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Inference in Near Singular Regression

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Abstract

This paper considers stationary regression models with near-collinear regressors. Limit theory is developed for regression estimates and test statistics in cases where the signal matrix is nearly singular in finite samples and is asymptotically degenerate. Examples include models that involve evaporating trends in the regressors that arise in conditions such as growth convergence. Structural equation models are also considered and limit theory is derived for the corresponding instrumental variable estimator, Wald test statistic, and overidentification test when the regressors are endogenous.

Suggested Citation

  • Peter C. B. Phillips, 2015. "Inference in Near Singular Regression," Cowles Foundation Discussion Papers 2009, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2009
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d20/d2009.pdf
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    Cited by:

    1. Christopher L. Skeels & Frank Windmeijer, 2018. "On the Stock–Yogo Tables," Econometrics, MDPI, vol. 6(4), pages 1-23, November.
    2. Kheifets, Igor L. & Phillips, Peter C.B., 2023. "Fully modified least squares cointegrating parameter estimation in multicointegrated systems," Journal of Econometrics, Elsevier, vol. 232(2), pages 300-319.
    3. M. Hashem Pesaran & Ron P. Smith, 2017. "Posterior Means and Precisions of the Coefficients in Linear Models with Highly Collinear Regressors," CESifo Working Paper Series 6785, CESifo.
    4. Pesaran, M. Hashem & Smith, Ron P., 2019. "A Bayesian analysis of linear regression models with highly collinear regressors," Econometrics and Statistics, Elsevier, vol. 11(C), pages 1-21.
    5. Igor Kheifets & Peter C.B. Phillips, 2019. "Fully Modified Least Squares for Multicointegrated Systems," Cowles Foundation Discussion Papers 2210, Cowles Foundation for Research in Economics, Yale University.
    6. Richard, Patrick, 2019. "Residual bootstrap tests in linear models with many regressors," Journal of Econometrics, Elsevier, vol. 208(2), pages 367-394.

    More about this item

    Keywords

    Endogeneity; Instrumental variable; Overidentification test; Regression; Singular Signal Matrix; Structural equation;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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