Hu, Xingwei
(2017):
*A Theory of Dichotomous Valuation with Applications to Variable Selection.*

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## 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.

Item Type: | MPRA Paper |
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Original Title: | A Theory of Dichotomous Valuation with Applications to Variable Selection |

English Title: | A Theory of Dichotomous Valuation with Applications to Variable Selection |

Language: | English |

Keywords: | unbiased multivariate Shapley value; variable selection; marginal effect; endowment bias; model uncertainty |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C57 - Econometrics of Games and Auctions C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty |

Item ID: | 80457 |

Depositing User: | Xingwei Hu |

Date Deposited: | 02 Aug 2017 09:34 |

Last Modified: | 11 Oct 2019 04:31 |

References: | [1] M. Arellano, S. Bond, Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations, Rev. Econ. 415 Stud. 58 (1991), 277-297. [2] O. Ashenfelter, A. Krueger, Estimates of the economic return to Schooling from a new sample of twins, Amer. Econ. Rev. 84(1994), 1157-1173. [3] O. Ashenfelter, C. Rouse, Income, schooling, and ability: evidence from a new sample of identical twins, Quart. J. Econ. 113(1998), 253-284. [4] R.J. Aumann, L.S. Shapley, Values of Non-Atomic Games. Princeton University Press, Princeton, NJ (1974). [5] J.F. Banzhaf, Weighted voting doesn't work: a mathematical analysis, Rutgers Law Rev. 19(1965), 317-343. [6] G.E.P. Box, Science and Statistics, J. of Amer. Stat. Assoc. 71(1976), 791-425 799. [7] N. Budina, B. Gracia, X. Hu, S. Saksonovs, Recognizing the Bias: Financial Cycles and Fiscal Policy, IMF Working Paper No. 15/246 (2015). [8] M. Clyde, E. I. George, Model Uncertainty, Statistical Science 19(2004), 81-94. [9] F. Devicienti, Shapley-value decomposition of changes in wage distributions: a note, J. Econ. Inequal 8(2010), 35-45. [10] D.A. Freedman, A Note on Screening Regression Equations, Amer. Statistician 37(1983), 152-155. [11] E.I. George, R.E. McCulloch, Approaches for Bayesian variable selection, 435 Statistica Sinica 7(1997), 339-373. [12] U. Gromping, Estimators of relative importance in linear regression based on variance decomposition, Amer. Statistician 61(2007), 1-9. [13] X. Hu, Value of Loss in n-Person Games, UCLA Comput. Appl. Math. Reports 02-53 (2002). [14] X. Hu, An asymmetric Shapley-Shubik power index, Intl. J. Game Theory 34(2006), 229-240. [15] O. Israeli, A Shapley-based decomposition of the R-Square of a linear regression, J. Econ. Inequal 5(2007), 199-212. [16] S. Lipovetsky, M. Conklin, Analysis of regression in game theory approach, Appl. Stoch. Models in Business Industry 17(2001), 319-330. [17] N. Megiddo, On Finding Additive, Superadditive and Subadditive Set-Function Subject to Linear Inequalities, RJ 6329 (61998) 7/11/88, Computer Science/Nathematics, IBM Almaden Research Center, San Jose, California. [18] D. Monderer, D. Samet, Variations on the Shapley Value. In: R.J. Aumann and S. Hart (eds) Handbook of Game Theory, vol 2, Chapter 54 (2002), pp.2055-2076. Elsevier Science, Netherlands. [19] R.B. O'Hara, M.J. Sillanpaa, A Review of Bayesian Variable Selection Methods: What, How and Which, Bayesian Analysis 4(2009), 85-118. [20] P.J. Rousseeuw, Multivariate estimation with high break-down point. In: W. Grossmann et al. (eds.) Mathematical Statistics and Applications, vol. B(1985), pp.283-297. Akademiai Kiado, Budapest. [21] L.S. Shapley, A value for n-person games. In: H.W. Kuhn and A.W. Tucker (eds.) Contributions to the Theory of Games, Annals of Math. Studies, vol. 28 (1953), pp.307-317. Princeton University Press, Princeton, New Jersey. [22] E. Winter, The Shapley Value. In: R.J. Aumann and S.Hart (eds) Handbook of Game Theory, vol 2, Chapter 53 (2002), pp.2025-2054. Elsevier Science, Netherlands. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/80457 |