IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/8768.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/8768/1/MPRA_paper_8768.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
    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. 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.
    4. Sala-i-Martin, Xavier X, 1996. "The Classical Approach to Convergence Analysis," Economic Journal, Royal Economic Society, vol. 106(437), pages 1019-1036, July.
    5. 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.
    6. Quah, Danny, 1997. "Empirics for growth and distribution," LSE Research Online Documents on Economics 2138, London School of Economics and Political Science, LSE Library.
    7. Galor, Oded, 1996. "Convergence? Inferences from Theoretical Models," Economic Journal, Royal Economic Society, vol. 106(437), pages 1056-1069, July.
    8. 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.
    9. 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..
    10. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    11. 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.
    12. 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.
    13. 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.
    14. Robert J. Barro, 1991. "Economic Growth in a Cross Section of Countries," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(2), pages 407-443.
    15. L. Wade, 1988. "Review," Public Choice, Springer, vol. 58(1), pages 99-100, July.
    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. Abramovitz, Moses, 1986. "Catching Up, Forging Ahead, and Falling Behind," The Journal of Economic History, Cambridge University Press, vol. 46(2), pages 385-406, June.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Jonathan R. W. Temple, 1998. "Robustness tests of the augmented Solow model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(4), pages 361-375.
    24. 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.
    25. Fiaschi, Davide & Lavezzi, Andrea Mario, 2003. "Distribution Dynamics and Nonlinear Growth," Journal of Economic Growth, Springer, vol. 8(4), pages 379-401, December.
    26. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    27. Johnson, Paul A., 2005. "A continuous state space approach to "Convergence by Parts"," Economics Letters, Elsevier, vol. 86(3), pages 317-321, March.
    28. 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.
    29. Jonathan Temple, 1999. "The New Growth Evidence," Journal of Economic Literature, American Economic Association, vol. 37(1), pages 112-156, March.
    30. Baumol, William J, 1986. "Productivity Growth, Convergence, and Welfare: What the Long-run Data Show," American Economic Review, American Economic Association, vol. 76(5), pages 1072-1085, December.
    31. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 407-437.
    32. M.‐Y. Cheng & P. Hall, 1998. "Calibrating the excess mass and dip tests of modality," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 579-589.
    33. 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.
    34. 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.
    35. 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.
    36. Elodie Guerre & I. Perrigne & Q.H. Vuong, 2000. "Optimal nonparametric estimation of first-price auctions [[Estimation nonparamétrique optimale des enchères au premier prix]]," Post-Print hal-02697497, HAL.
    37. 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..
    38. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    39. Quah, Danny, 1993. "Empirical cross-section dynamics in economic growth," European Economic Review, Elsevier, vol. 37(2-3), pages 426-434, April.
    40. Henderson, Daniel J. & Ullah, Aman, 2005. "A nonparametric random effects estimator," Economics Letters, Elsevier, vol. 88(3), pages 403-407, September.
    41. Quah, Danny, 1997. "Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs," CEPR Discussion Papers 1586, C.E.P.R. Discussion Papers.
    42. 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.
    43. 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.
    44. Xihong Lin & Raymond J. Carroll, 2006. "Semiparametric estimation in general repeated measures problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 69-88, February.
    45. Theofanis P. Mamuneas & Andreas Savvides & 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, January.
    46. Quah, D., 1990. "Galton'S Fallacy And The Tests Of The Convergence Hypothesis," Working papers 552, Massachusetts Institute of Technology (MIT), Department of Economics.
    47. 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.
    48. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    49. Danny Quah, 1997. "Empirics for Growth and Distribution," CEP Discussion Papers dp0324, Centre for Economic Performance, LSE.
    50. Su, Liangjun & Ullah, Aman, 2006. "Profile likelihood estimation of partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 92(1), pages 75-81, July.
    51. Quah, Danny T, 1997. "Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs," Journal of Economic Growth, Springer, vol. 2(1), pages 27-59, March.
    52. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
    53. Robert Summers & Alan Heston, 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.
    54. Clifford M. Hurvich & Jeffrey S. Simonoff & Chih‐Ling Tsai, 1998. "Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 271-293.
    55. Nazrul Islam, 1995. "Growth Empirics: A Panel Data Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(4), pages 1127-1170.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Valentin Zelenyuk & Leopold Simar, 2011. "To Smooth or Not to Smooth? The Case of Discrete Variables in Nonparametric Regressions," CEPA Working Papers Series WP102011, School of Economics, University of Queensland, Australia.
    2. Naima Chrid & Sami Saafi & Mohamed Chakroun, 2021. "Export Upgrading and Economic Growth: a Panel Cointegration and Causality Analysis," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 12(2), pages 811-841, June.
    3. Haupt, Harry & Meier, Verena, 2016. "Dealing with heterogeneity, nonlinearity and club misclassification in growth convergence: A nonparametric two-step approach," Center for Mathematical Economics Working Papers 455, Center for Mathematical Economics, Bielefeld University.
    4. Saafi Sami & Nouira Ridha, 2018. "Re-Examining the Relationship Between Export Upgrading and Economic Growth: Is there a Threshold Effect?," The Economic and Social Review, Economic and Social Studies, vol. 49(4), pages 437-454.
    5. 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.
    6. Mohamed Chakroun & Naima Chrid & Sami Saafi, 2021. "Does export upgrading really matter to economic growth? Evidence from panel data for high‐, middle‐ and low‐income countries," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5584-5609, October.
    7. Charalampos Agiropoulos & Michael L. Polemis & Michael Siopsis & Sotiris Karkalakos, 2022. "Revisiting the finance‐growth nexus: A socioeconomic approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(3), pages 2762-2783, July.
    8. Li, Degui & Simar, Léopold & Zelenyuk, Valentin, 2016. "Generalized nonparametric smoothing with mixed discrete and continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 424-444.
    9. Henderson, Daniel J. & Maasoumi, Esfandiar, 2012. "Searching for Rehabilitation in Nonparametric Regression Models with Exogenous Treatment Assignment," IZA Discussion Papers 6874, Institute of Labor Economics (IZA).
    10. Haupt, Harry & Schnurbus, Joachim & Semmler, Willi, 2018. "Estimation of grouped, time-varying convergence in economic growth," Econometrics and Statistics, Elsevier, vol. 8(C), pages 141-158.
    11. Cohen-Cole, Ethan B. & Durlauf, Steven N. & Rondina, Giacomo, 2012. "Nonlinearities in growth: From evidence to policy," Journal of Macroeconomics, Elsevier, vol. 34(1), pages 42-58.
    12. Roman Matousek & Nickolaos G. Tzeremes, 2021. "The asymmetric impact of human capital on economic growth," Empirical Economics, Springer, vol. 60(3), pages 1309-1334, March.
    13. Thomas Triebs & Subal C. Kumbhakar, 2012. "Management Practice in Production," ifo Working Paper Series 129, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    14. Neumann, Uwe, 2020. "Lebenslanges Lernen als Standortfaktor? Weiterbildungschancen im Vergleich der deutschen Bundesländer," RWI Materialien 138, RWI - Leibniz-Institut für Wirtschaftsforschung.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Paul Johnson & Chris Papageorgiou, 2020. "What Remains of Cross-Country Convergence?," Journal of Economic Literature, American Economic Association, vol. 58(1), pages 129-175, March.
    2. Steven N. Durlauf & Andros Kourtellos & Chih Ming Tan, 2008. "Empirics of Growth and Development," Chapters, in: Amitava Krishna Dutt & Jaime Ros (ed.), International Handbook of Development Economics, Volumes 1 & 2, volume 0, chapter 3, Edward Elgar Publishing.
    3. Falko Juessen, 2009. "A distribution dynamics approach to regional GDP convergence in unified Germany," Empirical Economics, Springer, vol. 37(3), pages 627-652, December.
    4. 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.
    5. Haupt, Harry & Schnurbus, Joachim & Semmler, Willi, 2018. "Estimation of grouped, time-varying convergence in economic growth," Econometrics and Statistics, Elsevier, vol. 8(C), pages 141-158.
    6. Marco Alfo & Giovanni Trovato & Robert J. Waldmann, 2008. "Testing for country heterogeneity in growth models using a finite mixture approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 487-514.
    7. 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.
    8. Cem Ertur & Julie Le Gallo & Catherine Baumont, 2006. "The European Regional Convergence Process, 1980-1995: Do Spatial Regimes and Spatial Dependence Matter?," International Regional Science Review, , vol. 29(1), pages 3-34, January.
    9. 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.
    10. Ezcurra, Roberto, 2007. "Is there cross-country convergence in carbon dioxide emissions?," Energy Policy, Elsevier, vol. 35(2), pages 1363-1372, February.
    11. Cristina D. Checherita, 2009. "Variations on economic convergence: The case of the United States," Papers in Regional Science, Wiley Blackwell, vol. 88(2), pages 259-278, June.
    12. Gordon Anderson & Oliver Linton & Teng Leo, 2012. "A polarization-cohesion perspective on cross-country convergence," Journal of Economic Growth, Springer, vol. 17(1), pages 49-69, March.
    13. Andreas Pyka & Jens J. Kruger & Uwe Cantner, 2003. "Twin Peaks: What the Knowledge-based Approach Can Say about the Dynamics of the World Income Distribution," Chapters, in: Pier Paolo Saviotti (ed.), Applied Evolutionary Economics, chapter 9, Edward Elgar Publishing.
    14. Andros Kourtellos, 2002. "Modeling Parameter Heterogeneity in Cross Country Growth Regression Models," University of Cyprus Working Papers in Economics 0212, University of Cyprus Department of Economics.
    15. Walheer, Barnabé, 2016. "Growth and convergence of the OECD countries: A multi-sector production-frontier approach," European Journal of Operational Research, Elsevier, vol. 252(2), pages 665-675.
    16. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    17. Azomahou, Théophile T. & El ouardighi, Jalal & Nguyen-Van, Phu & Pham, Thi Kim Cuong, 2011. "Testing convergence of European regions: A semiparametric approach," Economic Modelling, Elsevier, vol. 28(3), pages 1202-1210, May.
    18. Epstein, Philip & Howlett, Peter & Schulze, Max-Stephan, 2003. "Distribution dynamics: stratification, polarization, and convergence among OECD economies, 1870-1992," Explorations in Economic History, Elsevier, vol. 40(1), pages 78-97, January.
    19. Roberto Basile, 2009. "Productivity Polarization across Regions in Europe," International Regional Science Review, , vol. 32(1), pages 92-115, January.
    20. Fulvio Castellacci, 2007. "Evolutionary And New Growth Theories. Are They Converging?," Journal of Economic Surveys, Wiley Blackwell, vol. 21(3), pages 585-627, July.

    More about this item

    Keywords

    Nonparametric Kernel; Convergence; Modality Tests;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:8768. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.