Inference in near-singular regression
Inference in near-singular regression
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.
461-486
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Phillips, Peter C.B.
(2016)
Inference in near-singular regression.
In,
Gonzalez-Riviera, Gloria, Hill, R. Carter and Lee, Tae-Hwy
(eds.)
Essays in Honor of Aman Ullah.
(Advances in Econometrics, 36)
Bingley, GB.
Emerald Publishing, .
(doi:10.1108/S0731-905320160000036022).
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Book Section
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.
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e-pub ahead of print date: 23 June 2016
Organisations:
Economics
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Local EPrints ID: 400700
URI: http://eprints.soton.ac.uk/id/eprint/400700
PURE UUID: 689b187e-d6cf-4635-8ce2-981084949a6d
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Date deposited: 23 Sep 2016 13:25
Last modified: 15 Mar 2024 02:26
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Contributors
Editor:
Gloria Gonzalez-Riviera
Editor:
R. Carter Hill
Editor:
Tae-Hwy Lee
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