table F9.1 has just the observations, rounded to two digits. Here, we give the F21.4 version, see the examples for the F9.1 version. Note that age has some suspiciously low values (below one year) for some applicants. One of these differs between the F9.1 and F21.4 version.

Source

Online complements to Greene (2003). Table F21.4.

https://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm

References

Greene, W.H. (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall.

See Also

Greene2003

Examples

data("CreditCard")

## Greene (2003)
## 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)

## More examples can be found in:
## help("Greene2003")

Description

Tests the null hypothesis of equidispersion in Poisson GLMs against the alternative of overdispersion and/or underdispersion.

Usage

dispersiontest(object, trafo = NULL, alternative = c("greater", "two.sided", "less"))

Arguments

Details

The standard Poisson GLM models the (conditional) mean $\mathsf{E}[y] = \mu$ which is assumed to be equal to the variance $\mathsf{VAR}[y] = \mu$. dispersiontest assesses the hypothesis that this assumption holds (equidispersion) against the alternative that the variance is of the form:

$\mathsf{VAR}[y] \quad = \quad \mu \; + \; \alpha \cdot \mathrm{trafo}(\mu).$

Overdispersion corresponds to $\alpha > 0$ and underdispersion to $\alpha < 0$. The coefficient $\alpha$ can be estimated by an auxiliary OLS regression and tested with the corresponding t (or z) statistic which is asymptotically standard normal under the null hypothesis.

Common specifications of the transformation function $\mathrm{trafo}$ are $\mathrm{trafo}(\mu) = \mu^2$ or $\mathrm{trafo}(\mu) = \mu$. The former corresponds to a negative binomial (NB) model with quadratic variance function (called NB2 by Cameron and Trivedi, 2005), the latter to a NB model with linear variance function (called NB1 by Cameron and Trivedi, 2005) or quasi-Poisson model with dispersion parameter, i.e.,

$\mathsf{VAR}[y] \quad = \quad (1 + \alpha) \cdot \mu = \mathrm{dispersion} \cdot \mu.$

By default, for trafo = NULL, the latter dispersion formulation is used in dispersiontest. Otherwise, if trafo is specified, the test is formulated in terms of the parameter $\alpha$. The transformation trafo can either be specified as a function or an integer corresponding to the function function(x) x^trafo, such that trafo = 1 and trafo = 2 yield the linear and quadratic formulations respectively.

Value

An object of class "htest".

References

Cameron, A.C. and Trivedi, P.K. (1990). Regression-based Tests for Overdispersion in the Poisson Model. Journal of Econometrics, 46, 347–364.

Cameron, A.C. and Trivedi, P.K. (1998). Regression Analysis of Count Data. Cambridge: Cambridge University Press.

Cameron, A.C. and Trivedi, P.K. (2005). Microeconometrics: Methods and Applications. Cambridge: Cambridge University Press.

See Also

glm, poisson, glm.nb

Examples

data("RecreationDemand")
rd <- glm(trips ~ ., data = RecreationDemand, family = poisson)

## linear specification (in terms of dispersion)
dispersiontest(rd)
## linear specification (in terms of alpha)
dispersiontest(rd, trafo = 1)
## quadratic specification (in terms of alpha)
dispersiontest(rd, trafo = 2)
dispersiontest(rd, trafo = function(x) x^2)

## further examples
data("DoctorVisits")
dv <- glm(visits ~ . + I(age^2), data = DoctorVisits, family = poisson)
dispersiontest(dv)

data("NMES1988")
nmes <- glm(visits ~ health + age + gender + married + income + insurance,
  data = NMES1988, family = poisson)
dispersiontest(nmes)

Description

Dow Jones index time series computed at the end of the week where week is assumed to run from Thursday to Wednesday.

Usage

data("DJFranses")

Format

A weekly univariate time series from 1980(1) to 1994(42).

Source

Online complements to Franses (1998).

References

Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.

See Also

Franses1998

Examples

data("DJFranses")
plot(DJFranses)

Description

Time series of the Dow Jones Industrial Average (DJIA) index.

Usage

data("DJIA8012")

Format

A daily univariate time series from 1980-01-01 to 2012-12-31 (of class "zoo" with "Date" index).

Source

Online complements to Franses, van Dijk and Opschoor (2014).

https://www.cambridge.org/us/academic/subjects/economics/econometrics-statistics-and-mathematical-economics/time-series-models-business-and-economic-forecasting-2nd-edition

References

Franses, P.H., van Dijk, D. and Opschoor, A. (2014). Time Series Models for Business and Economic Forecasting, 2nd ed. Cambridge, UK: Cambridge University Press.

Examples

data("DJIA8012")
plot(DJIA8012)

# p.26, Figure 2.18
dldjia <- diff(log(DJIA8012))
plot(dldjia)

# p.141, Figure 6.4
plot(window(dldjia, start = "1987-09-01", end = "1987-12-31"))

# p.167, Figure 7.1
dldjia9005 <- window(dldjia, start = "1990-01-01", end = "2005-12-31")
qqnorm(dldjia9005)
qqline(dldjia9005, lty = 2)

# p.170, Figure 7.4
acf(dldjia9005,  na.action = na.exclude, lag.max = 250, ylim =  c(-0.1, 0.25))
acf(dldjia9005^2,  na.action = na.exclude, lag.max = 250, ylim =  c(-0.1, 0.25))
acf(abs(dldjia9005),  na.action = na.exclude, lag.max = 250, ylim =  c(-0.1, 0.25))

Description

Cross-section data originating from the 1977–1978 Australian Health Survey.

Usage

data("DoctorVisits")

Format

A data frame containing 5,190 observations on 12 variables.

visits

Number of doctor visits in past 2 weeks.

gender

Factor indicating gender.

age

Age in years divided by 100.

income

Annual income in tens of thousands of dollars.

illness

Number of illnesses in past 2 weeks.

reduced

Number of days of reduced activity in past 2 weeks due to illness or injury.

health

General health questionnaire score using Goldberg's method.

private

Factor. Does the individual have private health insurance?

freepoor

Factor. Does the individual have free government health insurance due to low income?

freerepat

Factor. Does the individual have free government health insurance due to old age, disability or veteran status?

nchronic

Factor. Is there a chronic condition not limiting activity?

lchronic

Factor. Is there a chronic condition limiting activity?

Source

Journal of Applied Econometrics Data Archive.

http://qed.econ.queensu.ca/jae/1997-v12.3/mullahy/

References

Cameron, A.C. and Trivedi, P.K. (1986). Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests. Journal of Applied Econometrics, 1, 29–53.

Cameron, A.C. and Trivedi, P.K. (1998). Regression Analysis of Count Data. Cambridge: Cambridge University Press.

Mullahy, J. (1997). Heterogeneity, Excess Zeros, and the Structure of Count Data Models. Journal of Applied Econometrics, 12, 337–350.

See Also

CameronTrivedi1998

Examples

data("DoctorVisits", package = "AER")
library("MASS")

## Cameron and Trivedi (1986), Table III, col. (1)
dv_lm <- lm(visits ~ . + I(age^2), data = DoctorVisits)
summary(dv_lm)

## Cameron and Trivedi (1998), Table 3.3 
dv_pois <- glm(visits ~ . + I(age^2), data = DoctorVisits, family = poisson)
summary(dv_pois)                  ## MLH standard errors
coeftest(dv_pois, vcov = vcovOPG) ## MLOP standard errors
logLik(dv_pois)
## standard errors denoted RS ("unspecified omega robust sandwich estimate")
coeftest(dv_pois, vcov = sandwich)

## Cameron and Trivedi (1986), Table III, col. (4)
dv_nb <- glm.nb(visits ~ . + I(age^2), data = DoctorVisits)
summary(dv_nb)
logLik(dv_nb)

Description

Time series of television and radio advertising expenditures (in real terms) in The Netherlands.

Usage

data("DutchAdvert")

Format

A four-weekly multiple time series from 1978(1) to 1994(13) with 2 variables.

tv

Television advertising expenditures.

radio

Radio advertising expenditures.

Source

Originally available as an online supplement to Franses (1998). Now available via online complements to Franses, van Dijk and Opschoor (2014).

https://www.cambridge.org/us/academic/subjects/economics/econometrics-statistics-and-mathematical-economics/time-series-models-business-and-economic-forecasting-2nd-edition

References

Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.

Franses, P.H., van Dijk, D. and Opschoor, A. (2014). Time Series Models for Business and Economic Forecasting, 2nd ed. Cambridge, UK: Cambridge University Press.

See Also

Franses1998

Examples

data("DutchAdvert")
plot(DutchAdvert)

## EACF tables (Franses 1998, Sec. 5.1, p. 99)
ctrafo <- function(x) residuals(lm(x ~ factor(cycle(x))))
ddiff <- function(x) diff(diff(x, frequency(x)), 1)
eacf <- function(y, lag = 12) {
  stopifnot(all(lag > 0))
  if(length(lag) < 2) lag <- 1:lag
  rval <- sapply(
    list(y = y, dy = diff(y), cdy = ctrafo(diff(y)),
         Dy = diff(y, frequency(y)), dDy = ddiff(y)),
    function(x) acf(x, plot = FALSE, lag.max = max(lag))$acf[lag + 1])
  rownames(rval) <- lag
  return(rval)
}

## Franses (1998, p. 103), Table 5.4
round(eacf(log(DutchAdvert[,"tv"]), lag = c(1:19, 26, 39)), digits = 3)

Description

Time series of retail sales index in The Netherlands.

Usage

data("DutchSales")

Format

A monthly univariate time series from 1960(5) to 1995(9).

Source

Online complements to Franses (1998).

References

Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.

See Also

Franses1998

Examples

data("DutchSales")
plot(DutchSales)

## EACF tables (Franses 1998, p. 99)
ctrafo <- function(x) residuals(lm(x ~ factor(cycle(x))))
ddiff <- function(x) diff(diff(x, frequency(x)), 1)
eacf <- function(y, lag = 12) {
  stopifnot(all(lag > 0))
  if(length(lag) < 2) lag <- 1:lag
  rval <- sapply(
    list(y = y, dy = diff(y), cdy = ctrafo(diff(y)),
         Dy = diff(y, frequency(y)), dDy = ddiff(y)),
    function(x) acf(x, plot = FALSE, lag.max = max(lag))$acf[lag + 1])
  rownames(rval) <- lag
  return(rval)
}

## Franses (1998), Table 5.3
round(eacf(log(DutchSales), lag = c(1:18, 24, 36)), digits = 3)

Description

Cost function data for 145 (+14) US electricity producers in 1955.

Usage

data("Electricity1955")

Format

A data frame containing 159 observations on 8 variables.

cost

total cost.

output

total output.

labor

wage rate.

laborshare

cost share for labor.

capital

capital price index.

capitalshare

cost share for capital.

fuel

fuel price.

fuelshare

cost share for fuel.

Details

The data contains several extra observations that are aggregates of commonly owned firms. Only the first 145 observations should be used for analysis.

Source

Online complements to Greene (2003). Table F14.2.

https://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm

References

Greene, W.H. (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall.

Nerlove, M. (1963) “Returns to Scale in Electricity Supply.” In C. Christ (ed.), Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld. Stanford University Press, 1963.

See Also

Greene2003, Electricity1970

Examples

data("Electricity1955")
Electricity <- Electricity1955[1:145,]

## Greene (2003)
## 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")

## 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)

## More examples can be found in:
## help("Greene2003")

Description

Cross-section data, at the firm level, on electric power generation.

Usage

data("Electricity1970")

Format

A data frame containing 158 cross-section observations on 9 variables.

cost

total cost.

output

total output.

labor

wage rate.

laborshare

cost share for labor.

capital

capital price index.

capitalshare

cost share for capital.

fuel

fuel price.

fuelshare

cost share for fuel.

Details

The data are from Christensen and Greene (1976) and pertain to the year 1970. However, the file contains some extra observations, the holding companies. Only the first 123 observations are needed to replicate Christensen and Greene (1976).

Source

Online complements to Greene (2003), Table F5.2.

https://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm

References

Christensen, L. and Greene, W.H. (1976). Economies of Scale in U.S. Electric Power Generation. Journal of Political Economy, 84, 655–676.

Greene, W.H. (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall.

See Also

Greene2003, Electricity1955

Examples

data("Electricity1970")

## Greene (2003), Ex. 5.6: a generalized Cobb-Douglas cost function
fm <- lm(log(cost/fuel) ~ log(output) + I(log(output)^2/2) + 
  log(capital/fuel) + log(labor/fuel), data=Electricity1970[1:123,])

Description

Analysis of citations of evolutionary biology papers published in 1998 in the top three journals (as judged by their 5-year impact factors in the Thomson Reuters Journal Citation Reports 2010).

Usage

data("EquationCitations")

Format

A data frame containing 649 observations on 13 variables.

journal

Factor. Journal in which the paper was published (The American Naturalist, Evolution, Proceedings of the Royal Society of London B: Biological Sciences).

authors

Character. Names of authors.

volume

Volume in which the paper was published.

startpage

Starting page of publication.

pages

Number of pages.

equations

Number of equations in total.

mainequations

Number of equations in main text.

appequations

Number of equations in appendix.

cites

Number of citations in total.

selfcites

Number of citations by the authors themselves.

othercites

Number of citations by other authors.

theocites

Number of citations by theoretical papers.

nontheocites

Number of citations by nontheoretical papers.

Details

Fawcett and Higginson (2012) investigate the relationship between the number of citations evolutionary biology papers receive, depending on the number of equations per page in the cited paper. Overall it can be shown that papers with many mathematical equations significantly lower the number of citations they receive, in particular from nontheoretical papers.

Source

Online supplements to Fawcett and Higginson (2012).

https://www.pnas.org/doi/suppl/10.1073/pnas.1205259109/suppl_file/sd01.xlsx

References

Fawcett, T.W. and Higginson, A.D. (2012). Heavy Use of Equations Impedes Communication among Biologists. PNAS – Proceedings of the National Academy of Sciences of the United States of America, 109, 11735–11739. doi:10.1073/pnas.1205259109

See Also

PhDPublications

Examples

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

## convenience function for summarizing NB models
nbtable <- function(obj, digits = 3) round(cbind(
  "OR" = exp(coef(obj)),
  "CI" = exp(confint.default(obj)),
  "Wald z" = coeftest(obj)[,3],
  "p" = coeftest(obj)[, 4]), digits = digits)


#################
## Replication ##
#################

## Table 1
m1a <- glm.nb(othercites ~ I(equations/pages) * pages + journal,
  data = EquationCitations)
m1b <- update(m1a, nontheocites ~ .)
m1c <- update(m1a, theocites ~ .)
nbtable(m1a)
nbtable(m1b)
nbtable(m1c)

## Table 2
m2a <- glm.nb(
  othercites ~ (I(mainequations/pages) + I(appequations/pages)) * pages + journal,
  data = EquationCitations)
m2b <- update(m2a, nontheocites ~ .)
m2c <- update(m2a, theocites ~ .)
nbtable(m2a)
nbtable(m2b)
nbtable(m2c)


###############
## Extension ##
###############

## nonlinear page effect: use log(pages) instead of pages+interaction
m3a <- glm.nb(othercites ~ I(equations/pages) + log(pages) + journal,
  data = EquationCitations)
m3b <- update(m3a, nontheocites ~ .)
m3c <- update(m3a, theocites ~ .)

## nested models: allow different equation effects over journals
m4a <- glm.nb(othercites ~ journal / I(equations/pages) + log(pages),
  data = EquationCitations)
m4b <- update(m4a, nontheocites ~ .)
m4c <- update(m4a, theocites ~ .)

## nested model best (wrt AIC) for all responses
AIC(m1a, m2a, m3a, m4a)
nbtable(m4a)
AIC(m1b, m2b, m3b, m4b)
nbtable(m4b)
AIC(m1c, m2c, m3c, m4c)
nbtable(m4c)
## equation effect by journal/response
##           comb nontheo theo
## AmNat     =/-  -       +
## Evolution =/+  =       +
## ProcB     -    -       =/+

Description

Statewide data on transportation equipment manufacturing for 25 US states.

Usage

data("Equipment")

Format

A data frame containing 25 observations on 4 variables.

valueadded

Aggregate output, in millions of 1957 dollars.

capital

Capital input, in millions of 1957 dollars.

labor

Aggregate labor input, in millions of man hours.

firms

Number of firms.

Source

Journal of Applied Econometrics Data Archive.

http://qed.econ.queensu.ca/jae/1998-v13.2/zellner-ryu/

Online complements to Greene (2003), Table F9.2.

https://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm

References

Greene, W.H. (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall.

Zellner, A. and Revankar, N. (1969). Generalized Production Functions. Review of Economic Studies, 36, 241–250.

Zellner, A. and Ryu, H. (1998). Alternative Functional Forms for Production, Cost and Returns to Scale Functions. Journal of Applied Econometrics, 13, 101–127.

See Also

Greene2003

Examples

## Greene (2003), Example 17.5
data("Equipment")

## 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)))

Description

Cross-section data on energy consumption for 20 European countries, for the year 1980.

Usage

data("EuroEnergy")

Format

A data frame containing 20 observations on 2 variables.

gdp

Real gross domestic product for the year 1980 (in million 1975 US dollars).

energy

Aggregate energy consumption (in million kilograms coal equivalence).

Source

The data are from Baltagi (2002).

References

Baltagi, B.H. (2002). Econometrics, 3rd ed. Berlin, Springer.

See Also

Baltagi2002

Examples

data("EuroEnergy")
energy_lm <- lm(log(energy) ~ log(gdp), data = EuroEnergy)
influence.measures(energy_lm)

Description

US traffic fatalities panel data for the “lower 48” US states (i.e., excluding Alaska and Hawaii), annually for 1982 through 1988.

Usage

data("Fatalities")

Format

A data frame containing 336 observations on 34 variables.

state

factor indicating state.

year

factor indicating year.

spirits

numeric. Spirits consumption.

unemp

numeric. Unemployment rate.

income

numeric. Per capita personal income in 1987 dollars.

emppop

numeric. Employment/population ratio.

beertax

numeric. Tax on case of beer.

baptist

numeric. Percent of southern baptist.

mormon

numeric. Percent of mormon.

drinkage

numeric. Minimum legal drinking age.

dry

numeric. Percent residing in “dry” countries.

youngdrivers

numeric. Percent of drivers aged 15–24.

miles

numeric. Average miles per driver.

breath

factor. Preliminary breath test law?

jail

factor. Mandatory jail sentence?

service

factor. Mandatory community service?

fatal

numeric. Number of vehicle fatalities.

nfatal

numeric. Number of night-time vehicle fatalities.

sfatal

numeric. Number of single vehicle fatalities.

fatal1517

numeric. Number of vehicle fatalities, 15–17 year olds.

nfatal1517

numeric. Number of night-time vehicle fatalities, 15–17 year olds.

fatal1820

numeric. Number of vehicle fatalities, 18–20 year olds.

nfatal1820

numeric. Number of night-time vehicle fatalities, 18–20 year olds.

fatal2124

numeric. Number of vehicle fatalities, 21–24 year olds.

nfatal2124

numeric. Number of night-time vehicle fatalities, 21–24 year olds.

afatal

numeric. Number of alcohol-involved vehicle fatalities.

pop

numeric. Population.

pop1517

numeric. Population, 15–17 year olds.

pop1820

numeric. Population, 18–20 year olds.

pop2124

numeric. Population, 21–24 year olds.

milestot

numeric. Total vehicle miles (millions).

unempus

numeric. US unemployment rate.

emppopus

numeric. US employment/population ratio.

gsp

numeric. GSP rate of change.

Details

Traffic fatalities are from the US Department of Transportation Fatal Accident Reporting System. The beer tax is the tax on a case of beer, which is an available measure of state alcohol taxes more generally. The drinking age variable is a factor indicating whether the legal drinking age is 18, 19, or 20. The two binary punishment variables describe the state's minimum sentencing requirements for an initial drunk driving conviction.

Total vehicle miles traveled annually by state was obtained from the Department of Transportation. Personal income was obtained from the US Bureau of Economic Analysis, and the unemployment rate was obtained from the US Bureau of Labor Statistics.

Source

Online complements to Stock and Watson (2007).

References

Ruhm, C. J. (1996). Alcohol Policies and Highway Vehicle Fatalities. Journal of Health Economics, 15, 435–454.

Stock, J. H. and Watson, M. W. (2007). Introduction to Econometrics, 2nd ed. Boston: Addison Wesley.

See Also

StockWatson2007

Examples

## data from Stock and Watson (2007)
data("Fatalities", package = "AER")
## add fatality rate (number of traffic deaths
## per 10,000 people living in that state in that year)
Fatalities$frate <- with(Fatalities, fatal/pop * 10000)
## add discretized version of minimum legal drinking age
Fatalities$drinkagec <- cut(Fatalities$drinkage,
  breaks = 18:22, include.lowest = TRUE, right = FALSE)
Fatalities$drinkagec <- relevel(Fatalities$drinkagec, ref = 4)
## any punishment?
Fatalities$punish <- with(Fatalities,
  factor(jail == "yes" | service == "yes", labels = c("no", "yes")))
## plm package
library("plm")

## for comparability with Stata we use HC1 below
## p. 351, Eq. (10.2)
f1982 <- subset(Fatalities, year == "1982")
fm_1982 <- lm(frate ~ beertax, data = f1982)
coeftest(fm_1982, vcov = vcovHC(fm_1982, type = "HC1"))

## p. 353, Eq. (10.3)
f1988 <- subset(Fatalities, year == "1988")
fm_1988 <- lm(frate ~ beertax, data = f1988)
coeftest(fm_1988, vcov = vcovHC(fm_1988, type = "HC1"))

## pp. 355, Eq. (10.8)
fm_diff <- lm(I(f1988$frate - f1982$frate) ~ I(f1988$beertax - f1982$beertax))
coeftest(fm_diff, vcov = vcovHC(fm_diff, type = "HC1"))

## pp. 360, Eq. (10.15)
##   (1) via formula
fm_sfe <- lm(frate ~ beertax + state - 1, data = Fatalities)
##   (2) by hand
fat <- with(Fatalities,
  data.frame(frates = frate - ave(frate, state),
  beertaxs = beertax - ave(beertax, state)))
fm_sfe2 <- lm(frates ~ beertaxs - 1, data = fat)
##   (3) via plm()
fm_sfe3 <- plm(frate ~ beertax, data = Fatalities,
  index = c("state", "year"), model = "within")

coeftest(fm_sfe, vcov = vcovHC(fm_sfe, type = "HC1"))[1,]
## uses different df in sd and p-value
coeftest(fm_sfe2, vcov = vcovHC(fm_sfe2, type = "HC1"))[1,]
## uses different df in p-value
coeftest(fm_sfe3, vcov = vcovHC(fm_sfe3, type = "HC1", method = "white1"))[1,]


## pp. 363, Eq. (10.21)
## via lm()
fm_stfe <- lm(frate ~ beertax + state + year - 1, data = Fatalities)
coeftest(fm_stfe, vcov = vcovHC(fm_stfe, type = "HC1"))[1,]
## via plm()
fm_stfe2 <- plm(frate ~ beertax, data = Fatalities,
  index = c("state", "year"), model = "within", effect = "twoways")
coeftest(fm_stfe2, vcov = vcovHC) ## different


## p. 368, Table 10.1, numbers refer to cols.
fm1 <- plm(frate ~ beertax, data = Fatalities, index = c("state", "year"), model = "pooling")
fm2 <- plm(frate ~ beertax, data = Fatalities, index = c("state", "year"), model = "within")
fm3 <- plm(frate ~ beertax, data = Fatalities, index = c("state", "year"), model = "within",
  effect = "twoways")
fm4 <- plm(frate ~ beertax + drinkagec + jail + service + miles + unemp + log(income),
  data = Fatalities, index = c("state", "year"), model = "within", effect = "twoways")
fm5 <- plm(frate ~ beertax + drinkagec + jail + service + miles,
  data = Fatalities, index = c("state", "year"), model = "within", effect = "twoways")
fm6 <- plm(frate ~ beertax + drinkage + punish + miles + unemp + log(income),
  data = Fatalities, index = c("state", "year"), model = "within", effect = "twoways")
fm7 <- plm(frate ~ beertax + drinkagec + jail + service + miles + unemp + log(income),
  data = Fatalities, index = c("state", "year"), model = "within", effect = "twoways")
## summaries not too close, s.e.s generally too small
coeftest(fm1, vcov = vcovHC)
coeftest(fm2, vcov = vcovHC)
coeftest(fm3, vcov = vcovHC)
coeftest(fm4, vcov = vcovHC)
coeftest(fm5, vcov = vcovHC)
coeftest(fm6, vcov = vcovHC)
coeftest(fm7, vcov = vcovHC)

## TODO: Testing exclusion restrictions

Description

Cross-section data from the 1980 US Census on married women aged 21–35 with two or more children.

Usage

data("Fertility")
data("Fertility2")

Format

A data frame containing 254,654 (and 30,000, respectively) observations on 8 variables.

morekids

factor. Does the mother have more than 2 children?

gender1

factor indicating gender of first child.

gender2

factor indicating gender of second child.

age

age of mother at census.

afam

factor. Is the mother African-American?

hispanic

factor. Is the mother Hispanic?

other

factor. Is the mother's ethnicity neither African-American nor Hispanic, nor Caucasian? (see below)

work

number of weeks in which the mother worked in 1979.

Details

Fertility2 is a random subset of Fertility with 30,000 observations.

There are conflicts in the ethnicity coding (see also examples). Hence, it was not possible to create a single factor and the original three indicator variables have been retained.

Not all variables from Angrist and Evans (1998) have been included.

Source

Online complements to Stock and Watson (2007).

References

Angrist, J.D., and Evans, W.N. (1998). Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size American Economic Review, 88, 450–477.

Stock, J.H. and Watson, M.W. (2007). Introduction to Econometrics, 2nd ed. Boston: Addison Wesley.

See Also

StockWatson2007

Examples

data("Fertility2")

## conflicts in ethnicity coding
ftable(xtabs(~ afam + hispanic + other, data = Fertility2))

## create convenience variables
Fertility2$mkids <- with(Fertility2, as.numeric(morekids) - 1)
Fertility2$samegender <- with(Fertility2, factor(gender1 == gender2))
Fertility2$twoboys <- with(Fertility2, factor(gender1 == "male" & gender2 == "male"))
Fertility2$twogirls <- with(Fertility2, factor(gender1 == "female" & gender2 == "female"))

## similar to Angrist and Evans, p. 462
fm1 <- lm(mkids ~ samegender, data = Fertility2)
summary(fm1)

fm2 <- lm(mkids ~ gender1 + gender2 + samegender + age + afam + hispanic + other, data = Fertility2)
summary(fm2)

fm3 <- lm(mkids ~ gender1 + twoboys + twogirls + age + afam + hispanic + other, data = Fertility2)
summary(fm3)

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

Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.

See Also

ArgentinaCPI, ChinaIncome, ConsumerGood, DJFranses, DutchAdvert, DutchSales, GermanUnemployment, MotorCycles, OlympicTV, PepperPrice, UKNonDurables, USProdIndex

Examples

###########################
## Convenience functions ##
###########################

## EACF tables (Franses 1998, p. 99)
ctrafo <- function(x) residuals(lm(x ~ factor(cycle(x))))
ddiff <- function(x) diff(diff(x, frequency(x)), 1)
eacf <- function(y, lag = 12) {
  stopifnot(all(lag > 0))
  if(length(lag) < 2) lag <- 1:lag
  rval <- sapply(
    list(y = y, dy = diff(y), cdy = ctrafo(diff(y)),
         Dy = diff(y, frequency(y)), dDy = ddiff(y)),
    function(x) acf(x, plot = FALSE, lag.max = max(lag))$acf[lag + 1])
  rownames(rval) <- lag
  return(rval)
}

#######################################
## Index of US industrial production ##
#######################################

data("USProdIndex", package = "AER")
plot(USProdIndex, plot.type = "single", col = 1:2)

## Franses (1998), Table 5.1
round(eacf(log(USProdIndex[,1])), digits = 3)

## Franses (1998), Equation 5.6: Unrestricted airline model
## (Franses: ma1 = 0.388 (0.063), ma4 = -0.739 (0.060), ma5 = -0.452 (0.069))
arima(log(USProdIndex[,1]), c(0, 1, 5), c(0, 1, 0), fixed = c(NA, 0, 0, NA, NA))

###########################################
## Consumption of non-durables in the UK ##
###########################################

data("UKNonDurables", package = "AER")
plot(UKNonDurables)

## Franses (1998), Table 5.2
round(eacf(log(UKNonDurables)), digits = 3)

## Franses (1998), Equation 5.51
## (Franses: sma1 = -0.632 (0.069))
arima(log(UKNonDurables), c(0, 1, 0), c(0, 1, 1))

##############################
## Dutch retail sales index ##
##############################

data("DutchSales", package = "AER")
plot(DutchSales)

## Franses (1998), Table 5.3
round(eacf(log(DutchSales), lag = c(1:18, 24, 36)), digits = 3)

###########################################
## TV and radio advertising expenditures ##
###########################################

data("DutchAdvert", package = "AER")
plot(DutchAdvert)

## Franses (1998), Table 5.4
round(eacf(log(DutchAdvert[,"tv"]), lag = c(1:19, 26, 39)), digits = 3)

Description

Monthly data on the price of frozen orange juice concentrate and temperature in the orange-growing region of Florida.

Usage

data("FrozenJuice")

Format

A monthly multiple time series from 1950(1) to 2000(12) with 3 variables.

price

Average producer price for frozen orange juice.

ppi

Producer price index for finished goods. Used to deflate the overall producer price index for finished goods to eliminate the effects of overall price inflation.

fdd

Number of freezing degree days at the Orlando, Florida, airport. Calculated as the sum of the number of degrees Fahrenheit that the minimum temperature falls below freezing (32 degrees Fahrenheit = about 0 degrees Celsius) in a given day over all days in the month: fdd = sum(max(0, 32 - minimum daily temperature)), e.g. for February fdd is the number of freezing degree days from January 11 to February 10.

Details

The orange juice price data are the frozen orange juice component of processed foods and feeds group of the Producer Price Index (PPI), collected by the US Bureau of Labor Statistics (BLS series wpu02420301). The orange juice price series was divided by the overall PPI for finished goods to adjust for general price inflation. The freezing degree days series was constructed from daily minimum temperatures recorded at Orlando area airports, obtained from the National Oceanic and Atmospheric Administration (NOAA) of the US Department of Commerce.

Source

Online complements to Stock and Watson (2007).

References

Stock, J.H. and Watson, M.W. (2007). Introduction to Econometrics, 2nd ed. Boston: Addison Wesley.

See Also

StockWatson2007

Examples

## load data
data("FrozenJuice")

## Stock and Watson, p. 594
library("dynlm")
fm_dyn <- dynlm(d(100 * log(price/ppi)) ~ fdd, data = FrozenJuice)
coeftest(fm_dyn, vcov = vcovHC(fm_dyn, type = "HC1"))

## equivalently, returns can be computed 'by hand'
## (reducing the complexity of the formula notation)
fj <- ts.union(fdd = FrozenJuice[, "fdd"],
  ret = 100 * diff(log(FrozenJuice[,"price"]/FrozenJuice[,"ppi"])))
fm_dyn <- dynlm(ret ~ fdd, data = fj)

## Stock and Watson, p. 595
fm_dl <- dynlm(ret ~ L(fdd, 0:6), data = fj)
coeftest(fm_dl, vcov = vcovHC(fm_dl, type = "HC1"))

## Stock and Watson, Table 15.1, p. 620, numbers refer to columns
## (1) Dynamic Multipliers 
fm1 <- dynlm(ret ~ L(fdd, 0:18), data = fj)
coeftest(fm1, vcov = NeweyWest(fm1, lag = 7, prewhite =  FALSE))
## (2) Cumulative Multipliers
fm2 <- dynlm(ret ~ L(d(fdd), 0:17) + L(fdd, 18), data = fj)
coeftest(fm2, vcov = NeweyWest(fm2, lag = 7, prewhite =  FALSE))
## (3) Cumulative Multipliers, more lags in NW
coeftest(fm2, vcov = NeweyWest(fm2, lag = 14, prewhite =  FALSE))
## (4) Cumulative Multipliers with monthly indicators
fm4 <- dynlm(ret ~ L(d(fdd), 0:17) + L(fdd, 18) + season(fdd), data = fj)
coeftest(fm4, vcov = NeweyWest(fm4, lag = 7, prewhite =  FALSE))
## monthly indicators needed?
fm4r <- update(fm4, . ~ . - season(fdd))
waldtest(fm4, fm4r, vcov= NeweyWest(fm4, lag = 7, prewhite = FALSE)) ## close ...

Description

Time series of unemployment rate (in percent) in Germany.

Usage

data("GermanUnemployment")

Format

A quarterly multiple time series from 1962(1) to 1991(4) with 2 variables.

unadjusted

Raw unemployment rate,

adjusted

Seasonally adjusted rate.

Source

Online complements to Franses (1998).

References

Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.

See Also

Franses1998

Examples

data("GermanUnemployment")
plot(GermanUnemployment, plot.type = "single", col = 1:2)

Description

Time series of gold and silver prices.

Usage

data("GoldSilver")

Format

A daily multiple time series from 1977-12-30 to 2012-12-31 (of class "zoo" with "Date" index).

gold

spot price for gold,

silver

spot price for silver.

Source

Online complements to Franses, van Dijk and Opschoor (2014).

https://www.cambridge.org/us/academic/subjects/economics/econometrics-statistics-and-mathematical-economics/time-series-models-business-and-economic-forecasting-2nd-edition

References

Franses, P.H., van Dijk, D. and Opschoor, A. (2014). Time Series Models for Business and Economic Forecasting, 2nd ed. Cambridge, UK: Cambridge University Press.

Examples

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

## p.31, daily returns
lgs <- log(GoldSilver)
plot(lgs[, c("silver", "gold")])

dlgs <- 100 * diff(lgs) 
plot(dlgs[, c("silver", "gold")])

## p.31, monthly log prices
lgs7812 <- window(lgs, start = as.Date("1978-01-01"))
lgs7812m <- aggregate(lgs7812, as.Date(as.yearmon(time(lgs7812))), mean)
plot(lgs7812m, plot.type = "single", lty = 1:2, lwd = 2)

## p.93, empirical ACF of absolute daily gold returns, 1978-01-01 - 2012-12-31
absgret <- abs(100 * diff(lgs7812[, "gold"]))
sacf <- acf(absgret, lag.max = 200, na.action = na.exclude, plot = FALSE)
plot(1:201, sacf$acf, ylim = c(0.04, 0.28), type = "l", xaxs = "i", yaxs = "i", las = 1)


## ARFIMA(0,1,1) model, eq. (4.44)
library("longmemo")
WhittleEst(absgret, model = "fARIMA", p = 0, q = 1, start = list(H = 0.3, MA = .25))

library("forecast")
arfima(as.vector(absgret), max.p = 0, max.q = 1)


## p.254: VAR(2), monthly data for 1986.1 - 2012.12
library("vars")

lgs8612 <- window(lgs, start = as.Date("1986-01-01"))
dim(lgs8612)

lgs8612m <- aggregate(lgs8612, as.Date(as.yearmon(time(lgs8612))), mean)
plot(lgs8612m)
dim(lgs8612m)

VARselect(lgs8612m, 5)
gs2 <- VAR(lgs8612m, 2)

summary(gs2)
summary(gs2)$covres

## ACF of residuals, p.256
acf(resid(gs2), 2, plot = FALSE)


## Figure 9.1, p.260 (somewhat different)
plot(irf(gs2, impulse = "gold", n.ahead = 50), ylim = c(-0.02, 0.1))
plot(irf(gs2, impulse = "silver", n.ahead = 50), ylim = c(-0.02, 0.1))


## Table 9.2, p.261
fevd(gs2)

## p.266
ls <- lgs8612[, "silver"]
lg <- lgs8612[, "gold"]

gsreg <- lm(lg ~ ls)
summary(gsreg)
sgreg <- lm(ls ~ lg)
summary(sgreg)

library("tseries")
adf.test(resid(gsreg), k = 0)
adf.test(resid(sgreg), k = 0)

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 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

#####################################
## 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)