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Testing Identification Strength

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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.

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File URL: http://www.sfu.ca/econ-research/RePEc/sfu/sfudps/dp12-17.pdf
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Paper provided by Department of Economics, Simon Fraser University in its series Discussion Papers with number dp12-17.

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Length: 60
Date of creation: Sep 2012
Date of revision: Jan 2017
Handle: RePEc:sfu:sfudps:dp12-17
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Department of Economics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

Phone: (778)782-3508
Fax: (778)782-5944
Web page: http://www.sfu.ca/economics.html

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Order Information: Postal: Working Paper Coordinator, Department of Economics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada
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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. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
  3. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  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. 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.
  7. 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.
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