A Theory of Attribution

Feldman, Barry (2007): A Theory of Attribution.

Abstract

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.

• Item Type: MPRA Paper
• Institution: Prism Analytics
• Language: English
• Keywords: Coalition formation; consistency; cost allocation; joint effects; proportional value; random order model; relative importance; restricted potential; Shapley value and variance decomposition
• Subjects: D - Microeconomics > D0 - General > D00 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General