REAT (version 1.3.2)

rca:

Description

This function provides the analysis of absolute regional economic convergence (beta and sigma convergence) for cross-sectional data.

Usage

rca(gdp1, time1, gdp2, time2, output = "all", sigma.measure = "cv", 
sigma.log = TRUE, sigma.norm = FALSE, sigma.weighting = NULL, digs = 5)

Arguments

gdp1

A numeric vector containing the GDP per capita (or another economic variable) at time t

time1

A single value of time t, e.g. the initial year

gdp2

A numeric vector containing the GDP per capita (or another economic variable) at time t+1

time2

A single value of time t+1

output

argument that indicates the type of function output: if output = "all" (default), the function returns a list containing the results. If output = "data", the function only returns the input variables and their transformations in a data.frame. If output = "lm", an lm object of the (linearized) model is returned.

sigma.measure

argument that indicates how the sigma convergence should be measured. The default is output = "cv", which means that a coefficient of variation is used. If output = "sd", the standard deviation is used.

sigma.log

Logical argument. Per default (sigma.log = TRUE), also in the sigma convergence analysis, the economic variables are transformed by natural logarithm. If the original values should be used, state sigma.log = FALSE

sigma.norm

Logical argument that indicates if a normalized coefficient of variation should be used instead

sigma.weighting

If the measure of statistical dispersion in the sigma convergence analysis (coefficient of variation or standard deviation) should be weighted, a weighting vector has to be stated

digs

The number of digits for the resulting values (default: digs = 5)

Value

If output = "all": a list containing the items

constant

The constant in the beta convergence OLS model

beta

The "slope" of the OLS model (beta convergence)

tinterval

Time interval between t and t+T, in units of time

lambda

Lambda, the speed of convergence (NA in absence of beta convergence)

halflife

H, the half-life value (NA in absence of beta convergence)

r.squared

R-Squared of the OLS model

N

Number of regarded regions

sigma

Difference in dispersion parameter between t and t+T

If output = "data": a data.frame containing the columns

gdp1

the input GDP per capita (or another economic variable) at time t

gdp2

the input GDP per capita (or another economic variable) at time t+T

diff

the absolute difference between gdp2 and gdp1 ((t+T) - t)

diff

the relative difference between gdp2 and gdp1 ((t+T) - t)

ln_growth

natural logarithm of the growth

ln_initial

natural logarithm of the initial value at time t

If output = "lm": A lm object of the estimated OLS model

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 \(t+T\)). Given two GDPs per capita or another economic variable, (absolute) beta convergence can be calculated as the "slope" of a linearized OLS regression model of \(\ln \Delta y_{i,t+T}\) against \(\ln y_{i,t}\). If there is beta convergence (\(-1 < \beta < 0\)), 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). 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 \(t+T\) (Furceri 2005).

This function needs 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 output = "all", it returns the estimation results of beta convergence and, if \(-1 < \beta < 0\), also the calculations of \(\lambda\) and \(H\) related to \(\beta\). The sigma convergence is operationalized as the difference between the dispersions of the regared variable (ln-transformed if sigma.log = TRUE): \(\sigma_t - \sigma_{t+T}\). If this value is positive, there is sigma convergence with respect to these points in time. The dispersions can be calculated as (weighted or non-weighted, standardized or non-standardized) standard deviation or coefficient of variation (see the function cv), to be stated by the function parameters sigma.measure, sigma.norm and sigma.weighting. State output = "lm" for the underlying regression model (lm object) only or output = "data" for the transformed dataset. As yet, the function only allows absolute beta convergence.

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.

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

cv

Examples

# Regional disparities / beta and sigma convergence in Germany
data(G.counties.gdp)
# GDP per capita for German counties (Landkreise)
rca (G.counties.gdp$gdppc2005, 2005, G.counties.gdp$gdppc2009, 2009, digs=5)
# returns a list
convergence <- rca (G.counties.gdp$gdppc2005, 2005, G.counties.gdp$gdppc2009, 2009, digs=5)
beta <- convergence$beta
# Beta convergence value