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Cointegrating Polynomial Regressions: Fully Modified Ols Estimation And Inference

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  • Wagner, Martin
  • Hong, Seung Hyun

Abstract

This paper develops a fully modified OLS (FM-OLS) estimator for cointegrating polynomial regressions, i.e., regressions that include as explanatory variables deterministic variables, integrated processes, and integer powers of integrated processes. The stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous. The paper extends the fully modified estimator of Phillips and Hansen (1990) from cointegrating regressions to cointegrating polynomial regressions. The FM-OLS estimator has a zero-mean Gaussian mixture limiting distribution that allows for standard asymptotic inference. Wald and LM specification tests as well as a KPSS-type test for cointegration are derived. The theoretical analysis is complemented by a simulation study which shows that this FM-OLS estimator, as well as tests based upon it, perform well in the sense that the performance advantages over OLS are largely similar to the performance advantages of FM-OLS over OLS in standard cointegrating regressions.

Suggested Citation

  • Wagner, Martin & Hong, Seung Hyun, 2016. "Cointegrating Polynomial Regressions: Fully Modified Ols Estimation And Inference," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1289-1315, October.
    • Handle: RePEc:cup:etheor:v:32:y:2016:i:05:p:1289-1315_00
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    Cited by:

    1. Jing Gao & Wen Xu & Lei Zhang, 2021. "Tourism, economic growth, and tourism-induced EKC hypothesis: evidence from the Mediterranean region," Empirical Economics, Springer, vol. 60(3), pages 1507-1529, March.
    2. Yicong Lin & Hanno Reuvers, 2022. "Fully Modified Estimation in Cointegrating Polynomial Regressions: Extensions and Monte Carlo Comparison," Tinbergen Institute Discussion Papers 22-093/III, Tinbergen Institute.
    3. Yicong Lin & Hanno Reuvers, 2019. "Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve," Papers 1908.02552, arXiv.org, revised Aug 2020.
    4. T. Daniel Coggin, 2023. "CO2, SO2 and economic growth: a cross-national panel study," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 47(2), pages 437-457, June.
    5. Fabian Knorre & Martin Wagner & Maximilian Grupe, 2021. "Monitoring Cointegrating Polynomial Regressions: Theory and Application to the Environmental Kuznets Curves for Carbon and Sulfur Dioxide Emissions," Econometrics, MDPI, vol. 9(1), pages 1-35, March.
    6. Wagner, Martin, 2023. "Fully modified least squares estimation and inference for systems of cointegrating polynomial regressions," Economics Letters, Elsevier, vol. 228(C).
    7. Olimpia Neagu, 2019. "The Link between Economic Complexity and Carbon Emissions in the European Union Countries: A Model Based on the Environmental Kuznets Curve (EKC) Approach," Sustainability, MDPI, vol. 11(17), pages 1-27, August.
    8. Yicong Lin & Hanno Reuvers, 2020. "Cointegrating Polynomial Regressions with Power Law Trends: Environmental Kuznets Curve or Omitted Time Effects?," Papers 2009.02262, arXiv.org, revised Dec 2021.
    9. Stypka, Oliver & Wagner, Martin, 2019. "The Phillips unit root tests for polynomials of integrated processes revisited," Economics Letters, Elsevier, vol. 176(C), pages 109-113.
    10. Stypka, Oliver & Wagner, Martin & Grabarczyk, Peter & Kawka, Rafael, 2017. "The Asymptotic Validity of "Standard" Fully Modified OLS Estimation and Inference in Cointegrating Polynomial Regressions," Economics Series 333, Institute for Advanced Studies.
    11. Bergmann, Philip, 2019. "Oil price shocks and GDP growth: Do energy shares amplify causal effects?," Energy Economics, Elsevier, vol. 80(C), pages 1010-1040.
    12. Wagner, Martin & Grabarczyk, Peter & Hong, Seung Hyun, 2020. "Fully modified OLS estimation and inference for seemingly unrelated cointegrating polynomial regressions and the environmental Kuznets curve for carbon dioxide emissions," Journal of Econometrics, Elsevier, vol. 214(1), pages 216-255.
    13. Francesca Di Iorio & Stefano Fachin, 2022. "Fiscal reaction functions for the advanced economies revisited," Empirical Economics, Springer, vol. 62(6), pages 2865-2891, June.
    14. Xu, Li & Wang, Xiuli & Wang, Lijun & Zhang, Di, 2022. "Does technological advancement impede ecological footprint level? The role of natural resources prices volatility, foreign direct investment and renewable energy in China," Resources Policy, Elsevier, vol. 76(C).
    15. Iancu, Aurel & Olteanu, Dan Constantin, 2023. "Debt Limit, Fiscal Space and Fiscal Fatigue in the Central and Eastern European Countries of EU," Working Papers of National Institute for Economic Research 230629, Institutul National de Cercetari Economice (INCE).
    16. Florian Flachenecker & Martin Kornejew, 2019. "The causal impact of material productivity on microeconomic competitiveness and environmental performance in the European Union," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 21(1), pages 87-122, January.
    17. Auld, T., 2022. "Betting and financial markets are cointegrated on election night," Cambridge Working Papers in Economics 2263, Faculty of Economics, University of Cambridge.
    18. Florian Flachenecker & Martin Kornejew & Mario Lorenzo Janiri, 2021. "The effects of publicly supported environmental innovations on firm growth in the European Union," SEEDS Working Papers 0721, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Jun 2021.
    19. Kyungsik Nam & Sungro Lee & Hocheol Jeon, 2020. "Nonlinearity between CO 2 Emission and Economic Development: Evidence from a Functional Coefficient Panel Approach," Sustainability, MDPI, vol. 12(24), pages 1-10, December.
    20. Kopp, Thomas & Nabernegg, Markus & Lange, Steffen, 2023. "The net climate effect of digitalization, differentiating between firms and households," Energy Economics, Elsevier, vol. 126(C).

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