Using the SHAPLEY value approach to variance decomposition in strategy research: Diversification, internationalization, and corporate group effects on affiliate profitability

• Author: Paul Kattuman,Dmitry Sharapov,Diego Rodriguez,F. Javier Velazquez
• Published date: 01 March 2021
• Date: 01 March 2021
• DOI: http://doi.org/10.1002/smj.3236

RESEARCH ARTICLE

Using the Shapley Value approach to variance

decomposition in strategy research:

Diversification, internationalization, and

corporate group effects on affiliate profitability

Dmitry Sharapov

1

| Paul Kattuman

2

| Diego Rodriguez

3

|

F. Javier Velazquez

3

1

Imperial College Business School,

London, UK

2

Cambridge Judge Business School,

University of Cambridge, Cambridge, UK

3

Facultad de Ciencias Económicas y

Empresariales, Universidad Complutense

de Madrid and GRIPICO, Madrid, Spain

Correspondence

Dmitry Sharapov, Imperial College

Business School, Tanaka Building,

South Kensington Campus, London SW7

2AZ, UK.

Email: dmitry.sharapov@imperial.ac.uk

Abstract

Research Summary: Variance decomposition methods

allow strategy scholars to identify key sources of het-

erogeneity 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 ran-

dom effects. In this paper, we propose the use of an axi-

omatically 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 internationaliza-

tion 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.

Managerial Summary: A key contribution of strategic

management research to managerial practice is identi-

fying drivers of firm performance that operate at firm,

corporation, industry, and national levels. A branch of

this research measures the relative importance of

Received: 5 September 2014 Revised: 17 August 2020 Accepted: 26 August 2020 Published on: 23 September 2020

DOI: 10.1002/smj.3236

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and

reproduction in any medium, provided the original work is properly cited.

© 2020 The Authors. Strategic Management Journal published by John Wiley & Sons Ltd.

608 Strat Mgmt J. 2021;42:608–623.wileyonlinelibrary.com/journal/smj

factors at these different levels in producing variation in

firm performance, thus helping top managers focus

efforts on aspects of their businesses most likely to yield

performance differences. However, estimates produced by

extant methods are sensitive to method used, and to

modeling choices made. This paper proposes the use of

the “Shapley Value”approach, which is free from such

sensitivity, shows its effectiveness compared to extant

methods, and uses it to explore how the importance of

factors at the level of the business group varies with group

diversification and internationalization.

KEYWORDS

corporate group, diversification, internationalization, Shapley value

regression, variance decomposition

Variance decomposition methods have been vital in research on whether sources of heterogene-

ity in firm performance reside at the business unit, corporation, or industry level

(e.g., Guo, 2017; McGahan & Porter, 1997; Misangyi, Elms, Greckhamer, & Lepine, 2006;

Rumelt, 1991; Schmalensee, 1985). More recently, these methods have also proven useful in

evaluating whether a range of other influences on firm performance actually “matter”in

explaining its variation across firms, including country and regional effects (Chan, Makino, &

Isobe, 2010; Ma, Tong, & Fitza, 2013; Makino, Isobe, & Chan, 2004; McGahan & Victer, 2010),

ownership (Fitza & Tihaniy, 2018), and Chief Executive Officers (Crossland & Hambrick, 2007;

Fitza, 2017; Quigley & Graffin, 2017).

However, 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 sensi-

tive 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

This implies that these methods produce estimates of the share of variance accounted

for by different effects that may be lower- or upper-bound estimates, or anywhere in between,

depending on the above choices.

In this paper, we draw on the statistical literature (Grömping, 2007; Pintér, 2011;

Young, 1985) to propose an axiomatically justified, unique, and effective solution to this limita-

tion: the Shapley Value approach. The Shapley Value for a given effect is its contribution to

model explanatory power, averaged (with weights) over all possible sequential orders in which

the effects could be introduced into the regression model. In the following sections, we intro-

duce the Shapley Value method, before showing its effectiveness compared to currently used

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. We provide a further discussion of the VCA

approach and compare the results that it generates to those produced by other methods below.

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