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Inference in Near-Singular Regression

In: Essays in Honor of Aman Ullah


  • 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 Publishing Ltd.
  • Handle: RePEc:eme:aecozz:s0731-905320160000036022

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

    JEL classification:

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


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