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Fully Modified Least Squares Cointegrating Parameter Estimation in Multicointegrated Systems

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  • Igor L. Kheifets
  • Peter C. B. Phillips

Abstract

Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional cointegrating links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals the explicit role that singularity of the long run conditional covariance matrix plays in determining multicointegration. The semiparametric framework has the advantage that short run dynamics do not need to be modeled and estimation by standard techniques such as fully modified least squares (FM-OLS) on the original I(1) system is straightforward. The paper derives FM-OLS limit theory in the multicointegrated setting, showing how faster rates of convergence are achieved in the direction of singularity and that the limit distribution depends on the distribution of the conditional one-sided long run covariance estimator used in FM-OLS estimation. Wald tests of restrictions on the regression coefficients have nonstandard limit theory which depends on nuisance parameters in general. The usual tests are shown to be conservative when the restrictions are isolated to the directions of singularity and, under certain conditions, are invariant to singularity otherwise. Simulations show that approximations derived in the paper work well in finite samples. The findings are illustrated empirically in an analysis of fiscal sustainability of the US government over the post-war period.

Suggested Citation

  • Igor L. Kheifets & Peter C. B. Phillips, 2021. "Fully Modified Least Squares Cointegrating Parameter Estimation in Multicointegrated Systems," Papers 2108.03486, arXiv.org.
  • Handle: RePEc:arx:papers:2108.03486
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    References listed on IDEAS

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    1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
    2. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
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    21. Peter C. B. Phillips, 2016. "Inference in Near-Singular Regression," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 461-486, Emerald Group Publishing Limited.
    22. Quintos, Carmela E, 1995. "Sustainability of the Deficit Process with Structural Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 409-417, October.
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    Cited by:

    1. Phillips, Peter C.B. & Kheifets, Igor L., 2024. "High-dimensional IV cointegration estimation and inference," Journal of Econometrics, Elsevier, vol. 238(2).
    2. Peter C.B. Phillips & Igor Kheifets, 2021. "On Multicointegration," Cowles Foundation Discussion Papers 2306, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    4. Suha Mahmoud Alawi & Wajih Abbassi & Rukhma Saqib & Madeeha Sharif, 2022. "Impact of Financial Innovation and Institutional Quality on Financial Development in Emerging Markets," JRFM, MDPI, vol. 15(3), pages 1-11, March.
    5. Skrobotov, Anton, 2021. "Structural breaks in cointegration models: Multivariate case," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 64, pages 83-106.

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    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
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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