Product Market Competition’s Effect on Earnings Management When Audit Quality Is Endogenous: Theory and Evidence

Andrew Samuel; Jeremy Schwartz

doi:10.1515/rle-2018-0044

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Product Market Competition’s Effect on Earnings Management When Audit Quality Is Endogenous: Theory and Evidence

Andrew Samuel und Jeremy Schwartz

Veröffentlicht/Copyright: 10. April 2019

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Aus der Zeitschrift Review of Law & Economics Band 15 Heft 3

Abstract

A long standing question is whether product market competition disciplines a firm’s incentive to engage in earnings management. This paper argues that this question cannot be investigated adequately without accounting for the quality of firms’ auditors, because auditors affect the probability of discovering earnings management. Since firms choose their auditor, a non-compliant firm can alter its own probability of being detected. Consequently, a firm’s decision to manage earnings is a function of its auditor’s quality, which is itself endogenously chosen by the firm. To study this issue we develop a game-theoretic model that captures the potential inter-relationship between industry competition, the firms’ choice of audit quality, and compliance with accounting regulations (or the degree of earnings manipulation). We show that the link between financial compliance and product market competition is affected by the endogenously chosen audit quality. We estimate this model’s structural parameters and find that greater competition reduces both compliance and the demand for high quality audits.

Keywords: Oligopoly; Cournot; auditing; earnings management

JEL Classification: L13; L15; K42

Acknowledgement

The authors would like to thank conference participants and discussants at the 2018 Center for Legal Theory and Empirical Jurisprudence Meetings, 2017 Canadian Law and Economics Conference, 2017 Public Economic Theory Conference (Paris), and seminar participants at the Judaical Behavior Seminar Series (Catholic University of Leuven), Towson University, and the brown bag workshop at Loyola University, Maryland. We also greatly appreciate Dr. Christoph Engel, Editor, Review of Law & Economics and an anonymous referee for their careful read of our paper and insightful comments. Finally, we acknowledge and are grateful for the generous support of the National Science Foundation (grant number 1626262) as part of the Major Research Instrument initiative that enabled some of the computational work forr this study. All remaining errors are ours.

A Theory Appendix

Proof of Lemma 1

The profit function for firm i is,

(10)πi=qiP+qi(1−γi)b+Tai+Bγiai−k0γi−k1γi22−gai22

Solving backwards, the first order condition with respect to ai yields,

ai∗=T+γiBg.

Substituting ai∗ into expression eq. (10), and yields,

qiα−βqi−βQ−i+(1−γi)b+T+Bγi2g2−k0γi−k1γi22

where Q−i is the sum of all firm’s quantities except firm i. The first order condition for γi, equation (3) implies that

γi=TB−gk0gk1−B2−gbgk1−B2qi

Since the first order condition for γi eq. (3) is a function only of qi, we substitute eqs. (3) into (2) to derive the Nash equilibrium. Further note that since γi is a function of only qi since firms observe each other’s quantities, they can also infer each others level of compliance (when making their audit decisions in stage 3). Substituting eqs. (3) into (2) yields,

α−2β−b2ggk1−B2⏟δqi−βQ−i+b1−TB−gk0gk−B2⏟C=0

α−qiδ−βQ−i+C.

Summing N firms FOCs and solving for a symmetric q∗ yields

q∗=α+Cδ+β(N−1),

where π‾∗=β(q∗)2−k‾(γ∗). Substituting the values for β and C into the expressions for q∗, γ∗ and π∗ yield the expressions identified in lemma 1.

Assumption 1

A standard Cournot assumption is that α > 0. Thus, when non-compliance generates a competition dependent benefit, i.e. b > 0, then the standard Cournot assumption is sufficient, and assumption 1 is redundant. When non-compliance generates a cost, i.e. b < 0, then Assumption 1 is required to ensure that firms do not shut-down for any value of γi.

Assumption 2

Assumption 2 is introduced in order to ensure that ai∈[0,1]. The derivative of profits with respect to ai is,

T+γiB−gai.

Therefore, a sufficient condition to ensure that a∗>0 is that T>|B|. To ensure that a∗<1, at a = 1 we need

g>T+B.

Assumption 3

Assumption 3 ensures that the profit function is quasiconcave in qi and γi and also ensures that γi<1 in equilibrium. Conditions for quasiconcavity require,

∂2πi∂qi2=−2β

which is negative since β > 0, and

∂2πi∂γi2=B2g−k1.

is negative if gk1−B2>0 which is the first part of Assumption 3.

(∂2πi∂qi2)(∂2πi∂γi2)−(∂2πi∂qi∂γi)2>0⇔

(−2β)(B2g−k1)−b2>0⇔k1>gb2+β2B22gβ≡kˆ

Next to ensure that γi≤1, we need

k1>(B2+BT−k0g)β(1+N)−αbgβ(1+N)g≡k′,

which follows directly from the expression for γ∗. Since BT−k0g must be positive for γ∗>0 and α+b>0 (from assumption 1) it follows that

(B2+BT−k0g)β(1+N)+α|b|gβ(1+N)g>k′,

regardless of whether b>/<0. The left hand side of the previous inequality is decreasing in N. Thus, if

(11)k1>gα|b|+(B2+BT−k0g)2β2βg,

it is satisfied for all N. (That is, since it is decreasing in N if it is satisfied at N = 2 it is satisfied for all N > 2.) Finally, the right hand size of condition eq. (11) is greater than k^ʹ; that is,

gα|b|+2β(B2+BT−k0g)2gβ>gb2+2βB22gβ⏟kˆ

Thus,

k1>(B2+BT−k0g)β(1+N)+α|b|gβ(1+N)g,

is sufficient to ensure that both γ∗<1 and that the quasi-concavity assumption is satisfied.

Note that we derive the above sufficient condition so that we can make one assumption to characterize the interior, symmetric, Nash equilibrium of Lemma 1. However, these conditions are not necessary, therefore, are only relevant to our structural estimation if the parameters achieve a corner solution.

Proof of Proposition 1

The first claim in proposition 1, that γ∗ is decreasing in N follows directly from taking the derivative of the expression for γ∗. Where

dγ∗dN=bgβ(TB−k0g)f+(gk−B2)(α+b)D2

where D is the denominator of the expression for γ∗. Note that the term inside the square brackets is the numerator of q∗ which is strictly positive under our assumptions. Thus, compliance is decreasing in N if b < 0. When b > 0, then γ∗ is increasing in N. Without re-deriving the expression for γ, this can be observed directly from the first order condition for γ, equation (3). We know that qi is always decreasing in N. Therefore if b > 0, then when N increases qi decreases and γi increases.

The second claim follows directly from the expression for a∗. Specifically, a∗ and γ∗ move in the same (opposite) direction with respect to N when B > 0 (< 0).

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Published Online: 2019-04-10

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https://doi.org/10.1515/rle-2018-0044

Schlagwörter für diesen Artikel

Oligopoly; Cournot; auditing; earnings management