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A Theory of Dichotomous Valuation with Applications to Variable Selection

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  • Hu, Xingwei

Abstract

An econometric or statistical model may undergo a marginal gain when a new variable is admitted, and marginal loss if an existing variable is removed. The value of a variable to the model is quantified by its expected marginal gain and marginal loss. Under a prior belief that all candidate variables should be treated fairly, we derive a few formulas which evaluate the overall performance of each variable. One formula is identical to that for the Shapley value. However, it is not symmetric with respect to marginal gain and marginal loss; moreover, the Shapley value favors the latter. Thus we propose a unbiased solution. Two empirical studies are included: the first being a multi-criteria model selection for a dynamic panel regression; the second being an analysis of effect on hourly wage given by additional years of schooling.

Suggested Citation

  • Hu, Xingwei, 2017. "A Theory of Dichotomous Valuation with Applications to Variable Selection," MPRA Paper 80457, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:80457
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    References listed on IDEAS

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    1. Mrs. Nina Budina & Mr. Borja Gracia & Xingwei Hu & Mr. Sergejs Saksonovs, 2015. "Recognizing the Bias: Financial Cycles and Fiscal Policy," IMF Working Papers 2015/246, International Monetary Fund.
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    4. Monderer, Dov & Samet, Dov, 2002. "Variations on the shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 54, pages 2055-2076, Elsevier.
    5. Ashenfelter, Orley & Krueger, Alan B, 1994. "Estimates of the Economic Returns to Schooling from a New Sample of Twins," American Economic Review, American Economic Association, vol. 84(5), pages 1157-1173, December.
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    7. Osnat Israeli, 2007. "A Shapley-based decomposition of the R-Square of a linear regression," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(2), pages 199-212, August.
    8. Winter, Eyal, 2002. "The shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 53, pages 2025-2054, Elsevier.
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    More about this item

    Keywords

    unbiased multivariate Shapley value; variable selection; marginal effect; endowment bias; model uncertainty;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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