frantz - 1999 - auditor's skill, auditing standards, litigation, and audit quality

When auditors’ levels of skill are unobservable, the introduction of either restrictions on costs awarded by the courts or an imperfection in the courts’ technology is shown to lead the

Article No bare.1999.0096, available online at http://www.idealibrary.com on

AUDITOR’S SKILL, AUDITING STANDARDS, LITIGATION, AND AUDIT QUALITY

PASCAL FRANTZ

London School of Economics and Political Science

This paper introduces a model of the market for audit services in which auditors differ

in their levels of skill, which may or may not be observable and capture differences in ability The model captures the interplay amongst auditing standards, litigation, and auditors’ levels of skill, which determines auditors’ responses to auditing standards The paper shows that the quality of audit supplied by any auditor is increasing in the auditor’s level of skill regardless of whether or not auditors’ levels of skill are observable.

An increase in the quality of audit prescribed by auditing standards is shown to induce some auditors endowed with low levels of skill to decrease the quality of their audits so that the average quality of audit and economic welfare may actually decline as auditing standards are raised Auditors’ choices of audit quality are furthermore shown to be increasing in trial awards Incentives for trials and out-of-court settlements are shown

to depend crucially on whether or not auditors’ levels of skill are observable Only when auditors’ levels of skill are unobservable do trials obtain with some probability When auditors’ levels of skill are unobservable, the introduction of either restrictions

on costs awarded by the courts or an imperfection in the courts’ technology is shown to lead the most skilled auditors to supply audits of a quality strictly exceeding the quality prescribed by the prevailing auditing standards When the courts err often enough, the most skilled auditors having exercised due care furthermore make offers to settle when sued.

 1999 Academic PressINTRODUCTION

The last decades have seen a dramatic increase in litigation against auditors.Although the litigation crisis is most profound1in the USA, it has not sparedthe UK, where Price Waterhouse and Ernst & Young face a multi-billion

This paper is based on Discussion Paper No 235, Financial Markets Group, London School of Economics and Political Science The author would like to thank Sudipto Bhattacharya, Michael Bromwich, Ronald Dye, Christopher Napier, Bharat Sarath, Marleen Willekens, and other participants

at various workshops, the 1996 Annual Congress of the European Accounting Association, and the

1996 International Symposium on Audit Research.

Please address all correspondence to: Pascal Frantz, Department of Accounting and Finance, London School of Economics and Political Science, Houghton Street, London WC2A 2AE.

Received February 1998; revised September 1998; accepted November 1998.

dollar writ in connection with audits of the collapsed Bank of Credit andCommerce International This paper introduces a model of the marketfor auditing services designed to capture the interplay amongst auditingstandards, litigation, and auditors’ levels of skill, which determines auditors’responses to auditing standards and other legal parameters The model is avehicle for asking the following questions: How is the choice of audit qualityrelated to an auditor’s level of skill? Why do some auditors settle out-of-courtwhile others go to trial? What effect does the increasing number of auditingstandards have on both the equilibrium schedule of audit quality chosen byauditors and the resulting frequency of trial? Do limits on trial awards reducethe average quality of audit? How do restrictions on litigation costs awarded

by the courts or a move from the English to the American rule on litigationcosts affect the equilibrium schedule of audit quality and the resultingfrequency of trial? How does an imperfection in the courts’ technologyaffect the average quality of audit supplied or the frequency of trial?

The accounting literature suggests that audit firms differ in the quality

of the audits supplied (Palmrose, 1988)2 Dye (1993) explains systematicdifferences in the quality of audit supplied by various auditors through

differences in auditors’ levels of wealth Nelson et al (1988) show how the

quality of an audit is related to the quality of the client’s internal controlsystem This paper explains differences in audit quality through differences

in levels of skill, which may or may not be observable and capture differences

in ability Any auditor, whatever his level of skill, can supply audits of anyquality The direct cost of an audit of any quality is however strictlydecreasing in the auditor’s level of skill Differences in auditors’ levels ofskill may be explained by differences in knowledge3 or audit technology4.This paper also differs from the above papers by explicitly modelling thelitigation phase Related papers in the legal literature include Hylton (1993),Hay (1995), and Hughes & Snyder (1995)

As in the contemporaneous literature, the quality of an audit is assumednot to be observable either at the time the audit is purchased or performed,incentives to supply high quality audits are provided by the threat oflitigation (Moore & Scott, 1988; Sarath & Wolfson, 1988; Balachandran &Nagarajan, 1991; Narayanan, 1994; Thoman, 1996; Schwartz, 1997) Themodel captures the following features of litigation against auditors in the

UK Auditors owe a duty of care to the company5 Litigation against auditors

is initiated by insolvency practitioners such as receivers and liquidators infinancially distressed firms6 Auditors are liable under a rule of joint andseveral liability Courts’ decisions are based on a rule of negligence Therelevant law on litigation costs is defined by the English rule7

The paper considers exogenous differences in levels of skill amongstauditors and examines the dependence of the quality of audit supplied by anauditor and the subsequent litigation choices made by this auditor if sued

on his level of skill, trial awards, litigation costs, and auditing standards.Regardless of whether or not auditors’ levels of skill are observable, the

quality of audit supplied by any auditor is shown to be increasing in theauditor’s level of skill An increase in the quality of audit prescribed byauditing standards is shown to induce some auditors endowed with lowlevels of skill to decrease the quality of their audits so that the averagequality of audit and economic welfare may actually decline as auditingstandards are raised Auditors’ choices of audit quality are furthermoreshown to be increasing in trial awards Incentives for trials and out-of-courtsettlements are shown to depend crucially on whether or not auditors’ levels

of skill are observable Only when auditors’ levels of skill are unobservable

do trials obtain with some probability When auditors’ levels of skill areunobservable, the introduction of either restrictions on costs awarded by thecourts or an imperfection in the courts’ technology is shown to lead the mostskilled auditors to supply audits of a quality strictly exceeding the qualityprescribed by the prevailing auditing standards When the courts err oftenenough, the most skilled auditors having exercised due care furthermoremake offers to settle if sued

The paper proceeds as follows Section 2 introduces the basic modeland derives an auditor’s equilibrium litigation and audit quality choices as

a function of his level of skill, trial awards, litigation costs, and auditingstandards Section 3 analyses in typical legal environments the effect ofchanges in the quality of audit prescribed by auditing standards on thequality of audit adopted by auditors, economic welfare, and the resultingfrequency of trial Section 4 analyses the effect of changes in legal parameters

on the quality of audit adopted by auditors and the resulting frequency oftrial Section 5 considers the effect of restrictions on costs awarded bythe courts Section 6 introduces an imperfection in the courts’ technology.Section 7 presents a brief summary of the paper

AUDITOR’S SKILL AND AUDIT QUALITY

This section first introduces a model of the market for audit services inwhich auditors differ in their levels of skill and audits may or may not

be discretionary It then analyses an auditor’s litigation and audit qualitychoices as a function of his level of skill, trial awards, litigation costs, andauditing standards

The basic model

Demand for audit services is generated by the sale of firms by one generation

to another generation of risk-neutral8 investors for life-cycle reasons Each

firm sold may ultimately turn out to be either a success (denoted by S), generating cash-flow X S , or a failure (denoted by F), generating cash-flow

X F , with 0<X F <X L <X S and X L representing the cash-flow that can beobtained from an early liquidation of the firm If investors could distinguishbetween successful and failing firms, they would thus liquidate9 the latter

firms Investors however cannot10distinguish between successful and failingfirms Only the fraction of successful firms11 in the population, p2.0, 1/,

is known

Audit technology Auditors own a technology that aids in distinguishing

between successful and failing firms The audit process may be summarized

as follows Every firm that hires an auditor requests him to attest to the reportthat it is ultimately successful In his duties, the auditor acquires additionalinformation about the audited firm’s type Based on this information, theauditor either agrees to attest to the firm’s original favourable report andissues an unqualified opinion (denoted by ‘S’) or, instead, disagrees with theproposed report and issues a going concern qualification12(denoted by ‘F’).The relation between the audit report, the audited firm’s actual condition,

and the quality q of the audit is summarized by the following conditional

probabilities: nPr.‘F’jF, q/ Dq

That is, if the auditor adopts an audit of quality q, the likelihood that he

correctly issues a qualified report, given that the audited firm ultimately

fails, is q Conversely, if the audited firm is ultimately successful, the auditor

is assumed not to obtain any information indicating that the firm might failand thus always issues an unqualified opinion for such firms13,14

Auditor’s level of skill and audit cost Each auditor is a utility-maximizing,

risk-neutral agent, who has the ability to audit at most one firm in a period

He strategically chooses how hard to work, that is his level of effort e, and thus the quality q of his audit, which is strictly increasing in the level of effort supplied Both the level of effort e and the quality of audit q are

assumed not to be observable either at the time the audit is purchased or

performed Auditors differ in a factor n, which may or may not be publicly

observable and will be referred to as skill Any auditor, whatever his level

of skill, can supply audits of any quality in the interval 

q, 1

, where q

is a lower bound on audit quality The direct cost of an audit of quality

q supplied by an auditor of skill n, C.q, n/, is however strictly increasing

in q on q, 1

, C q >0, and strictly decreasing in n, C n<0 The marginal

cost of producing an audit of quality q strictly increases in q , C qq>0, and

strictly decreases in n, C qn<015 C.q, n/ furthermore satisfies the following boundary conditions: 8n, C.q, n/D0, C q q, n/D0, and lim q!1 C.q, n/DC1.

The distribution of auditors’ skill has a density w.n/ with support [0, nmax] Its associated distribution function is denoted by W n/.

Auditor’s liability Unless disciplined, an auditor would always choose the

lowest level of audit quality q The incentive to supply higher quality

audits is provided by the threat of litigation: conditional on a firm’s failure,the firm’s auditor may be sued on behalf of the ‘company’ by the firm’s

insolvency practitioner The relevant law is defined by a rule of negligenceand the courts own a technology allowing them to discover the defendant’sbehaviour without error16 There is some level of audit quality qŁprescribed

by the prevailing auditing standards such that, conditional on the failure ofthe firm and issuance of an unqualified opinion by the firm’s auditor, the

auditor is only liable if the quality q of his audit is strictly lower than qŁ17,18.The relevant law on litigation costs is defined by the English rule: the loser

at trial pays the litigation costs of both parties

Suits need not end up in trials: the defendant, that is, the auditor, canmake a settlement offer and the plaintiff, that is, the insolvency practitioner,can accept the offer or go to trial More formally, the litigation process is

as follows The plaintiff, who believes that the defendant is negligent withsome probability p, must decide whether or not to file suit on behalf of thecompany The defendant, who knows whether or not he is negligent, thenresponds with a settlement offer (a settlement offer of zero is equivalent

to no settlement offer) The plaintiff finally chooses between accepting thesettlement offer and going to trial (acceptance of a zero settlement offer

is equivalent to dropping the action) Both parties, who are assumed to

be risk-neutral, take their decisions knowing that, if the defendant is found

negligent by the courts, he must pay trial awards A to the plaintiff in addition

to the plaintiff’s litigation costs P and his own litigation costs D19 Neitherparty incurs any costs20 if the plaintiff drops the case before trial or if thecase is settled

Demand for audit services Audits may be discretionary or mandatory As in

Dye (1995), the audit market operates as follows Each potential auditorchooses which fee to charge Firms’ owners observe the posted audit fees(and levels of skill when observable) and conjecture about both the quality

of audit supplied by each potential auditor and the expected value derivedfrom hiring each potential auditor The owners of each firm then either hire

an auditor from amongst those offering the highest audit value or hire none,depending on which decision makes them better off (the latter alternativebeing only available when audits are discretionary)

The benefit derived by a firm’s owners from an audit gross of the auditfee that is, the gross value of an audit, lies in the rise in the firm’s expectedselling price An audit increases the firm’s expected selling price for thefollowing reasons First, it assists in identifying and liquidating firms whoseliquidating values exceed their going-concern values (information value of

an audit) Second, it provides gains from litigation if the firm subsequentlyfails, the auditor did not issue a going concern qualification, and the auditwas negligent (litigation value of an audit) Equilibrium audit fees aredetermined as follows In any market equilibrium, as all firms are ex-anteidentical, the net value of an audit, that is, the gross value of an audit lessthe audit fee, must be the same across all firms that hire auditors and acrossall potential auditors seeking to be employed

Strategic analysis

This subsection analyses the schedule of audit quality supplied by auditorsand litigation choices made by insolvency practitioners and auditors Theanalysis is based on the concept of a perfect Bayesian equilibrium (PBE) Aset of strategies and beliefs constitutes a PBE if it is sequentially rational,that is, if at any stage of the game, the strategies are optimal given beliefs andbeliefs are obtained from equilibrium strategies and observed actions usingBayes’ rule In addition, we impose the condition that weakly dominatedstrategies be excluded21

Equilibrium litigation choices The equilibrium litigation choices made

by auditors and insolvency practitioners depend on whether or notauditors’ levels of skill are observable When auditors’ levels of skill areunobservable, there are two possible sequences of equilibrium litigationstrategies: no suit and semi-separating suit equilibrium strategies If theinsolvency practitioners’ expected return from trial is non-positive, that

is, pA 1 p/.P C D/  0, the insolvency practitioners do not sue and

the no suit sequence of equilibrium litigation strategies obtains If theinsolvency practitioners’ expected return from trial is strictly positive, that

is, pA 1 p/.P CD/>0, the semi-separating suit sequence of equilibrium

litigation strategies described in Lemma 1 obtains

LEMMA1: Assuming that auditors’ levels of skill are unobservable and that insolvency practitioners’ expected return from trial is strictly positive, that is,

A 1 /.P C D/ > 0, the following sequence of strategies are equilibrium

strategies22:

Insolvency practitioners file suit;

Negligent auditors make offers of A with probability A 1 /.PCD/A , and make no offer to settle with the complementary probability;

Careful auditors make no offer to settle;

Insolvency practitioners accept offers to settle of A, but in response to no offer

to settle, drop their actions with probability ACPCDPCD , and go to trial with the complementary probability.

PROOF: A proof of Lemma 1 can be found in the Appendix

In the semi-separating suit sequence of equilibrium strategies, a portion of negligent auditors thus reveal their types through offers to settle.The complementary proportion of negligent auditors mimic the behaviour

pro-of the careful auditors by making no settlement pro-offer The informationcontent of a refusal to settle is thus clouded Some insolvency practitionersrespond by bringing their cases to trial while others drop their actions

COROLLARY1: Conditional on the failure of a firm and the firm’s auditor having filed an unqualified report, the probabilities of the various litigation outcomes are:

1  for trial;



1 1  PCDA 

for settlement;

.1 /PCDA for the action being dropped.

COROLLARY2: Conditional on the failure of a firm and the firm’s auditor having filed an unqualified report, the expected payoffs to the various parties arising from litigation are as follows:

A gain of A 1 /.PCD/ for insolvency practitioners;

A loss of A for negligent auditors;

No gain or loss for careful auditors.

When auditors’ levels of skill are observable, there are two possiblesequences of equilibrium litigation strategies: no suit and separating suitequilibrium strategies If no auditor is negligent, insolvency practitionersnever sue and the no suit sequence of equilibrium litigation strategiesobtains Conversely, if some auditors are negligent, the separating suitsequence of equilibrium litigation strategies described in Lemma 2 obtains

LEMMA2: Assuming that auditors’ levels of skill are observable and that some auditors are negligent, the following sequence of strategies are equilibrium litigation strategies23:

Insolvency practitioners file suit;

Negligent auditors make offers of A;

Careful auditors make no offers to settle;

Insolvency practitioners accept offers to settle of A, and in response to no offer to settle, drop their actions.

PROOF: In the event of failure, the insolvency practitioner infers from

the equilibrium schedule of audit quality q.n/ and from knowledge of the auditor level of skill n the quality of audit supplied There is no asymmetry

of information between the auditor and the insolvency practitioner and notrial ever takes place

Litigation outcomes depend on the level of care taken by the auditor inonly two sequences of equilibrium litigation strategies: the semi-separatingand separating suit sequences of equilibrium strategies In the no suitsequence of equilibrium strategies, no suits are filed and there are thus noincentives for auditors to perform audits whose quality exceeds the lower

bound on audit quality q The lack of filing of any suits can thus only arise

in equilibrium if the quality level qŁ prescribed by the prevailing auditing

standards does not exceed the lower bound on audit quality q, which is not

very interesting As equilibrium strategies arising in the litigation phase, weshall therefore adopt those described in Lemma 1 when auditors’ levels ofskill are unobservable and those described in Lemma 2 when auditors’ levels

of skill are observable Whether or not auditors’ levels of skill are observable,

there is thus no gain or loss in the litigation stage for careful auditors and

the expected loss of a negligent auditor is equal to trial awards A.

Equilibrium choices of audit quality As the quality of an audit is not publicly

observable when the auditor’s report is issued, the equilibrium choice ofaudit quality made by an auditor is the one minimizing the total cost ofthe audit, with the total cost of an audit being the sum of the direct cost

C.q, n/ and the expected loss arising from any litigation by the insolvency

practitioner working on behalf of the auditee in the event of the auditee’sfailure An auditor can only be sued if the audited firm fails and the auditordid not issue a going concern qualification Conditional on performing an

audit of quality q, an auditor’s expected cost arising from litigation can thus

be written as l.q/d.q, qŁ/A, where l.q/.1 p/.1 q/ represents the auditor’s

joint probability of auditing a failing firm and issuing an unqualified report

and d.q, qŁ/, with d.q, qŁ/1 if q<qŁ and d.q, qŁ/0 if q½qŁ, is an indicator

of auditor’s negligence (d.q, qŁ/ D 1 indicates that the auditor supplied a

negligent audit while d.q, qŁ/D0 indicates that the auditor exercised due

care) An auditor of skill n thus chooses the level of audit quality (and hence the level of effort) minimizing the function fC.q, n/Cl.q/d.q, qŁ/Ag

over

q, 1

As shown in Figure 1, this function presents a discontinuity: it

follows the function fC.q, n/Cl.q/Ag up to the quality qDqŁ, whereupon it

follows the function fC.q, n/g.

Figure 1 Total expected cost of an audit.

This analysis confines attention to ‘typical legal environments’, withtypical legal environments satisfying the following definitions:

DEFINITION1: A legal environment is defined as the set fqŁ, A, P, Dg.

DEFINITION2: A legal environment is said to be typical if the following conditions are satisfied:

At least one employed auditor elects to be negligent;

At least one employed auditor elects to exercise due care.

Restricting the analysis to legal environments in which at least oneemployed auditor elects to supply a negligent audit does not entail muchloss of generality If all employed auditors elect to exercise due care and

the quality level qŁ prescribed by the prevailing auditing standards strictly

exceeds the lower bound on audit quality q, no equilibrium can obtain24 Theintuition is as follows If all employed auditors exercise due care, there is noincentive for insolvency practitioners to file suit But, given that insolvencypractitioners do not file any suits, all auditors supply negligent audits

Audit cost functions corresponding to different levels of skill n in a typical

legal environment are shown in Figure 2

LEMMA3: The level of effort e supplied by an auditor of skill n if employed,

e.n/, and hence the quality q of the audit supplied, q.n/, are increasing in n.

Figure 2 Total expected cost for auditors with various levels of skill.

PROOF: A proof of Lemma 3 can be found in the Appendix The intuition

is as follows Any auditor, whatever his level of skill, can supply audits ofany quality The direct cost of an audit of any quality is however strictlydecreasing in the auditor’s level of skill The level of effort supplied by

an auditor if employed, and hence the quality of audit supplied, are thusincreasing in the auditor’s level of skill

From Figure 2, it can be inferred that, for any level of audit quality qŁprescribed by the prevailing auditing standards, there exists a critical level

of skill n B such that an auditor of this level of skill would be indifferentbetween being negligent and exactly meeting the level of quality prescribed

by the prevailing auditing standards More formally, this condition may berewritten as:

min

q fC.q, n B /Cl.q/AgDC.qŁ, n B/ 2/The solution to the left-hand side of this equality may be characterized bythe first order condition:

PROOF: A proof of Proposition 1 can be found in the Appendix

As illustrated in Figure 3, auditors with lower levels of skill thus choose tosupply negligent audits Auditors with higher levels of skill elect to provideaudits of the quality prescribed by the prevailing auditing standards The

equilibrium schedule of audit quality q.n/ is furthermore discontinuous at

n B

PROPOSITION2: The expected cost of an audit supplied by an auditor of skill n strictly decreases in n over [0, nmax] When auditors’ levels of skill are

unobservable, there thus existsbnB½0 such that the set of levels of skill employed

auditors are endowed with is the interval

bnB, nmax

.

PROOF: A proof of Proposition 2 can be found in the Appendix

When auditors’ levels of skill are unobservable, the set of employedauditors thus consists of the most skilled auditors The intuition is asfollows When auditors’ levels of skill are unobservable, the fee related to

Figure 3 Equilibrium schedule of audit quality.

the audit supplied by any auditor is independent of the auditor’s level ofskill25 The expected cost of an audit supplied by any auditor howeverstrictly decreases in the auditor’s level of skill The profit expected from

an audit thus strictly increases in the auditor’s level of skill As the set ofauditors willing to enter the market consists of those endowed with levels ofskill for which the profit expected from an audit is non negative, the set ofemployed auditors thus consists of the most skilled auditors26

Unconditional frequencies of litigation outcomes Let us define the unconditional

frequency of a given litigation outcome as the probability of an audit beingfollowed by litigation leading to that litigation outcome When auditors’

levels of skill are observable, Pr.Trial j F, ‘S’/ D 0 and the unconditional frequency of trial, Pr.Trial j F, ‘S’/Pr.F j ‘S’/Pr.‘S’/, is thus nil When auditors’ levels of skill are unobservable, from Corollary 1, Pr.TrialjF, ‘S’/D

1 p As the set of employed auditors is the interval 

bn B , nmax

, Pr.F j

‘S’/Pr.‘S’/DRnmax

bn B l[q.n/]w.n/dn bn B/, and the unconditional frequency

of trial is thus 1 p/ .bnB/ But by Bayes’ rule, 1 p D.n B/

COROLLARY3: When auditors’ levels of skill are observable, the unconditional frequency of trial is nil When auditors’ levels of skill are unobservable,

The unconditional frequency of trial is .nB/;

The unconditional frequency of settlement is .bnB/ .nB/ PCDA .nB/;

The unconditional frequency of dropping of a suit is PCDA .nB/.

AUDITORS’ RESPONSES TO AUDITING STANDARDSThis section analyses in typical legal environments the effect of changes

in the quality of audit prescribed by auditing standards on the quality ofaudit adopted by auditors if employed, economic welfare, and the resultingfrequency of trial As in Dye (1993), an increase in the quality of auditprescribed by auditing standards may not lead to an increase in the averagequality of audit supplied The effect of an increase in the quality of auditprescribed by auditing standards on the quality of audit supplied by varioustypes of auditors, if employed, is summarized in Proposition 3:

PROPOSITION3: For any move from auditing standards prescribing audit quality

qŁto auditing standards prescribing a strictly higher audit quality qŁ 0

, there is one constant nB0 satisfying 0<nB<nB0 such that the move will:

1 Have no effect on the quality of the negligent audits adopted by employed auditors, whose levels of skill are strictly lower than nB;

2 Strictly decrease the quality of the audits adopted by employed auditors, whose levels of skill exceed nBbut are strictly lower than nB 0

endowed with the level of skill n B This auditor is thus indifferent betweencomplying with the prevailing auditing standards and providing an audit of

quality q Neg n B/arg minq2

q,qŁ C.q, nB /Cl.q/A The cost of supplying the

latter audit is independent of the quality of audit prescribed by the auditingstandards If the quality of audit prescribed by the auditing standards were

to increase to qŁ0, this auditor would thus strictly prefer to supply the

negligent audit of quality q Neg n B / All auditors with levels of skill n B <n<n B0

also revert to negligent audits when the quality of audit prescribed by the

auditing standards increases to qŁ 0

The effect of an increase in the auditquality prescribed by auditing standards on the quality of audit supplied byvarious types of auditors, if employed, is illustrated in Figure 4

COROLLARY4: When auditors’ levels of skill are unobservable27, an increase

in the quality of audit prescribed by auditing standards leads to a decrease in

Figure 4 Effect of an increase in the quality of audit prescribed by auditing standards on audit quality.

the unconditional frequency of trial Furthermore, in settings in which either all potential auditors are employed or audits are mandatory, an increase in the quality

of audit prescribed by auditing standards leads to a decrease in the absolute number

the information value of an audit supplied by an auditor of skill n is equal

of employed auditors When auditors’ levels of skill are unobservable, the

gross value of an audit supplied by an auditor of skill n is thus equal to 1 p/.X L X F/R

E q.n/w.n/dnC[pA 1 p/.PCD/]R

E l[q.n/]w.n/dn, which

is independent of the auditor’s level of skill In contrast, when auditors’levels of skill are observable, the gross value of an audit supplied by an

auditor of skill n is equal to 1 p/q.n/.X L X F /Cl[q.n/]d.q.n/, qŁ/A, which

depends on the auditor’s level of skill

COROLLARY6: The gross value of an audit increases in the gain derived from an early liquidation of the failing firms and increases in firms’ risk When auditors’ levels of skill are observable, the gross value of an audit supplied by an auditor exercising due care increases in the quality qŁ prescribed by auditing standards When auditors’ levels of skill are unobservable, as the average quality of audit may not increase in qŁ, the gross value of an audit may however not increase in

qŁ even in settings in which either audits are mandatory or all potential auditors are employed.

PROOF: The proof of Corollary 6 is straightforward and is thus omitted.The value of an audit to the economy (economic value of an audit)lies in the audit’s ability to identify and liquidate firms whose liquidatingvalues exceed their going-concern values (information value of the audit)

The economic value of an audit supplied by an auditor of skill n is given

by 1 p/q.n/.X L X F/ C.q.n/, n/28 Let us denote the quality of audit

supplied by an auditor of skill n maximizing the economic value of his audit,

arg maxq2

q,1 .1 p/q.X L X F/ C.q, n/, by q Best n/ It can be shown that

q Best n/ is strictly increasing in n over the interval [0, nmax] A social planner

maximizing economic welfare thus selects the set of auditing standardsmaximizing the sum of the economic values of the audits carried out in theeconomy:R

E [.1 p/q.n/.X L X F / C.q.n/, n/] w.n/dn.

PROPOSITION4: Economic welfare may not increase in the quality of audit prescribed by auditing standards even in settings in which either all potential auditors are employed or audits are mandatory.

PROOF: The proof of Proposition 4 is straightforward and is thus omitted.The intuition is as follows Consider a setting in which audits are

mandatory and investors’ loss X L X F strictly exceeds trial awards A.

An increase in the quality of audit prescribed by auditing standards causessome auditors endowed with lower levels of skill who would otherwise haveexercised due care to supply negligent audits and auditors endowed withhigher levels of skill to raise the quality of their audits to implement the new

standards As q Best n/ is strictly increasing in n, the auditors endowed with

the highest levels of skill may supply audits of higher economic values underthe new standards Auditors endowed with lower levels of skill implementingthe new standards may however supply audits of lower economic valuesunder the new standards As investors’ loss strictly exceeds trial awards,auditors endowed with even lower levels of skill supplying negligent auditsunder the new standards but exercising due care under the old standardsmay furthermore supply audits of lower economic values under the newstandards29 An increase in the quality of audit prescribed by auditingstandards may thus cause economic welfare to decrease.

COMPARATIVE STATICSThis section analyses in typical legal environments the effect of changes

in legal parameters—trial awards, plaintiffs’ and defendants’ litigationcosts—on both the quality of audit adopted by auditors, if employed,and the resulting frequency of trial

Effect of an increase in trial awards

PROPOSITION5: For any move from trial awards A to strictly higher trial awards A0, there exists one constant nB0 satisfying 0<nB0<nBsuch that the move

to the higher trial awards will:

1 Strictly increase the quality of the negligent audits supplied by employed auditors with levels of skill strictly lower than nB0;

2 Strictly increase the quality of the audits supplied by employed auditors with levels of skill exceeding nB0 and strictly lower than nB to the standard quality

is fairly intuitive Consider an auditor endowed with the level of skill n B

Given trial awards A, this auditor is indifferent between complying with

the prevailing auditing standards and supplying a negligent audit of quality

q Neg n B/arg minq2

q,qŁ C.q, n B /Cl.q/A The cost of supplying the latter audit increases in trial awards If trial awards were to increase to A0, thisauditor would thus strictly prefer to comply with the prevailing auditing

standards All auditors with levels of skill n B0n<n B also comply with the

prevailing auditing standards when trial awards increase to A0 The effect of

an increase in trial awards on the quality of audit supplied by the varioustypes of auditors, if employed, is illustrated in Figure 5

Figure 5 Effect of higher trial awards on audit quality.

COROLLARY7: When auditors’ levels of skill are unobservable30, an increase

in trial awards leads to an increase31 in the unconditional frequency of trial Furthermore, in settings in which either all potential auditors are employed or audits are mandatory, an increase in trial awards leads to an increase in the absolute number of trials.

COROLLARY8: In settings in which either all potential auditors are employed or audits are mandatory and auditors’ levels of skill are unobservable, an increase in trial awards leads to an increase in the average quality of audit supplied.

PROOF: When auditors’ levels of skill are unobservable, an increase in trial

awards leads to a decrease in the threshold level n Band thus an increase inthe unconditional frequency of trial In settings in which either all potentialauditors are employed or audits are mandatory and auditors’ levels of skillare unobservable, an increase in trial awards has no effect on either thenumber of audits or the set of employed auditors, but leads to an increase

in the quality of audit supplied by negligent auditors and thus to an increase

in the average quality of audit

Effect of an increase in plaintiffs’ or defendants’ litigation costs

PROPOSITION6: An increase in plaintiffs’ or defendants’ litigation costs has no effect32 on the equilibrium quality of audit supplied by any auditor, if employed, and hence, no effect on the unconditional frequency of trial.