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A Ridge-Regularized Jackknifed Anderson-Rubin Test.

Max-Sebastian Dovì1, Anders Bredahl Kock2, Sophocles Mavroeidis2

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PubMed
Summary
This summary is machine-generated.

A new ridge-regularized Anderson-Rubin (AR) test effectively controls statistical errors in instrumental variable regression, even with numerous instruments and weak instrument validity. This method enhances hypothesis testing accuracy for complex economic models.

Keywords:
High dimensional modelsInstrumental variablesRidge regressionWeak identification

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Area of Science:

  • Econometrics
  • Statistical Inference
  • Applied Microeconometrics

Background:

  • Instrumental variable (IV) regression is crucial for causal inference when endogeneity is present.
  • Traditional hypothesis testing in IV models faces challenges with many instruments (overidentification) and weak instruments.
  • Existing methods may lack robustness to heteroscedasticity or require more instruments than observations.

Purpose of the Study:

  • To develop a robust hypothesis testing method for instrumental variable regression models.
  • To address challenges posed by a large number of instruments, potentially exceeding sample size.
  • To ensure reliable statistical inference under weak instrument conditions and heteroscedasticity.

Main Methods:

  • A ridge-regularized version of the jackknifed Anderson and Rubin (AR) test is proposed.
  • The method is designed to control asymptotic size under heteroscedasticity and weak instruments.
  • The approach extends to situations with more instruments than observations (many-instrument problem).

Main Results:

  • The proposed ridge-regularized jackknifed AR test demonstrates asymptotic size control.
  • It achieves size control under weaker assumptions compared to existing jackknifed AR tests.
  • Monte Carlo simulations show favorable finite-sample size and power properties against alternatives.

Conclusions:

  • Ridge-regularization offers a powerful extension to jackknifed AR tests for many-instrument settings.
  • The method provides a reliable tool for hypothesis testing in challenging instrumental variable scenarios.
  • Empirical application confirms its practical utility in economic research, such as analyzing labor markets.