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Identification-Robust Nonparametric Inference in a Linear IV Model

Author

Listed:
  • Antoine, Bertille
  • Lavergne, Pascal

Abstract

For a linear IV regression, we propose two new inference procedures on parameters of endogenous variables that are robust to any identification pattern, do not rely on a linear first-stage equation, and account for heteroskedasticity of unknown form. Building on Bierens (1982), we first propose an Integrated Conditional Moment (ICM) type statistic constructed by setting the parameters to the value under the null hypothesis. The ICM procedure tests at the same time the value of the coefficient and the specification of the model. We then adopt the conditionality principle used by Moreira (2003) to condition on a set of ICM statistics that informs on identification strength. Our two procedures uniformly control size irrespective of identification strength. They are powerful irrespective of the nonlinear form of the link between instruments and endogenous variables and are competitive with existing procedures in simulations and applications.

Suggested Citation

  • Antoine, Bertille & Lavergne, Pascal, 2019. "Identification-Robust Nonparametric Inference in a Linear IV Model," TSE Working Papers 19-1004, Toulouse School of Economics (TSE), revised Mar 2020.
  • Handle: RePEc:tse:wpaper:122916
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    References listed on IDEAS

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    1. Sellars, Emily A. & Alix-Garcia, Jennifer, 2018. "Labor scarcity, land tenure, and historical legacy: Evidence from Mexico," Journal of Development Economics, Elsevier, vol. 135(C), pages 504-516.
    2. Moreira, Humberto AtaĆ­de & Moreira, Marcelo J., 2015. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 764, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    3. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    4. Lavergne, Pascal & Patilea, Valentin, 2013. "Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory," Journal of Econometrics, Elsevier, vol. 177(1), pages 47-59.
    5. Cattaneo, Matias D. & Farrell, Max H., 2013. "Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators," Journal of Econometrics, Elsevier, vol. 174(2), pages 127-143.
    6. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    7. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
    8. 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.
    9. Kasy Maximilian, 2019. "Uniformity and the Delta Method," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-19, January.
    10. Dreier, I. & Kotz, S., 2002. "A note on the characteristic function of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 221-224, April.
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    Citations

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    Cited by:

    1. Bertille Antoine & Xiaolin Sun, 2020. "Partially Linear Models with Endogeneity: a conditional moment based approach," Discussion Papers dp20-06, Department of Economics, Simon Fraser University.
    2. Xiaohong Chen & Sokbae Lee & Myung Hwan Seo, 2020. "Powerful Inference," Papers 2008.11140, arXiv.org.
    3. Jiafeng Chen & Daniel L. Chen & Greg Lewis, 2020. "Mostly Harmless Machine Learning: Learning Optimal Instruments in Linear IV Models," Papers 2011.06158, arXiv.org.

    More about this item

    Keywords

    Weak Instruments; Hypothesis Testing; Semiparametric Model;

    JEL classification:

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

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