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.
This paper was written during a cross-Canada rail journey in June 2015. It originated in a Yale Take Home Examination given in the Fall, 2014. The author thanks two referees for helpful comments and acknowledges support of the NSF under Grant SES 12-58258.
Phillips, P.C.B. (2016), "Inference in Near-Singular Regression", Essays in Honor of Aman Ullah (Advances in Econometrics, Vol. 36), Emerald Group Publishing Limited, Bingley, pp. 461-486. https://doi.org/10.1108/S0731-905320160000036022
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