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Testing Over-Identifying Restrictions without Consistent Estimation of the Asymptotic Covariance Matrix

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Abstract

This paper extends Kiefer, Vogelsang, and Bunzel (2000) and Kiefer and Vogelsang (2002b) to propose a class of over-identifying restrictions (OIR) tests that are robust to heteroskedasticity and serial correlations of unknown form. These OIR tests do not require consistent estimation of the asymptotic covariance matrix and hence avoid choosing the bandwidth in nonparametric kernel estimation. By employing a suitable normalizing matrix to eliminate the nuisance parameters in the limit, these tests remain asymptotically pivotal. As opposed of the conventional OIR test, the proposed tests require only a consistent, but not necessarily optimal, GMM estimator. It is also shown that the asymptotic local power of these tests is invariant with respect to the choice of the weighting matrix for preliminary GMM estimator. Our simulations demonstrate that the proposed tests are properly sized in most cases and may have power comparable with that of the conventional OIR test.

Suggested Citation

  • Wei-Ming Lee & Chung-Ming Kuan & Yu-Chin Hsu, 2014. "Testing Over-Identifying Restrictions without Consistent Estimation of the Asymptotic Covariance Matrix," IEAS Working Paper : academic research 14-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    • Handle: RePEc:sin:wpaper:14-a001
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    1. Lee, Wei-Ming & Kuan, Chung-Ming & Hsu, Yu-Chin, 2014. "Testing over-identifying restrictions without consistent estimation of the asymptotic covariance matrix," Journal of Econometrics, Elsevier, vol. 181(2), pages 181-193.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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