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Testing Identification Strength

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Abstract

We consider models defined by a set of moment restrictions that may be subject to weak identification. We propose a testing procedure to assess whether instruments are ”too weak” for standard (Gaussian) asymptotic theory to be reliable. Since the validity of standard asymptotics for GMM rests upon a Taylor expansion of the first order conditions, we distinguish two cases: (i) models that are either linear or separable in the parameters of interest (ii) general models that are neither linear nor separable. Our testing procedure is similar in both cases, but our null hypothesis of weak identification for a nonlinear model is broader than the popular one. Our test is straightforward to apply and allows to test the null hypothesis of weak identification of specific subvectors without assuming identification of the components not under test. In the linear case, it can be seen as a generalization of the popular first-stage F-test but allows us to fix its shortcomings in case of heteroskedasticity. In simulations, our test is well behaved when compared to contenders, both in terms of size and power. In particular, the focus on subvectors allows us to have power to reject the null of weak identification on some components of interest. This observation may explain why, when applied to the estimation of the Elasticity of Intertemporal Substitution, our test is the only one to find matching results for every country under the two symmetric popular specifications: the intercept parameter is always found strongly identified, whereas the slope parameter is always found weakly identified.

Suggested Citation

  • Bertille Antoine & Eric Renault, 2012. "Testing Identification Strength," Discussion Papers dp12-17, Department of Economics, Simon Fraser University, revised Jan 2017.
  • Handle: RePEc:sfu:sfudps:dp12-17
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    File URL: http://www.sfu.ca/econ-research/RePEc/sfu/sfudps/dp12-17.pdf
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    3. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    4. Dridi, Ramdan & Guay, Alain & Renault, Eric, 2007. "Indirect inference and calibration of dynamic stochastic general equilibrium models," Journal of Econometrics, Elsevier, vol. 136(2), pages 397-430, February.
    5. Chaudhuri, Saraswata & Zivot, Eric, 2011. "A new method of projection-based inference in GMM with weakly identified nuisance parameters," Journal of Econometrics, Elsevier, vol. 164(2), pages 239-251, October.
    6. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    7. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
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    More about this item

    Keywords

    GMM; Weak IV; Test; Subvector;

    JEL classification:

    • 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
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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