¶ Using the SHAPLEY value approach to variance decomposition in strategy research

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¶ BibTeX

@article{sharapov2021using,
  title={Using the SHAPLEY value approach to variance decomposition in strategy research: Diversification, internationalization, and corporate group effects on affiliate profitability},
  author={Sharapov, Dmitry and Kattuman, Paul and Rodriguez, Diego and Velazquez, F Javier},
  journal={Strategic Management Journal},
  volume={42},
  number={3},
  pages={608--623},
  year={2021},
  publisher={Wiley Online Library}
}

¶ Abstract

Variance decomposition methods allow strategy scholars to identify key sources of heterogeneity in firm performance. However, most extant approaches produce estimates that depend on the order in which sources are considered, the ways they are nested, and which sources are treated as fixed or random effects. In this paper, we propose the use of an axiomatically justified, unique, and effective solution to this limitation: the “Shapley Value” approach. We show its effectiveness compared to extant methods using both simulated and real data, and use it to explore how the importance of business group effects varies with group diversification and internationalization in a large, representative sample of European firms. We thus demonstrate the method’s superior accuracy and its usefulness in asking and answering new questions.

¶ Notes and Excerpts

while the methods used for variance decomposition have been improved in a number of ways (for an overview, see Guo, 2017, pp. 1328–1330), most extant approaches share an important limitation: unless the effects under study are orthogonal, the estimates are sensitive to choices regarding the order in which the effects are introduced into the models; which effects are treated as fixed versus random; and which effects are considered to be nested in others.1
1 While random effects variance decomposition methods, which we will refer to as Variance Components Analysis (VCA), do not share this order-dependence limitation when used to estimate models without a nesting structure, this is because they make strong assumptions regarding effect distributions

Alternative approaches have also been used, including simultaneous equation modeling (Brush, Bromiley, & Hendrickx, 1999), nonparametric estimation (Ruefli & Wiggins, 2003), and multilevel modeling (Guo, 2017; Hough, 2006; Misangyi et al., 2006). These are not exempt from criticism (Guo, 2017; Hough, 2006; McGahan & Porter, 2005). The multilevel approach appears to be the most promising, as it explicitly takes the cross-nested structure of variation in firm performance into account. Examples include observations across time being nested within firms, and firms in turn being cross-nested within both business groups and industries (Misangyi et al., 2006), or firms being nested within corporate groups (Majumdar & Bhattacharjee, 2014). Thus, this approach allows for the estimation of random effects variance components like the VCA method but allows for general multilevel error structures in deriving more accurate variance component estimates (Guo, 2017; Hough, 2006). It can produce estimates of the dispersion importance of both random and fixed effects. However the estimates produced by a cross-nested multilevel approach will also depend on choices of which effects are considered to be nested in others, and which cross-nesting effects (e.g., industry or corporate group) are treated as being random versus fixed (see Misangyi et al., 2006, pp. 580–581).3

This paper goes on to compare SHAPLEY and other variance decomposition techniques on a simulated dataset.

CF lundberg2017unified