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Testing Over- and Underidentification in Linear Models, with Applications to Dynamic Panel Data and Asset-Pricing Models

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  • Frank Windmeijer

Abstract

This paper develops the links between overidentification tests, underidentification tests, score tests and the Cragg-Donald (1993, 1997) and Kleibergen-Paap (2006) rank tests in linear instrumental variables (IV) models. This general framework shows that standard underidentification tests are (robust) score tests for overidentification in an auxiliary linear model, x_1 = X_2 δ + ε_1, where X = [x_1 X_2] are the endogenous explanatory variables in the original model, estimated by IV estimation methods using the same instruments as for the original model. This simple structure makes it possible to establish valid robust underidentification tests for linear IV models where these have not been proposed or used before, like clustered dynamic panel data models estimated by GMM. The framework also applies to general tests of rank, including the I test of Arellano, Hansen and Sentana (2012), and, outside the IV setting, for tests of rank of parameter matrices estimated by OLS. Invariant rank tests are based on LIML or continuously updated GMM estimators of the first-stage parameters. This insight leads to the proposal of a new two-step invariant asymptotically efficient GMM estimator, and a new iterated GMM estimator that converges to the continuously updated GMM estimator.

Suggested Citation

  • Frank Windmeijer, 2018. "Testing Over- and Underidentification in Linear Models, with Applications to Dynamic Panel Data and Asset-Pricing Models," Bristol Economics Discussion Papers 18/696, School of Economics, University of Bristol, UK.
  • Handle: RePEc:bri:uobdis:18/696
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    References listed on IDEAS

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    Cited by:

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    2. Sokullu, Senay, 2023. "More Is Better, Or Not? An Empirical Analysis of Buyer Preferences for Variety on the E-Market," Journal of Economic Behavior & Organization, Elsevier, vol. 209(C), pages 450-470.
    3. Van de Sijpe, Nicolas & Windmeijer, Frank, 2023. "On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference," Journal of Econometrics, Elsevier, vol. 235(1), pages 82-104.
    4. Lenzen, Sabrina & Gannon, Brenda & Rose, Christiern, 2020. "A dynamic microeconomic analysis of the impact of physical activity on cognition among older people," Economics & Human Biology, Elsevier, vol. 39(C).
    5. Sebastian Kripfganz, 2019. "Generalized method of moments estimation of linear dynamic panel-data models," London Stata Conference 2019 17, Stata Users Group.
    6. Frank Windmeijer, 2019. "Two-stage least squares as minimum distance," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 1-9.
    7. Walter Beckert, 2019. "A Note on Specification Testing in Some Structural Regression Models," CeMMAP working papers CWP22/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Laurin James & Michael Koelle & Simon Quinn, 2019. "Do Capital Grants Improve Microenterprise Productivity?," CSAE Working Paper Series 2019-13, Centre for the Study of African Economies, University of Oxford.

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    More about this item

    Keywords

    Overidentification; Underidentification; Rank tests; Dynamic Panel Data Models; Asset Pricing Models.;
    All these keywords.

    JEL classification:

    • 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
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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