Package 'desk'

Description

Calculates the autocorrelation coefficient between a vector and its k-period lag. This can be used as an estimator for rho in an AR(1) process.

Usage

acc(x, lag = 1)

Arguments

Value

Autocorrelation coefficient of lag k, numeric value.

References

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/eda/section3/eda35c.htm.

See Also

lagk, acf.

Examples

## Simulate AR(1) Process with 30 observations and positive autocorrelation
X <- ar1sim(n = 30, u0 = 2.0, rho = 0.7, var.e = 0.1)
acc(X$u.sim, lag = 1)

## Equivalent result using acf (stats)
acf(X$u.sim, lag.max = 1, plot = FALSE)$acf[2]

Description

Simulates an autoregressive process of order 1.

Usage

ar1sim(n = 50, rho, u0 = 0, var.e = 1, details = FALSE, seed = NULL)

Arguments

Value

A list object including:

Note

Objects generated by ar1sim() can be plotted using the regular plot() command.

plot.what = "time" plots simulated AR(1) values over time. Available options are

plot.what = "lag" plots simulated AR(1) values over its lagged values. Available options are

Examples

## Generate 30 positively autocorrelated errors
my.ar1 <- ar1sim(n = 30, rho = 0.9, var.e = 0.1, seed = 511)
my.ar1
plot(my.ar1$u.sim, type = 'l')

## Illustrate the effect of Rho on the AR(1)
set.seed(12)
parOrg = par(c("mfrow", "mar"))
par(mfrow = c(2,4), mar = c(1,1,1,1))
rhovalues <- c(0.1, 0.5, 0.8, 0.99)
for (i in c(0, 0.3)){
  for (rho in rhovalues){
    u.data <- ar1sim(n = 20, u0 = 2, rho = rho, var.e = i)
    plot(u.data$u.sim, plot.what = "lag", cex.legend = 0.7, xlim = c(-2.5,2.5), ylim = c(-2.5,2.5),
         acc.line = TRUE, ols.line = TRUE)
  }
}
par(mfrow = parOrg$"mfrow", mar = parOrg$"mar")

## Illustrate the effect of Rho on the (non-)stationarity of the AR(1)
set.seed(1324)
parOrg = par(c("mfrow", "mar"))
par(mfrow = c(2, 4), mar = c(1,1,1,1))
for (rho in c(0.1, 0.9, 1, 1.04, -0.1, -0.9, -1, -1.04)){
  u.data <- ar1sim(n = 25, u0 = 5, rho = rho, var.e = 0)
  plot(u.data$u.sim, plot.what = "time", ylim = c(-8,8))
}
par(mfrow = parOrg$"mfrow", mar = parOrg$"mar")

Description

Shows the arguments and their default values of a function.

Usage

arguments(fun, width = options("width")$width)

Arguments

Value

None.

See Also

args.

Examples

arguments(repeat.sample)

Description

Finds lambda-values for which the one dimensional Box-Cox model has lowest SSR.

Usage

bc.model(mod, data = list(), range = seq(-2, 2, 0.1), details = FALSE)

Arguments

Value

A list object including:

Examples

y <- c(4,1,3)
x <- c(1,2,4)
my.mod <- ols(y ~ x)
bc.model(my.mod)

Description

Box-Cox test for functional form. Compares a base model with non transformed endogenous variable to a model with logarithmic endogenous variable. Exogenous variables can be transformed or non-transformed. The object of test results returned by this command can be plotted using the plot() function.

Usage

bc.test(
  basemod,
  data = list(),
  exo = "same",
  sig.level = 0.05,
  details = TRUE,
  hyp = TRUE
)

Arguments

Value

A list object including:

References

Box, G.E.P. & Cox, D.R. (1964): An Analysis of Transformations. Journal of the Royal Statistical Society, Series B. 26, 211-243.

See Also

boxcox.

Examples

## Box-Cox test between a semi-logarithmic model and a logarithmic model
semilogmilk.est <- ols(milk ~ log(feed), data = data.milk)
results <- bc.test(semilogmilk.est, details = TRUE)

## Plot the test results
plot(results)

## Example with transformed exogenous variables
lin.est <- ols(rent ~ mult + mem + access, data = data.comp)
A <- lin.est$data
bc.test(lin.est, exo = log(cbind(A$mult, A$mem, A$access)))

Description

Breusch-Pagan test for heteroskedastic errors. The object of test results returned by this command can be plotted using the plot() function.

Usage

bp.test(
  mod,
  data = list(),
  varmod = NULL,
  koenker = TRUE,
  sig.level = 0.05,
  details = FALSE,
  hyp = TRUE
)

Arguments

Value

List object including:

References

Breusch, T.S. & Pagan, A.R. (1979): A Simple Test for Heteroscedasticity and Random Coefficient Variation. Econometrica 47, 1287-1294.

Koenker, R. (1981): A Note on Studentizing a Test for Heteroscedasticity. Journal of Econometrics 17, 107-112.

See Also

wh.test, bptest.

Examples

## BP test with Koenker's studentized residuals
X <- bp.test(wage ~ educ + age, data = data.wage, koenker = FALSE)
X

## A white test for the same model (auxiliary regression specified by \code{varmod})
bp.test(wage ~ educ + age, varmod = ~ (educ + age)^2 + I(educ^2) + I(age^2), data = data.wage)

## Similar test
wh.test(wage ~ educ + age, data = data.wage)

## Plot the test result
plot(X)

Description

If autocorrelated errors can be modeled by an AR(1) process (rho as parameter) then this function performs a Cochrane-Orcutt iteration. If model coefficients and the estimated rho value converge with the number of iterations, this procedure provides valid solutions. The object returned by this command can be plotted using the plot() function.

Usage

cochorc(
  mod,
  data = list(),
  iter = 10,
  tol = 0.0001,
  pwt = TRUE,
  details = FALSE
)

Arguments

Value

A list object including:

References

Cochrane, E. & Orcutt, G.H. (1949): Application of Least Squares Regressions to Relationships Containing Autocorrelated Error Terms. Journal of the American Statistical Association 44, 32-61.

Examples

## In this example only 2 iterations are needed to achieve (convergence of rho at the 5th digit)
sales.est <- ols(sales ~ price, data = data.filter)
cochorc(sales.est)

## For a higher precision we need 6 iterations
cochorc(sales.est, tol = 0.0000000000001)

## Direct usage of a model formula
X <- cochorc(sick ~ jobless, data = data.sick[1:14,], details = TRUE)

## See iterated regression results
X$all.regs

## Print full details
X

## Suppress details
print(X, details = FALSE)

## Plot rho over iterations to see convergence
plot(X)

## Example with interaction
dummy <-  as.numeric(data.sick$year >= 2005)
kstand.str.est <- ols(sick ~ dummy + jobless + dummy*jobless, data = data.sick)
cochorc(kstand.str.est)

Description

This data set comprises four individual x-y-data sets which have the same statistical properties (mean, variance, correlation, regression line, etc.), yet are quite different.

Usage

data.anscombe

Format

A data frame of 4 data sets, each with 11 observations of the two variables x and y.

Details

In Auer et al. (2024, Chap. 3) these data are used to illustrate the simple regression model and the importance to visually evaluate datasets before a numerical analysis is performed.

Source

This dataset was manually generated from: Anscombe, F.J. (1973): Graphs in Statistical Analysis. American Statistician, 27(1), 17-21. Also available in the R package datasets.

References

Tufte, E.R. (1989): The Visual Display of Quantitative Information, 13-14. Graphics Press.

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the prices and qualitative characteristics of US-cars sold in 1979.

Usage

data.auto

Format

A data frame with 52 observations on the following nine variables:

Details

In Auer et al. (2024, Chap. 13) these data are used to illustrate the selection process of exogenous variables.

Source

This data frame was imported from an SAS dataset provided by York University, CA

References

Originally published in: Chambers, J.M, Cleveland, W.S., Kleiner, B., Tukey, P.A. (1983): Graphical Methods for Data Analysis, Wadsworth International Group, pages 352-355.

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the percentage of defective units in the production of ball bearings.

Usage

data.ballb

Format

A data frame with six observations on the following two variables:

Details

In Auer (2023, Chap. 16) and Auer et al. (2024, Chap. 16) these hypothetical data are used to illustrate the consequences of error terms with an expected value deviating from zero.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the monthly number of burglaries and the number of power blackouts in a small town.

Usage

data.burglary

Format

A data frame with 12 observations on the following three variables:

Details

In Auer et al. (2024, Chap. 15) these hypothetical data are used to illustrate the consequences of a structural break.

Source

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

The data give the speed of cars and the distances taken to stop. The data were recorded in the 1920s.

Usage

data.cars

Format

A data frame of 50 observations with the following two variables:

Details

In Auer et al. (2024, Chaps. 5, 6, 7 & 16) the data are used to illustrate the simple regression model and the consequences of truncated data.

Source

R package datasets (object cars). Originally published in: Ezekiel, M. (1930): Methods of Correlation Analysis, Wiley.

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This data set can be used to model a Cobb-Douglas production process.

Usage

data.cobbdoug

Format

A data frame with 100 observations on the following three variables:

Details

In Auer et al. (2024, Chap. 14) these hypothetical data are used to illustrate the functional specification of a non-linear regression model.

Source

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the monthly rentals of computers of different quality during the 1960s.

Usage

data.comp

Format

A data frame with 34 observations on the following four variables:

Details

In Auer et al. (2024, Chaps. 13 & 14) these data are used to illustrate the specification of a multivariate regression model.

Source

The dataset was originally published by Chow (1967). For the purpose of desk it was imported from 3.5 inch floppy disk in ASCII format included in Berndt (1990). The dataset also available in the original format on Github.

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Chow, G.C. (1967): Technological Change and the Demand for Computers. The American Economic Review, 57, 1117–1130.

Berndt, E.R. (1990): The Practice of Econometrics: Classic and Contemporary. Addison-Wesley, 136-142.

Description

This is a data set on the shares of total EU-expenditures received by the individual member states of the EU-25 in 2005. Furthermore, the data describe some relevant characteristics (population share, gross domestic product, etc.) of these member states.

Usage

data.eu

Format

A data frame with 25 observations on the following seven variables:

Source

Imported 2007 from the Website of the EU commission and Eurostat. Published by Auer (2008).

References

Auer, L.v. (2008): Gestaltungspolitik oder Kuhhandel? Eine empirische Analyse der EU-Ausgabenpolitik, in H. Gischer, P. Reichling, T. Spengler, A. Wenig (eds.), Transformation in der Oekonomie - Festschrift fuer Gerhard Schwoediauer zum 65. Geburtstag, Gabler.

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the use of fertilizers (phosphate and nitrogen) in the cultivation of barley.

Usage

data.fertilizer

Format

A data frame with 30 observations on the following three variables:

Details

In Auer (2023, Chap. 9) and Auer et al. (2024, Chap. 9). These hypothetical data are used to illustrate the estimation of a multivariate linear regression model.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the prices and sales figures of water filters (in 1000 pcs.).

Usage

data.filter

Format

A data frame with 24 observations on the following two variables:

Details

In Auer (2023, Chap. 18) and Auer et al. (2024, Chap. 18) these hypothetical data are used to illustrate the consequences of autocorrelated error terms.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the yearly expenditures of the US-States in 2013. Furthermore, the data describe some relevant characteristics of these states.

Usage

data.govexpend

Format

A data frame with 50 observations on the following 5 variables:

Details

In Auer et al. (2024, Chap. 17) these data are used to illustrate the consequences of heteroscedastic error terms.

Source

Different datasets based on National Association of State imported in 2015:

State Expenditure Report, Table 1: Total State Expenditures - Capital Inclusive from (Budget Officers).

Annual Surveys of State and Local Government Finances, Table 1: State and Local Government Finances by Level of Government and by State 2012-13 from U.S. Census.

Real GDP by State, 2011-2014, Table 1 from U.S. Bureau of Economic Analysis.

Annual Estimates of the Resident Population for the United States, Regions, States, and Puerto Rico, Table 1 from U.S. Census.

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This hypothetical data set is on the daily revenues from selling ice cream and the daily average temperature in some town on a sample of 35 working days.

Usage

data.icecream

Format

A data frame with 35 observations on the following two variables:

Details

In Auer et al. (2024, Chap. 7) these hypothetical data are used to illustrate the estimation of the simple linear regression model.

Source

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This data set describes major macroeconomic variables determining the differences in per capita income of 75 countries in 1985.

Usage

data.income

Format

A data frame with 75 observations on the following three variables:

Details

In Auer (2023, Chap. 19) and Auer et al. (2024, Chap. 19) these data are used to illustrate the detection and consequences of error terms that are not normally distributed.

Source

Mankiw, N.G., Romer, D. & Weil, D.N. (1992): A Contribution to the Empirics of Economic Growth. Quarterly Journal of Economics, 107, 407-437

Summers, R., Heston, A. (1988): A new set of International Comparisons of Real Product and Price Levels Estimates for 130 Countries, 1950–1985, Review of Income and Wealth, 34(1), 1-25

References

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the ability and success of salespersons in selling insurance contracts.

Usage

data.insurance

Format

A data frame with 30 observations on the following four variables:

Details

In Auer (2023, Chap. 20) and Auer et al. (2024, Chap. 20) these hypothetical data illustrate the use of two stage least squares estimation with an instrumental variable.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This data set is on the use of instrumental variables.

Usage

data.iv

Format

A data frame with 8 observations on the following five variables:

Details

In Auer et al. (2024, Chap. 20) these hypothetical data are used to illustrate the use of two stage least squares estimation with instrumental variables.

Source

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

A data set describing the life satisfaction and per capita income in 40 countries in 2010.

Usage

data.lifesat

Format

A data frame of 40 observations with the following three variables:

Details

In Auer et al. (2024, Chap. 3) these data are used to illustrate the use of the simple linear regression model.

Source

Imported from World Value Survey, Inglehart et al. (2014).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Inglehart, R. et al. (2014): World Values Survey: All Rounds - Country-Pooled Datafile Version, R. Inglehart, C. Haerpfer, A. Moreno, C. Welzel, K. Kizilova, J. Diez-Medrano, M. Lagos, P. Norris, E. Ponarin & B. Puranen (eds.), Madrid: JD Systems Institute.

Description

This is a (time series) data set on macroeconomic data from Germany covering 129 consecutive quarters (Q1 1990 – Q1 2023).

Usage

data.macro

Format

A data frame with 129 observations on the following seven variables:

Details

These National Accounts data are measured in real quantities (billions of chained 2015 Euros) and are calendar and seasonally-adjusted (method: X13 JDemetra+). Theoretically, private consumption, gross investment, government expenditure, and net exports should exactly sum up to the gross domestic product. However, in practice, there are often some minor discrepancies in the data. As a result, for didactical purposes, we calculated gross investment as residuals rather than using the actual data.

Source

Imported from Federal Statistical Office of Germany, data ID: 81000-0020.

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a hypothetical data set on the use of concentrated feed for cows and their milk output.

Usage

data.milk

Format

A data frame with 12 observations on the following two variables:

Details

In Auer (2023, Chap. 14) and Auer et al. (2024, Chap. 14) these hypothetical data are used to illustrate transformations in non-linear relationships.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on quarterly commercials data of a pharmaceutical company.

Usage

data.pharma

Format

A data frame with 24 quarterly observations on the following four variables:

Details

In Auer (2023, Chap. 23) and Auer et al. (2024, Chap. 23) these hypothetical data are used to illustrate the estimation of simultaneous equation econometric models.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the prices and qualitative characteristics of laser printers from 1992 to 2001.

Usage

data.printer

Format

A data frame with 44 observations on the following five variables:

Details

In Auer (2023, Chap. 21) and Auer et al. (2024, Chap. 21) these hypothetical data are used to illustrate the consequences of multicollinear exogenous variables.

Source

Data from computer magazin c't (February 1992 to August 2001).

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on regional wages and the regional levels of the cost of living. The data set covers the 401 counties and cities of Germany.

Usage

data.regional

Format

A data frame with 401 observations on the following seven variables:

Details

In Auer et al. (2024, Chap. 22) these data are used to illustrate the estimation of simultaneous equations models.

Source

The wage data are taken from Fuchs (2018) while the cost of living data are taken from Auer and Weinand (2022). The unemployment data can be found in the report "Arbeitsmarkt in Zahlen" provided by the Bundesagentur für Arbeit. For each German State and each month, one report is published. Each report is available as Excel-sheet.

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Auer, L.v., Weinand, S. (2022): A nonlinear generalization of the Country-Product-Dummy method, Discussion Paper No. 45/2022, Deutsche Bundesbank.

Fuchs, M. (2018): Aktuelle Daten und Indikatoren - Regionale Lohnunterschiede zwischen Männern und Frauen in Deutschland, Februar 2018, Institut für Arbeitsmarkt- und Berufsforschung (IAB).

Description

This is a hypothetical data set on twelve districts of a city. The data describe the district's distance to the city center and the average basic rent (it excludes additional costs).

Usage

data.rent

Format

A data frame with 12 observations on the following four variables:

Details

In Auer (2023, Chap. 17) and Auer et al. (2024, Chap. 17) these hypothetical data are used to illustrate the consequences of heteroskedastic error terms.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de)..

Description

This data set describes the savings behavior of 50 countries in 1960-1970. The data set includes demographical variables as well as variables on disposable income.

Usage

data.savings

Format

A data frame with 50 observations on the following five variables.

Details

Under the life-cycle savings hypothesis as developed by Franco Modigliani, the savings ratio (aggregate personal saving divided by disposable income) is explained by per-capita disposable income, the percentage rate of change in per-capita disposable income, and two demographic variables: the percentage of population less than 15 years old and the percentage of the population over 75 years old. The data are averaged over the decade 1960-1970 to remove the business cycle or other short-term fluctuations.

In Auer et al. (2024, Chaps. 9, 10 & 12) the data set is used to illustrate the econometric analysis of a multivariate linear regression model.

Source

R package datasets (object LifeCycleSavings).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the unemployment rates and the sick leave in Germany in the years 1992 to 2014.

Usage

data.sick

Format

A data frame with 23 observations on the following three variables:

Details

In Auer et al. (2024, Chap. 18) these data are used to illustrate the consequences of autocorrelated error terms.

Source

Imported from Federal Statistical Office of Germany.

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a hypothetical (time series) data set on business data of a software company covering 36 consecutive months.

Usage

data.software

Format

A data frame with 36 observations on the following three variables:

Details

In Auer (2023, Chap. 22) and Auer et al. (2024, Chap. 22) these hypothetical data are used to illustrate the estimation of dynamic regression models.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

The variables in this data set are non-stationary and help to understand spurious regression in the context of time series analysis.

Usage

data.spurious

Format

A data frame with yearly observations from 1880 to 2022 on the following five variables:

Details

In Auer et al. (2024, Chap. 22) these data are used to illustrate the estimation of dynamic regression models.

Source

NASA (GISTEMP Team, 2023: GISS Surface Temperature Analysis (GISTEMP), version 4. NASA Goddard Institute for Space Studies. Dataset accessed 2023-05-11 at https://data.giss.nasa.gov/gistemp/).

IUPAC (https://iupac.org/what-we-do/periodic-table-of-elements/).

LBMA (retrieved from Deutsche Bundesbank Zeitreihen-Datenbanken, BBEX3.A.XAU.USD.EA.AC.C08).

OECD (retrieved from FRED, https://fred.stlouisfed.org/series/CPALTT01USA661S).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Lenssen, N., Schmidt, G., Hansen, J., Menne, M., Persin, A., Ruedy, R., & Zyss, D. (2019): Improvements in the GISTEMP uncertainty model. J. Geophys. Res. Atmos., 124, no. 12, 6307-6326, doi:10.1029/2018JD029522.

Description

This is a data set on the bills and the corresponding tips given in a restaurant of only 3 guests. Is can be used as minimal example to illustrate simple linear regression. The larger version of this dataset (20 guests) is available as data.tip.all.

Usage

data.tip

Format

A data frame with three observations on the following two variables:

Details

In Auer (2023, Chap. 3) and Auer et al. (2024, Chap. 3) these hypothetical data provide a minimal data set for estimating a simple linear regression model.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a hypothetical data set on the bills and the corresponding tips given in a restaurant. A reduced version of this dataset (only 3 observations) is also available as data.tip.

Usage

data.tip

Format

A data frame with 20 observations on the following two variables:

Details

In Auer (2023, Chap. 3) and Auer et al. (2024, Chap. 3) these hypothetical data provide a data set for estimating a simple linear regression model.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on German trade with its 27 EU-partners in 2014.

Usage

data.trade

Format

A data frame with 27 observations on the following five variables:

Details

In Auer et al. (2024, Chaps. 9 & 14) these data are used to illustrate the estimation and functional specification of a multivariate linear regression model.

Source

Imported from Eurostat Eurostat. Distances computed with FreeMapTools.

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on German economic growth and unemployment rates from 1992 to 2021.

Usage

data.unempl

Format

A data frame with 30 observations on the following three variables:

Details

In Auer (2023, Chap. 15) and Auer et al. (2024, Chap. 15) these yearly data are used to illustrate the estimation of regression models that exhibit a structural break.

Source

Imported from Genesis, Federal Statistical Office of Germany.

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the wage structure in a company.

Usage

data.wage

Format

A data frame with 20 observations on the following six variables:

Details

In Auer (2023, Chap. 13) and Auer et al. (2024, Chap. 13) these hypothetical data are used to illustrate the selection of the relevant exogenous variables.

Source

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

References

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

This is a data set on the business statistics of 248 branches of a car glass service company in 2015.

Usage

data.windscreen

Format

A data frame with 248 observations on the following eight variables:

Details

In Auer et al. (2024, Chap. 20) these hypothetical data illustrate the use of two stage least squares estimation with instrumental variables.

Source

Auer, L.v., Hoffmann, S. & Kranz, T. (2024): Ökonometrie - Das R-Arbeitsbuch, 2nd ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Description

Generates a table of data set names and descriptions available in package desk.

Usage

datasets()

Value

An object of class table.

Examples

datasets()

Description

Calculates density values of the null distribution in the Durbin Watson test. Uses the saddlepoint approximation by Paolella (2007).

Usage

ddw(x, mod, data = list())

Arguments

Details

The Durbin Watson Null-Distribution depends on values of the exogenous variables. That is why it must be calculated from each specific data set, respectively.

Value

Numerical density value(s).

References

Durbin, J. & Watson, G.S. (1950): Testing for Serial Correlation in Least Squares Regression I. Biometrika 37, 409-428.

Paolella (2007): Intermediate Probability - A Computational Approach, Wiley.

See Also

dw.test, pdw.

Examples

filter.est <- ols(sales ~ price, data = data.filter)
ddw(x = c(0.9, 1.7, 2.15), filter.est)

Description

Calculates the lambda deformed exponential.

Usage

def.exp(x, lambda = 0, normalize = FALSE)

Arguments

Value

The function value of the lambda deformed exponential at x.

See Also

def.log.

Examples

def.exp(3)   # Natural exponential of 3
def.exp(3,2) # Deformed by lambda = 2

Description

Calculates the lambda deformed logarithm.

Usage

def.log(x, lambda = 0, normalize = FALSE)

Arguments

Value

The function value of the lambda deformed logarithm at x.

See Also

def.exp.

Examples

def.log(3)   # Natural log of 3
def.log(3,2) # Deformed by lambda = 2

Description

Durbin-Watson Test on AR(1) autocorrelation of errors in a linear model. The object of test results returned by this command can be plotted using the plot() function.

Usage

dw.test(
  mod,
  data = list(),
  dir = c("left", "right", "both"),
  method = c("pan1", "pan2", "paol", "spa"),
  crit.val = TRUE,
  sig.level = 0.05,
  details = FALSE,
  hyp = TRUE
)

Arguments

Value

A list object including:

References

Durbin, J. & Watson, G.S. (1950): Testing for Serial Correlation in Least Squares Regression I. Biometrika 37, 409-428.

Paolella (2007): Intermediate Probability - A Computational Approach, Wiley.

See Also

ddw, pdw.

Examples

## Estimate a simple model
filter.est <- ols(sales ~ price, data = data.filter)

## Perform Durbin Watson test for positive autocorrelation rho > 0 (i.e. d < 2)
test.results <- dw.test(filter.est)

## Print the test results
test.results

## Calculate DW null-distribution and plot the test results
plot(test.results)

Description

Goldfeld-Quandt test for heteroskedastic errors. The object of test results returned by this command can be plotted using the plot() function.

Usage

gq.test(
  mod,
  data = list(),
  split = 0.5,
  omit.obs = 0,
  ah = c("increasing", "unequal", "decreasing"),
  order.by = NULL,
  sig.level = 0.05,
  details = FALSE,
  hyp = TRUE
)

Arguments

Value

A list object including:

References

Goldfeld, S.M. & Quandt, R.E. (1965): Some Tests for Homoskedasticity. Journal of the American Statistical Association 60, 539-547.

See Also

wh.test, gqtest.

Examples

## 5 observations in group 1 with the hypothesis that the variance of group 2 is larger
gq.test(rent ~ dist, split = 5, ah = "increasing", data = data.rent)

## Ordered by population size
eu.mod <- ols(expend ~ pop + gdp + farm + votes + mship, data = data.eu)
results <- gq.test(eu.mod, split = 13, order.by = data.eu$pop, details = TRUE)
results

plot(results)

Description

Calculates Whites (1980) heteroskedasticity corrected covariance matrix in a linear model.

Usage

hcc(mod, data = list(), digits = 4)

Arguments

Value

The heteroskedasticity corrected covariance matrix.

References

White, H. (1980): A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica 48, 817-838.

See Also

wh.test, bptest.

Examples

rent.est <- ols(rent ~ dist, data = data.rent)
hcc(rent.est)

hcc(wage ~ educ + age, data = data.wage)

Description

If autocorrelated errors can be modeled by an AR(1) process (rho as parameter) then this function finds the rho value that that minimizes SSR in a Prais-Winsten transformed linear model. This is known as Hildreth and Lu estimation. The object returned by this command can be plotted using the plot() function.

Usage

hilu(mod, data = list(), range = seq(-1, 1, 0.01), details = FALSE)

Arguments

Value

A list object including:

References

Hildreth, C. & Lu, J.Y. (1960): Demand Relations with Autocorrelated Disturbances. AES Technical Bulletin 276, Michigan State University.

Examples

sales.est <- ols(sales ~ price, data = data.filter)

## In this example regressions over 199 rho values between -1 and 1 are carried out
## The one with minimal SSR is printed out
hilu(sales.est)

## Direct usage of a model formula
X <- hilu(sick ~ jobless, data = data.sick[1:14,], details = TRUE)

## Print full details
X

## Suppress details
print(X, details = FALSE)

## Plot SSR over rho-values to see minimum
plot(X)

Description

Performs a two-stage least squares regression on a single equation including endogenous regressors Y and exogenous regressors X on the right hand-side. Note that by specifying the set of endogenous regressors Y by endog the set of remaining regressors X are assumed to be exogenous and therefore automatically considered as part of the instrument in the first stage of the 2SLS. These variables are not to be specified in the iv argument. Here only instrumental variables outside the equation under consideration are specified.

Usage

ivr(formula, data = list(), endog, iv, contrasts = NULL, details = FALSE, ...)

Arguments

Value

A list object including:

References

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Wooldridge, J.M. (2013): Introductory Econometrics: A Modern Approach, 5th Edition, Cengage Learning, Datasets available for download at Cengage Learning

Examples

## Numerical Illustration 20.1 in Auer (2023)
ivr(contr ~ score, endog = "score", iv = "contrprev", data = data.insurance, details = TRUE)

## Replicating an example of Ani Katchova (econometric academy)
## (https://www.youtube.com/watch?v=lm3UvcDa2Hc)
## on U.S. Women's Labor-Force Participation (data from Wooldridge 2013)
library(wooldridge)
data(mroz)

# Select only working women
mroz = mroz[mroz$"inlf" == 1,]
mroz = mroz[, c("lwage", "educ", "exper", "expersq", "fatheduc", "motheduc")]
attach(mroz)

# Regular ols of lwage on educ, where educ is suspected to be endogenous
# hence estimators are biased
ols(lwage ~ educ, data = mroz)

# Manual calculation of ols coeff
Sxy(educ, lwage)/Sxy(educ)

# Manual calculation of iv regression coeff
# with fatheduc as instrument for educ
Sxy(fatheduc, lwage)/Sxy(fatheduc, educ)

# Calculation with 2SLS
educ_hat = ols(educ ~ fatheduc)$fitted
ols(lwage ~ educ_hat)

# Verify that educ_hat is completely determined by values of fatheduc
head(cbind(educ,fatheduc,educ_hat), 10)

# Calculation with ivr()
ivr(lwage ~ educ, endog = "educ", iv = "fatheduc", data = mroz, details = TRUE)

# Multiple regression model with 1 endogenous regressor (educ)
# and two exogenous regressors (exper, expersq)

# Biased ols estimation
ols(lwage ~ educ + exper + expersq, data = mroz)

# Unbiased 2SLS estimation with fatheduc and motheduc as instruments
# for the endogenous regressor educ
ivr(lwage ~ educ + exper + expersq,
    endog = "educ", iv = c("fatheduc", "motheduc"),
    data = mroz)

# Manual 2SLS
# First stage: Regress endog. regressor on all exogen. regressors
# and instruments -> get exogenous part of educ
stage1.mod = ols(educ ~ exper + expersq + fatheduc + motheduc)
educ_hat = stage1.mod$fitted

# Second stage: Replace endog regressor with predicted value educ_hat
# See the uncorrected standard errors!
stage2.mod = ols(lwage ~ educ_hat + exper + expersq, data = mroz)

## Simple test for endogeneity of educ:
## Include endogenous part of educ into model and see if it is signif.
## (is signif. at 10% level)
uhat = ols(educ ~ exper + expersq + fatheduc + motheduc)$resid
ols(lwage ~ educ + exper + expersq + uhat)
detach(mroz)

Description

Jarque-Bera test for normality. The object of test results returned by this command can be plotted using the plot() function.

Usage

jb.test(x, data = list(), sig.level = 0.05, details = FALSE, hyp = TRUE)

Arguments

Details

Under H0 the test statistic of the Jarque-Bera test follows a chi-squared distribution with 2 degrees of freedom. If moment of order 3 (skewness) differs significantly from 0 and/or moment of order 4 (kurtosis) differs significantly from 3, H0 is rejected.

Value

A list object including:

References

Jarque, C.M. & Bera, A.K. (1980): Efficient Test for Normality, Homoscedasticity and Serial Independence of Residuals. Economics Letters 6 Issue 3, 255-259.

See Also

'jarque.test()' in Package 'moments'.

Examples

## Test response variable for normality
X <- jb.test(data.income$loginc)
X

## Estimate linear model
income.est <- ols(loginc ~ logsave + logsum, data = data.income)
## Test residuals for normality, print details
jb.test(income.est, details = TRUE)

## Equivalent test
jb.test(loginc ~ logsave + logsum, data = data.income, details = TRUE)

## Plot the test result
plot(X)

Description

Generates a matrix of a given vector and its 1 to k-period lags. Missing values due to lag are filled with NAs.

Usage

lagk(u, lag = 1, delete = TRUE)

Arguments

Value

Matrix of vector u and its 1 to k-period lags.

Examples

u = round(rnorm(10),2)
lagk(u)
lagk(u,lag = 3)
lagk(u,lag = 3, delete = FALSE)

Description

This command generates a data frame of two variables, x and y, which can be both transformed by a normalized, lambda-deformed logarithm (aka. Box-Cox-transformation). The purpose of this command is to generate data sets that represent a non-linear relationship between exogenous and endogenous variable. These data sets can be used to train linearization and heteroskedasticity issues. Note that the error term is also transformed to make it normal and homoscedastic after re-transformation to linearity. This is why generated data sets may have non-constant variance depending on the transformation parameters.

Usage

makedata.bc(
  lambda.x = 1,
  lambda.y = 1,
  a = 0,
  x.max = 5,
  n = 200,
  sigma = 1,
  seed = NULL
)

Arguments

Value

Data frame of x- and y-values.

Examples

## Compare 4 data sets generated differently
parOrg = par("mfrow")
par(mfrow = c(2,2))

## Linear data shifted by 3
A.dat <- makedata.bc(a = 3)

## Log transformed y-data
B.dat <- makedata.bc(lambda.y = 0, n = 100, sigma = 0.2, x.max = 2, seed = 123)

## Concave scatter
C.dat <- makedata.bc(lambda.y = 6, sigma = 0.4, seed = 12)

## Concave scatter, x transf.
D.dat <- makedata.bc(lambda.x = 0, lambda.y = 6, sigma = 0.4, seed = 12)

plot(A.dat, main = "linear data shifted by 3")
plot(B.dat, main = "log transformed y-data")
plot(C.dat, main = "concave scatter")
plot(D.dat, main = "concave scatter, x transf.")
par(mfrow = parOrg)

Description

This command generates a data frame of exogenous normal regression data with given correlation between the variables. This can, for example, be used for analyzing the effects of autocorrelation.

Usage

makedata.corr(n = 10, k = 2, CORR, sample = FALSE)

Arguments

Value

The generated data frame of exogenous variables.

Examples

## Generate desired correlation structure
corr.mat <- cbind(c(1, 0.7),c(0.7, 1))

## Generate 10 observations of 2 exogenous variables
X <- makedata.corr(n = 10, k = 2, CORR = corr.mat)
cor(X) # not exact values of corr.mat

## Same structure applied to a sample
X <- makedata.corr(n = 10, k = 2, CORR = corr.mat, sample = TRUE)
cor(X) # exact values of corr.mat

Description

For a given set of regressors this command calculates the coefficient of determination of a regression of one specific regressor on all combinations of the remaining regressors. This provides an overview of potential multicollinearity. Needs at least three variables. For just two regressors the square of cor() can be used.

Usage

mc.table(x, intercept = TRUE, digits = 3)

Arguments

Value

Matrix of R-squared values. The column headers indicate the respective endogenous variables that is projected on a combination of exogenous variables. Example: If we have 4 regressors x1, x2, x3, x4, then the fist column of the returned matrix has 7 rows including the R-squared values of the following regressions:

1. x1 ~ x2 + x3 + x4

2. x1 ~ x3 + x4

3. x1 ~ x2 + x4

4. x1 ~ x2 + x3

5. x1 ~ x4

6. x1 ~ x3

7. x1 ~ x2

The second column corresponds to the regressions:

1. x2 ~ x1 + x3 + x4

2. x2 ~ x3 + x4

3. x2 ~ x1 + x4

4. x2 ~ x1 + x3

5. x2 ~ x4

6. x2 ~ x3

7. x2 ~ x1

and so on.

Examples

## Replicate table 21.3 in the textbook
mc.table(data.printer[,-1])

Description

new.session removes all objects from global environment, removes all plots, clears the console, and restores parameter settings. As default, sets the working directory to source file loction in case the function is used from an R script. As an option, resets the scientific notation (e.g., 1e-04).

Usage

new.session(cd = TRUE, sci = FALSE)

Arguments

Value

None.

Examples

# No example available to avoid possibly unwanted object deletion in user environment.

Description

Estimates linear models using ordinary least squares estimation. Generated objects should be compatible with commands expecting objects generated by lm(). The object returned by this command can be plotted using the plot() function.

Usage

ols(
  formula,
  data = list(),
  na.action = NULL,
  contrasts = NULL,
  details = FALSE,
  ...
)

Arguments

Details

Let X be a model object generated by ols() then plot(X, ...) accepts the following arguments:

Value

A list object including:

Examples

## Minimal simple regression model
check <- c(10,30,50)
tip <- c(2,3,7)
tip.est <- ols(tip ~ check)

## Equivalent estimation using data argument
tip.est <- ols(y ~ x, data = data.tip)

## Show estimation results
tip.est

## Show details
print(tip.est, details = TRUE)

## Plot scatter and regression line
plot(tip.est)

## Plot confidence (dark) and prediction bands (light), residuals and two center lines
plot(tip.est, pred.int = TRUE, conf.int = TRUE, residuals = TRUE, center = TRUE)

## Multiple regression model
fert.est <- ols(barley ~ phos + nit, data = log(data.fertilizer), details = TRUE)
fert.est

Description

Checks if a linear model included a constant level parameter (alpha).

Usage

ols.has.const(mod)

Arguments

Value

A logical value: TRUE (has contant) or FALSE (has no constant).

Examples

my.modA = ols(y ~ x, data = data.tip)
my.modB = ols(y ~ 0 + x, data = data.tip)
ols.has.const(my.modA)
ols.has.const(my.modB)

Description

Calculates three common information criteria of models estimated by ols().

Usage

ols.infocrit(mod, which = "all", scaled = FALSE)

Arguments

Value

A data frame of AIC, SIC, and PC values.

Examples

wage.est <- ols(wage ~ educ + age, data = data.wage)
ols.infocrit(wage.est) # Return all criteria unscaled
ols.infocrit(wage.est, scaled = TRUE) # Return all criteria scaled
ols.infocrit(wage.est, which = "pc") # Return Prognostic Criterion unscaled

Description

Calculates different types of intervals in a linear model.

Usage

ols.interval(
  mod,
  data = list(),
  type = c("confidence", "prediction", "acceptance"),
  which.coef = "all",
  sig.level = 0.05,
  q = 0,
  dir = c("both", "left", "right"),
  xnew,
  details = FALSE
)

Arguments

Value

A list object including:

Examples

fert.est <- ols(barley ~ phos + nit, data = log(data.fertilizer))
my.mat = cbind(x1 = log(c(6,3,9)), x2 = log(c(5,3,10)))

## 95% CI for all parameters
ols.interval(fert.est)

## 95% CI for intercept and beta2
ols.interval(fert.est, which.coef = c(1,3))

## 95% CI around three true, constant y-values
ols.interval(fert.est, xnew = my.mat)

## AI for H0:beta1 = 0.5 and H0:beta2 = 0.5
ols.interval(fert.est, type = "acc", which.coef = c(2,3), q = 0.5)

## AI for H0:beta1 <= 0.5
ols.interval(fert.est, type = "acc", which.coef = 2, dir = "right", q = 0.5)

## PI (Textbook p. 285)
ols.interval(fert.est, type = "pred", xnew = c(x1 = log(29), x2 = log(120)), details = TRUE)

## Three PI
ols.interval(fert.est, type = "pred", xnew = my.mat, details = TRUE)

Description

Calculates the predicted values of a linear model based on specified values of the exogenous variables. Optionally the estimated variance of the prediction error is returned.

Usage

ols.predict(mod, data = list(), xnew, antilog = FALSE, details = FALSE)

Arguments

Value

A list object including:

Examples

## Estimate logarithmic model
fert.est <- ols(barley ~ phos + nit, data = log(data.fertilizer))

## Set new x data
my.mat = cbind(x1 = log(c(6,3,9)), x2 = log(c(5,3,10)))

## Returns fitted values
ols.predict(fert.est)

## Returns predicted values at new x-values
ols.predict(fert.est, xnew = my.mat)

## Returns re-transformed predicted values and est. var. of pred. error
ols.predict(fert.est, xnew = my.mat, antilog = TRUE, details = TRUE)

Description

Performs an F-test (non-directional) on multiple (L) linear combinations of parameters in a linear model.

Usage

par.f.test(
  mod,
  data = list(),
  nh,
  q = rep(0, dim(nh)[1]),
  sig.level = 0.05,
  details = FALSE,
  hyp = TRUE
)

Arguments

Details

Objects x generated by par.f.test can be plotted using plot(x, plot.what = ...). Argument plot.what can have the following values:

If plot.what = "ellipse" is specified, further arguments can be passed to plot():

Value

A list object including:

Examples

## H0: beta1 = 0.33 and beta2 = 0
x <- par.f.test(barley ~ phos + nit, data = log(data.fertilizer),
                 nh = rbind(c(0,1,0), c(0,0,1)),
                 q = c(0.33,0.33),
                 details = TRUE)
x # Show the test results

plot(x) # Visualize the test result
plot(x, plot.what = "ellipse", q = c(0.33, 0.33))

Description

Performs a t-test on a single parameter hypothesis or a hypothesis containing a linear combination of parameters of a linear model. The object of test results returned by this command can be plotted using the plot() function.

Usage

par.t.test(
  mod,
  data = list(),
  nh,
  q = 0,
  dir = c("both", "left", "right"),
  sig.level = 0.05,
  details = FALSE,
  hyp = TRUE
)

Arguments

Value

A list object including:

Examples

## Test H1: "phos + nit <> 1"
fert.est <- ols(barley ~ phos + nit, data = log(data.fertilizer))
x = par.t.test(fert.est, nh = c(0,1,1), q = 1, details = TRUE)
x # Show the test results

plot(x) # Visualize the test result

## Test H1: "phos > 0.5"
x = par.t.test(fert.est, nh = c(0,1,0), q = 0.5, dir = "right")
plot(x)

Description

Performs prognostic Chow test on structural break. The object of test results returned by this command can be plotted using the plot() function.

Usage

pc.test(
  mod,
  data = list(),
  split,
  sig.level = 0.05,
  details = FALSE,
  hyp = TRUE
)

Arguments

Value

A list object including:

References

Chow, G.C. (1960): Tests of Equality Between Sets of Coefficients in Two Linear Regressions. Econometrica 28, 591-605.

Examples

## Estimate model
unemp.est <- ols(unempl ~ gdp, data = data.unempl[1:14,])

## Test for immediate structural break after t = 13
X <- pc.test(unemp.est, split = 13, details = TRUE)
X

plot(X)

Description

Calculates cumulative distribution values of the null distribution in the Durbin-Watson test. Uses saddle point approximation by Paolella (2007).

Usage

pdw(x, mod, data = list())

Arguments

Details

Distribution depends on values of the exogenous variables. That is why it must be calculated from each specific data set, respectively.

Value

Numerical density value(s).

References

Paolella, M.S. (2007): Intermediate Probability - A Computational Approach, Wiley.

See Also

ddw, dw.test.

Examples

filter.est <- ols(sales ~ price, data = data.filter)
pdw(x = c(0.9, 1.7, 2.15), filter.est)

Description

This function implements an S3 method for plotting regression- and test-results generated by functions of the desk package. Used for internal purposes.

Usage

## S3 method for class 'desk'
plot(x, ...)

Arguments

Value

No return value. Called for side effects.

Examples

## Test H1: "phos + nit <> 1"
fert.est <- ols(barley ~ phos + nit, data = log(data.fertilizer))
x = par.t.test(fert.est, nh = c(0,1,1), q = 1, details = TRUE)
x # Show the test results
class(x) # Check its class
plot(x) # Visualize the test result

## Plot confidence (dark) and prediction bands (light), residuals and two center lines
## in a simple regression model
tip.est <- ols(y ~ x, data = data.tip)
class(x) # Check its class
plot(tip.est, pred.int = TRUE, conf.int = TRUE, residuals = TRUE, center = TRUE)

Description

This function implements an S3 method for printing regression- and test-results generated by functions of the desk package. Used for internal purposes.

Usage

## S3 method for class 'desk'
print(x, details, digits = 4, ...)

Arguments

Value

No return value. Called for side effects.

Examples

## Simple regression model
tip.est <- ols (y ~ x, data = data.tip)

## Check its class
class(tip.est)
#> [1] "desk" "lm"

## Standard regression output
print(tip.est) # same as tip.est

## Regression output with details rounded to 2 digits
print(tip.est, details = TRUE, digits = 2)

Description

Calculates critical values for Quandt Likelihood Ratio-test (QLR) for structural breaks with unknown break date.

Usage

qlr.cv(tAll, from = round(0.15*tAll), to = round(0.85*tAll),
L = 2, sig.level = list(0.05, 0.01, 0.1))

Arguments

Value

A list object including:

References

Quandt, R.E. (1960): Tests of the Hypothesis That a Linear Regression Obeys Two Separate Regimes. Journal of the American Statistical Association 55, 324–30.

Hansen, B. (1996): “Inference When a Nuisance Parameter is Not Identified under the Null Hypothesis,” Econometrica, 64, 413–430.

Examples

qlr.cv(20, L = 2, sig.level = 0.01)

Description

Performs Quandt Likelihood Ratio-test (QLR) for structural breaks with unknown break date. The object returned by this command can be plotted using the plot() function.

Usage

qlr.test(mod, data = list(), from, to, sig.level = 0.05, details = FALSE)

Arguments

Value

A list object including:

References

Quandt, R.E. (1960): Tests of the Hypothesis That a Linear Regression Obeys Two Separate Regimes. Journal of the American Statistical Association 55, 324–30.

Examples

unemp.est <- ols(unempl ~ gdp, data = data.unempl)
my.qlr <- qlr.test(unemp.est, from = 13, to = 17, details = TRUE)
my.qlr # Print test results

plot(my.qlr) # Plot test results

Description

This command simulates repeated samples given fixed data of the exogenous predictors and given (true) regression parameters. For each sample generated the results from an OLS regression with level parameter and confidence intervals (CIs) as well as prediction intervals are calculated.

Usage

repeat.sample(
  x,
  true.par,
  omit = 0,
  mean = 0,
  sd = 1,
  rep = 100,
  xnew = x,
  sig.level = 0.05,
  seed = NULL
)

Arguments

Details

Let X be an object generated by repeat.sample() then plot(X, ...) accepts the following arguments:

Value

A list of named data structures. Let s = number of samples, n = sample size, k = number of coefficients, t = number of new data points in xnew then:

Examples

## Generate data of two predictors
x1 = c(1,2,3,4,5)
x2 = c(2,4,5,5,6)
x = cbind(x1,x2)

## Generate list of data structures and name it "out"
out = repeat.sample(x, true.par = c(2,1,4), rep = 10)

## Extract some data
out$coef[2,8] # Extract estimated beta1 (i.e. 2nd coef) in the 8th sample
out$coef["beta1","SMPL8"] # Same as above using internal names
out$confint["beta1","upper","SMPL5"] # Extract only upper bound of CI of beta 1 from 5th sample
out$confint[,,5] # Extract CIs (upper and lower bound) for all parameters from 5th sample
out$confint[,,"SMPL5"] # Same as above using internal names
out$confint["beta1",,"SMPL5"] # Extract CI of beta 1 from 5th sample
out$u.hat[,"SMPL7"] # Extract residuals from OLS estimation of sample 7

## Generate prediction intervals at three specified points of exogenous data (xnew)
out = repeat.sample(x, true.par = c(2,1,4), rep = 10,
      xnew = cbind(x1 = c(1.5,6,7), x2 = c(1,3,5.5)))
out$predint[,,6] # Prediction intervals at the three data points of xnew in 6th sample
out$sd.pe[,6] # Estimated standard deviations of prediction errors in 6th sample
out$outside.pi # Percentage of how many intervals miss true y0 realization

## Illustrate that the relative shares of cases when the interval does not cover the
## true value approaches the significance level
out = repeat.sample(x, true.par = c(2,1,4), rep = 1000)
out$outside.ci

## Illustrate omitted variable bias
out.unbiased = repeat.sample(x, true.par = c(2,1,4))
mean(out.unbiased$coef["beta1",]) # approx. equal to beta1 = 1
out.biased = repeat.sample(x, true.par = c(2,1,4), omit = 2) # omit x2
mean(out.biased$coef["beta1",]) # not approx. equal to beta1 = 1
out.biased$bias.coef # show the true bias in coefficients

## Simulate a regression with given correlation structure in exogenous data
corr.mat = cbind(c(1, 0.9),c(0.9, 1)) # Generate desired corr. structure (high autocorrelation)
X = makedata.corr(n = 10, k = 2, CORR = corr.mat) # Generate 10 obs. of 2 exogenous variables
out = repeat.sample(X, true.par = c(2,1,4), rep = 1) # Simulate a regression
out$vcov.coef

## Illustrate confidence intervals
out = repeat.sample(c(10, 20, 30,50), true.par = c(0.2,0.13), rep = 10, seed = 12)
plot(out, plot.what = "confint")

## Plots confidence intervals of alpha with specified \code{xlim} values.
plot(out, plot.what = "confint", which.coef = 1, xlim = c(-15,15))

## Illustrate normality of dependent variable
out = repeat.sample(c(10,30,50), true.par = c(0.2,0.13), rep = 200)
plot(out, plot.what = "scatter")

## Illustrate confidence bands in a regression
plot(out, plot.what = "reglines")

Description

Ramsey's RESET for non-linear functional form. The object of test results returned by this command can be plotted using the plot() function.

Usage

reset.test(
  mod,
  data = list(),
  m = 2,
  sig.level = 0.05,
  details = FALSE,
  hyp = TRUE
)

Arguments

Value

A list object including:

References

Ramsey, J.B. (1969): Tests for Specification Error in Classical Linear Least Squares Regression Analysis. Journal of the Royal Statistical Society, Series B 31, 350-371.

See Also

resettest.

Examples

## Numerical illustration 14.2. of the textbook
X <- reset.test(milk ~ feed, m = 4, data = data.milk)
X

## Plot the test result
plot(X)

Description

Removes all objects from global environment, except those that are specified by argument keep.

Usage

rm.all(keep = NULL)

Arguments

Value

None.

Examples

# No example available to avoid possibly unwanted object deletion in user environment.

Description

Helps to (visually) detect whether a time series is stationary or non-stationary. A time series is a data-generating process with every observation - as a random variable - following a distribution. When expectational value, variance, and covariance (between different points in time) are constant, the time series is indicated as weekly dependent and seen as stationary. This desired property is a requirement to overcome the problem of spurious regression. Since there is no distribution but only one observation for each point in time, adjacent observations will be used as stand-in to calculate the indicators. Therefore, the chosen window should not be too large.

Usage

roll.win(x, window = 3, indicator = "mean", tau = NULL)

Arguments

Value

a vector of the calculated indicators.

Note

Objects generated by roll.win() can be plotted using the regular plot() command.

Examples

## Plot the expected values with a window of width 5
exp.values <- roll.win(1:100, window = 5, indicator = "mean")
plot(exp.values)

## Spurious regression example
set.seed(123)
N <- 10^3
p.values <- rep(NA, N)

for (i in 1:N) {
  x <- 1:100 + rnorm(100) # time series with trend
  y <- 1:100 + rnorm(100) # time series with trend
  p.values[i] <- summary(ols(y ~ x))$coef[2,4]
}
sum(p.values < 0.05)/N    # share of significant results (100%)

for (i in 1:N) {
  x <- rnorm(100)         # time series without trend
  y <- 1:100 + rnorm(100) # time series with trend
  p.values[i] <- summary(ols(y ~ x))$coef[2,4]
}
sum(p.values < 0.05)/N    # share of significant results (~ 5%)

Description

Adds a specified R command to file "Rprofile.site" for automatic execution during startup.

Usage

rprofile.add(line)

Arguments

Value

None.

Examples

if (FALSE) rprofile.add("library(desk)") # Makes package desk to be loaded at startup

Description

Opens the user R startup file "Rprofile.site" for viewing or editing.

Usage

rprofile.open()

Value

None.

Examples

if (FALSE) rprofile.open() # Open the file if statement = TRUE

Description

Calculates the variation of one variable or the covariation of two different variables.

Usage

Sxy(x, y = x, na.rm = FALSE)

Arguments

Value

The variaion of x or the covariation of x and y.

Examples

x = c(1, 2)
y = c(4, 1)
Sxy(x) # variation
Sxy(x, y) # covariation

## Second example illustrating the na.rm option
x = c(1, 2, NA, 4)
Sxy(x)
Sxy(x, na.rm = TRUE)

Description

White's test for heteroskedastic errors.

Usage

wh.test(mod, data = list(), sig.level = 0.05, details = FALSE, hyp = TRUE)

Arguments

Value

A list object including:

References

White, H. (1980): A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica 48, 817-838.

See Also

bptest.

Examples

## White test for a model with two regressors
X <- wh.test(wage ~ educ + age, data = data.wage)

## Show the auxiliary regression results
X$hreg

## Prettier way
print(X, details = TRUE)

## Plot the test result
plot(X)