This function calculates the beta convergence speed and half-life based on a given beta value and time interval.
betaconv.speed(beta, tinterval, print.results = TRUE)Beta value
Time interval (in time units, such as years)
Logical argument that indicates if the function shows the results or not
A matrix containing the following objects:
Lambda value (convergence speed)
Half-life values
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.
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.
betaconv.nls, betaconv.ols, sigmaconv, sigmaconv.t, cv, sd2, var2
# NOT RUN {
speed <- betaconv.speed(-0.008070533, 1)
speed[1] # lambda
speed[2] # half-life
# }
Run the code above in your browser using DataLab