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Fully Modified Least Squares Estimation and Inference for Systems of Cointegrating Polynomial Regressions

Author

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  • Wagner, Martin

    (Department of Economics University of Klagenfurt, Austria, Bank of Slovenia Ljubljana, Slovenia and Institute for Advanced Studies Vienna, Austria)

Abstract

We consider fully modified least squares estimation for systems of cointegrating polynomial regressions, i. e., systems of regressions that include deterministic variables, integrated processes and their powers as regressors. The errors are allowed to be correlated across equations, over time and with the regressors. Whilst, of course, fully modified OLS and GLS estimation coincide – for any regular weighting matrix – without restrictions on the parameters and with the same regressors in all equations, this equivalence breaks down, in general, in case of parameter restrictions and/or different regressors across equations. Consequently, we discuss in detail restricted fully modified GLS estimators and inference based upon them.

Suggested Citation

  • Wagner, Martin, 2023. "Fully Modified Least Squares Estimation and Inference for Systems of Cointegrating Polynomial Regressions," IHS Working Paper Series 44, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihswps:44
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    File URL: https://irihs.ihs.ac.at/id/eprint/6431
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    References listed on IDEAS

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    1. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    2. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(1), pages 95-131, April.
    3. Hyungsik Roger Moon & Benoit Perron, 2005. "Efficient Estimation of the Seemingly Unrelated Regression Cointegration Model and Testing for Purchasing Power Parity," Econometric Reviews, Taylor & Francis Journals, vol. 23(4), pages 293-323.
    4. 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.
    5. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    6. Grabarczyk, Peter & Wagner, Martin & Frondel, Manuel & Sommer, Stephan, 2018. "A cointegrating polynomial regression analysis of the material kuznets curve hypothesis," Resources Policy, Elsevier, vol. 57(C), pages 236-245.
    7. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    8. Labson B. Stephen & Crompton Paul L., 1993. "Common Trends in Economic Activity and Metals Demand: Cointegration and the Intensity of Use Debate," Journal of Environmental Economics and Management, Elsevier, vol. 25(2), pages 147-161, September.
    9. Lars E. O. Svensson, 1992. "An Interpretation of Recent Research on Exchange Rate Target Zones," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 119-144, Fall.
    10. Park, J.Y. & Ogaki, M., 1991. "Seemingly Unrelated Canonical Cointegrating Regressions," RCER Working Papers 280, University of Rochester - Center for Economic Research (RCER).
    11. Martin Wagner, 2015. "The Environmental Kuznets Curve, Cointegration and Nonlinearity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(6), pages 948-967, September.
    12. 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.
    13. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1449-1459, December.
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    1. Yugang He, 2024. "E-commerce and foreign direct investment: pioneering a new era of trade strategies," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-14, December.

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    More about this item

    Keywords

    Fully Modified Estimation; Cointegrating Polynomial Regression; Generalized; Least Squares; Hypothesis Testing;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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