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Weak Identification in Maximum Likelihood: A Question of Information

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  • Isaiah Andrews
  • Anna Mikusheva

Abstract

In this paper we connect the discrepancy between two estimates of Fisher information, one based on the quadratic variation of the score and the other based on the negative Hessian of the log-likelihood, to weak identification. Classical asymptotic approximations assume that these two estimates are asymptotically equivalent, but we show that this equivalence fails in many weakly identified models, which can distort the behavior of the MLE. Using a stylized DSGE model we show that the discrepancy between information estimates is large when identification is weak.

Suggested Citation

  • Isaiah Andrews & Anna Mikusheva, 2014. "Weak Identification in Maximum Likelihood: A Question of Information," American Economic Review, American Economic Association, vol. 104(5), pages 195-199, May.
    • Handle: RePEc:aea:aecrev:v:104:y:2014:i:5:p:195-99
    Note: DOI: 10.1257/aer.104.5.195
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    References listed on IDEAS

    as
    1. Canova, Fabio & Sala, Luca, 2009. "Back to square one: Identification issues in DSGE models," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 431-449, May.
    2. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    3. Nikolay Iskrev, 2010. "Evaluating the strength of identification in DSGE models. An a priori approach," 2010 Meeting Papers 1117, Society for Economic Dynamics.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    Cited by:

    1. Tetsuya Kaji, 2019. "Theory of Weak Identification in Semiparametric Models," Papers 1908.10478, arXiv.org, revised Aug 2020.
    2. Denni Tommasi & Alexander Wolf, 2016. "Overcoming Weak Identification in the Estimation of Household Resource Shares," Working Papers ECARES ECARES 2016-12, ULB -- Universite Libre de Bruxelles.
    3. Giovanni Angelini & Giuseppe Cavaliere & Luca Fanelli, 2022. "Bootstrap inference and diagnostics in state space models: With applications to dynamic macro models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 3-22, January.
    4. Lynda Khalaf & Beatriz Peraza López, 2020. "Simultaneous Indirect Inference, Impulse Responses and ARMA Models," Econometrics, MDPI, vol. 8(2), pages 1-26, April.
    5. Tommasi, Denni & Wolf, Alexander, 2018. "Estimating household resource shares: A shrinkage approach," Economics Letters, Elsevier, vol. 163(C), pages 75-78.

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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical

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