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GEL statistics under weak identification

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  • Guggenberger, Patrik
  • Ramalho, Joaquim J.S.
  • Smith, Richard J.

Abstract

The central concern of this paper is the provision in a time series moment condition framework of practical recommendations of confidence regions for parameters whose coverage probabilities are robust to the strength or weakness of identification. To this end we develop Pearson-type test statistics based on GEL implied probabilities formed from general kernel smoothed versions of the moment indicators. We also modify the statistics suggested in Guggenberger and Smith (2008) for a general kernel smoothing function. Importantly for our conclusions, we provide GEL time series counterparts to GMM and GEL conditional likelihood ratio statistics given in Kleibergen (2005) and Smith (2007). Our analysis not only demonstrates that these statistics are asymptotically (conditionally) pivotal under both classical asymptotic theory and weak instrument asymptotics of Stock and Wright (2000) but also provides asymptotic power results in the weakly identified time series context. Consequently, the empirical null rejection probabilities of the associated tests and, thereby, the coverage probabilities of the corresponding confidence regions, should not be affected greatly by the strength or otherwise of identification. A comprehensive Monte Carlo study indicates that a number of the tests proposed here represent very competitive choices in comparison with those suggested elsewhere in the literature.

Suggested Citation

  • Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.
  • Handle: RePEc:eee:econom:v:170:y:2012:i:2:p:331-349
    DOI: 10.1016/j.jeconom.2012.05.009
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    Cited by:

    1. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.
    2. Francesco Bravo, 2016. "Local Information Theoretic Methods for smooth Coefficients Dynamic Panel Data Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(5), pages 690-708, September.
    3. Philip Kostov & Julie Le Gallo, 2018. "What role for human capital in the growth process: new evidence from endogenous latent factor panel quantile regressions," Scottish Journal of Political Economy, Scottish Economic Society, vol. 65(5), pages 501-527, November.

    More about this item

    Keywords

    Asymptotically pivotal statistics; Conditional likelihood ratio statistic; Generalised empirical likelihood; Implied probabilities; Nonlinear moment conditions; Weak identification;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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