×

Q-convergence with interquartile ranges. (English) Zbl 1198.91173

Summary: We introduce a new convergence concept “Q-convergence” which defines convergence in national incomes as a shrinking interquartile range (IQR) of the national income distribution. Compared with the other convergence definitions in the literature, Q-convergence has the following advantages. First, IQR, which represents dispersion and inequality of the income distribution, is also closely linked to the two-group clustering with the lower and upper quartiles being the “centers” of the two groups. Second, IQR is equivariant to increasing transformations and thus reconciles better conflicting empirical findings using level or log data. Third, IQR is insensitive to outliers, leading to robust statistical inferences. Panel data are analyzed to find that the absolute income gap between the poor and rich countries has increased in terms of IQR, but the widening gap is rather small and insignificant when compared with the income increase of the poor countries.

MSC:

91B82 Statistical methods; economic indices and measures
62H30 Classification and discrimination; cluster analysis (statistical aspects)
60E05 Probability distributions: general theory
62E10 Characterization and structure theory of statistical distributions

Software:

bootstrap; clusfind
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Barro, R. J.; Sala-i-Martin, X., Convergence, Journal of Political Economy, 100, 223-251 (1992)
[2] Barro, R. J.; Sala-i-Martin, X., Economic Growth (1995), McGraw-Hill: McGraw-Hill New York
[3] Beaudry, P., Collard, F., Green, D.A., 2002. Decomposing the twin-peaks in the world distribution of output-per-worker. Unpublished paper.; Beaudry, P., Collard, F., Green, D.A., 2002. Decomposing the twin-peaks in the world distribution of output-per-worker. Unpublished paper.
[4] Bernard, A. B.; Durlauf, S. N., Convergence in international output, Journal of Applied Econometrics, 10, 97-108 (1995)
[5] Bernard, A. B.; Durlauf, S. N., Interpreting tests of the convergence hypothesis, Journal of Econometrics, 71, 161-174 (1996) · Zbl 0842.62094
[6] Bianchi, M., Testing for convergenceevidence from non-parametric multimodality tests, Journal of Applied Econometrics, 12, 393-409 (1997)
[7] Deaton, A., The Analysis of Household Surveys (1997), Johns Hopkins University Press: Johns Hopkins University Press Baltimore, MD
[8] Durlauf, S. N.; Quah, D., The new empirics of economic growth, (Taylor, J. B.; Woodford, M., Handbook of Macroeconomics, vol. 1 (1999), North-Holland: North-Holland Amsterdam), 234-308
[9] Efron, B.; Tibshirani, R. J., An Introduction to the Bootstrap (1993), Chapman & Hall: Chapman & Hall London · Zbl 0835.62038
[10] Evans, P., Using panel data to evaluate growth theories, International Economic Review, 39, 295-306 (1998)
[11] Hall, P.; York, M., On the calibration of Silverman’s test for multimodality, Statistica Sinica, 11, 515-536 (2001) · Zbl 1026.62047
[12] Islam, N., Growth empiricsa panel data approach, Quarterly Journal of Economics, 110, 1127-1170 (1995) · Zbl 0836.90032
[13] Islam, N., What have we learnt from the convergence debate?, Journal of Economic Surveys, 17, 309-362 (2003)
[14] Jones, C. I., On the evolution of the world income distribution, Journal of Economic Perspectives, 11, 19-36 (1997)
[15] Jones, M. C.; Marron, J. S.; Sheather, S. J., A brief survey of bandwidth selection for density estimation, Journal of the American Statistical Association, 91, 401-407 (1996) · Zbl 0873.62040
[16] Kaufman, L.; Rousseeuw, P. J., Finding Groups in DataAn Introduction to Cluster Analysis (1990), Wiley: Wiley New York
[17] Koenker, R.; Bassett, G., Regression quantiles, Econometrica, 46, 33-50 (1978) · Zbl 0373.62038
[18] Lee, M. J., Mode regression, Journal of Econometrics, 42, 337-349 (1989) · Zbl 0692.62092
[19] Lee, K.; Pesaran, M. H.; Smith, R., Growth and convergence in a multi-country empirical stochastic Solow model, Journal of Applied Econometrics, 12, 357-392 (1997)
[20] Mankiw, N. G.; Romer, D.; Weil, D. N., A contribution to the empirics of economic growth, Quarterly Journal of Economics, 107, 407-437 (1992) · Zbl 0825.90191
[21] Park, B. U.; Turlach, B. A., Practical performance of several data driven bandwidth selector, Computational Statistics, 7, 251-270 (1992) · Zbl 0775.62100
[22] Pesaran, M.H., 2004. A pair-wise approach to testing for output and growth convergence. Unpublished paper.; Pesaran, M.H., 2004. A pair-wise approach to testing for output and growth convergence. Unpublished paper. · Zbl 1418.62529
[23] Pollard, D., Strong consistency of k-means clustering, Annals of Statistics, 9, 135-140 (1981) · Zbl 0451.62048
[24] Pollard, D., A central limit theorem for k-means clustering, Annals of Probability, 10, 919-926 (1982) · Zbl 0502.62055
[25] Quah, D., Empirics for economic growth and convergence, European Economic Review, 40, 1353-1375 (1996)
[26] Quah, D., Twin peaksgrowth and convergence in models of distribution dynamics, Economic Journal, 106, 1045-1055 (1996)
[27] Sheather, S. J.; Jones, M. C., A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Association, 53, Series B, 683-690 (1991) · Zbl 0800.62219
[28] Silverman, B. W., Using kernel density estimates to investigate multimodality, Journal of the Royal Statistical Society, 43, Series B, 97-99 (1981)
[29] Silverman, B. W., Density Estimation for Statistics and Data Analyses (1986), Chapman & Hall: Chapman & Hall London · Zbl 0617.62042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.