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Stein-Like Shrinkage Estimators for Coefficients of a Single-Equation in Simultaneous Equation Systems

Author

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  • Ali Mehrabani

    (Department of Economics, University of Kansas, Lawrence, KS 66045)

Abstract

Two stein-like shrinkage estimators are introduced to modify the 2SLS and the LIML estimators for coefficients of a single equation in a simultaneous system of equations. The proposed estimators are weighted averages of the 2SLS/LIML estimators and the OLS estimator. The shrinkage weight depends on the Wu-Hausman misspecification test statistic which evaluates the null of exogeneity against the alternative hypothesis of endogeneity. The approximate finite sample bias, mean squared errors, and density functions of the Stein-like shrinkage estimators are obtained using small-disturbance approximations. The dominance conditions of the Stein-like shrinkage estimators over the 2SLS/LIML estimator under the mean squared error and the concentration probability are obtained. The proposed method is further illustrated by simulation studies which demonstrate the good finite sample performance of the method, and is also applied to an empirical application of returns to education.

Suggested Citation

  • Ali Mehrabani, 2024. "Stein-Like Shrinkage Estimators for Coefficients of a Single-Equation in Simultaneous Equation Systems," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202414, University of Kansas, Department of Economics.
    • Handle: RePEc:kan:wpaper:202410
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    File URL: https://kuwpaper.ku.edu/2024Papers/202414.pdf
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    Keywords

    Words: Stein-like Estimator; Small;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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