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A Test for Multimodality of Regression Derivatives with an Application to Nonparametric Growth Regressions

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  • Henderson, Daniel J.

Abstract

This paper presents a method to test for multimodality of an estimated kernel density of parameter estimates from a local-linear least-squares regression derivative. The procedure is laid out in seven simple steps and a suggestion for implementation is proposed. A Monte Carlo exercise is used to examine the finite sample properties of the test along with those from a calibrated version of it which corrects for the conservative nature of Silverman-type tests. The test is included in a study on nonparametric growth regressions. The results show that in the estimation of unconditional β-convergence, the distribution of the parameter estimates is multimodal with one mode in the negative region (primarily OECD economies) and possibly two modes in the positive region (primarily non-OECD economies) of the parameter estimates. The results for conditional β-convergence show that the density is predominantly negative and unimodal. Finally, the application attempts to determine why particular observations posess positive marginal effects on initial income in both the unconditional and conditional frameworks.

Suggested Citation

  • Henderson, Daniel J., 2008. "A Test for Multimodality of Regression Derivatives with an Application to Nonparametric Growth Regressions," MPRA Paper 8768, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:8768
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    File URL: https://mpra.ub.uni-muenchen.de/8768/1/MPRA_paper_8768.pdf
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    1. Paapaa, Richard & van Dijk, Herman K., 1998. "Distribution and mobility of wealth of nations," European Economic Review, Elsevier, vol. 42(7), pages 1269-1293, July.
    2. Maria Grazia Pittau, 2005. "Fitting Regional Income Distributions in the European Union," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(2), pages 135-161, April.
    3. Maasoumi, Esfandiar & Racine, Jeff & Stengos, Thanasis, 2007. "Growth and convergence: A profile of distribution dynamics and mobility," Journal of Econometrics, Elsevier, vol. 136(2), pages 483-508, February.
    4. Bianchi, Marco, 1997. "Testing for Convergence: Evidence from Non-parametric Multimodality Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(4), pages 393-409, July-Aug..
    5. Quah, Danny T, 1996. "Twin Peaks: Growth and Convergence in Models of Distribution Dynamics," Economic Journal, Royal Economic Society, vol. 106(437), pages 1045-1055, July.
    6. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    7. Sala-i-Martin, Xavier X, 1996. "The Classical Approach to Convergence Analysis," Economic Journal, Royal Economic Society, vol. 106(437), pages 1019-1036, July.
    8. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    9. Vaona, A. & Schiavo, S., 2007. "Nonparametric and semiparametric evidence on the long-run effects of inflation on growth," Economics Letters, Elsevier, vol. 94(3), pages 452-458, March.
    10. Quah, Danny, 1993. "Empirical cross-section dynamics in economic growth," European Economic Review, Elsevier, vol. 37(2-3), pages 426-434, April.
    11. Galor, Oded, 1996. "Convergence? Inferences from Theoretical Models," Economic Journal, Royal Economic Society, vol. 106(437), pages 1056-1069, July.
    12. Durlauf, Steven N & Johnson, Paul A, 1995. "Multiple Regimes and Cross-Country Growth Behaviour," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 365-384, Oct.-Dec..
    13. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    14. Durlauf, Steven N. & Kourtellos, Andros & Minkin, Artur, 2001. "The local Solow growth model," European Economic Review, Elsevier, vol. 45(4-6), pages 928-940, May.
    15. Ketteni, Elena & Mamuneas, Theofanis P. & Stengos, Thanasis, 2007. "Nonlinearities in economic growth: A semiparametric approach applied to information technology data," Journal of Macroeconomics, Elsevier, vol. 29(3), pages 555-568, September.
    16. Barro, Robert J & Lee, Jong-Wha, 2001. "International Data on Educational Attainment: Updates and Implications," Oxford Economic Papers, Oxford University Press, vol. 53(3), pages 541-563, July.
    17. Robert J. Barro, 1991. "Economic Growth in a Cross Section of Countries," The Quarterly Journal of Economics, Oxford University Press, vol. 106(2), pages 407-443.
    18. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 407-437.
    19. L. Wade, 1988. "Review," Public Choice, Springer, vol. 58(1), pages 99-100, July.
    20. Durlauf, Steven N. & Quah, Danny T., 1999. "The new empirics of economic growth," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 4, pages 235-308 Elsevier.
    21. Charles I. Jones, 1997. "On the Evolution of the World Income Distribution," Journal of Economic Perspectives, American Economic Association, vol. 11(3), pages 19-36, Summer.
    22. Kalaitzidakis, Pantelis & Mamuneas, Theofanis P. & Savvides, Andreas & Stengos, Thanasis, 2001. "Measures of Human Capital and Nonlinearities in Economic Growth," Journal of Economic Growth, Springer, vol. 6(3), pages 229-254, September.
    23. Hsiao, Cheng & Li, Qi & Racine, Jeffrey S., 2007. "A consistent model specification test with mixed discrete and continuous data," Journal of Econometrics, Elsevier, vol. 140(2), pages 802-826, October.
    24. Daniel J. Henderson & Christopher F. Parmeter & R. Robert Russell, 2008. "Modes, weighted modes, and calibrated modes: evidence of clustering using modality tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 607-638.
    25. Ozkan Eren & Daniel J. Henderson, 2008. "The impact of homework on student achievement," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 326-348, July.
    26. Andreas Savvides & Theofanis P. Mamuneas & Thanasis Stengos, 2006. "Economic development and the return to human capital: a smooth coefficient semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 111-132.
    27. Kelley, Allen C, 1988. "Economic Consequences of Population Change in the Third World," Journal of Economic Literature, American Economic Association, vol. 26(4), pages 1685-1728, December.
    28. Fiaschi, Davide & Lavezzi, Andrea Mario, 2003. "Distribution Dynamics and Nonlinear Growth," Journal of Economic Growth, Springer, vol. 8(4), pages 379-401, December.
    29. Winford H. Masanjala & Chris Papageorgiou, 2004. "The Solow model with CES technology: nonlinearities and parameter heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(2), pages 171-201.
    30. Johnson, Paul A., 2005. "A continuous state space approach to "Convergence by Parts"," Economics Letters, Elsevier, vol. 86(3), pages 317-321, March.
    31. Daniel J. Henderson & R. Robert Russell, 2005. "Human Capital And Convergence: A Production-Frontier Approach ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(4), pages 1167-1205, November.
    32. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    33. Quah, Danny, 1993. " Galton's Fallacy and Tests of the Convergence Hypothesis," Scandinavian Journal of Economics, Wiley Blackwell, vol. 95(4), pages 427-443, December.
    34. Jonathan Temple, 1999. "The New Growth Evidence," Journal of Economic Literature, American Economic Association, vol. 37(1), pages 112-156, March.
    35. Roberto Zelli & Maria Grazia Pittau, 2006. "Empirical evidence of income dynamics across EU regions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 605-628.
    36. Liu, Zhenjuan & Stengos, Thanasis, 1999. "Non-linearities in Cross-Country Growth Regressions: A Semiparametric Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 527-538, Sept.-Oct.
    37. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
    38. Summers, Robert & Heston, Alan, 1988. "A New Set of International Comparisons of Real Product and Price Levels Estimates for 130 Countries, 1950-1985," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 34(1), pages 1-25, March.
    39. Nazrul Islam, 1995. "Growth Empirics: A Panel Data Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 110(4), pages 1127-1170.
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    Cited by:

    1. Michael S. Delgado & Daniel J. Henderson & Christopher F. Parmeter, 2014. "Does Education Matter for Economic Growth?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 334-359, June.
    2. Henderson, Daniel J. & Maasoumi, Esfandiar, 2012. "Searching for Rehabilitation in Nonparametric Regression Models with Exogenous Treatment Assignment," IZA Discussion Papers 6874, Institute for the Study of Labor (IZA).

    More about this item

    Keywords

    Nonparametric Kernel; Convergence; Modality Tests;

    JEL classification:

    • O10 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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