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Endogeneity in High Dimensions.

Jianqing Fan1, Yuan Liao2

  • 1Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544.

Annals of Statistics
|January 13, 2015
PubMed
Summary
This summary is machine-generated.

High-dimensional statistics often assume exogenous regressors, but incidental endogeneity can cause errors. This study introduces a penalized focused generalized method of moments (FGMM) to address endogeneity and ensure model consistency.

Keywords:
Conditional moment restrictionEndogenous variablesEstimating equationFocused GMMGlobal minimizationOracle propertyOver identificationSemi-parametric efficiencySparsity recovery

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • High-dimensional statistics commonly assume exogenous regressors, meaning no correlation with the regression error.
  • Incidental endogeneity, arising from numerous regressors, can lead to inconsistent penalized least-squares methods and erroneous scientific findings.

Purpose of the Study:

  • To formally prove the inconsistency of penalized regression methods due to incidental endogeneity.
  • To develop a novel method that effectively handles endogeneity in high-dimensional regression.
  • To ensure model selection consistency and reliable scientific discoveries in the presence of endogenous predictors.

Main Methods:

  • Derivation of a necessary condition for model selection consistency in penalized regression.
  • Construction of a penalized focused generalized method of moments (FGMM) criterion function.
  • Application of instrumental variable methods within the FGMM framework.

Main Results:

  • Formal proof of inconsistency for penalized methods when incidental endogeneity is present.
  • Demonstration that FGMM achieves dimension reduction and handles endogeneity.
  • Proof that FGMM possesses the oracle property even with endogenous predictors.
  • The FGMM solution is shown to be near a global minimum under over-identification.

Conclusions:

  • Incidental endogeneity poses a significant challenge to standard high-dimensional statistical methods.
  • The proposed penalized FGMM method offers a robust solution for high-dimensional regression with endogenous predictors.
  • The FGMM method ensures model selection consistency and enables semi-parametric efficiency through a two-step estimation approach.