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Endogeneity in ultrahigh dimension

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  • Fan, Jianqing
  • Liao, Yuan

Abstract

Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity arises easily in high-dimensional regression due to a large pool of regressors and this causes the inconsistency of the penalized least-squares methods and possible false scientic discoveries. A necessary condition for model selection of a very general class of penalized regression methods is given, which allows us to prove formally the inconsistency claim. To cope with the possible endogeneity, we construct a novel penalized focussed generalized method of moments (FGMM) criterion function and oer a new optimization algorithm. The FGMM is not a smooth function. To establish its asymptotic properties, we rst study the model selection consistency and an oracle property for a general class of penalized regression methods. These results are then used to show that the FGMM possesses an oracle property even in the presence of endogenous predictors, and that the solution is also near global minimum under the over-identication assumption. Finally, we also show how the semi-parametric efficiency of estimation can be achieved via a two-step approach.

Suggested Citation

  • Fan, Jianqing & Liao, Yuan, 2012. "Endogeneity in ultrahigh dimension," MPRA Paper 38698, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:38698
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    References listed on IDEAS

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    Cited by:

    1. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    2. Zhu, Ying, 2015. "Sparse Linear Models and l1−Regularized 2SLS with High-Dimensional Endogenous Regressors and Instruments," MPRA Paper 81217, University Library of Munich, Germany.
    3. Mehmet Caner & Xu Han & Yoonseok Lee, 2018. "Adaptive Elastic Net GMM Estimation With Many Invalid Moment Conditions: Simultaneous Model and Moment Selection," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 24-46, January.
    4. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    5. Achim Ahrens & Arnab Bhattacharjee, 2015. "Two-Step Lasso Estimation of the Spatial Weights Matrix," Econometrics, MDPI, vol. 3(1), pages 1-28, March.
    6. Ben Gillen & Erik Snowberg & Leeat Yariv, 2015. "Experimenting with Measurement Error: Techniques with Applications to the Caltech Cohort Study," NBER Working Papers 21517, National Bureau of Economic Research, Inc.
    7. Task Force Members Include: Lilli Japec & Frauke Kreuter & Marcus Berg & Paul Biemer & Paul Decker & Cliff Lampe & Julia Lane & Cathy O'Neil & Abe Usher, "undated". "AAPOR Report on Big Data," Mathematica Policy Research Reports 4eb9b798fd5b42a8b53a9249c, Mathematica Policy Research.

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    More about this item

    Keywords

    Focused GMM; Sparsity recovery; Endogenous variables; Oracle property; Conditional moment restriction; Estimating equation; Over identi cation; Global minimization; Semi-parametric efficiency;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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