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Inference in Second-Order Identi?ed Models

Author

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  • Prosper Dovonon
  • Alastair Hall
  • Frank Kleibergen

Abstract

We explore the local power properties of di?erent test statistics for conducting inference in moment condition models that only identify the parameters locally to second order. We consider the conventional Wald and LM statistics, and also the Generalized Anderson Rubin (GAR) statistic (Anderson and Rubin, 1949; Dufour, 1997; Staiger and Stock, 1997; Stock and Wright, 2000), KLM statistic (Kleibergen, 2002, 2005) and the GMM extension of Moreira’s (2003) (GMM-M) conditional likelihood ratio statistic. The GAR, KLM and GMM-M statistics are so-called “identi?cation robust” since their (conditional) limiting distribution is the same under ?rst-order, weak and therefore also second order identi?cation. For inference about the model speci?cation, we consider the identi?cation-robust J statistic (Kleibergen, 2005) and the GAR statistic. Interestingly, we ?nd that the limiting distribution of the Wald statistic under local alternatives not only de-pends on the distance to the null hypothesis but also on the convergence rate of the Jacobian. We speci?cally analyze two empirically relevant models with second order identi?cation. In the panel autoregressive model of order one, our analysis indicates that the Wald test of a unit root value of the autoregressive parameter has better power compared to the corresponding GAR test which, in turn, dominates the KLM, GMM-M and LM tests. For the conditionally heteroskedastic factor model, we compare Kleibergen’s (2005) J and the GAR statistics to Hansen’s (1982) overidentifying restrictions test (previously analyzed in this context by Dovonon and Renault, 2013) and ?nd the power ranking depends on the sample size. Collectively, our results suggest that tests with meaningful power can be conducted in second-order identi?ed models.

Suggested Citation

  • Prosper Dovonon & Alastair Hall & Frank Kleibergen, 2018. "Inference in Second-Order Identi?ed Models," CIRANO Working Papers 2018s-36, CIRANO.
    • Handle: RePEc:cir:cirwor:2018s-36
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    References listed on IDEAS

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    Keywords

    Generalized Method of Moments estimation; First-order identi?cation failure; Identi?cation-robust inference;
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