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Antoine, Bertille and Renault, Eric (2020) Testing identification strength. Journal of Econometrics, 218 (2). pp. 271-293. doi:10.1016/j.jeconom.2020.04.017 ISSN 0304-4076.
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Official URL: https://doi.org/10.1016/j.jeconom.2020.04.017
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.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Social Sciences > Economics | ||||||||
Journal or Publication Title: | Journal of Econometrics | ||||||||
Publisher: | Elsevier BV * North-Holland | ||||||||
ISSN: | 0304-4076 | ||||||||
Official Date: | October 2020 | ||||||||
Dates: |
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Volume: | 218 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 271-293 | ||||||||
DOI: | 10.1016/j.jeconom.2020.04.017 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 5 February 2019 | ||||||||
Date of first compliant Open Access: | 18 May 2022 | ||||||||
Related URLs: | |||||||||
Open Access Version: |
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