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A Theory of Attribution


  • Feldman, Barry


Attribution of economic joint effects is achieved with a random order model of their relative importance. Random order consistency and elementary axioms uniquely identify linear and proportional marginal attribution. These are the Shapley (1953) and proportional (Feldman (1999, 2002) and Ortmann (2000)) values of the dual of the implied cooperative game. Random order consistency does not use a reduced game. Restricted potentials facilitate identification of proportional value derivatives and coalition formation results. Attributions of econometric model performance, using data from Fair (1978), show stability across models. Proportional marginal attribution (PMA) is found to correctly identify factor relative importance and to have a role in model construction. A portfolio attribution example illuminates basic issues regarding utility attribution and demonstrates investment applications. PMA is also shown to mitigate concerns (e.g., Thomas (1977)) regarding strategic behavior induced by linear cost attribution.

Suggested Citation

  • Feldman, Barry, 2007. "A Theory of Attribution," MPRA Paper 3349, University Library of Munich, Germany, revised 29 May 2007.
  • Handle: RePEc:pra:mprapa:3349

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    References listed on IDEAS

    1. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612.
    2. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    3. Eduardo Walker, 2006. "Optimal Portfolios In Defined Contribution Pension Systems," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 9(2), pages 99-129.
    4. Detemple, Jerome & Garcia, Rene & Rindisbacher, Marcel, 2006. "Asymptotic properties of Monte Carlo estimators of diffusion processes," Journal of Econometrics, Elsevier, vol. 134(1), pages 1-68, September.
    5. Giacomo Scandolo, 2004. "Models of Capital Requirements in Static and Dynamic Settings," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 33(3), pages 415-435, November.
    6. Suleyman Basak & Alex Shapiro & Lucie Teplá, 2006. "Risk Management with Benchmarking," Management Science, INFORMS, vol. 52(4), pages 542-557, April.
    7. M. Prigent & M. De Palma, 2003. "Optimal portfolio positioning," THEMA Working Papers 2003-24, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    8. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    9. Srinivas, P.S. & Whitehouse, Edward & Yermo, Juan, 2000. "Regulating private pension funds'structure, performance, and investments : cross-country evidence," Social Protection and Labor Policy and Technical Notes 23302, The World Bank.
    10. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2004. "Dynamic monetary risk measures for bounded discrete-time processes," Papers math/0410453,
    12. Wolfram Horneff & Raimond Maurer & Michael Stamos, 2006. "Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal?," Working Papers wp146, University of Michigan, Michigan Retirement Research Center.
    13. Charupat, Narat & Milevsky, Moshe A., 2002. "Optimal asset allocation in life annuities: a note," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 199-209, April.
    14. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    15. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    16. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    17. Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
    18. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    More about this item


    Coalition formation; consistency; cost allocation; joint effects; proportional value; random order model; relative importance; restricted potential; Shapley value and variance decomposition;

    JEL classification:

    • D00 - Microeconomics - - General - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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