Evidence of Convergence Clubs Using Mixture Models

REFERENCES

• Aitkin, M., Rubin, D. B. (1985). Estimation and hypothesis testing in finite mixture models. Journal of the Royal Statistical Society (B) 47:67–75.
   Google Scholar
• Anderson, G., Linton, O., Teng Wah, L. (2012a). A polarization–cohesion perspective on cross–country convergence. Journal of Economic Growth 17:49–69.
   Web of Science ®Google Scholar
• Anderson, G., Linton, O., Whang, Y. J. (2012b). Nonparametric estimation and inference about the overlap of two distributions. Journal of Econometrics 171:1–23.
   Web of Science ®Google Scholar
• Andrews, R. A., Currim, I. S. (2003). A comparison of segment retention criteria for finite mixture logit's models. Journal of Marketing Research 40:235–43.
   Web of Science ®Google Scholar
• Battisti, M., Parmeter, C. (2013). Clustering and polarization in the distribution of output: A multivariate perspective. Journal of Macroeconomics 35:144–162.
   Web of Science ®Google Scholar
• Bianchi, M. (1997). Testing for convergence: Evidence from non-parametric multimodality tests. Journal of Applied Econometrics 12:393–409.
   Web of Science ®Google Scholar
• Bickel, P. J., Rosenblatt, M. (1973). On some global measures of the deviation of the density function estimates. The Annals of Statistics 28:152–157.
   Google Scholar
• Biernacki, C., Celeux, G., Govaert, G. (2000). Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence 22:719–25.
   Web of Science ®Google Scholar
• Bloom, D. E., Canning, D., Sevilla, J. (2003). Geography and Poverty Traps. Journal of Economic Growth 8:355–78.
   Web of Science ®Google Scholar
• Bowman, A. W. (1992). Density based tests of goodness-of-fit. Journal of Statistical Computation and Simulation 40:1–13.
   Google Scholar
• Bowman, A., Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations. Oxford: Oxford University Press.
   Google Scholar
• Cameron, S. V., Heckman, J. J. (1998). Life cycle schooling and dynamic selection bias: Models and evidence for five Cohorts of American males. Journal of Political Economy 106:262–333.
   Web of Science ®Google Scholar
• Cameron, A. C., Trivedi, P. K. (2005). Microeconometrics. Methods and Applications. New York: Cambridge University Press.
   Google Scholar
• Chaudhuri, P., Marron, J. S. (1999). SiZer for exploration in curves. Journal of the American Statistical Association 94:807–823.
   Web of Science ®Google Scholar
• Chen, J., Kalbfleisch, J. D. (1996). Penalized minimum distance estimates in finite mixture models. Canadian Journal of Statistics 24:167–175.
   Web of Science ®Google Scholar
• Chen, X., Ponomareva, M., Tamer, E. (2014). Likelihood inference in some finite mixture models. Journal of Econometrics 182:87–99.
   Web of Science ®Google Scholar
• Deb, P., Trivedi, P. (2002). The Structure of Demand for Health Care: Latent Class versus two-part Models. Journal of Health Economics 21:601–625.
   PubMed Web of Science ®Google Scholar
• Deaton, A., Heston, A. (2010). Understanding PPPs and PPP-based national accounts. American Economic Journal: Macroeconomics 2:4, 1–35.
   Google Scholar
• Dempster, A. P., Laird, N. M., Rubin, D. B. (1977). Maximum likelihood from incomplete data via EM algorithm. Journal of the Royal Statistical Society (B) 69:1–38.
   Google Scholar
• Dmitrienko, A., Tamhane, A. C., Wang, X. Chen X. (2006). Stepwise gatekeeping procedures in clinical trials applications. Biometrical Journal 48:984–991.
   PubMed Web of Science ®Google Scholar
• Durlauf, S. N., Johnson, P. A., Temple, J. (2005). Growth Econometrics. In: Aghion, P. Durlauf, S. N. eds. Handbook of Economic Growth. Amsterdam: Elsevier, pp. 1063–1114.
   Google Scholar
• Fan, Y. (1994). Testing the goodness of fit of a parametric density function by kernel method. Econometric Theory 10:316–356.
   Web of Science ®Google Scholar
• Fan, Y. (1995). Bootstrapping a consistent non parametric Goodness-of-Fit Test. Econometrics Reviews 14:367–82.
   Google Scholar
• Fan, Y., Ullah, A. (1999). On Goodness-of-fit tests for weakly dependent processes using kernel method. Journal of Nonparametric Statistics 11:337–360.
   Web of Science ®Google Scholar
• Farcomeni, A., Finos, L. (2013). FDR control with Pseudo-gatekeeping based on a possibly data driven order of the hypotheses. Biometrics 69:606–613.
   PubMed Web of Science ®Google Scholar
• Feng, Z., McCulloch, C. (1994). On the likelihood ratio test statistic for the number of components in a normal mixture with unequal variances. Biometrics 50:1158–1162.
   PubMed Web of Science ®Google Scholar
• Figueiredo, M. A. T. and Jain, A. K. (2002). Unsupervised learning of finite mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(3):381–396.
   Web of Science ®Google Scholar
• Flachaire, E., Nunez, O. (2007). Estimation of the income distribution and detection of subpopulations: An exploratory model. Computational Statistics & Data Analysis 51:3368–3380.
   Web of Science ®Google Scholar
• Fraley, C., Raftery, A. E. (1998). How many clusters? Which clustering method? Answers via model based cluster analysis. Computer Journal 41:578–88.
   Web of Science ®Google Scholar
• Ghosh, J. K., Sen, P. K. (1985). On the asymptotic performance of the log likelihood ratio statistics for the mixture model and related results. Proceedings of the Berkeley Conference in Honor of J. Neyman and J. Kiefer 2:789–806.
   Google Scholar
• Hartigan, J. A., Hartigan, P. M. (1985). The dip test of unimodality. The Annals of Statistics 13:70–84.
   Web of Science ®Google Scholar
• Henderson, D. J., Russell, R. R. (2005). Human capital and convergence: A production-frontier approach. International Economic Review 46:1167–1205.
   Web of Science ®Google Scholar
• Henderson, D. J., Parmeter, C., Russell, R. R. (2008). Modes, weighted modes, and calibrated modes: Evidence of clustering using modality tests. Journal of Applied Econometrics 23:607–638.
   Web of Science ®Google Scholar
• Heston, A., Summers, R., Aten, B. (2012). Penn World Table Version 7.1. Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania.
   Google Scholar
• Huang, T., Peng, H., Zhang, K. (2013). Model selection for Gaussian mixture models, arXIv:1301.3558v1.
   Google Scholar
• James, L. F., Priebe, C. E., Marchette, J. (2001). Consistent estimation of mixture complexity. The Annals of Statistics 29(5):1281–1296.
   Web of Science ®Google Scholar
• Johnson, S., Larson, W., Papageorgiou, C., Subramamian, A. (2013). Is newer better? Penn World Table Revisions and their impact on growth estimates. Journal of Monetary Economics 60:255–274.
   Web of Science ®Google Scholar
• Jones, M. C., Marron, J. S., Sheather, S. J. (1996). A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association 91:401–407.
   Web of Science ®Google Scholar
• Jones, C. (1997). On the evolution of the world income distribution. Journal of Economic Perspectives 11:19–36.
   Web of Science ®Google Scholar
• Kass, R. E., Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association 90:773–795.
   Web of Science ®Google Scholar
• Kamakura, W. A., Russell, G. J. (1989). A probabilistic choice model for market segmentation and elasticity structuring. Journal of Marketing Research 26:379–390.
   Web of Science ®Google Scholar
• Keane, M. P., Wolpin, K. I. (1997). The career decisions of Young men. Journal of Political Economy 105:473–522.
   Web of Science ®Google Scholar
• Kim, H. J., Entsuah, A. R., Shults, J. (2011). The union closure method for testing a fixed sequence of families of hypotheses. Biometrika 98:391–401.
   Web of Science ®Google Scholar
• Leroux, B. G. (1992). Consistent estimation of a mixing distribution. The Annals of Statistics 20:1350–1360.
   Web of Science ®Google Scholar
• Marron, J. S., Wand, M. P. (1992). Exact mean integrated squared error. The Annals of Statistics 2:712–736.
   Web of Science ®Google Scholar
• McLachlan, G. (1987). On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Journal of the Royal Statistical Society C 36:318–324.
   Google Scholar
• McLachlan, G., Peel, D. (2000). Finite Mixture Models. New York: Wiley.
   Google Scholar
• Melnykov, V., Maitra, R. (2010). Finite mixture models and model-based clustering. Statistics Surveys 4:80–116.
   Google Scholar
• Maitra, R., Melnykov, V. (2010). Simulating data to study performance of finite mixture modeling and clustering algorithm. Journal of Computational and Graphical Statistics 19:354–376.
   Web of Science ®Google Scholar
• Morduch, J. J., Stern, H. S. (1997). Using mixture models to detect sex bias in health outcomes in Bangladesh. Journal of Econometrics 77:259–276.
   Web of Science ®Google Scholar
• Paap, R., van Dijk, H. K. (1998). Distribution and mobility of wealth of nations. European Economic Review 42:1269–93.
   Web of Science ®Google Scholar
• Pittau, M. G. (2005). Fitting regional income distributions in the European union. Oxford Bulletin of Economics and Statistics 67(2):135–162.
   Web of Science ®Google Scholar
• Pittau, M. G., Zelli, R. (2006). Empirical evidence of income dynamics across EU regions. Journal of Applied Econometrics 21:605–628.
   Web of Science ®Google Scholar
• Pittau, M. G., Zelli, R. (2007). Exploring patterns of income polarization using siZer. Journal of Quantitative Economics 5:101–111.
   Google Scholar
• Pittau, M. G., Zelli, R., Johnson, P. A. (2010). Mixture models, convergence clubs and polarization. Review of Income and Wealth 56:102–122.
   Web of Science ®Google Scholar
• Quah, D. (1993). Empirical cross-section dynamics in economic growth. European Economic Review 37:426–434.
   Web of Science ®Google Scholar
• Quah, D. (1997). Empirics for growth and distribution: Polarization, stratification, and convergence clubs. Journal of Economics Growth 2:25–59.
   Google Scholar
• R Core Team (2012). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. Available at http://www.R-project.org/. last accessed November 2013.
   Google Scholar
• Ray, S., Lindasy, B. (2008). Model selection in high dimensions: A quadratic-risk-based approach. Journal of the Royal Statistical Society (B) 70:95–118.
   Google Scholar
• Rosenblatt, M. (1975). A quadratic measure of deviation of two dimensional density estimates and a test of independence. The Annals of Statistics 3:1–14.
   Web of Science ®Google Scholar
• Ruppert, D., Sheather, S. J., Wand, M. P. (1995). An effective bandwidth selector for local least squares regression. Journal of the American Statistical Association 90:1257–1270.
   Web of Science ®Google Scholar
• Sheather, S. J., Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of Royal Statistical Society (B) 53:683–690.
   Google Scholar
• Silverman, B. W. (1981). Using Kernel Density Estimates to Investigate Multimodality. Journal of Royal Statistical Society (B) 43:97–99.
   Google Scholar
• Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.
   Google Scholar
• Simonoff, J. S. (1996). Smoothing Methods in Statistics. New York: Springer.
   Google Scholar
• Woo, M., Sriram, T. N. (2006). Robust etimation of mixture complexity. Journal of the American Statistical Association 101:1475–1486.
   Web of Science ®Google Scholar
• Whindam, M. P., Cutler, A. (1992). Information ratios for validating mixture analyses. Journal of the American Statistical Association 87:1188–1192.
   Web of Science ®Google Scholar