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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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    Cited by:

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    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.

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    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

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