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Inference in Near-Singular Regression

In: Essays in Honor of Aman Ullah

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  • Peter C. B. Phillips

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 (IV) estimator, Wald test statistic, and overidentification test when the regressors are endogenous. It is shown that near-singular designs of the type considered here are not completely fatal to least squares inference, but do inevitably involve size distortion except in special Gaussian cases. In the endogenous case, IV estimation is inconsistent and both the block Wald test and Sargan overidentification test are conservative, biasing these tests in favor of the null.

Suggested Citation

  • 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.
    • Handle: RePEc:eme:aecozz:s0731-905320160000036022
    DOI: 10.1108/S0731-905320160000036022
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    Cited by:

    1. 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.
    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," BCAM Working Papers 1707, Birkbeck Centre for Applied Macroeconomics.
    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. Richard, Patrick, 2019. "Residual bootstrap tests in linear models with many regressors," Journal of Econometrics, Elsevier, vol. 208(2), pages 367-394.
    6. Christopher L. Skeels & Frank Windmeijer, 2018. "On the Stock–Yogo Tables," Econometrics, MDPI, vol. 6(4), pages 1-23, November.

    More about this item

    Keywords

    Endogeneity; instrumental variable; singular signal matrix; size distortion; structural equation; C23;
    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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