‘Williamson’s Fallacy’ in Estimation of Inter-Regional Inequality

Gluschenko, Konstantin (2015): ‘Williamson’s Fallacy’ in Estimation of Inter-Regional Inequality.

Abstract

When estimating regional inequality, many economists use inequality indices weighted by the regions’ shares in the national population. Although this approach is widespread, its adequacy has not received attention in the regional science literature. This paper proves that such approach is conceptually inconsistent, yielding an estimate of interpersonal inequality among the whole population of the country rather than an estimate of regional inequality. Nevertheless, as a measure of interpersonal inequality, such an estimate is very rough (up to misleading) and does not always have an intuitive interpretation. Moreover, the population-weighted inequality indices do not meet the requirements for an adequate inequality measure.

• Item Type: MPRA Paper
• Language: English
• Keywords: Inequality index, Weighting by population, Williamson coefficient of variation, inequality axioms
• Subjects: D - Microeconomics > D3 - Distribution > D31 - Personal Income, Wealth, and Their Distributions; D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R10 - General

References

Akita, T., Kurniawan, P. A. & Miyata, S. (2011) Structural changes and regional income inequality in Indonesia: a bidimensional decomposition analysis, Asian Economic Journal 25, 55–77.

Cowell, F. A. (2000) Measurement of inequality, in: A.B. Atkinson & F. Bourguignon (eds), Handbook of Income Distribution, vol. 1, pp. 86–166, Amsterdam, North Holland.

Deiwiks, C., Cederman, L. & Gleditsch, K. S. (2012) Inequality and conflict in federations, Journal of Peace Research, 49, 289–304.

Doran, J. & Jordan, D. (2013) Decomposing European NUTS2 regional inequality from 1980 to 2009: national and European policy implications, Journal of Economic Studies, 40, 22–38.

Enflo, K. & Rosés, J. R. (2015) Coping with regional inequality in Sweden: structural change, migrations, and policy, 1860–2000, Economic History Review 68, 191–217.

Ezcurra, R. & Rodríguez-Pose, A. (2009) Measuring the regional divide, in: R. Capello & P. Nijkamp (eds) Handbook of Regional Growth and Development Theories, pp. 329–353, Cheltenham, Edward Elgar.

Ezcurra, R. & Rodríguez-Pose, A. (2014) Trade openness and spatial inequality in emerging countries, Spatial Economic Analysis, 9, 162–201.

Fisch, O. (1984) Regional income inequality and economic development, Regional Science and Urban Economics, 14, 89–111.

Firebaugh, G. (2003) The New Geography of Global Income Inequality, Cambridge, MA, Harvard University Press. Friedman, M. (1992) Do old fallacies ever die? Journal of Economic Literature, 30, 2129–2132.

Gisbert F.J.G. (2003) Weighted samples, kernel density estimators and convergence, Empirical Economics, 28, 335–351.

Goskomstat of Russia (1996) Methodological Regulations on Statistics, Moscow. [In Russian.]

Jenkins, S. P. & van Kerm, P. (2009) The measurement of economic inequality, in: V. Salvedra, B. Nolan & T.M. Smeeding (eds), The Oxford Handbook of Economic Inequality, pp. 40–67, Oxford, Oxford University Press.

Kanwal, R.P. (2004) Generalized Functions: Theory and applications, Boston, Birkhäuser.

Kapp, L. (2016) General and flag officers in the U.S. Armed Forces: background and considerations for Congress. Congressional Research Service Report R44389, February 18, 2016. http://www.fas.org/sgp/crs/natsec/R44389.pdf

Kyriacou, A. P. & Roca-Sagalés O. (2014) Regional disparities and government quality: redistributive conflict crowds out good government, Spatial Economic Analysis, 9, 183–201.

Lambert, P. (2001) The Distribution and Redistribution of Income, Manchester, Manchester University Press.

Lessmann, C. (2014) Spatial inequality and development – Is there an inverted-U relationship? Journal of Development Economics, 106, 35–51.

Li, C. & Gibson, J. (2013) Rising regional inequality in China: fact or artifact? World Development, 2013, 47, 16–29.

Martínez-Galarraga, J., Rosés, J. R. & Tirado, D. A. (2015) The long-term patterns of regional income inequality in Spain, 1860–2000, Regional Studies, 49, 502–517.

Metwally, M. M. & Jensen R. C. (1973) A note on the measurement of regional income dispersion, Economic Development and Cultural Change, 22, 135–136.

Milanovic, B. (2005) Worlds apart: measuring international and global inequality, Princeton, MA, Princeton University Press.

Milanovic, B. (2012) Global inequality recalculated and updated: the effect of new PPP estimates on global inequality and 2005 estimates, Journal of Economic Inequality, 10, 1–18.

Mussini, M. (2015) Decomposing changes in inequality and welfare between EU regions: the roles of population change, re-ranking and income growth, Social Indicators Research, DOI 10.1007/s11205-015-1184-2

Parr, J. B. (1974) Welfare differences within a nation: a comment, Papers of the Regional Science Association, 32, 83–91.

Petrakos, G. & Psycharis, Y. (2016) The spatial aspects of economic crisis in Greece, Cambridge Journal of Regions, Economy and Society, 9,137–152.

Petrakos, G., Rodríguez-Pose, A. & Rovolis, A. (2005) Growth, integration, and regional disparities in the European Union, Environment and Planning A, 37,1837–1855.

Portnov, B.A. & Felsenstein D. (2010) On the suitability of income inequality measures for regional analysis: some evidence from simulation analysis and bootstrapping tests, Socio-Economic Planning Sciences, 44, 212–219.

Quah, D. (1993) Galton’s fallacy and tests of the convergence hypothesis, Scandinavian Journal of Economics, 95, 427–443.

Ravallion, M. (2005) Competing concepts of inequality in the globalization debate, in: S.M .Collins & C.L. Graham (eds), Brookings Trade Forum: 2004: Globalization, Poverty, and Inequality, pp. 1–38, Washington, D.C., Brookings Institution Press.

Sacchi, A. & Salotti, S. (2014) How regional inequality affects fiscal decentralisation: accounting for the autonomy of subcentral governments, Environment and Planning C: Government and Policy 32, 144–162.

Shorrocks, A. & Wan, G. (2005) Spatial decomposition of inequality, Journal of Economic Geography, 2005, 5, 59–81.

Silverman, B.W. (1986) Density estimation for statistics and data analysis, London, Chapman & Hall.

Theil, H. (1967) Economics and Information Theory, Amsterdam, North Holland.

Wijerathna, D., Bandara, J. S., Smith, C. & Naranpanawa, A. (2014) Regional disparities in Sri Lanka: an empirical analysis, Asia-Pacific Development Journal 21, 77–102.

Williamson, J. G. (1965) Regional inequality and the process of national development: a description of patterns, Economic Development and Cultural Change, 13, 1–84.

Wodon, Q. & Yitzhaki, S. (2006) Convergence forward and backward? Economics Letters, 92, 47–51.

Yitzhaki, S. and Schechtman, E. (2013) The Gini Methodology. A Primer on a Statistical Methodology, New York, Springer. Zubarevich, N.V. & Safronov, S.G. (2011) Regional inequality in large post-Soviet countries, Regional Research of Russia, 1, 15–26.

Zubarevich, N.V. & Safronov, S.G. (2011) Regional inequality in large post-Soviet countries, Regional Research of Russia, 1, 15–26.