Economics Letters 117 (2012) 743–745

Contents lists available at SciVerse ScienceDirect

Economics Letters

journal homepage: www.elsevier.com/locate/ecolet

Disentangling disproportionalityThomas Poulsen ∗

Copenhagen Business School, Department of International Economics and Management, Porcelaenshaven 24 A, 2000 Frederiksberg, Denmark

a r t i c l e i n f o

Article history:Received 21 March 2011Received in revised form22 August 2012Accepted 23 August 2012Available online 27 August 2012

JEL classification:G32G34

Keywords:Ownership structureDisproportionalityVoting powerFirm value

a b s t r a c t

The literature on deviations from one share-one vote seems to ignore that a difference between influenceand investment, i.e., disproportionality, may exist without control enhancing mechanisms such as dualclass shares. I propose a method to disentangle disproportionality and argue for its relevance. Theconsequences are documented on a testing data set.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

A certain type of agency problem follows from ownershipstructures with both large and small shareholders. When a largeshareholder controls a firm, the standard assumption that the firmshould be run so as to maximize its value may conflict with thelarge shareholder’s utility maximization.1 A series of papers find anegative relationship between the size of the largest shareholderand the value of outside equity, indicating that such a conflictof interest indeed exists.2,3 This conflict is easily aggravated bycontrol enhancing mechanisms such as dual-class shares sincethey provide the owner of the superior voting shares with moreinfluence (voting rights) thanwhat is warranted by her investment(cash flow rights).

When economic rents are distributed according to influence(voting rights) but paid according to investment (cash flowrights), a difference between voting rights and cash flow rightsclearly creates obscure incentives. The effect has been studied by

∗ Tel.: +45 38152372.E-mail address: tpo.int@cbs.dk.

1 Note that this is not a formal agency problem in the sense that no explicitcontracts exist. Rather, it is a conflict of interest.2 This strand of literature dates back to Stulz (1988), Morck et al. (1988), and

McConnell and Servaes (1990). Recent reviews can be found in Burkart and Lee(2008) and Adams and Ferreira (2008).3 Trying to account for the endogeneity of ownership structures, this relationship

has been questioned by e.g. Demsetz and Lehn (1985) andHimmelberg et al. (1999).

0165-1765/$ – see front matter© 2012 Elsevier B.V. All rights reserved.doi:10.1016/j.econlet.2012.08.036

e.g. Claessens et al. (2002) who find that an approximation ofTobin’s Q increases with the largest shareholder’s cash flow rightsbut decreases with the wedge between voting rights and cashflow rights. What this paper and other papers on deviations fromone share-one vote seem to ignore is that a difference betweeninfluence and investment may exist without control enhancingmechanisms. The ownership structure in itself may provide thelargest shareholder with more influence than what is warrantedby her investment. This can be realized if one thinks of influence interms of voting power rather than voting rights.

Papers on disproportionality ought to notice the differencebetween these two types. In the next section, I will propose amethod to disentangle them. Then, I will present a testing data setand illustrate the importance of noticing the difference. Section 4concludes.

2. Methodology

Power always manifests itself in a relational manner.4 Onecannot meaningfully say that a particular shareholder has powerwithout specifying the role of the remaining shareholders in therelationship as well. For this reason, the method is groundedin the game theoretic idea of voting power instead of the

4 The terms ‘‘influence’’ and ‘‘power’’ are used as synonyms. However, one canmake a distinction between influence as a more general concept and power asintended influence.

744 T. Poulsen / Economics Letters 117 (2012) 743–745

simple dichotomy between control and no control based on somearbitrary criterion in terms of the voting rights of the largestshareholder.

Before presenting the voting power index, it is important tomention that power indices measure a priori voting power. Ingeneral, game theory represents an abstract model of decisionmaking, not the social reality of decision making itself. A priorivoting power is the component of a posteriori voting powerthat shareholders derive solely from the decision rule, computedwithout regard to specific interests and preferences and the natureof the proposal to be voted upon. One can think of it as formalpower as given by the constitutional rules of a collectivity.

2.1. Choosing the right index

A simple voting game is a pair (N, v), where N = {1, . . . , n}is a set of shareholders and v is a characteristic function mappingeach non-empty subset S ⊆ N (a coalition where s represents thenumber of shareholders in the coalition) to 0 (non-winning) or 1(winning), such that:1. v (∅) = 0 (the empty coalition is non-winning) and v (N) = 1

(the coalition of all shareholders is winning),2. there exists at least one subset S ⊆ N such that v (S) = 1 (there

is at least one winning coalition),3. for all subsets S, T ⊆ N, S ⊆ T implies v(S) ≤ v(T ) (a superset

of a winning coalition is also winning),4. for all subsets S ⊆ N, v (S) + v(N \ S) ≤ 1 (for any partition of

the set of shareholders into two disjoint coalitions, at most oneis winning).Such a game is fully specified once the distribution of voting

weights and the decision-making rule are given. A power index isa function Φ that maps a voting game to a vector of real numbers,{φ1, . . . , φn}, and φi is the voting power of shareholder i. TheBanzhaf (1965) index (Bz) and the Shapley and Shubik (1954) index(SS) are instances of such functions:• ΦBz ({N, v}) := φ {φ1, . . . , φn}, where

φi =1

2n−1

S⊆N,i∈S

[v (S) − v(S \ {i})] . (1)

• ΦSS ({N, v}) := φ {φ1, . . . , φn}, where

φi =

S⊆N,i∈S

(s − 1)! (n − s)!n!

[v (S) − v(S \ {i})] . (2)

For the Banzhaf index, we can say that shareholder i is pivotalfor a particular coalition if i’s leaving this coalition turns it from awinning to a non-winning one. The Banzhaf index for shareholderi can then be interpreted as the proportion among all possiblecoalitions (2n) for which shareholder i is pivotal.

For the Shapley–Shubik index, consider all possible sequencesin which the n shareholders can join a coalition one by one.We canthen say that shareholder i is pivotal for a particular sequence if i’sjoining the coalition of all shareholders preceding i in the sequenceturns this coalition from a non-winning to a winning one. TheShapley–Shubik index can thus be interpreted as the proportionamong all such sequences (n!) for which shareholder i is pivotal.

The Banzhaf index does not consider the order or the sequenceof shareholders in a coalition important; it simply considers allpossible coalitions. The Shapley–Shubik index on the other handis analogous to stating that if a coalition is large enough to win,it should avoid accepting additional shareholders, since thesenew shareholders will demand a share of the payoff available tothe winning coalition without contributing essential votes to thecoalition. In other words, a smaller winning coalition is preferablebecause it has a larger group of minority shareholders to extractrents from. This index seems to fit the agency problem betweenlarge and small shareholders well.

2.2. Disproportionality and how to disentangle it

With the distinction between voting rights and voting power,proportionality should no longer be one share-one vote or votingrights according to cash flow rights but rather voting poweraccording to cash flow rights. This means that disproportionalityshould be defined as φ1/c1, where φ1 is the largest shareholder’sShapley–Shubik index and c1 is her relative share of the cash flowrights, instead of v1/c1, where v1 is her relative share of the votingrights.

In order to disentangle disproportionality, it is necessary to bemore careful though. The set of shareholders, N , can be definedeither in terms of voting rights or in terms of cash flow rights andthen voting power reflects either actual influence (φv

1 ) or influencein the situation where the voting rights equals cash flow rights(φc

1). There may be disproportionality in the above sense in bothcases. The difference is due to thewedge between voting rights andcash flow rights. Disproportionality can thus be disentangled in thefollowing way:

Aggregate ≡φv1

c1(3)

Structural ≡φc1

c1(4)

Non-structural ≡φv1

c1−

φc1

c1. (5)

Structural assumes no wedge between voting rights and cashflow rights; it is the disproportionality that the ownership struc-ture in itself may cause. Non-structural is the disproportionalitythat the control enhancing mechanisms may cause. Previous pa-pers have only focused on aggregate disproportionality using vot-ing rights instead of voting power.

3. Data and results

To estimate voting power, one needs an account of theownership structure. This data requirement is different from(more demanding than) that of the largest shareholder’s relativeshare of the voting rights. In most countries, however, smallshareholders are exempted fromdisclosing their ownership stakes,necessitating an assumption about these small shareholders. Twoprocedures can be found in the literature. One assumes that theunobserved shareholders are not influential, the other assumesthat they are influential with some positive probability. BecauseI do not want to inflict powerlessness on small shareholders byconstruction, I assume that each small shareholder holds onepercent of the votes and then add shareholders until the joint votesof all shareholders add up to 100%.

I use the publicly available ownership structure data fromFaccio and Lang (2002). This data provides information aboutownership structures (subject to the limitations set by disclosurerequirements) and deviations from one share-one vote for listedfirms in thirteen European countries. I augment the data withfinancial information from the Worldscope database in order totest the effect of differences between voting rights and cash flowrights on the value of outside equity.

Having compiled a feasible testing data set, I estimate Huberregression coefficients from the following model:

Yi = β0 + β1 Disproportionalityi

+ β2 Disproportionalityi ∗ Quality +

k

βkXi,k + ui (6)

where Yi is an approximation of Tobin’s Q for firm i,Disproportionalityi is a measure of deviation from proportionality

T. Poulsen / Economics Letters 117 (2012) 743–745 745

Table 1The effect of disproportionality in the value of outside equity.

Wedge Voting powerAggregate Structural Non-structural

Disproportionality −0.830***−0.021***

−0.140***−0.012

(0.174) (0.006) (0.030) (0.007)Disproportionality *Quality

0.335*** 0.011*** 0.019*** 0.007***

(0.064) (0.002) (0.004) (0.003)Control variables Yes Yes Yes YesIndustry dummies Yes Yes Yes Yes

Sample size 2868 2868 2868 2868R2 0.196 0.199 0.206 0.206

Note: Standard errors in parentheses.*** Indicate that the coefficient estimates are statistically significantly differentfrom 0 at the 1% level.

between influence and investment, and Xi contains relevant firmcharacteristics identified in the literature.5 Disproportionality isinteracted with a measure of institutional quality instead of hav-ing a country dummy in Xi. This is preferable because it allows aranking of countries. ui is a random error. Table 1 presents the re-sults.

For comparison, the table presents the result when dispropor-tionality is defined as the difference between the largest share-holder’s voting rights and cash flow rights (wedge). The result is inlinewith the existing literature, i.e., there is a negative relationshipbetween the approximation of Tobin’s Q and the wedge betweenvoting rights and cash flow rights. As one would expect, institu-tional quality alleviates the negative effect. I then substitute thewedge with the aggregate disproportionality from Eq. (3) and re-run themodel. The result is also in line with the existing literature,i.e., it is also capable of capturing the negative relationship. And,again, institutional quality alleviates the effect. Notewhat happenswhen disproportionality is disentangled into structural and non-structural disproportionality: structural disproportionality drivesthe aggregate effect. By far, it has the largest impact on the valueof outside equity.

5 I use themarket-to-book ratio as my approximation of Tobin’s Q . I use the anti-director index by La Porta et al. (1998) as my approximation of institutional quality.Xi contains the largest shareholder’s investment and approximations of firm size,leverage, tangibility, and sales growth.

4. Conclusion

Using a straightforward measure such as the differencebetween voting rights and cash flow rights to investigate theeffect of disproportionality on the value of outside equity is notideal. I propose a measure based on voting power rather thanvoting rights and show the importance of noticing the difference;it is a fallacy to equate disproportionality and the mere existenceof control enhancing mechanisms because a difference betweeninfluence and investment may exist without these mechanisms. Ihave shown how this can be realized if one thinks of influence interms of voting power rather than voting rights.

References

Adams, R., Ferreira, D., 2008. One share-one vote: the empirical evidence. Review ofFinance 12, 51–91.

Banzhaf, J., 1965. Weighted voting doesn’t work: a mathematical analysis. RutgersLaw Review 19, 317–343.

Burkart, M., Lee, S., 2008. One share-one vote: the theory. Review of Finance 12,1–49.

Claessens, S., Djankov, S., Fan, J., Lang, L., 2002. Disentangling the incentiveand entrenchment effects of large shareholdings. The Journal of Finance 57,2741–2771.

Demsetz, H., Lehn, K., 1985. The structure of corporate ownership: causes andconsequences. Journal of Political Economy 93, 1155–1177.

Faccio, M., Lang, L., 2002. The ultimate ownership of Western Europeancorporations. Journal of Financial Economics 65, 365–395.

Himmelberg, C., Hubbard, R., Palia, D., 1999. Understanding the determinantsof managerial ownership and the link between ownership structure andperformance. Journal of Financial Economics 53, 353–384.

La Porta, R., Lopez de Silanes, F., Shleifer, A., Vishny, R., 1998. Law and finance.Journal of Political Economy 106, 1113–1155.

McConnell, J., Servaes, H., 1990. Additional evidence on equity ownership andcorporate value. Journal of Financial Economics 27, 595–612.

Morck, R., Shleifer, A., Vishny, R., 1988. Management ownership and marketvaluation: an empirical analysis. Journal of Financial Economics 20, 293–316.

Shapley, L., Shubik, M., 1954. A method for evaluating the distribution ofpower in a committee system. The American Political Science Review 48,787–792.

Stulz, R., 1988.Managerial control of voting rights: financing policies and themarketfor corporate control. Journal of Financial Economics 20, 25–54.