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Estimation and inference in a possibly multicointegrated system with a fixed number of instruments

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  • Sun, Yixiao
  • Phillips, Peter C.B.
  • Kheifets, Igor L.

Abstract

This paper shows that the mixed normal asymptotic limit of the trend IV estimator with a fixed number of deterministic instruments (fTIV) holds in both singular (multicointegrated) and nonsingular cointegration systems, thereby relaxing the exogeneity condition in (Phillips and Kheifets, 2024, Theorem 1(ii)). The mixed normality of the limiting distribution of fTIV allows for asymptotically pivotal F and t tests about the cointegration parameters and for simple efficiency comparisons of the estimators for different numbers K of instruments, as well as comparisons with the trend IV estimator when K→∞ with the sample size.

Suggested Citation

  • Sun, Yixiao & Phillips, Peter C.B. & Kheifets, Igor L., 2025. "Estimation and inference in a possibly multicointegrated system with a fixed number of instruments," Economics Letters, Elsevier, vol. 250(C).
    • Handle: RePEc:eee:ecolet:v:250:y:2025:i:c:s016517652500134x
    DOI: 10.1016/j.econlet.2025.112297
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    References listed on IDEAS

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    1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(1), pages 116-142, February.
    2. Hwang, Jungbin & Sun, Yixiao, 2018. "SIMPLE, ROBUST, AND ACCURATE F AND t TESTS IN COINTEGRATED SYSTEMS," Econometric Theory, Cambridge University Press, vol. 34(5), pages 949-984, October.
    3. Hwang, Jungbin & Sun, Yixiao, 2017. "Asymptotic F and t tests in an efficient GMM setting," Journal of Econometrics, Elsevier, vol. 198(2), pages 277-295.
    4. Phillips, Peter C.B., 2014. "Optimal estimation of cointegrated systems with irrelevant instruments," Journal of Econometrics, Elsevier, vol. 178(P2), pages 210-224.
    5. Phillips, Peter C.B. & Kheifets, Igor L., 2024. "High-dimensional IV cointegration estimation and inference," Journal of Econometrics, Elsevier, vol. 238(2).
    6. Yixiao Sun, 2023. "Some Extensions of AsymptoticFandtTheory in Nonstationary Regressions," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Theory, volume 45, pages 319-347, Emerald Group Publishing Limited.
    7. Peter C.B. Phillips & Igor Kheifets, 2021. "On Multicointegration," Cowles Foundation Discussion Papers 2306, Cowles Foundation for Research in Economics, Yale University.
    8. Vogelsang, Timothy J. & Wagner, Martin, 2014. "Integrated modified OLS estimation and fixed-b inference for cointegrating regressions," Journal of Econometrics, Elsevier, vol. 178(2), pages 741-760.
    9. Ulrich K. Müller & Mark W. Watson, 2018. "Long†Run Covariability," Econometrica, Econometric Society, vol. 86(3), pages 775-804, May.
    10. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
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    Cited by:

    1. Jungbin Hwang & Yixiao Sun, 2025. "Asymptotic F and t Tests in Cointegrating Regressions with Asymptotically Homogeneous Functions," Working papers 2025-01, University of Connecticut, Department of Economics.

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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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