CUE with many weak instruments and nearly singular design

Mehmet Caner and Neşe Yıldız

Journal of Econometrics, 2012, vol. 170, issue 2, 422-441

Abstract: This paper analyzes many weak moment asymptotics under the possibility of similar moments. The possibility of highly related moments arises when there are many of them. Knight and Fu (2000) designate the issue of similar regressors as the “nearly singular” design in the least squares case. In the nearly singular design, the sample variance converges to a singular limit term. However, Knight and Fu (2000) assume that on the nullspace of the limit term, the difference between the sample variance and the singular matrix converges in probability to a positive definite matrix when multiplied by an appropriate rate. We consider specifically Continuous Updating Estimator (CUE) with many weak moments under nearly singular design. We show that the nearly singular design affects the form of the limit of the many weak moment asymptotics that is introduced by Newey and Windmeijer (2009a). However, the estimator is still consistent and the Wald test has the standard χ2 limit.

Keywords: Singular matrix; Variance; Bias (search for similar items in EconPapers)
JEL-codes: C13 C30 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:170:y:2012:i:2:p:422-441

DOI: 10.1016/j.jeconom.2012.05.014

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