Package 'REAT'

Description

In regional and urban economics and economic geography, very frequent research fields are the existence and evolution of agglomerations due to (internal and external) agglomeration economies, regional economic growth and regional disparities, where these concepts and relationships are closely related to each other (Capello/Nijkamp 2009, Dinc 2015, Farhauer/Kroell 2013, McCann/van Oort 2009). Also accessibility and spatial interaction modeling is mostly regarded as related to these disciplines (Aoyama et al. 2011, Guessefeldt 1999). The group of the related analysis methods is sometimes summarized by the term regional analysis or regional economic analysis (Dinc 2015, Guessefeldt 1999, Isard 1960).

This package contains a collection of models and analysis methods used in regional and urban economics and (quantitative) economic geography. The functions in this package can be divided into seven groups:

(1) Inequality, concentration and dispersion, including Gini coefficient, Lorenz curve, Herfindahl-Hirschman-coefficient, Theil coefficient, Hoover coefficient and (weighted) coefficient of variation

(2) Specialization of regions and spatial concentration of industries, including location quotient, spatial Gini coefficients for regional specialization and industry concentration and Krugman coefficients for regional specialization and industry concentration

(3) Regional disparities and regional convergence, especially analysis of beta and sigma convergence for cross-sectional data

(4) Regional growth, including portfolio matrix, several types of shift-share analysis and commercial area prognosis ("GIFPRO")

(5) Spatial interaction and accessibility models, including Huff model and Hansen accessibility

(6) Proximity analysis, including calculation of distance matrices and buffers

(7) Additional tools for data preparation und visualization, such as for creating dummy variables and calculating standardized regression coefficients. The package also contains data examples.

Author(s)

Thomas Wieland

Maintainer: Thomas Wieland [email protected]

References

Aoyama, Y./Murphy, J. T./Hanson, S. (2011): “Key Concepts in Economic Geography”. London: SAGE.

Capello, R./Nijkamp, P. (2009): “Introduction: regional growth and development theories in the twenty-first century - recent theoretical advances and future challenges”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 1-16.

Dinc, M. (2015): “Introduction to Regional Economic Development. Major Theories and Basic Analytical Tools”. Cheltenham: Elgar.

Farhauer, O./Kroell, A. (2013): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden: Springer.

Guessefeldt, J. (1999): “Regionalanalyse”. Muenchen: Oldenbourg.

Isard, W. (1960): “Methods of Regional Analysis: an Introduction to Regional Science”. Cambridge: M.I.T. Press.

McCann, P./van Oort, F. (2009): “Theories of agglomeration and regional economic growth: a historical review”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 19-32.

Description

Calculating the Atkinson Inequality Index e.g. with respect to regional income

Usage

atkinson(x, epsilon = 0.5, na.rm = TRUE)

Arguments

Details

The Atkinson Inequality Index ($AI$) varies between 0 (no inequality/concentration) and 1 (complete inequality/concentration). It can be used for economic inequality and/or regional disparities (Portnov/Felsenstein 2010).

Value

A single numeric value of the Atkinson Inequality Index ($0 < AI < 1$).

Author(s)

Thomas Wieland

References

Portnov, B.A./Felsenstein, D. (2010): “On the suitability of income inequality measures for regional analysis: Some evidence from simulation analysis and bootstrapping tests”. In: Socio-Economic Planning Sciences, 44, 4, p. 212-219.

See Also

cv, gini, gini2, herf, theil, hoover, coulter, dalton, disp

Examples

atkinson(c(100,0,0,0), epsilon = 0.8)

atkinson(c(100,100,100,100), epsilon = 0.8)

Description

Top 20 automotive industry companies, including their manufacturing quantity and turnovers (Table from wikipedia)

Usage

data("Automotive")

Format

A data frame with 20 observations on the following 8 variables.

Rank

Rank of the company

Company

Name of the company (German)

Country

Origin county of the company (German)

Quantity2014

Quantity of produced vehicles in 2014

Quantity2014_car

Quantity of produced cars in 2014

Turnover2008

Annual turnover 2008 (in billion dollars)

Turnover2012

Annual turnover 2012 (in billion dollars)

Turnover2013

Annual turnover 2013 (in billion dollars)

Source

Wikipedia (2018): “Automobilindustrie — Wikipedia, Die freie Enzyklopaedie”. https://de.wikipedia.org/wiki/Automobilindustrie (accessed October 14, 2018). Own postprocessing.

References

Wikipedia (2018): “Automobilindustrie — Wikipedia, Die freie Enzyklopaedie”. https://de.wikipedia.org/wiki/Automobilindustrie (accessed October 14, 2018).

Examples

# Market concentration in automotive industry

data(Automotive)

gini(Automotive$Turnover2008, lsize=1, lc=TRUE, le.col = "black", 
lc.col = "orange", lcx = "Shares of companies", lcy = "Shares of turnover / cars", 
lctitle = "Automotive industry: market concentration", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Turnover 2008:", lcg.lab.x = 0, lcg.lab.y = 1)
# Gini coefficient and Lorenz curve for turnover 2008

gini(Automotive$Turnover2013, lsize=1, lc = TRUE, add.lc = TRUE, lc.col = "red", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Turnover 2013:", lcg.lab.x = 0, lcg.lab.y = 0.85)
# Adding Gini coefficient and Lorenz curve for turnover 2013

gini(Automotive$Quantity2014_car, lsize=1, lc = TRUE, add.lc = TRUE, lc.col = "blue", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Cars 2014:", lcg.lab.x = 0, lcg.lab.y = 0.7)
# Adding Gini coefficient and Lorenz curve for cars 2014

Description

This function provides the analysis of absolute and conditional regional economic beta convergence for cross-sectional data using a nonlineaer least squares (NLS) technique.

Usage

betaconv.nls(gdp1, time1, gdp2, time2, conditions = NULL, conditions.formula = NULL, 
conditions.startval = NULL, beta.plot = FALSE, beta.plotPSize = 1, 
beta.plotPCol = "black", beta.plotLine = FALSE, beta.plotLineCol = "red", 
beta.plotX = "Ln (initial)", beta.plotY = "Ln (growth)", 
beta.plotTitle = "Beta convergence", beta.bgCol = "gray95", beta.bgrid = TRUE, 
beta.bgridCol = "white", beta.bgridSize = 2, beta.bgridType = "solid", 
print.results = TRUE)

Arguments

Details

From the regional economic perspective (in particular the neoclassical growth theory), regional disparities are expected to decline. This convergence can have different meanings: Sigma convergence ($\sigma$) means a harmonization of regional economic output or income over time, while beta convergence ($\beta$) means a decline of dispersion because poor regions have a stronger economic growth than rich regions (Capello/Nijkamp 2009). Regardless of the theoretical assumptions of a harmonization in reality, the related analytical framework allows to analyze both types of convergence for cross-sectional data (GDP p.c. or another economic variable, $y$, for $i$ regions and two points in time, $t$ and $t+T$), or one starting point ($t$) and the average growth within the following $n$ years ($t+1, t+2, ..., t+n$), respectively. Beta convergence can be calculated either in a linearized OLS regression model or in a nonlinear regression model. When no other variables are integrated in this model, it is called absolute beta convergence. Implementing other region-related variables (conditions) into the model leads to conditional beta convergence. If there is beta convergence ($\beta < 0$), it is possible to calculate the speed of convergence, $\lambda$, and the so-called Half-Life $H$, while the latter is the time taken to reduce the disparities by one half (Allington/McCombie 2007, Goecke/Huether 2016). There is sigma convergence, when the dispersion of the variable ($\sigma$), e.g. calculated as standard deviation or coefficient of variation, reduces from $t$ to $t+T$. This can be measured using ANOVA for two years or trend regression with respect to several years (Furceri 2005, Goecke/Huether 2016).

This function calculates absolute and/or conditional beta convergence using a nonlinear least squares approach for estimation. It needs at least two vectors (GDP p.c. or another economic variable, $y$, for $i$ regions) and the related two points in time ($t$ and $t+T$). If the beta coefficient is negative (using OLS) or positive (using NLS), there is beta convergence.

Value

A list containing the following objects:

Author(s)

Thomas Wieland

References

Allington, N. F. B./McCombie, J. S. L. (2007): “Economic growth and beta-convergence in the East European Transition Economies”. In: Arestis, P./Baddely, M./McCombie, J. S. L. (eds.): Economic Growth. New Directions in Theory and Policy. Cheltenham: Elgar. p. 200-222.

Capello, R./Nijkamp, P. (2009): “Introduction: regional growth and development theories in the twenty-first century - recent theoretical advances and future challenges”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 1-16.

Dapena, A. D./Vazquez, E. F./Morollon, F. R. (2016): “The role of spatial scale in regional convergence: the effect of MAUP in the estimation of beta-convergence equations”. In: The Annals of Regional Science, 56, 2, p. 473-489.

Furceri, D. (2005): “Beta and sigma-convergence: A mathematical relation of causality”. In: Economics Letters, 89, 2, p. 212-215.

Goecke, H./Huether, M. (2016): “Regional Convergence in Europe”. In: Intereconomics, 51, 3, p. 165-171.

Young, A. T./Higgins, M. J./Levy, D. (2008): “Sigma Convergence versus Beta Convergence: Evidence from U.S. County-Level Data”. In: Journal of Money, Credit and Banking, 40, 5, p. 1083-1093.

See Also

rca, betaconv.ols, betaconv.speed, sigmaconv, sigmaconv.t, cv, sd2, var2

Examples

data (G.counties.gdp)
# Loading GDP data for Germany (counties = Landkreise)
betaconv.nls (G.counties.gdp$gdppc2010, 2010, G.counties.gdp$gdppc2011, 2011, 
conditions = NULL, print.results = TRUE)
# Two years, no conditions (Absolute beta convergence)

Description

This function provides the analysis of absolute and conditional regional economic beta convergence for cross-sectional data using ordinary least squares (OLS) technique.

Usage

betaconv.ols(gdp1, time1, gdp2, time2, conditions = NULL, beta.plot = FALSE, 
beta.plotPSize = 1, beta.plotPCol = "black", beta.plotLine = FALSE, 
beta.plotLineCol = "red", beta.plotX = "Ln (initial)", beta.plotY = "Ln (growth)", 
beta.plotTitle = "Beta convergence", beta.bgCol = "gray95", beta.bgrid = TRUE,
beta.bgridCol = "white", beta.bgridSize = 2, beta.bgridType = "solid", 
print.results = FALSE)

Arguments

Details

From the regional economic perspective (in particular the neoclassical growth theory), regional disparities are expected to decline. This convergence can have different meanings: Sigma convergence ($\sigma$) means a harmonization of regional economic output or income over time, while beta convergence ($\beta$) means a decline of dispersion because poor regions have a stronger economic growth than rich regions (Capello/Nijkamp 2009). Regardless of the theoretical assumptions of a harmonization in reality, the related analytical framework allows to analyze both types of convergence for cross-sectional data (GDP p.c. or another economic variable, $y$, for $i$ regions and two points in time, $t$ and $t+T$), or one starting point ($t$) and the average growth within the following $n$ years ($t+1, t+2, ..., t+n$), respectively. Beta convergence can be calculated either in a linearized OLS regression model or in a nonlinear regression model. When no other variables are integrated in this model, it is called absolute beta convergence. Implementing other region-related variables (conditions) into the model leads to conditional beta convergence. If there is beta convergence ($\beta < 0$), it is possible to calculate the speed of convergence, $\lambda$, and the so-called Half-Life $H$, while the latter is the time taken to reduce the disparities by one half (Allington/McCombie 2007, Goecke/Huether 2016). There is sigma convergence, when the dispersion of the variable ($\sigma$), e.g. calculated as standard deviation or coefficient of variation, reduces from $t$ to $t+T$. This can be measured using ANOVA for two years or trend regression with respect to several years (Furceri 2005, Goecke/Huether 2016).

This function calculates absolute and/or conditional beta convergence using ordinary least squares regression (OLS) for estimation. It needs at least two vectors (GDP p.c. or another economic variable, $y$, for $i$ regions) and the related two points in time ($t$ and $t+T$). If the beta coefficient is negative (using OLS) or positive (using NLS), there is beta convergence.

Value

A list containing the following objects:

Author(s)

Thomas Wieland

References

Allington, N. F. B./McCombie, J. S. L. (2007): “Economic growth and beta-convergence in the East European Transition Economies”. In: Arestis, P./Baddely, M./McCombie, J. S. L. (eds.): Economic Growth. New Directions in Theory and Policy. Cheltenham: Elgar. p. 200-222.

Capello, R./Nijkamp, P. (2009): “Introduction: regional growth and development theories in the twenty-first century - recent theoretical advances and future challenges”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 1-16.

Dapena, A. D./Vazquez, E. F./Morollon, F. R. (2016): “The role of spatial scale in regional convergence: the effect of MAUP in the estimation of beta-convergence equations”. In: The Annals of Regional Science, 56, 2, p. 473-489.

Furceri, D. (2005): “Beta and sigma-convergence: A mathematical relation of causality”. In: Economics Letters, 89, 2, p. 212-215.

Goecke, H./Huether, M. (2016): “Regional Convergence in Europe”. In: Intereconomics, 51, 3, p. 165-171.

Young, A. T./Higgins, M. J./Levy, D. (2008): “Sigma Convergence versus Beta Convergence: Evidence from U.S. County-Level Data”. In: Journal of Money, Credit and Banking, 40, 5, p. 1083-1093.

See Also

rca, betaconv.nls, betaconv.speed, sigmaconv, sigmaconv.t, cv, sd2, var2

Examples

data (G.counties.gdp)

betaconv.ols (G.counties.gdp$gdppc2010, 2010, G.counties.gdp$gdppc2011, 2011, 
conditions = NULL, print.results = TRUE)
# Two years, no conditions (Absolute beta convergence)

regionaldummies <- to.dummy(G.counties.gdp$regional)
# Creating dummy variables for West/East
G.counties.gdp$West <- regionaldummies[,2]
G.counties.gdp$East <- regionaldummies[,1]
# Adding dummy variables to data

betaconv.ols (G.counties.gdp$gdppc2010, 2010, G.counties.gdp$gdppc2011, 2011, 
conditions = G.counties.gdp[c(70,71)], print.results = TRUE)
# Two years, with condition (dummy for West/East)
# (Absolute and conditional beta convergence)

betaconverg1 <- betaconv.ols (G.counties.gdp$gdppc2010, 2010, G.counties.gdp$gdppc2011, 2011,
conditions = G.counties.gdp[c(70,71)], print.results = TRUE)
# Store results in object
betaconverg1$cbeta$estimates
# Addressing estimates for the conditional beta model


betaconv.ols (G.counties.gdp$gdppc2010, 2010, G.counties.gdp[65:66], 2012, 
conditions = NULL, print.results = TRUE)
# Three years (2010-2012), no conditions (Absolute beta convergence)

betaconv.ols (G.counties.gdp$gdppc2010, 2010, G.counties.gdp[65:66], 2012, 
conditions = G.counties.gdp[c(70,71)], print.results = TRUE)
# Three years (2010-2012), with conditions (Absolute and conditional beta convergence)

betaconverg2 <- betaconv.ols (G.counties.gdp$gdppc2010, 2010, G.counties.gdp[65:66],
2012, conditions = G.counties.gdp[c(70,71)], print.results = TRUE)
# Store results in object
betaconverg2$cbeta$estimates
# Addressing estimates for the conditional beta model

Description

This function calculates the beta convergence speed and half-life based on a given beta value and time interval.

Usage

betaconv.speed(beta, tinterval, print.results = TRUE)

Arguments

Details

From the regional economic perspective (in particular the neoclassical growth theory), regional disparities are expected to decline. This convergence can have different meanings: Sigma convergence ($\sigma$) means a harmonization of regional economic output or income over time, while beta convergence ($\beta$) means a decline of dispersion because poor regions have a stronger economic growth than rich regions (Capello/Nijkamp 2009). Regardless of the theoretical assumptions of a harmonization in reality, the related analytical framework allows to analyze both types of convergence for cross-sectional data (GDP p.c. or another economic variable, $y$, for $i$ regions and two points in time, $t$ and $t+T$), or one starting point ($t$) and the average growth within the following $n$ years ($t+1, t+2, ..., t+n$), respectively. Beta convergence can be calculated either in a linearized OLS regression model or in a nonlinear regression model. When no other variables are integrated in this model, it is called absolute beta convergence. Implementing other region-related variables (conditions) into the model leads to conditional beta convergence. If there is beta convergence ($\beta < 0$), it is possible to calculate the speed of convergence, $\lambda$, and the so-called Half-Life $H$, while the latter is the time taken to reduce the disparities by one half (Allington/McCombie 2007, Goecke/Huether 2016). There is sigma convergence, when the dispersion of the variable ($\sigma$), e.g. calculated as standard deviation or coefficient of variation, reduces from $t$ to $t+T$. This can be measured using ANOVA for two years or trend regression with respect to several years (Furceri 2005, Goecke/Huether 2016).

This function calculates the speed of convergence, $\lambda$, and the Half-Life, $H$, based on a given $\beta$ value and time interval.

Value

A matrix containing the following objects:

Author(s)

Thomas Wieland

References

Allington, N. F. B./McCombie, J. S. L. (2007): “Economic growth and beta-convergence in the East European Transition Economies”. In: Arestis, P./Baddely, M./McCombie, J. S. L. (eds.): Economic Growth. New Directions in Theory and Policy. Cheltenham: Elgar. p. 200-222.

Capello, R./Nijkamp, P. (2009): “Introduction: regional growth and development theories in the twenty-first century - recent theoretical advances and future challenges”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 1-16.

Dapena, A. D./Vazquez, E. F./Morollon, F. R. (2016): “The role of spatial scale in regional convergence: the effect of MAUP in the estimation of beta-convergence equations”. In: The Annals of Regional Science, 56, 2, p. 473-489.

Furceri, D. (2005): “Beta and sigma-convergence: A mathematical relation of causality”. In: Economics Letters, 89, 2, p. 212-215.

Goecke, H./Huether, M. (2016): “Regional Convergence in Europe”. In: Intereconomics, 51, 3, p. 165-171.

Young, A. T./Higgins, M. J./Levy, D. (2008): “Sigma Convergence versus Beta Convergence: Evidence from U.S. County-Level Data”. In: Journal of Money, Credit and Banking, 40, 5, p. 1083-1093.

See Also

betaconv.nls, betaconv.ols, sigmaconv, sigmaconv.t, cv, sd2, var2

Examples

speed <- betaconv.speed(-0.008070533, 1)
speed[1] # lambda
speed[2] # half-life

Description

Calculating three measures of industry concentration (Gini, Krugman, Hoover) for a set of $I$ industries

Usage

conc(e_ij, industry.id, region.id, na.rm = TRUE)

Arguments

Details

This function is a convenient wrapper for all functions calculating measures of spatial concentration of industries (Gini, Krugman, Hoover)

Value

A matrix with three columns (Gini coefficient, Krugman coefficient, Hoover coefficient) and $I$ rows (one for each regarded industry).

Author(s)

Thomas Wieland

References

Farhauer, O./Kroell, A. (2014): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Schaetzl, L. (2000): “Wirtschaftsgeographie 2: Empirie”. Paderborn : Schoeningh.

See Also

gini.conc, krugman.conc2, hoover

Examples

data(G.regions.industries)

conc_i <- conc (e_ij = G.regions.industries$emp_all, 
industry.id = G.regions.industries$ind_code,
region.id = G.regions.industries$region_code)

Description

Calculating the breaking point between two cities or retail locations

Usage

converse(P_a, P_b, D_ab)

Arguments

Details

The breaking point formula by Converse (1949) is a modification of the law of retail gravitation by Reilly (1929, 1931) (see the functions reilly and reilly.lambda). The aim of the calculation is to determine the boundaries of the market areas between two locations/cities in consideration of their attractivity/population size and the transport costs (e.g. distance) between them. The models by Reilly and Converse are simple spatial interaction models and are considered as deterministic market area models due to their exact allocation of demand origins to locations. A probabilistic approach including a theoretical framework was developed by Huff (1962) (see the function huff).

Value

a list with two values (B_a: distance from location $a$ to breaking point, B_b: distance from location $b$ to breaking point)

Author(s)

Thomas Wieland

References

Berman, B. R./Evans, J. R. (2012): “Retail Management: A Strategic Approach”. 12th edition. Bosten : Pearson.

Converse, P. D. (1949): “New Laws of Retail Gravitation”. In: Journal of Marketing, 14, 3, p. 379-384.

Huff, D. L. (1962): “Determination of Intra-Urban Retail Trade Areas”. Los Angeles : University of California.

Levy, M./Weitz, B. A. (2012): “Retailing management”. 8th edition. New York : McGraw-Hill Irwin.

Loeffler, G. (1998): “Market areas - a methodological reflection on their boundaries”. In: GeoJournal, 45, 4, p. 265-272

Reilly, W. J. (1929): “Methods for the Study of Retail Relationships”. Studies in Marketing, 4. Austin : Bureau of Business Research, The University of Texas.

Reilly, W. J. (1931): “The Law of Retail Gravitation”. New York.

See Also

huff, reilly

Examples

# Example from Huff (1962):
converse (400000, 200000, 80)
# two cities (population 400.000 and 200.000 with a distance separating them of 80 miles)

Description

Calculating the Coulter Coefficient e.g. with respect to regional income

Usage

coulter(x, weighting = NULL, na.rm = TRUE)

Arguments

Details

The Coulter Coefficient ($CC$) varies between 0 (no inequality/concentration) and 1 (complete inequality/concentration). It can be used for economic inequality and/or regional disparities (Portnov/Felsenstein 2010).

Value

A single numeric value of the Coulter Coefficient ($0 < CC < 1$).

Author(s)

Thomas Wieland

References

Portnov, B.A./Felsenstein, D. (2010): “On the suitability of income inequality measures for regional analysis: Some evidence from simulation analysis and bootstrapping tests”. In: Socio-Economic Planning Sciences, 44, 4, p. 212-219.

See Also

cv, gini, gini2, herf, theil, hoover, atkinson, dalton, disp

Examples

bip <- c(400,400,400, 400, NA)
bev <- c(1,1,1,200, NA)
coulter(bip, bev)

Description

Curve fitting (similar to SPSS and Excel)

Usage

curvefit(x, y, y.max = NULL, extrapol = NULL, 
plot.curves = TRUE, pcol = "black", ptype = 19, psize = 1,
lin.col = "blue", pow.col = "green", exp.col = "orange", logi.col = "red",
plot.title = "Curve fitting", plot.legend = TRUE,
xlab = "x", ylab = "y", y.min = NULL, ..., print.results = TRUE)

Arguments

Details

Curve fitting for a given independent and dependent variable ($y = f(x)$). Similar to curve fitting in SPSS or Excel. Fitting of nonlinear regression models (power, exponential, logistic) via intrinsically linear models (Rawlings et al. 1998).

Value

A data frame containing the regression results (Parameters a and b, std. errors, t values, ...)

Author(s)

Thomas Wieland

References

Rawlings, J. O./Pantula, S. G./Dickey, D. A. (1998): “Applied Regression Analysis”. Springer. 2nd edition.

Examples

x <- 1:20
y <- 3-2*x
curvefit(x, y, plot.curves = TRUE)
# fit with plot
curvefit(x, y, extrapol=10, plot.curves = TRUE)
# fit and extrapolation with plot

x <- runif(20, min = 0, max = 100)
# some random data

# linear
y_resid <- runif(20, min = 0, max = 10)
# random residuals
y <- 3+(-0.112*x)+y_resid
curvefit(x, y)

# power
y_resid <- runif(20, min = 0.1, max = 0.2)
# random residuals
y <- 3*(x^-0.112)*y_resid
curvefit(x, y)

# exponential
y_resid <- runif(20, min = 0.1, max = 0.2)
# random residuals
y <- 3*exp(-0.112*x)*y_resid
curvefit(x, y)

# logistic
y_resid <- runif(20, min = 0.1, max = 0.2)
# random residuals
y <- 100/(1+exp(3+(-0.112*x)))*y_resid
curvefit(x, y)

Description

Calculating the coefficient of variation (cv), standardized and non-standardized, weighted and non-weighted

Usage

cv (x, is.sample = TRUE, coefnorm = FALSE, weighting = NULL, 
wmean = FALSE, na.rm = TRUE)

Arguments

Details

The coefficient of variation, $v$, is a dimensionless measure of statistical dispersion ($0 < v < \infty$), based on variance and standard deviation, respectively. From a regional economic perspective, it is closely linked to the concept of sigma convergence ($\sigma$) which means a harmonization of regional economic output or income over time, while the other type of convergence, beta convergence ($\beta$), means a decline of dispersion because poor regions have a stronger growth than rich regions (Capello/Nijkamp 2009). The cv allows to summarize regional disparities (e.g. disparities in regional GDP per capita) in one indicator and is more frequently used for this purpose than the standard deviation, especially in analyzing of $\sigma$ convergence over a long period (e.g. Lessmann 2005, Huang/Leung 2009, Siljak 2015). But the cv can also be used for any other types of disparities or dispersion, such as disparities in supply (e.g. density of physicians or grocery stores).

The cv (variance, standard deviation) can be weighted by using a second weighting vector. As there is more than one way to weight measures of statistical dispersion, this function uses the formula for the weighted cv ($v_w$) from Sheret (1984). The cv can be standardized, while this function uses the formula for the standardized cv ($v*$, with $0 < v* < 1$) from Kohn/Oeztuerk (2013). The vector x is automatically treated as a sample (such as in the base sd function), so the denominator of variance is $n-1$, if it is not, set is.sample = FALSE.

Value

Single numeric value. If coefnorm = FALSE the function returns the non-standardized cv ($0 < v < \infty$). If coefnorm = TRUE the standardized cv ($0 < v* < 1$) is returned.

Author(s)

Thomas Wieland

References

Bahrenberg, G./Giese, E./Mevenkamp, N./Nipper, J. (2010): “Statistische Methoden in der Geographie. Band 1: Univariate und bivariate Statistik”. Stuttgart: Borntraeger.

Capello, R./Nijkamp, P. (2009): “Introduction: regional growth and development theories in the twenty-first century - recent theoretical advances and future challenges”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 1-16.

Lessmann, C. (2005): “Regionale Disparitaeten in Deutschland und ausgesuchten OECD-Staaten im Vergleich”. ifo Dresden berichtet, 3/2005. https://www.ifo.de/DocDL/ifodb_2005_3_25-33.pdf.

Huang, Y./Leung, Y. (2009): “Measuring Regional Inequality: A Comparison of Coefficient of Variation and Hoover Concentration Index”. In: The Open Geography Journal, 2, p. 25-34.

Kohn, W./Oeztuerk, R. (2013): “Statistik fuer Oekonomen. Datenanalyse mit R und SPSS”. Berlin: Springer.

Sheret, M. (1984): “The Coefficient of Variation: Weighting Considerations”. In: Social Indicators Research, 15, 3, p. 289-295.

Siljak, D. (2015): “Real Economic Convergence in Western Europe from 1995 to 2013”. In: International Journal of Business and Economic Development, 3, 3, p. 56-67.

See Also

gini, herf, hoover, rca

Examples

# Regional disparities / sigma convergence in Germany
data(G.counties.gdp)
# GDP per capita for German counties (Landkreise)
cvs <- apply (G.counties.gdp[54:68], MARGIN = 2, FUN = cv)
# Calculating cv for the years 2000-2014
years <- 2000:2014
plot(years, cvs, "l", ylim=c(0.3,0.6), xlab = "year", 
ylab = "CV of GDP per capita")
# Plot cv over time

Description

Calculating the Dalton Inequality Index e.g. with respect to regional income

Usage

dalton(x, na.rm = TRUE)

Arguments

Details

The Dalton Inequality Index ($\delta$) can be used for economic inequality and/or regional disparities (Portnov/Felsenstein 2010).

Value

A single numeric value of the Dalton Inequality Index.

Author(s)

Thomas Wieland

References

Portnov, B.A./Felsenstein, D. (2010): “On the suitability of income inequality measures for regional analysis: Some evidence from simulation analysis and bootstrapping tests”. In: Socio-Economic Planning Sciences, 44, 4, p. 212-219.

See Also

cv, gini, gini2, herf, theil, hoover, coulter, dalton, disp

Examples

dalton (c(10,10,10,10))

dalton (c(10,0,0,0))

dalton (c(10,1,1,1))

Description

Calculating a set of concentration/inequality/dispersion measures

Usage

disp(x, weighting = NULL, at.epsilon = 0.5, na.rm = TRUE)

Arguments

Details

This function is a convenient wrapper for all functions calculating concentration/inequality measures.

Value

A matrix containing the concentration/inequality measures.

Author(s)

Thomas Wieland

References

Gluschenko, K. (2018): “Measuring regional inequality: to weight or not to weight?” In: Spatial Economic Analysis, 13, 1, p. 36-59.

Portnov, B.A./Felsenstein, D. (2010): “On the suitability of income inequality measures for regional analysis: Some evidence from simulation analysis and bootstrapping tests”. In: Socio-Economic Planning Sciences, 44, 4, p. 212-219.

See Also

atkinson, coulter, dalton, cv, gini2, herf, hoover, sd2, theil, williamson

Examples

data(Automotive)

disp(Automotive$Turnover2008)
disp(Automotive[4:8])

Description

Counting points within a buffer of a given distance with points with given coordinates

Usage

dist.buf(startpoints, sp_id, lat_start, lon_start, endpoints, ep_id, lat_end, lon_end, 
ep_sum = NULL, bufdist = 500, extract_local = TRUE, unit = "m")

Arguments

Details

The function is based on the idea of a buffer analysis in GIS (Geographic Information System), e.g. to count the points of interest within a given buffer distance.

Value

The function returns a list containing:

Author(s)

Thomas Wieland

References

de Lange, N. (2013): “Geoinformatik in Theorie und Praxis”. 3rd edition. Berlin : Springer Spektrum.

Krider, R. E./Putler, R. S. (2013): “Which Birds of a Feather Flock Together? Clustering and Avoidance Patterns of Similar Retail Outlets”. In: Geographical Analysis, 45, 2, p. 123-149

See Also

dist, dist.mat

Examples

citynames <- c("Goettingen", "Karlsruhe", "Freiburg")
lat <- c(51.556307, 49.009603, 47.9874)
lon <- c(9.947375, 8.417004, 7.8945)
citynames <- c("Goettingen", "Karlsruhe", "Freiburg")
cities <- data.frame(citynames, lat, lon)
dist.mat (cities, "citynames", "lat", "lon", cities, "citynames", "lat", "lon")
# Euclidean distance matrix (3 x 3 cities = 9 distances)
dist.buf (cities, "citynames", "lat", "lon", cities, "citynames", "lat", "lon", bufdist = 300000)
# Cities within 300 km

Description

Calculation of the euclidean distance between two points with stated coordinates (lat, lon)

Usage

dist.calc(lat1, lon1, lat2, lon2, unit = "km")

Arguments

Value

A single numeric value

Author(s)

Thomas Wieland

See Also

dist.buf, dist.mat

Examples

dist.calc(51.556307, 9.947375, 49.009603, 8.417004)
# about 304 kilometers

Description

Calculation of an euclidean distance matrix between points with stated coordinates (lat, lon)

Usage

dist.mat(startpoints, sp_id, lat_start, lon_start, endpoints, ep_id, 
lat_end, lon_end, unit = "km")

Arguments

Details

The function calculates an euclidean distance matrix between points with stated coordinates (lat and lon). While $m$ start points and $n$ end points are given, the output is a linear $m * n$ distance matrix.

Value

The function returns a data.frame containing 4 columns: The start point IDs (from), the end point IDs (to), the combination of both (from_to) and the calculated distance (distance).

Author(s)

Thomas Wieland

References

de Lange, N. (2013): “Geoinformatik in Theorie und Praxis”. 3rd edition. Berlin : Springer Spektrum.

Krider, R. E./Putler, R. S. (2013): “Which Birds of a Feather Flock Together? Clustering and Avoidance Patterns of Similar Retail Outlets”. In: Geographical Analysis, 45, 2, p. 123-149

See Also

dist, dist.buf

Examples

citynames <- c("Goettingen", "Karlsruhe", "Freiburg")
lat <- c(51.556307, 49.009603, 47.9874)
lon <- c(9.947375, 8.417004, 7.8945)
citynames <- c("Goettingen", "Karlsruhe", "Freiburg")
cities <- data.frame(citynames, lat, lon)
dist.mat (cities, "citynames", "lat", "lon", cities, "citynames", "lat", "lon")
# Euclidean distance matrix (3 x 3 cities = 9 distances)
dist.buf (cities, "citynames", "lat", "lon", cities, "citynames", "lat", "lon", bufdist = 300000)
# Cities within 300 km

Description

Calculating the relative diversity index (RDI) by Duranton and Puga based on regional industry data (normally employment data)

Usage

durpug(e_ij, e_i)

Arguments

Value

A single numeric value of $RDI$

Author(s)

Thomas Wieland

References

Duranton, G./Puga, D. (2000): “Diversity and Specialisation in Cities: Why, Where and When Does it Matter?”. In: Urban Studies, 37, 3, p. 533-555.

Farhauer, O./Kroell, A. (2013): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

See Also

gini.spec, krugman.spec, hoover

Examples

# Example Goettingen:

data(Goettingen)
# Loads the data

durpug (Goettingen$Goettingen2008[2:13], Goettingen$BRD2008[2:13])
# Returns the Duranton-Puga RDI for Goettingen

Description

Calculating the Agglomeration Index by Ellison and Glaeser for a single industry $i$

Usage

ellison.a(e_ik, e_j, regions, print.results = TRUE)

Arguments

Details

The Ellison-Glaeser Agglomeration Index is not standardized. A value of $\gamma_i = 0$ indicates a spatial distribution of firms equal to a dartboard approach. Values below zero indicate spatial dispersion, values greater than zero indicate clustering.

Value

A matrix with five columns ($\gamma_i$, $G_i$, $z_{G_i}$, $K_i$ and $HHI_i$).

Author(s)

Thomas Wieland

References

Ellison G./Glaeser, E. (1997): “Geographic concentration in u.s. manufacturing industries: A dartboard approach”. In: Journal of Political Economy, 105, 5, p. 889-927.

Farhauer, O./Kroell, A. (2014): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Nakamura R./Morrison Paul, C. (2009): “Measuring agglomeration”. In: Capello, R./Nijkamp, P. (eds): Handbook of Regional Growth and Development Theories, p. 305-328.

See Also

gini.conc, gini.spec, locq, locq2, howard.cl, howard.xcl, howard.xcl2, litzenberger, litzenberger2

Examples

# Example from Farhauer/Kroell (2014):
j <- c("Wien", "Wien", "Wien", "Wien", "Wien", "Linz", 
"Linz", "Linz", "Linz", "Graz")
E_ik <- c(200,650,12000,100,50,16000,13000,1500,1500,25000)
E_j <- c(500000,400000,100000)
ellison.a(E_ik, E_j, j)
# 0.05990628

Description

Calculating the Agglomeration Index by Ellison and Glaeser for a given number of $I$ industries

Usage

ellison.a2(e_ik, industry, region, print.results = TRUE)

Arguments

Details

The Ellison-Glaeser Agglomeration Index is not standardized. A value of $\gamma_i = 0$ indicates a spatial distribution of firms equal to a dartboard approach. Values below zero indicate spatial dispersion, values greater than zero indicate clustering.

Value

A matrix with five columns ($\gamma_i$, $G_i$, $z_{G_i}$, $K_i$ and $HHI_i$) and $I$ rows (one for each industry).

Author(s)

Thomas Wieland

References

Ellison G./Glaeser, E. (1997): “Geographic concentration in u.s. manufacturing industries: A dartboard approach”. In: Journal of Political Economy, 105, 5, p. 889-927.

Farhauer, O./Kroell, A. (2014): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Nakamura R./Morrison Paul, C. (2009): “Measuring agglomeration”. In: Capello, R./Nijkamp, P. (eds): Handbook of Regional Growth and Development Theories, p. 305-328.

See Also

ellison.a, gini.conc, gini.spec, locq, locq2, howard.cl, howard.xcl, howard.xcl2, litzenberger, litzenberger2

Examples

# Example data from Farhauer/Kroell (2014):
data(FK2014_EGC)

ellison.a2 (FK2014_EGC$emp_firm, FK2014_EGC$industry, 
FK2014_EGC$region)

Description

Calculating the Coagglomeration Index by Ellison and Glaeser for one set of $U$ industries

Usage

ellison.c(e_ik, industry, region, e_j = NULL, c.industries = NULL)

Arguments

Details

The Ellison-Glaeser Coagglomeration Index is not standardized. A value of $\gamma_c = 0$ indicates a spatial distribution of firms equal to a dartboard approach. Values below zero indicate spatial dispersion, values greater than zero indicate clustering.

Value

A single value of $\gamma_c$

Author(s)

Thomas Wieland

References

Ellison G./Glaeser, E. (1997): “Geographic concentration in u.s. manufacturing industries: A dartboard approach”. In: Journal of Political Economy, 105, 5, p. 889-927.

Farhauer, O./Kroell, A. (2014): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Nakamura R./Morrison Paul, C. (2009): “Measuring agglomeration”. In: Capello, R./Nijkamp, P. (eds): Handbook of Regional Growth and Development Theories, p. 305-328.

See Also

ellison.a, ellison.a2, ellison.c2, gini.conc, gini.spec, locq, locq2, howard.cl, howard.xcl, howard.xcl2, litzenberger, litzenberger2

Examples

# Example from Farhauer/Kroell (2014):
data(FK2014_EGC)

ellison.c(FK2014_EGC$emp_firm, FK2014_EGC$industry, 
FK2014_EGC$region, FK2014_EGC$emp_region)

Description

Calculating the Coagglomeration Index by Ellison and Glaeser for $IxI$ sets of two industries

Usage

ellison.c2(e_ik, industry, region, e_j = NULL, print.results = TRUE)

Arguments

Details

The Ellison-Glaeser Coagglomeration Index is not standardized. A value of $\gamma^c = 0$ indicates a spatial distribution of firms equal to a dartboard approach. Values below zero indicate spatial dispersion, values greater than zero indicate clustering.

Value

A single value of $\gamma^c$

Author(s)

Thomas Wieland

References

Ellison G./Glaeser, E. (1997): “Geographic concentration in u.s. manufacturing industries: A dartboard approach”. In: Journal of Political Economy, 105, 5, p. 889-927.

Farhauer, O./Kroell, A. (2014): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Nakamura R./Morrison Paul, C. (2009): “Measuring agglomeration”. In: Capello, R./Nijkamp, P. (eds): Handbook of Regional Growth and Development Theories, p. 305-328.

See Also

ellison.a, ellison.a2, ellison.c, gini.conc, gini.spec, locq, locq2, howard.cl, howard.xcl, howard.xcl2, litzenberger, litzenberger2

Examples

# Example from Farhauer/Kroell (2014):
data(FK2014_EGC)

ellison.c2(FK2014_EGC$emp_firm, FK2014_EGC$industry, 
FK2014_EGC$region, FK2014_EGC$emp_region)
# this may take a while

Description

Employment data for EU countires 2004-2016 (Source: Eurostat)

Usage

data("EU28.emp")

Format

A data frame with 3000 observations on the following 7 variables.

unit

measuring unit: thousand persones (THS_PER)

nace_r2

NACE industry classification

s_adj

Adjustement of data: Not seasonally adjusted data (NSA)

na_item

a factor with levels SAL_DC

geo

NUTS nation code

time

year

emp1000

Industry-specific employment in thousand persons

Source

Eurostat (2018): Breakdowns of GDP aggregates and employment data by main industries and asset classes, Tab. code namq_10_a10_e. http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=namq_10_a10_e. Own postprocessing.

Examples

data(EU28.emp)
EU28.emp[EU28.emp$time == 2016,]
# only data for 2016

Description

Dataset with 42 firms from 4 industries in 3 regions (fictional sample data from Farhauer/Kroell 2014)

Usage

data("FK2014_EGC")

Format

A data frame with 42 observations on the following 5 variables.

region

unique ID of the region

industry

name of the industry (German language)

firm

firm ID

emp_firm

each firm's no. of employees

emp_region

total employment of the region

Source

Farhauer, O./Kroell, A. (2014): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

References

Farhauer, O./Kroell, A. (2014): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Examples

# Example from Farhauer/Kroell (2014):
data(FK2014_EGC)

ellison.c(FK2014_EGC$emp_firm, FK2014_EGC$industry, 
FK2014_EGC$region, FK2014_EGC$emp_region)

Description

Dataset with industry-specific employment in Freiburg and Germany in the years 2008 and 2014

Usage

data("Freiburg")

Format

A data frame with 9 observations on the following 8 variables.

industry

a factor with levels for the regarded industry based on the German official economic statistics (WZ2008)

e_Freiburg2008

a numeric vector with industry-specific employment in Freiburg 2008

e_Freiburg2014

a numeric vector with industry-specific employment in Freiburg 2014

e_g_Freiburg_0814

a numeric vector containing the growth of industry-specific employment in Freiburg 2008-2014, percentage

e_Germany2008

a numeric vector with industry-specific employment in Germany 2008

e_Germany2014

a numeric vector with industry-specific employment in Germany 2014

e_g_Germany_0814

a numeric vector containing the growth of industry-specific employment in Germany 2008-2014, percentage

color

a factor containg colors (blue, brown, ...)

Source

Statistische Aemter des Bundes und der Laender: Regionaldatenbank Deutschland, Tab. 254-74-4, own calculations

Examples

data(Freiburg)
# Loads the data
growth(Freiburg$e_Freiburg2008, Freiburg$e_Freiburg2014, growth.type = "rate")
# Industry-specific growth rates for Freiburg 2008 to 2014

Description

The dataset contains the Gross Domestic Product (GDP) absolute and per capita (in EUR, at current prices) for the 402 German counties (Landkreise) from 1992 to 2014.

Usage

data("G.counties.gdp")

Format

A data frame with 402 observations on the following 68 variables.

region_code_EU

a factor containing der EU regional code

region_code

a factor containing the German regional code

gdp1992

a numeric vector containing the GDP for German counties (Landkreise) for 1992

gdp1994

a numeric vector containing the GDP for German counties (Landkreise) for 1994

gdp1995

a numeric vector containing the GDP for German counties (Landkreise) for 1995

gdp1996

a numeric vector containing the GDP for German counties (Landkreise) for 1996

gdp1997

a numeric vector containing the GDP for German counties (Landkreise) for 1997

gdp1998

a numeric vector containing the GDP for German counties (Landkreise) for 1998

gdp1999

a numeric vector containing the GDP for German counties (Landkreise) for 1999

gdp2000

a numeric vector containing the GDP for German counties (Landkreise) for 2000

gdp2001

a numeric vector containing the GDP for German counties (Landkreise) for 2001

gdp2002

a numeric vector containing the GDP for German counties (Landkreise) for 2002

gdp2003

a numeric vector containing the GDP for German counties (Landkreise) for 2003

gdp2004

a numeric vector containing the GDP for German counties (Landkreise) for 2004

gdp2005

a numeric vector containing the GDP for German counties (Landkreise) for 2005

gdp2006

a numeric vector containing the GDP for German counties (Landkreise) for 2006

gdp2007

a numeric vector containing the GDP for German counties (Landkreise) for 2007

gdp2008

a numeric vector containing the GDP for German counties (Landkreise) for 2008

gdp2009

a numeric vector containing the GDP for German counties (Landkreise) for 2009

gdp2010

a numeric vector containing the GDP for German counties (Landkreise) for 2010

gdp2011

a numeric vector containing the GDP for German counties (Landkreise) for 2011

gdp2012

a numeric vector containing the GDP for German counties (Landkreise) for 2012

gdp2013

a numeric vector containing the GDP for German counties (Landkreise) for 2013

gdp2014

a numeric vector containing the GDP for German counties (Landkreise) for 2014

pop1992

a numeric vector containing the population for German counties (Landkreise) for 1992

pop1994

a numeric vector containing the population for German counties (Landkreise) for 1994

pop1995

a numeric vector containing the population for German counties (Landkreise) for 1995

pop1996

a numeric vector containing the population for German counties (Landkreise) for 1996

pop1997

a numeric vector containing the population for German counties (Landkreise) for 1997

pop1998

a numeric vector containing the population for German counties (Landkreise) for 1998

pop1999

a numeric vector containing the population for German counties (Landkreise) for 1999

pop2000

a numeric vector containing the population for German counties (Landkreise) for 2000

pop2001

a numeric vector containing the population for German counties (Landkreise) for 2001

pop2002

a numeric vector containing the population for German counties (Landkreise) for 2002

pop2003

a numeric vector containing the population for German counties (Landkreise) for 2003

pop2004

a numeric vector containing the population for German counties (Landkreise) for 2004

pop2005

a numeric vector containing the population for German counties (Landkreise) for 2005

pop2006

a numeric vector containing the population for German counties (Landkreise) for 2006

pop2007

a numeric vector containing the population for German counties (Landkreise) for 2007

pop2008

a numeric vector containing the population for German counties (Landkreise) for 2008

pop2009

a numeric vector containing the population for German counties (Landkreise) for 2009

pop2010

a numeric vector containing the population for German counties (Landkreise) for 2010

pop2011

a numeric vector containing the population for German counties (Landkreise) for 2011

pop2012

a numeric vector containing the population for German counties (Landkreise) for 2012

pop2013

a numeric vector containing the population for German counties (Landkreise) for 2013

pop2014

a numeric vector containing the population for German counties (Landkreise) for 2014

gdppc1992

a numeric vector containing the GDP per capita for German counties (Landkreise) for 1992

gdppc1994

a numeric vector containing the GDP per capita for German counties (Landkreise) for 1994

gdppc1995

a numeric vector containing the GDP per capita for German counties (Landkreise) for 1995

gdppc1996

a numeric vector containing the GDP per capita for German counties (Landkreise) for 1996

gdppc1997

a numeric vector containing the GDP per capita for German counties (Landkreise) for 1997

gdppc1998

a numeric vector containing the GDP per capita for German counties (Landkreise) for 1998

gdppc1999

a numeric vector containing the GDP per capita for German counties (Landkreise) for 1999

gdppc2000

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2000

gdppc2001

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2001

gdppc2002

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2002

gdppc2003

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2003

gdppc2004

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2004

gdppc2005

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2005

gdppc2006

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2006

gdppc2007

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2007

gdppc2008

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2008

gdppc2009

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2009

gdppc2010

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2010

gdppc2011

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2011

gdppc2012

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2012

gdppc2013

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2013

gdppc2014

a numeric vector containing the GDP per capita for German counties (Landkreise) for 2014

regional

Region West or East

Details

For the years 1992 to 1999, the GDP data is incomplete.

Source

Arbeitskreis "Volkswirtschaftliche Gesamtrechnungen der Laender" im Auftrag der Statistischen Aemter der 16 Bundeslaender, des Statistischen Bundesamtes und des Buergeramtes, Statistik und Wahlen, Frankfurt a. M. (2016): “Bruttoinlandsprodukt, Bruttowertschoepfung in den kreisfreien Staedten und Landkreisen der Bundesrepublik Deutschland 1992 und 1994 bis 2014”.

References

Arbeitskreis "Volkswirtschaftliche Gesamtrechnungen der Laender" im Auftrag der Statistischen Aemter der 16 Bundeslaender, des Statistischen Bundesamtes und des Buergeramtes, Statistik und Wahlen, Frankfurt a. M. (2016): “Bruttoinlandsprodukt, Bruttowertschoepfung in den kreisfreien Staedten und Landkreisen der Bundesrepublik Deutschland 1992 und 1994 bis 2014”.

Examples

# Regional disparities / sigma convergence in Germany
data(G.counties.gdp)
# GDP per capita for German counties (Landkreise)
cvs <- apply (G.counties.gdp[54:68], MARGIN = 2, FUN = cv)
# Calculating cv for the years 2000-2014
years <- 2000:2014
plot(years, cvs, "l", ylim=c(0.3,0.6), xlab = "year", 
ylab = "CV of GDP per capita")
# Plot cv over time

Description

The dataset contains the industry-specific employment in the German region ("Bundeslaender") for the years 2008 to 2014.

Usage

data("G.regions.emp")

Format

A data frame with 1428 observations on the following 4 variables.

industry

a factor containing the industry (in German language, e.g. "Baugewerbe" = construction, "Handel, Gastgewerbe, Verkehr (G-I)" = retail, hospitality industry and transport industry)

region

a factor containing the names of the German regions (Bundeslaender)

year

a numeric vector containing the related year

emp

a numeric vector containing the related number of employees

Source

Statistische Aemter des Bundes und der Laender, Regionaldatenbank (2017): Sozialversicherungspflichtig Beschaeftigte: Beschaeftigte am Arbeitsort nach Geschlecht, Nationalitaet und Wirtschaftszweigen (Beschaeftigungsstatistik der Bundesagentur fuer Arbeit) - Stichtag 30.06. - regionale Ebenen(Tab. 254-74-4-B).

References

Statistische Aemter des Bundes und der Laender, Regionaldatenbank (2017): Sozialversicherungspflichtig Beschaeftigte: Beschaeftigte am Arbeitsort nach Geschlecht, Nationalitaet und Wirtschaftszweigen (Beschaeftigungsstatistik der Bundesagentur fuer Arbeit) - Stichtag 30.06. - regionale Ebenen(Tab. 254-74-4-B).

Examples

data(G.regions.emp)
# Concentration of construction industry in Germany
# based on 16 German regions (Bundeslaender) for the year 2008
construction2008 <- G.regions.emp[(G.regions.emp$industry == "Baugewerbe (F)" | 
G.regions.emp$industry == "Insgesamt") & G.regions.emp$year == "2008",]
# only data for construction industry (Baugewerbe) and all-over (Insgesamt)
# for the 16 German regions in the year 2008
construction2008 <- construction2008[construction2008$region != "Insgesamt",]
# delete all-over data for all industries
gini.conc(construction2008[construction2008$industry=="Baugewerbe (F)",]$emp, 
construction2008[construction2008$industry=="Insgesamt",]$emp)

# Concentration of financial industry in Germany 2008 vs. 2014
# based on 16 German regions (Bundeslaender) for 2008 and 2014
finance2008 <- G.regions.emp[(G.regions.emp$industry == 
"Erbringung von Finanz- und Vers.leistungen (K)" | 
G.regions.emp$industry == "Insgesamt") & G.regions.emp$year == "2008",]
finance2008 <- finance2008[finance2008$region != "Insgesamt",]
# delete all-over data for all industries
gini.conc(finance2008[finance2008$industry == 
"Erbringung von Finanz- und Vers.leistungen (K)",]$emp, 
finance2008[finance2008$industry=="Insgesamt",]$emp)
finance2014 <- G.regions.emp[(G.regions.emp$industry == 
"Erbringung von Finanz- und Vers.leistungen (K)" | G.regions.emp$industry ==
"Insgesamt") & G.regions.emp$year == "2014",]
finance2014 <- finance2014[finance2014$region != "Insgesamt",]
# delete all-over data for all industries
gini.conc(finance2014[finance2014$industry == 
"Erbringung von Finanz- und Vers.leistungen (K)",]$emp, 
finance2014[finance2014$industry=="Insgesamt",]$emp)

Description

The dataset contains the industry-specific firm stock and employment in the German regions ("Bundeslaender") for 2015.

Usage

data("G.regions.industries")

Format

A data frame with 272 observations on the following 9 variables.

year

a numeric vector containing the related year

region

a factor containing the names of the German regions (Bundeslaender)

region_code

a factor containing the codes of the German regions (Bundeslaender)

ind_code

a factor containing the codes of the industries (WZ2008)

ind_name

a factor containing the names of the industries (WZ2008)

firms

a numeric vector containing the related number of firms

emp_all

a numeric vector containing the related number of employees (incl. self-employed)

pop

a numeric vector containing the related population

area_sqkm

a numeric vector containing the related region size (in sqkm)

Source

Compiled from:

Statistisches Bundesamt (2019): Tab. 11111-0001 - Gebietsflaeche: Bundeslaender, Stichtag.

Statistisches Bundesamt (2019): Tab. 12411-0010 - Bevoelkerung: Bundeslaender, Stichtag.

Statistisches Bundesamt (2019): Tab. 13311-0002 - Erwerbstaetige, Arbeitnehmer, Selbstaendige und mithelfende Familienangehoerige (im Inland): Bundeslaender, Jahre, Wirtschaftszweige (Arbeitskreis "Erwerbstaetigenrechnung des Bundes und der Laender").

Statistisches Bundesamt (2019): Tab. 52111-0004 - Betriebe (Unternehmensregister-System): Bundeslaender, Jahre, Wirtschaftszweige (Abschnitte), Beschaeftigtengroessenklassen.

Examples

data (G.regions.industries)

lqs <- locq2(e_ij = G.regions.industries$emp_all, 
G.regions.industries$ind_code, G.regions.industries$region_code, 
LQ.output = "df")
# output as data frame

lqs_sort <- lqs[order(lqs$LQ, decreasing = TRUE),]
# Sort decreasing by size of LQ

lqs_sort[1:5,]

Description

This function contains the basic GIFPRO model for commercial area prognosis (GIFPRO = Gewerbe- und Industrieflaechenprognose)

Usage

gifpro(e_ij, a_i, sq_ij, rq_ij, ru_ij = NULL, ai_ij, time.base, tinterval = 1, 
industry.names = NULL, output = "short")

Arguments

Details

In municipal land use planning (mostly in Germany), the future need of local commercial area (which is a type of land use, defined in official land-use plans) is mostly forecasted by models founded on the GIFPRO model (Gewerbe- und Industrieflaechenbedarfsprognose, prognosis of future demand of commercial area). GIFPRO is a demand-side model, which means predicting the demand of commercial area based on a prognosis of future employment in different industries (Bonny/Kahnert 2005). The key parameters of the model are the (assumed) shares of employees located in commercial areas ($a_i$), the (assumed) quotas of resettlement ($sq_{ij}$), relocation ($rq_{ij}$) and (sometimes) reuse ($ru_{ij}$) as well as the (assumed) area requirement per employee ($ai_{ij}$). Outgoing from current employment in $i$ industries in region $j$, $e_{ij}$, the future employment is predicted based on the quotas mentioned above and, finally, multiplied by the industry-specific (and maybe region-specific) areal index. The GIFPRO model has been modified and extended several times, especially with respect to industry- and region-specific employment growth, quotas and areal indices (Deutsches Institut fuer Urbanistik 2010, Vallee et al. 2012).

Value

A list containing the following objects:

Author(s)

Thomas Wieland

References

Bonny, H.-W./Kahnert, R. (2005): “Zur Ermittlung des Gewerbeflaechenbedarfs: Ein Vergleich zwischen einer Monitoring gestuetzten Prognose und einer analytischen Bestimmung”. In: Raumforschung und Raumordnung, 63, 3, p. 232-240.

Deutsches Institut fuer Urbanistik (ed.) (2010): “Stadtentwicklungskonzept Gewerbe fuer die Landeshauptstadt Potsdam”. Berlin. https://www.potsdam.de/sites/default/files/documents/STEK_Gewerbe_Langfassung_2010.pdf (accessed October 13, 2017).

Vallee, D./Witte, A./Brandt, T./Bischof, T. (2012): “Bedarfsberechnung fuer die Darstellung von Allgemeinen Siedlungsbereichen (ASB) und Gewerbe- und Industrieansiedlungsbereichen (GIB) in Regionalplaenen”. Im Auftrag der Staatskanzlei des Landes Nordrhein-Westfalen. Abschlussbericht Oktober 2012. Aachen.

See Also

gifpro.tbs, portfolio, shift, shiftd, shifti

Examples

# Data for the city Kempten (2012):
emp2012 <- c(7228, 12452, 11589)
sharesCA <- c(100, 40, 10)
rsquote <- c(0.3, 0.3, 0.3)
rlquote <- c(0.7, 0.7, 0.7)
arealindex <- c(148, 148, 148)
industries <- c("Manufacturing", "Wholesale and retail trade, Transportation 
and storage, Information and communication", "Other services")

gifpro (e_ij = emp2012, a_i = sharesCA,  sq_ij = rsquote,
rq_ij = rlquote, ai_ij = arealindex, time.base = 2012, 
tinterval = 13, industry.names = industries, output = "short")
# short output

gifpro (e_ij = emp2012, a_i = sharesCA,  sq_ij = rsquote,
rq_ij = rlquote, ai_ij = arealindex, time.base = 2012, 
tinterval = 13, industry.names = industries, output = "full")
# full output

gifpro_results <- gifpro (e_ij = emp2012, a_i = sharesCA,  sq_ij = rsquote,
rq_ij = rlquote, ai_ij = arealindex, time.base = 2012, 
tinterval = 13, industry.names = industries, output = "short")
# saving results as gifpro object

gifpro_results$components
# single components

gifpro_results$results
# results (as shown in full output)

Description

This function contains the TBS-GIFPRO model for commercial area prognosis (TBS-GIFPRO = Trendbasierte und standortspezifische Gewerbe- und Industrieflaechenprognose; trend-based and location-specific commercial area prognosis)

Usage

gifpro.tbs(e_ij, a_i, sq_ij, rq_ij, ru_ij = NULL, ai_ij, 
time.base, tinterval = 1, prog.func = rep("lin", nrow(e_ij)), 
prog.plot = TRUE, plot.single = FALSE,
multiplot.col = NULL, multiplot.row = NULL,
industry.names = NULL, emp.only = FALSE, output = "short")

Arguments

Details

In municipal land use planning (mostly in Germany), the future need of local commercial area (which is a type of land use, defined in official land-use plans) is mostly forecasted by models founded on the GIFPRO model (Gewerbe- und Industrieflaechenbedarfsprognose, prognosis of future demand of commercial area). GIFPRO is a demand-side model, which means predicting the demand of commercial area based on a prognosis of future employment in different industries (Bonny/Kahnert 2005). The key parameters of the model are the (assumed) shares of employees located in commercial areas ($a_i$), the (assumed) quotas of resettlement ($sq_{ij}$), relocation ($rq_{ij}$) and (sometimes) reuse ($ru_{ij}$) as well as the (assumed) area requirement per employee ($ai_{ij}$). Outgoing from current employment in $i$ industries in region $j$, $e_{ij}$, the future employment is predicted based on the quotas mentioned above and, finally, multiplied by the industry-specific (and maybe region-specific) areal index. The GIFPRO model has been modified and extended several times, especially with respect to industry- and region-specific employment growth, quotas and areal indices (Deutsches Institut fuer Urbanistik 2010, Vallee et al. 2012).

This function contains the TBS-GIFPRO model for commercial area prognosis (TBS-GIFPRO = Trendbasierte und standortspezifische Gewerbe- und Industrieflaechenprognose; trend-based and location-specific commercial area prognosis) (Deutsches Institut fuer Urbanistik 2010).

Value

A list containing the following objects:

Author(s)

Thomas Wieland

References

Bonny, H.-W./Kahnert, R. (2005): “Zur Ermittlung des Gewerbeflaechenbedarfs: Ein Vergleich zwischen einer Monitoring gestuetzten Prognose und einer analytischen Bestimmung”. In: Raumforschung und Raumordnung, 63, 3, p. 232-240.

Deutsches Institut fuer Urbanistik (ed.) (2010): “Stadtentwicklungskonzept Gewerbe fuer die Landeshauptstadt Potsdam”. Berlin. https://www.potsdam.de/sites/default/files/documents/STEK_Gewerbe_Langfassung_2010.pdf (accessed October 13, 2017).

Vallee, D./Witte, A./Brandt, T./Bischof, T. (2012): “Bedarfsberechnung fuer die Darstellung von Allgemeinen Siedlungsbereichen (ASB) und Gewerbe- und Industrieansiedlungsbereichen (GIB) in Regionalplaenen”. Im Auftrag der Staatskanzlei des Landes Nordrhein-Westfalen. Abschlussbericht Oktober 2012.

See Also

gifpro, portfolio, shift, shiftd, shifti

Examples

# Data for Goettingen:
data(Goettingen)

anteileGOE <- rep(100,15)
nvquote <- rep (0.3, 15)
vlquote <- rep (0.7, 15)

gifpro.tbs (e_ij = Goettingen[2:16,3:12], 
a_i = anteileGOE, sq_ij = nvquote,
rq_ij = vlquote, tinterval = 12, prog.func = 
rep("lin", nrow(Goettingen[2:16,3:12])),
ai_ij = 150, time.base = 2008, output = "full",
industry.names = Goettingen$WZ2008_Code[2:16],
prog.plot = TRUE, plot.single = FALSE)

Description

Calculating the Gini coefficient of inequality (or concentration), standardized and non-standardized, and optionally plotting the Lorenz curve

Usage

gini(x, coefnorm = FALSE, weighting = NULL, na.rm = TRUE, lc = FALSE, 
lcx = "% of objects", lcy = "% of regarded variable", 
lctitle = "Lorenz curve", le.col = "blue", lc.col = "black",
lsize = 1, ltype = "solid",
bg.col = "gray95", bgrid = TRUE, bgrid.col = "white", 
bgrid.size = 2, bgrid.type = "solid",
lcg = FALSE, lcgn = FALSE, lcg.caption = NULL, 
lcg.lab.x = 0, lcg.lab.y = 1, add.lc = FALSE)

Arguments

Details

The Gini coefficient (Gini 1912) is a popular measure of statistical dispersion, especially used for analyzing inequality or concentration. The Lorenz curve (Lorenz 1905), though developed independently, can be regarded as a graphical representation of the degree of inequality/concentration calculated by the Gini coefficient ($G$) and can also be used for additional interpretations of it. In an economic-geographical context, these methods are frequently used to analyse the concentration/inequality of income or wealth within countries (Aoyama et al. 2011). Other areas of application are analyzing regional disparities (Lessmann 2005, Nakamura 2008) and concentration in markets (sales turnover of competing firms) which makes Gini and Lorenz part of economic statistics in general (Doersam 2004, Roberts 2014).

The Gini coefficient ($G$) varies between 0 (no inequality/concentration) and 1 (complete inequality/concentration). The Lorenz curve displays the deviations of the empirical distribution from a perfectly equal distribution as the difference between two graphs (the distribution curve and a diagonal line of perfect equality). This function calculates $G$ and plots the Lorenz curve optionally. As there are several ways to calculate the Gini coefficient, this function uses the formula given in Doersam (2004). Because the maximum of $G$ is not equal to 1, also a standardized coefficient ($G*$) with a maximum equal to 1 can be calculated alternatively. If a Gini coefficient for aggregated data (e.g. income classes with averaged incomes) or the Gini coefficient has to be weighted, use a weighting vector (e.g. size of the income classes).

Value

A single numeric value of the Gini coefficient ($0 < G < 1$) or the standardized Gini coefficient ($0 < G* < 1$) and, optionally, a plot of the Lorenz curve.

Author(s)

Thomas Wieland

References

Aoyama, Y./Murphy, J. T./Hanson, S. (2011): “Key Concepts in Economic Geography”. London : SAGE.

Bahrenberg, G./Giese, E./Mevenkamp, N./Nipper, J. (2010): “Statistische Methoden in der Geographie. Band 1: Univariate und bivariate Statistik”. Stuttgart: Borntraeger.

Cerlani, L./Verme, P. (2012): “The origins of the Gini index: extracts from Variabilita e Mutabilita (1912) by Corrado Gini”. In: The Journal of Economic Inequality, 10, 3, p. 421-443.

Doersam, P. (2004): “Wirtschaftsstatistik anschaulich dargestellt”. Heidenau : PD-Verlag.

Gini, C. (1912): “Variabilita e Mutabilita”. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. Bologna : Cuppini.

Lessmann, C. (2005): “Regionale Disparitaeten in Deutschland und ausgesuchten OECD-Staaten im Vergleich”. ifo Dresden berichtet, 3/2005. https://www.ifo.de/DocDL/ifodb_2005_3_25-33.pdf.

Lorenz, M. O. (1905): “Methods of Measuring the Concentration of Wealth”. In: Publications of the American Statistical Association, 9, 70, p. 209-219.

Nakamura, R. (2008): “Agglomeration Effects on Regional Economic Disparities: A Comparison between the UK and Japan”. In: Urban Studies, 45, 9, p. 1947-1971.

Roberts, T. (2014): “When Bigger Is Better: A Critique of the Herfindahl-Hirschman Index's Use to Evaluate Mergers in Network Industries”. In: Pace Law Review, 34, 2, p. 894-946.

See Also

cv, gini.conc, gini.spec, herf, hoover

Examples

# Market concentration (example from Doersam 2004):
sales <- c(20,50,20,10)
# sales turnover of four car manufacturing companies
gini (sales, lc = TRUE, lcx = "percentage of companies", lcy = "percentrage of sales", 
lctitle = "Lorenz curve of sales", lcg = TRUE, lcgn = TRUE)
# returs the non-standardized Gini coefficient (0.3) and 
# plots the Lorenz curve with user-defined title and labels 
gini (sales, coefnorm = TRUE)
# returns the standardized Gini coefficient (0.4)

# Income classes (example from Doersam 2004):
income <- c(500, 1500, 2500, 4000, 7500, 15000)
# average income of 6 income classes
sizeofclass <- c(1000, 1200, 1600, 400, 200, 600)
# size of income classes
gini (income, weighting = sizeofclass)
# returns the non-standardized Gini coefficient (0.5278)

# Market concentration in automotive industry
data(Automotive)
gini(Automotive$Turnover2008, lsize=1, lc=TRUE, le.col = "black", 
lc.col = "orange", lcx = "Shares of companies", lcy = "Shares of turnover / cars", 
lctitle = "Automotive industry: market concentration", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Turnover 2008:", lcg.lab.x = 0, lcg.lab.y = 1)
# Gini coefficient and Lorenz curve for turnover 2008
gini(Automotive$Turnover2013, lsize=1, lc = TRUE, add.lc = TRUE, lc.col = "red", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Turnover 2013:", lcg.lab.x = 0, lcg.lab.y = 0.85)
# Adding Gini coefficient and Lorenz curve for turnover 2013
gini(Automotive$Quantity2014_car, lsize=1, lc = TRUE, add.lc = TRUE, lc.col = "blue", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Cars 2014:", lcg.lab.x = 0, lcg.lab.y = 0.7)
# Adding Gini coefficient and Lorenz curve for cars 2014

# Regional disparities in Germany:
gdp <- c(460.69, 549.19, 124.16, 65.29, 31.59, 109.27, 263.44, 39.87, 258.53, 
645.59, 131.95, 35.03, 112.66, 56.22, 85.61, 56.81)
# GDP of german regions (Bundeslaender) 2015 (in billion EUR)
gini(gdp)
# returs the non-standardized Gini coefficient (0.5009)

Description

Calculating the Gini coefficient of spatial industry concentration based on regional industry data (normally employment data)

Usage

gini.conc(e_ij, e_j, lc = FALSE, lcx = "% of objects", 
lcy = "% of regarded variable", lctitle = "Lorenz curve", 
le.col = "blue", lc.col = "black", lsize = 1, ltype = "solid",
bg.col = "gray95", bgrid = TRUE, bgrid.col = "white", 
bgrid.size = 2, bgrid.type = "solid", lcg = FALSE, lcgn = FALSE, 
lcg.caption = NULL, lcg.lab.x = 0, lcg.lab.y = 1, 
add.lc = FALSE, plot.lc = TRUE)

Arguments

Details

The Gini coefficient of spatial industry concentration ($G_{i}$) is a special spatial modification of the Gini coefficient of inequality (see the function gini()). It represents the rate of spatial concentration of the industry $i$ referring to $j$ regions (e.g. cities, counties, states). The coefficient $G_{i}$ varies between 0 (perfect distribution, respectively no concentration) and 1 (complete concentration in one region). Optionally a Lorenz curve is plotted (if lc = TRUE).

Value

A single numeric value ($0 < G_{i} < 1$)

Author(s)

Thomas Wieland

References

Farhauer, O./Kroell, A. (2013): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Nakamura, R./Morrison Paul, C. J. (2009): “Measuring agglomeration”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 305-328.

See Also

gini, gini.spec

Examples

# Example from Farhauer/Kroell (2013):
E_ij <- c(500,500,1000,7000,1000)
# employment of the industry in five regions
E_j <- c(20000,15000,20000,40000,5000)
# employment in the five regions
gini.conc (E_ij, E_j)
# Returns the Gini coefficient of industry concentration (0.4068966)

data(G.regions.emp)
# Concentration of construction industry in Germany
# based on 16 German regions (Bundeslaender) for the year 2008
construction2008 <- G.regions.emp[(G.regions.emp$industry == "Baugewerbe (F)" | 
G.regions.emp$industry == "Insgesamt") & G.regions.emp$year == "2008",]
# only data for construction industry (Baugewerbe) and all-over (Insgesamt)
# for the 16 German regions in the year 2008
construction2008 <- construction2008[construction2008$region != "Insgesamt",]
# delete all-over data for all industries
gini.conc(construction2008[construction2008$industry=="Baugewerbe (F)",]$emp, 
construction2008[construction2008$industry=="Insgesamt",]$emp)

# Concentration of financial industry in Germany 2008 vs. 2014
# based on 16 German regions (Bundeslaender) for 2008 and 2014
finance2008 <- G.regions.emp[(G.regions.emp$industry == 
"Erbringung von Finanz- und Vers.leistungen (K)" | 
G.regions.emp$industry == "Insgesamt") & G.regions.emp$year == "2008",]
finance2008 <- finance2008[finance2008$region != "Insgesamt",]
# delete all-over data for all industries
gini.conc(finance2008[finance2008$industry == 
"Erbringung von Finanz- und Vers.leistungen (K)",]$emp, 
finance2008[finance2008$industry=="Insgesamt",]$emp)
finance2014 <- G.regions.emp[(G.regions.emp$industry == 
"Erbringung von Finanz- und Vers.leistungen (K)" | G.regions.emp$industry ==
"Insgesamt") & G.regions.emp$year == "2014",]
finance2014 <- finance2014[finance2014$region != "Insgesamt",]
# delete all-over data for all industries
gini.conc(finance2014[finance2014$industry == 
"Erbringung von Finanz- und Vers.leistungen (K)",]$emp, 
finance2014[finance2014$industry=="Insgesamt",]$emp)

Description

Calculating the Gini coefficient of regional specialization based on regional industry data (normally employment data)

Usage

gini.spec(e_ij, e_i, lc = FALSE, lcx = "% of objects", 
lcy = "% of regarded variable", lctitle = "Lorenz curve", 
le.col = "blue", lc.col = "black", lsize = 1, ltype = "solid",
bg.col = "gray95", bgrid = TRUE, bgrid.col = "white", 
bgrid.size = 2, bgrid.type = "solid", lcg = FALSE, lcgn = FALSE, 
lcg.caption = NULL, lcg.lab.x = 0, lcg.lab.y = 1, 
add.lc = FALSE, plot.lc = TRUE)

Arguments

Details

The Gini coefficient of regional specialization ($G_{j}$) is a special spatial modification of the Gini coefficient of inequality (see the function gini()). It represents the degree of regional specialization of the region $j$ referring to $i$ industries. The coefficient $G_{j}$ varies between 0 (no specialization) and 1 (complete specialization). Optionally a Lorenz curve is plotted (if lc = TRUE).

Value

A single numeric value ($0 < G_{j} < 1$)

Author(s)

Thomas Wieland

References

Farhauer, O./Kroell, A. (2013): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Nakamura, R./Morrison Paul, C. J. (2009): “Measuring agglomeration”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 305-328.

See Also

gini, gini.conc

Examples

# Example from Farhauer/Kroell (2013):
E_ij <- c(700,600,500,10000,40000)
# employment of five industries in the region
E_i <- c(30000,15000,10000,60000,50000)
# over-all employment in the five industries
gini.spec (E_ij, E_i)
# Returns the Gini coefficient of regional specialization (0.6222222)

# Example Freiburg
data(Freiburg)
# Loads the data
E_ij <- Freiburg$e_Freiburg2014
# industry-specific employment in Freiburg 2014
E_i <- Freiburg$e_Germany2014
# industry-specific employment in Germany 2014
gini.spec (E_ij, E_i)
# Returns the Gini coefficient of regional specialization (0.2089009)

# Example Goettingen
data(Goettingen)
# Loads the data
gini.spec(Goettingen$Goettingen2017[2:16], Goettingen$BRD2017[2:16])
# Returns the Gini coefficient of regional specialization 2017 (0.359852)

Description

Calculating the Gini coefficient of inequality (or concentration), standardized and non-standardized, and optionally plotting the Lorenz curve

Usage

gini2(x, weighting = NULL, coefnorm = FALSE, na.rm = TRUE)

Arguments

Details

The Gini coefficient (Gini 1912) is a popular measure of statistical dispersion, especially used for analyzing inequality or concentration. In an economic-geographical context, the Gini coefficient is frequently used to analyse the concentration/inequality of income or wealth within countries (Aoyama et al. 2011). Other areas of application are analyzing regional disparities (Lessmann 2005, Nakamura 2008) and concentration in markets (sales turnover of competing firms).

The Gini coefficient ($G$) varies between 0 (no inequality/concentration) and 1 (complete inequality/concentration). This function calculates $G$. As there are several ways to calculate the Gini coefficient, this function uses the formula given in Doersam (2004). Because the maximum of $G$ is not equal to 1, also a standardized coefficient ($G*$) with a maximum equal to 1 can be calculated alternatively. If a Gini coefficient for aggregated data (e.g. income classes with averaged incomes) or the Gini coefficient has to be weighted, use a weighting vector (e.g. size of the income classes).

Value

A single numeric value of the Gini coefficient ($0 < G < 1$) or the standardized Gini coefficient ($0 < G* < 1$) and, optionally, a plot of the Lorenz curve.

Author(s)

Thomas Wieland

References

Aoyama, Y./Murphy, J. T./Hanson, S. (2011): “Key Concepts in Economic Geography”. London : SAGE.

Bahrenberg, G./Giese, E./Mevenkamp, N./Nipper, J. (2010): “Statistische Methoden in der Geographie. Band 1: Univariate und bivariate Statistik”. Stuttgart: Borntraeger.

Cerlani, L./Verme, P. (2012): “The origins of the Gini index: extracts from Variabilita e Mutabilita (1912) by Corrado Gini”. In: The Journal of Economic Inequality, 10, 3, p. 421-443.

Doersam, P. (2004): “Wirtschaftsstatistik anschaulich dargestellt”. Heidenau : PD-Verlag.

Gini, C. (1912): “Variabilita e Mutabilita”. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. Bologna : Cuppini.

Lessmann, C. (2005): “Regionale Disparitaeten in Deutschland und ausgesuchten OECD-Staaten im Vergleich”. ifo Dresden berichtet, 3/2005. https://www.ifo.de/DocDL/ifodb_2005_3_25-33.pdf.

Lorenz, M. O. (1905): “Methods of Measuring the Concentration of Wealth”. In: Publications of the American Statistical Association, 9, 70, p. 209-219.

Nakamura, R. (2008): “Agglomeration Effects on Regional Economic Disparities: A Comparison between the UK and Japan”. In: Urban Studies, 45, 9, p. 1947-1971.

Roberts, T. (2014): “When Bigger Is Better: A Critique of the Herfindahl-Hirschman Index's Use to Evaluate Mergers in Network Industries”. In: Pace Law Review, 34, 2, p. 894-946.

See Also

cv, gini.conc, gini.spec, herf, hoover

Examples

# Market concentration (example from Doersam 2004):
sales <- c(20,50,20,10)
# sales turnover of four car manufacturing companies
gini (sales, lc = TRUE, lcx = "percentage of companies", lcy = "percentrage of sales", 
lctitle = "Lorenz curve of sales", lcg = TRUE, lcgn = TRUE)
# returs the non-standardized Gini coefficient (0.3) and 
# plots the Lorenz curve with user-defined title and labels 
gini (sales, coefnorm = TRUE)
# returns the standardized Gini coefficient (0.4)

# Income classes (example from Doersam 2004):
income <- c(500, 1500, 2500, 4000, 7500, 15000)
# average income of 6 income classes
sizeofclass <- c(1000, 1200, 1600, 400, 200, 600)
# size of income classes
gini (income, weighting = sizeofclass)
# returns the non-standardized Gini coefficient (0.5278)

# Market concentration in automotive industry
data(Automotive)
gini(Automotive$Turnover2008, lsize=1, lc=TRUE, le.col = "black", 
lc.col = "orange", lcx = "Shares of companies", lcy = "Shares of turnover / cars", 
lctitle = "Automotive industry: market concentration", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Turnover 2008:", lcg.lab.x = 0, lcg.lab.y = 1)
# Gini coefficient and Lorenz curve for turnover 2008
gini(Automotive$Turnover2013, lsize=1, lc = TRUE, add.lc = TRUE, lc.col = "red", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Turnover 2013:", lcg.lab.x = 0, lcg.lab.y = 0.85)
# Adding Gini coefficient and Lorenz curve for turnover 2013
gini(Automotive$Quantity2014_car, lsize=1, lc = TRUE, add.lc = TRUE, lc.col = "blue", 
lcg = TRUE, lcgn = TRUE, lcg.caption = "Cars 2014:", lcg.lab.x = 0, lcg.lab.y = 0.7)
# Adding Gini coefficient and Lorenz curve for cars 2014

# Regional disparities in Germany:
gdp <- c(460.69, 549.19, 124.16, 65.29, 31.59, 109.27, 263.44, 39.87, 258.53, 
645.59, 131.95, 35.03, 112.66, 56.22, 85.61, 56.81)
# GDP of german regions (Bundeslaender) 2015 (in billion EUR)
gini(gdp)
# returs the non-standardized Gini coefficient (0.5009)