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RELEVANT MOMENT SELECTION UNDER MIXED IDENTIFICATION STRENGTH

Published online by Cambridge University Press:  16 January 2023

Prosper Dovonon ,
Firmin Doko Tchatoka  and
Michael Aguessy
Prosper Dovonon*
Affiliation:
Department of Economics, Concordia University
Firmin Doko Tchatoka
Affiliation:
School of Economics and Public Policy, The University of Adelaide
Michael Aguessy
Affiliation:
Department of Economics, Concordia University
*
Address correspondence to Prosper Dovonon, Department of Economics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, QC H3G 1M8, Canada; e-mail: [email protected].
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Abstract

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This paper proposes a robust moment selection method aiming to pick the best model even if this is a moment condition model with mixed identification strength, that is, moment conditions including moment functions that are local to zero uniformly over the parameter set. We show that the relevant moment selection procedure of Hall et al. (2007, Journal of Econometrics 138, 488–512) is inconsistent in this setting as it does not explicitly account for the rate of convergence of parameter estimation of the candidate models which may vary. We introduce a new moment selection procedure based on a criterion that automatically accounts for both the convergence rate of the candidate model’s parameter estimate and the entropy of the estimator’s asymptotic distribution. The benchmark estimator that we consider is the two-step efficient generalized method of moments estimator, which is known to be efficient in this framework as well. A family of penalization functions is introduced that guarantees the consistency of the selection procedure. The finite-sample performance of the proposed method is assessed through Monte Carlo simulations.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 5 , October 2024 , pp. 1003 - 1064
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Footnotes

The paper has benefited from many comments of the Co-Editor (Michael Jansson), the Editor (Peter Phillips), and two anonymous referees. We thank Jean-Jacques Forneron, Christian Gouriéroux, Zhongjun Qu, Eric Renault, Rami Tabri, Brendan K. Beare, and Ye Lu for helpful comments. We also thank the participants of the 2018 Africa Meeting of the Econometric Society in Benin and the 2018 Canadian Econometric Study Group meeting in Ottawa, and seminar participants at Boston University, York University, and the University of Sydney for helpful discussions. This research is supported by the Social Sciences and Humanities Research Council of Canada and by the Australian Research Council grant DP200101498.

References

REFERENCES

Andrews, D.W. & Stock, J.H. (2007) Testing with many weak instruments. Journal of Econometrics 138(1), 24–46.CrossRefGoogle Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariant matrix estimation. Econometrica 59(3), 817–858.CrossRefGoogle Scholar
Andrews, D.W.K. (1999) Consistent moment selection procedures for generalized method of moments estimation. Econometrica 67(3), 543–563.CrossRefGoogle Scholar
Andrews, D.W.K. & Cheng, X. (2012) Estimation and inference with weak, semi-strong, and strong identification. Econometrica 80(5), 2153–2211.Google Scholar
Andrews, D.W.K. & Lu, B. (2001) Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models. Journal of Econometrics 101(1), 123–164.CrossRefGoogle Scholar
Antoine, B. & Renault, E. (2009) Efficient GMM with nearly-weak instruments. The Econometrics Journal 12, S135–S171.CrossRefGoogle Scholar
Antoine, B. & Renault, E. (2012) Efficient minimum distance estimation with multiple rates of convergence. Journal of Econometrics 170(2), 350–367.CrossRefGoogle Scholar
Antoine, B. & Renault, E. (2017) On the relevance of weaker instruments. Econometric Reviews 36, 928–945.CrossRefGoogle Scholar
Antoine, B. & Renault, E. (2020) Testing identification strength. Journal of Econometrics 218, 271–293.CrossRefGoogle Scholar
Belloni, A., Chen, D., Chernozhukov, V., & Hansen, C. (2012) Sparse models and methods for optimal instruments with an application to eminent domain. Econometrica 80(6), 2369–2429.Google Scholar
Breusch, T., Qian, H., Schmidt, P., & Wyhowski, D. (1999) Redundancy of moment conditions. Journal of Econometrics 91, 89–111.CrossRefGoogle Scholar
Caner, M. (2009) Testing, estimation in GMM and CUE with nearly-weak identification. Econometric Reviews 29(3), 330–363.CrossRefGoogle Scholar
Caner, M. & Fan, Q. (2015) Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive Lasso. Journal of Econometrics 187(1), 256–274.CrossRefGoogle Scholar
Chao, J.C. & Swanson, N.R. (2005) Consistent estimation with a large number of weak instruments. Econometrica 73(5), 1673–1692.CrossRefGoogle Scholar
Cheng, X. & Liao, Z. (2015) Select the valid and relevant moments: An information-based Lasso for GMM with many moments. Journal of Econometrics 186(2), 443–464.CrossRefGoogle Scholar
Donald, S.G. & Newey, W.K. (2001) Choosing the number of instruments. Econometrica 69(5), 1161–1191.CrossRefGoogle Scholar
Dovonon, P. & Atchadé, Y.F. (2020) Efficiency bounds for semiparametric models with singular score functions. Econometric Reviews 39, 612–648.CrossRefGoogle Scholar
Dovonon, P., Atchadé, Y.F., and Doko Tchatoka, F. (2022) Efficiency bounds for moment condition models with mixed identification strength. Technical report, Department of Economics, Concordia University.Google Scholar
Dovonon, P. & Hall, A.R. (2018) The asymptotic properties of GMM and indirect inference under second-order identification. Journal of Econometrics 205(1), 76–111.CrossRefGoogle Scholar
Dovonon, P. & Renault, E. (2013) Testing for common conditionally heteroskedastic factors. Econometrica 81(6), 2561–2586.Google Scholar
Dovonon, P. and Renault, E. (2020). GMM overidentification test with first-order underidentification. Technical report, Department of Economics, Concordia University.Google Scholar
Gagliardini, P., Gourieroux, C., & Renault, E. (2011) Efficient derivative pricing by the extended method of moments. Econometrica 79(4), 1181–1232.Google Scholar
Hahn, J. & Kuersteiner, G. (2002) Discontinuities of weak instrument limiting distributions. Economics Letters 75(3), 325–331.CrossRefGoogle Scholar
Hall, A.R., Inoue, A., Jana, K., & Shin, C. (2007) Information in generalized method of moments estimation and entropy-based moment selection. Journal of Econometrics 138(2), 488–512.CrossRefGoogle Scholar
Hall, A.R., Inoue, A., & Shin, C. (2008) Entropy-based moment selection in the presence of weak identification. Econometric Reviews 27(4–6), 398–427.CrossRefGoogle Scholar
Hall, A.R. & Peixe, F.P. (2003) A consistent method for the selection of relevant instruments. Econometric Reviews 22(3), 269–287.CrossRefGoogle Scholar
Han, S. & McCloskey, A. (2019) Estimation and inference with a (nearly) singular Jacobian. Quantitative Economics 10(3), 1019–1068.CrossRefGoogle Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50(4), 1029–1054.CrossRefGoogle Scholar
Inoue, A. & Shintani, M. (2018) Quasi-Bayesian model selection. Quantitative Economics 9(3), 1265–1297.CrossRefGoogle Scholar
Kabaila, P. & Leeb, H. (2006) On the large-sample minimal coverage probability of confidence intervals after model selection. Journal of the American Statistical Association 101(474), 619–629.CrossRefGoogle Scholar
Lee, J.H. & Liao, Z. (2018) On standard inference for GMM with local identification failure of known forms. Econometric Theory 34(4), 790–814.CrossRefGoogle Scholar
Magnus, J.R. & Neudecker, H. (2002) Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley.Google Scholar
Newey, W.K. & Smith, R.J. (2004) Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 72(1), 219–255.CrossRefGoogle Scholar
Pötscher, B.M. (1991) Effects of model selection on inference. Econometric Theory 7, 163–185.CrossRefGoogle Scholar
Staiger, D. & Stock, J. (1997) Instrumental variables regression with weak instruments. Econometrica 65(3), 557–586.CrossRefGoogle Scholar
Stock, J.H. & Yogo, M. (2005) Testing for weak instruments in linear IV regression. In Andrews, D.W.K. & Stock, J.H. (eds.), Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg, pp. 80–108. Cambridge University Press.CrossRefGoogle Scholar
Windmeijer, F., Farbmacher, H., Davies, N., & Smith, D.G. (2019) On the use of the Lasso for instrumental variables estimation with some invalid instruments. Journal of the American Statistical Association 114, 1339–1350.CrossRefGoogle ScholarPubMed
Ziegler, K. (1997) Functional central limit theorems for triangular arrays of function-indexed processes under uniformly integrable entropy conditions. Journal of Multivariate Analysis 62(2), 233–272.CrossRefGoogle Scholar
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