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This is to certify that the
dissertation entitled
Commercial bank loan loss

provision discretion: Signals
and signal-jamming

presented by

Malcolm J. McLelland

has been accepted towards fulﬁllment
of the requirements for

PhD degree in Account ing

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Date 7 ’ 020 ’9 ?

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1M c/CIW.w6-p.14

COMMERCIAL BANK LOAN LOSS PROVISION DISCRETION:
SIGNALS AND SIGNAL-JAMMING

By

Malcolm J. McLelland

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Accounting
1 999

£8 IECT

COMMERCIAL BANK LOAN LOSS PROVISION DISCRETION:
SIGNALS AND SIGNAL-JAMMI'NG

By

Malcolm J. McLelland

In contrast to common notions of the information content of ﬁnancial disclosures and
accounting variables, this dissertation provides theory and empirical evidence suggesting
that accounting discretion can result in disinformative signals to equity traders. A
disinfonnative signal is deﬁned as a signal that results in equity traders revising their
distributions over some pricing-relevant variable such that their expectations become less
precise. A hypothesis is developed, based on Scharfstein and Stein’s (1990) herd behavior
model—and, more generally, on learning, herd behavior, and noise trading models in the
information and ﬁnancial economics literatures—that discretionary disclosures can be
disinformative to equity traders under certain conditions. Empirical evidence consistent
with this hypothesis is presented in simultaneous long- and short-window associations
between bank loan loss provision components, equity return variance, and share volume.
Accordingly, this study presents both theory and empirical evidence suggesting that

discretionary accounting disclosures can be disinforrmtive under certain conditions. I

To Diane, Andrew, and Stewart

For-helpingmeunderstandwhyitallwas,is,andwillbemeaningﬁrl.

AC 0 S

I am deeply indebted to my dissertation committee—Drs. Joseph H. Anthony (Chair),
Matthew J. Anderson, Craig E. Leﬁrnowicz, and Jeﬁi'ey M. Wooldridge—for many
interesting and valuable comments, insights, and ﬁ'eely-given hours of instruction. In
particular, I am indebted to Joseph Anthony for teaching me about the insights to be
gained ﬁ'om prelinrinarily characterizing any economic phenomenon as an equilibrium, for
repeatedly guiding me toward the ﬁnancial economics and industrial organimtion
literatures, forhelpingme understandtherelationships betweenthose literaturesandthe
ﬁnancialaccounting literature,andforreﬁningmyunderstandingof(his)ideasaboutthe
endogeneity of accounting information. I am indebted to Matthew Anderson for teaching
me the importance of philosophy of science in academic accounting inquiry, the
importance of rigorous logic and clear writing, and for guiding me towards the literature
on the rational expectations hypothesis. I am indebted to Craig Lefanowicz for helping me
interpret much of the ﬁnancial accounting literature in terms of corporate ﬁnance theory,
helping me understand current econometric practice in the accounting literature, and for
teaching me the many implications ofmairrtained hypotheses in empirical research. I am
indebted to Jeﬁ'ey Wooldridge for helping me understand the fundamental native and
limitations of econometric methods, teaching me the necessity of explicit linkage between
theoretical models and empirical models (and how that linkage is formed), and for
teaching me about the frmdamental nature and implications of mathematical proof.

I am also indebted to Dr. Richard Sirnonds for teaching me about insights to be

gained ﬁom intense study of simple models in ﬁnancial economics, and how to go about

iv

building theoretical models; to Dr. Maria Herrero for helping me understand
microeconomic theory by introducing me to alternative concepts of equilibrium and
repeatedly showing me the links between algebra, geometry, theoretical interpretation, and
intuition; and, to Dr. James Hannon for a rigorous overview of the mathematical
foundations of probability and statistical theory, an introduction to the limitations of
asymptotic theory, and for introducing me to the notion that linear theories are routinely
used to describe an inherently nonlinear world.

Finally, I am indebted to other doctoral students at Michigan State University who
have each become close ﬁiends of mine: to Gregory Gerard (now at Florida State
University) for many hours of interesting discussions about accounting theory and
research,candidcritiquesofmyideasandwriting,andforﬁeunuseofhis extensive
hbrary; to Ranana Sonti for many hours of interesting discussion about investment theory
and accounting theory, about ﬁnancial economic theory and econometrics, and for patient
. assistance with many mathematical proofs and derivations; and, to Adam Kepka (now at
the Technical University of Lodz, Poland) for teaching me most of what I know about
fornal mathematics and analysis, and for leading me to profound insights about the central
role of nathematics in social scientiﬁc research. A

I thank the American Institute of Certiﬁed Public Accountants and its Doctoral
Fellowship Program for generous ﬁrancial assistance that signiﬁcantly accelerated my

completion of this dissertation. I

O O S

LIST OF TABLES .................................................................................................... vii
LIST OF FIGURES ..................................................................................................... x
LIST OF ABBREVIATIONS ...................................................................................... xi
CHAPTER 1: INTRODUCTION ............................................................................... 1
CHAPTER 2: COMMERCIAL BANK INSTITUTIONAL CHARACTERISTICS 4
2.1 Financial irrtermediation and information asymmetry ....................................... 4

2.2 Commercial bank loan loss disclosures ........................................................... 7

2.3 Implications of commercial bank institutional characeristics ............................ 9
CHAPTER 3: RELATED RESEARCH ..................................................................... 10
3.1 Commercialbankaccounting literature ........................................................... 10
3.1.1 Loanlossdisclosurepricingstudies .................................................... 11

3.1.2 Loan loss disclosure discretion studies ............................................... 12

3.1.3 Implications of loan loss disclosure studies .......................................... 12

3.2 Signal-jamming equilibrimn ............................................................................ 13

3.3 Disclosure and equity market response ........................................................... 16
3.4 Implications of related research ...................................................................... 22
CHAPTER 4: HYPOTHESES ................................................................................... 24
4.1 Informational characteristics of discretionary accounting signals ..................... 24
4.2 Informative loan loss provision signals ............................................................ 26

4.3 Disinformative loan loss provision signals ....................................................... 28
CHAPTER 5: RESEARCH DESIGN ........................................................................ 32
5.] Population, sample, and data set ..................................................................... 32

5.2 Unexpected equity return variance and share transaction volume .................... 32

5.3 Unexpected loan loss provision components ................................................... 35

5.4 Empirical models and hypothesis tests ............................................................ 37

CHAPTER 6: EMPIRICAL RESULTS AND SENSITIVITY ANALYSES .............. 41

6.1 Informative loan loss provision discretion results ............................................ 41

6.2 Disinformative loan loss provision discretion results ....................................... 44
6.2.1 Hypotheses 2.1 and 2.2: Equityreturnvarianceresults ......................... 46

6.2.2 Hypotheses 3.1 and 3.2: Equity share volume results ........................... 47

6.3 Sensitivity analyses ......................................................................................... 48
CHAPTER 7: SUMMARY AND CONCLUSIONS ................................................... 61
APPENDICES ......................................................................................................... 63
Appendix 1: Tables .............................................................................................. 64
Appendix 2: Figures ............................................................................................ 88
Appendix 3: Infornative, noninformative, and disinformative signals ................... 101
Appendix 4: Discretionary and nondiscretionary accounting disclosure ................ 110
Appendix 5: Disinformative signals, noise traders, and equity prices ..................... 112
REFERENCES .......................................................................................................... 114

Ianlsﬂ
1212112
MEL;
Table—4
1:321:54.

Table 5.2

Table 6.1

Table 6.2

Table 6.3

Table 7.1

Table 7.2

Table 7.3

MM
mm
M
11111194
I.a_lﬂ§_9._2
1%

LIST 0 T S

Disclosure and equity market respome ................................................. 65
Deﬁnitions of signal types ..................................................................... 66
Necessary conditions for disclosure type observability .......................... 67
Loan loss disclosure expectatiora model SUR estimation results ........... 68
Expectations model residual regression results and hypothesis test

of lagged loan loss provision residuals (Full data set) ............................ 69
Expectations model residual regression results and hypothesis test

of lagged loan loss provision residuals (Reduced data set) .................... 70
Equity return variance (ﬁr-f) hypotheses tests:

FGLS estimated marginal effects and related signiﬁcance tests .............. 71
Equity retm'n variance (127:) hypotheses tests:

LAD estinated marginal effects and related signiﬁcance tests ............... 72

Equity return variance (ﬁrf) hypotheses tests:
Prais-Winsten estimated marginal effects and related signiﬁcance tests... 73

Equity share volume (riva) hypotheses tests:

FGLS estimated marginal effects and related signiﬁcance tests .............. 74
Equity share volume (1%,) hypotheses tests:
LAD estimated marginal effects and related signiﬁcance tests ............... 75

Equity share volume (1%,) hypotheses tests:
Prais-Winsten estinated marginal effects and related signiﬁcance tests... 76

Equity return variance (121;?) model FGLS estimation results ................ 77
Equity return variance (131;?) model LAD estimation results .................. 78

Equity return variance (1%,?) model Prais-Winsten estimation results ..... 79
Equity share volume (riva) model FGLS estimation results ................... 80
Equity share volume (rivn) model LAD estimation results ..................... 81
Equity share volume (rivﬂ) model Prais~Winsten estimation results ....... 82

Mic—104 Expectations model sensitivity analysis of 131'} hypotheses tests:

FGLS estimated marginal effects and related signiﬁcance tests .............. 83
M Expectations model sensitivity analysis of 13v, hypotheses tests:

FGLS estimated marginal effects and related signiﬁcance tests .............. 84
IAbLLL-l. Equity return variance (121;?) model FGLS estimation results

with additional conditioning on expected Ilp components ...................... 85
Table 11.2 Equity renn'n variance (1%,) model FGLS estimation results

with additional conditioning on expected Ilp components ...................... 86
Table 12 Descriptive statistics ............................................................................. 87

LIST OF FIG S

Plot of FGLS estimated long-window marginal effects of loan loss

provisiondiscretionwm, rim)onequityretrmnvariance(1ir2) ........

Plot of FGLS estimated short-window marginal effects of loan loss

provision discretion(13w, 13”,) on equity returnvar'ance (ﬁrz) ........

Plot of LAD estimated long-window marginal effects of loan loss

provision discretion(1im, 13w)onequityretm'nvariance (121-2) ........

Plot of LAD estimated short-window marginal effects of loan loss

provision discretion (17m, 1?“) on equityreturnvariance (111-2) ........

Plot of Prais-Winsten estimated long-window marginal effects of
loan loss provision discretion (13m, 13”,) on equity return variance

(ﬁrz) ..................................................................................................

Plot of Prais-Winsten estimated short-window marginal effects of ,

loan loss provision discretion (13”, 12“,) on equity return variance

(131'2) ..................................................................................................

Plot of FGLS estimated long-window marginal effects of loan loss

provision discretion (13m, 17%) on unexpected share volurne(1iv)

Plot of FGLS estimated short-window marginal eﬁ‘ects of loan loss

provision discretion (rim, 11“,“) on unexpected share volume (13v)

Plot of LAD estimated long-window marginal effects of loan loss

provision discretion (1?” , 1?”) on unexpected share volume (13v)

Plot of LAD estimated short-window marginal effects of loan loss

provision discretion (13m, 12”,) on unexpected share volume (riv)

Plot of Prais-Winsten estimated long-window marginal effects of
loan loss provision discretion (1? 17%) on unexpected share

uco’

volume (13v) .......................................................................................

Plot of Prais-Winsten estimated short-window marginal effects of
loan loss provision discretion (12 11“,) on unexpected share

1100’

89

90

91

92

93

94

95

96

97

98

99

volume(1'iv) ...................................................................................... 100

Abbreviation

Eano"

éHAllan

Ila
Alla
Ilp

"CO

npl

plle

R)

nan,"

“Ala .11

LIST OF ONS

Description
Equal to one if ﬁr} and ﬁvnfall within 11 day disclosure period; else

I

ZCI'O.

Expected net loan charge-offs for ﬁrm i, time t estimated at time (-1 (as
proxy for nondiscretionary nco).

Expected loan loss allowance change for ﬁrm 1', time t estimated at t—l
(as proxy for nondiscretiorary Alla).

Loan loss allowance; deﬁned by the identity - Ila, = -Ila,_l + nco, - llp, .
Change in loan loss allowance; deﬁned as Alla, = -lla, — (—Ila _,) .

Loan loss provision; decomposed as Ilp = nco + Alla .

Net loan charge-offs.

Non-performing loans.

Change, in non-performing loans; deﬁned as Anpl, = npl, — nle.
Pre-loan loss earnings deﬁned by plle = net income +le .

Unexpected net loan charge—oﬁ’s for ﬁrm 1', time t (as proxy for
discretionary nco); deﬁned as 13m, = 11cc, —E,nco, .

Unexpected loan loss allowance change for ﬁrm 1', time t estimated at
time t-l (as proxy for discretionary Alla); deﬁned as
am, =11a, —1‘3,11a,,. '

Squared unexpected (residual) equity return for ﬁrm 1', time t.
Unexpected (residual) equity slare volume for ﬁrm 1', time 1.

Parameter ofAR(1) residual process: 11, = p-u,_, + e,; e, ~ N(0,02).

CHAPTER 1

INTRODUCTION

Apnvalentviewhtheﬁmmhlaccthglheratmeisthﬁacwmtingvarablescmbe
either informative or noninformative to equity traders: rational traders and inforrnationally
eﬂicient equity markets presumably ensure that disinformative signals in the form of
ﬁnancial reporting and disclosure manipulations are not impounded in equity prices (cf.
Beaver, 1981; and Verrecchia, 1979). The term disinformation is used in the following
sense: a disinformative disclosure results in equity traders revising their distributions over
some pricing-relevant variable such that their expectations become less precise.1 As an
example, a disinformative disclosure decreases the ability of equity traders to make precise
inferences about exogenous factors that inﬂuence expected proﬁts. In this connection
Beaver (1968, p. 69m8) states: “It should be apparent that in a dynamic situation . . . a
decision maker may be more uncertain about a given event alter receiving a message about
the event than he was before he received the message.” Based generally on herd behavior

and learning models developed in the ﬁnancial and information economics literatures, this

 

' In the ﬁnance literature, the term disinformation as used in this study would generally
be referred to simply as noise. Similarly, in the accounting literature the term
disinformation as used here would be referred to alternatively as noise (cf. Collins and
Kothari, 1989), increases in the uncertainty of information contained in an accounting
signal (cf. Kim and Verrecchia, 1994), or reporting bias (cf. Fischer and Verrecchia,
1998). Thus, the notion of disinformation used in this study subsurnes two different types
of noise: white noise with expectation E(u,)= E(1t, |x,) = O,Vt; and non-white “noise”

with unconditioral expectation E(u,) = 0 and conditional expectation, E(u, |x,) at O,Vt .

study develops the hypothesis that under certain conditions managers use accounting
discretion to generate disinformative disclosures which “jam” inferences of equity traders.

A sample of commercial banks is selected for testing the hypothesis that
discretionary accounting disclosures can result in disinformative signals to equity traders
since the economic conditions faced by banks are analogous to those required for the
optimality of “signal-jamming” derived in Scharfstein and Stein (1990).2 Since loan loss
provisions represent one of the prirrary discretionary components of commercial bank
earnings, this hypothesis is tested by examining the empirical association between: (a)
unexpected equity return variance and the unexpected components of loan loss provisions;
and, (b) unexpected equity share transaction volume and the unexpected components of
loan loss provisions. Unexpected equity return variance and share transaction volume are
selected as measures of pricing-relevant information available to the equity traders based
primarily on theoretical models developed in Holthausen and Verrecchia (1988), and Kim
and Verrecchia (1994), respectively.

Consistent with the signal-jamming hypothesis, characteristics of the empirical
association between unexpected loan loss provision components, unexpected equity return
variance, and unexpected share transaction volume suggest that discretion over loan loss
provisions is used to emit disinformative signals to equity traders. This study contributes

to the accounting literature by: (1) providing theory and empirical evidence suggesting

 

2 Although Scharfstein and Stein (1990) model herd behavior in a managerial labor
market setting, such behavior results in jamming labor market inferences about
managerial ability. Hence the term signal-jamming introduced to the economics literature
in Fudenberg and Tirole (1986) is used in this study.

2

that discretionary accounting signals can be disinformative to equity traders; (2)
introducing an alterrative explanation for the use of accounting discretion; and (3)
providing additional evidence with respect to existing explanations of the widely
documented anomalous positive association between equity returns and unexpected loan
loss provision components.3

The remainder of this dissertation is organized as follows: Chapter 2, Commercial
Bank Institutional Characteristics; Chapter 3, Related Research; Chapter 4, Hypotheses;
Chapter 5, Research Design; Chapter 6, Empirical Results; and Chapter 7, Summary and

Conclusions. I

 

3 This association is anomalous in several senses: increases in loan loss provisions are
generally thought to be associated with decreases in future, expected returns of loan
principal and interest; and, unexpected earnings has been shown to be positively associated
with equity returns in the empirical accounting literature. Further, since bank managers
lave discretion over loan loss provisions, and since such unexpected loan loss provisions
have been shown to be positively associated with (ﬁrture) expected earnings before loan
losses, this association las been attributed to “signaling” behavior by bank managers.
However, it is difﬁcult to test hypotheses of signaling behavior since the underlying theory
predicts that under certain conditions it is optimal for agents to reveal their private, ex
ante (and ex post) unobservable information. Indeed, Milgrom and Roberts (1987) note in
their discussion of asymmetric information game theory that “the central object in the
theory [i.e., private information] is, by its very nature, unobservable” (p. 191).
Accordingly, studies of the information content and pricing of the unexpected component
of loan loss provisions generally represent relatively indirect tests of hypotheses based on

signaling theory.

CHAPTER 2

COMMERCIAL BANK INSTITUTIONAL CHARACTERISTICS

Thecomnercialbankingindusmywasselectedforthisstudyduetotleunique
informational characteristics of the asset portfolios held by most larger commercial banks.
Inparticular,commercialandindustrial loans, amangotherloanclassesthatusually
contain unobservable, heterogeneous credit (loan default) risk characteristics often
comprise a substant'al portion of a commercial banks assets. This characteristic, in
combination with the uncertainty over the economic factors that inﬂuence commercial loan
loss realizations and bank managers’ ability to renegotiate loan contracts, reasonably
results in a high level of managerial discretion over accounting recognition of loan losses.
This chapter examines how these characteristics result in persistent information
asymmetries between bank managers, auditors, regulators, and equity traders, and why it
maybeoptimalforbankmanagersto takeactionsthattendtomaimtainorincreasesuch
information asymmetries.

2.1 Financial intermediation and information asymmetry
Commercalbanksdealprhmrﬂymﬁmmialmntszassetswmpﬁsedprhmﬁlyof
loans and investment securities, and liabilities comprised primarily of deposit contracts and
other ﬁnancial obligations. The valuation of ﬁnancial instruments is highly dependent on
information (e.g., information about credit risk, interest rate environment, etc.). Since that
information is costly to acquire or is unobservable, information asymmetries exist between
borrowers and lenders that create economic opportunities for ﬁrancial intermediation

(Greenbaum and Thakor, 1995). Indeed, Greenbaum and Thakor (1995) suggest tlat

persistent information asymmetries between net buyers (e.g., commerc'al borrowers) and
net sellers (e.g., bank depositors) of ﬁmds is necessary for the existence of ﬁnancial
intermediaries in their information processing and asset transformation role.

With respect to accounting-related information asymmetries, Stigum and Branch
(1983) suggest that bank managers use accounting discretion over the timing and,
realizationofsecmitiesgainsandlossesto eﬁ‘ectsrmothmcreasingearningstrendsto
mﬂmmemnkandym’mmbmofﬁskwhﬂemMgMamlystsmawamofthis
manipulation. Theyﬁnthersuggestthatcommnercialbanksgenerally“stickwiththeher ”
with respect to investment, ﬁnancing and accounting policies in order to maintain
perceived risk proﬁles consistent with their peer group (see, e.g., p. 183). This suggestion
is consistent with the pervasive use of comparative peer group bank analysis by regulators
and analysts discussed in many bank ﬁrancial management texts (e.g., Hempel and
Simonson, 1991).

These institutional characteristics suggest that ﬁnancial reporting and related
disclosures represent the prirrary source of information available to the money, debt and

equity markets with respect to the risk-retum characteristics of commercial bank assets.

Thus, these characteristics provide incentives for bank managers to exercise accounting
discretion to inﬂuence risk—retina inferences made by the capital markets.4
Greenbaum and Tlakor (1995), and Stigrrrn and Branch (1983), characterize banks

asmeedpmﬁt-mathzemandmtethmmeprmmynsksbanksmusteﬁ‘ectively

 

’ Tlﬁsstudyassumesthat—fortheselectedsampleofwmmercalbanks—rmmgers
primarily use accounting discretion for the purpose of inﬂuencing equity trader risk
perceptions rather than for (short-run) manipulation of manager cormpensatiom and
performance contracting variables. According to positive agency theory, “maximizing
agents minimize the agency costs in any contracting relationship” in the long-run, and
rehtedly, “the organimtional form, [mpresented by] its contracts, will be those that
minimize the agency costs” (Jensen, 1983, p. 331). Under this maintained hypothesis, the
coexisting expected proﬁt-maximizing and agency explarations of managers’ use of
discretion over loan loss disclosures essentially reduce to one of expected proﬁt
maximization conditional on whether a bank is not failed or falling, or likely to be involved
in a corporate control transaction.

In the context of this study, a reasonable assumption following ﬁomr this maintained
hypothesis is that banks which have not failed or been involved in a corporate control
transaction (negotiation) are those whose managers are likely maximizing an expected
utility function with bank proﬁts as its primary argument (i.e., manager-shareholder
incentives are aligned), ceteris paribus. These conditions are approximated in this study by
using only bank-year observations ﬁom banks existing during the three years ended
12/31/96 that survive through 12/31/97 (see Chapter 5, Section 5.1, Population, sample,
and data set).

manage on a day-to-day basis are credit risk, liquidity risk and interest rate risks Further,
theymtethatthesemreesomcesofﬁskmenecessaﬁlymtemeatedMacwrdmgly,
banks’ decisions with respect to these risks are made jointly. Stigum and Branch (1983)
provide a number of examples of large commercial banks where unfavorable credit risk
information has resulted in increased liquidity risk (i.e., increased diﬂiculty in obtaining
adequateﬁlnding)andarelatedincreaseinimterest costsasaresultofthe informational
claracteristics of ﬁnancial intermediaries. This suggests the use of loan loss disclosure-
related accounting discretion to inﬂuence the market’s perception of the nature and level
of risk over a bank’s expected loan losses.

2.2 Commercial bank loan loss disclosures

Loan loss provisions represent one of the primary sources of earnings-based accounting
discretion and are only one of several disclosures related to loan losses. Loan loss
disclosures not given accounting recognition consist primarily of “non-performing” loan
(an) disclosures origirally required under Regulation S-X of the Securities and Exchange
Commission. Loan loss disclosures given accounting recognition consist of loan loss
allowances (Ila), loan loss provisions (lip), and net loan charge-oﬂ‘s (nco) and can be

summarizedinthefollowingaccountingidentityattimen

 

5 Creditriskistheriskofﬁrﬂuretoﬁrﬂyreahzetheprincipalandinterest paymentsdue
ﬁ'om a borrower under the terms of a lending contract. Liquidity risk is the risk that a
bank will be unable to meet its contractual obligations on a ﬁnely basis. Interest rate risk
is the risk that changes in the level or term structure of interest rates over time will result
inchangesinthevalueofitsassetsandliabilities.

— Ila, 2 —IIa,_, - le, + nco, [l]

where —IIa... denotes the exogenous component of —Ila..6 Note that an absolute increase
in any variable in equation [1] represents an increase in either expected or actual loan loss
realizations since, under existing accormting standards, Ila represents the amount
necessary to state loans at their expected net realizable value and nco represents loan loss
realizations. Thusllpisanaccountingcoratructthatcombinesbothactualloanloss
realizations and managers’ expectations of ﬁrture loan loss realimtions. To see this more

clearly, deﬁne Alla, a -lIa, - (410,4) , substitute this term into equation (1), and

rearrange to obtain:

11]), = nco, + Alla, [2]

where nco denotes current loan loss realizations, and Alla denotes changes in estimated
unrealized loan losses, respectively. Equation [2] was introduced to the commercial bank
accounting literature by Moyer (1990) and segregates the more discretionary component
(Alla) ﬁom the less discretionary component (nco) of recognized loan losses (llp). This
decomposition is further suggested by Beatty, Chamberlain, and Magliolo (1995), and
Collins, Shackelford, and Wahlen (1995) which both provide evidence suggesting bank
managers simultaneously exercise discretion over both llp and nco.

Net loan charge-oﬁ‘s, nco, are less discretionary since economic events associated

with loan loss realizations are observable to a bank’s independent auditors and regulators

 

6 A summary ofnotation used in this paper is presented on p. xi, List ofAbbreviations.

during the ﬁnancial reporting process. The change in loan loss allowance, Alla, is more
discretionary since the combination of uncertainty over expected loan losses and inherent
information asymmetries between bank managers, independent auditors, and regulators
reasonably allows a wide range of discretion over this component of recognized loan
losses (cf. AICPA, 1986).

2.3 Implications of commercial bank institutional characteristies

As ﬁnancial intermediaries, commercial banks obtain economic proﬁts primarily from
transforming pools of loans and other ﬁnancial assets with heterogeneous, unobservable
risks into relatively low- and homogenous-risk ﬁnancial instruments that are sold to
depositors, shareholders, and others. Since buyers of these ﬁnancial instruments must
primarily use information contained in the ﬁnancial disclosures of commercial banks to
makeinferencesabouttheserisksmanagershave incentivesto inﬂuencetheinferencesof
the money, debt and equity markets.

The risk characteristics of commercial bank loan asset portfolios, in conjunction
with loan loss accounting and disclosure requirements, suggest tlat bank managers have
substantial discretion over loan loss provisions. Moreover, the commercial bank
institutional literature suggests tlat accounting and ﬁrancial discretion is often used to
maintainabank’srisk—returnproﬁlesuchtlatitissimilarto otherbanksthereby,

inﬂuencing risk—return inferences made by the capital markets. I

CHAPTER 3

RELATED RESEARCH

This chapter discusses three literatures relevant to this study: the commercial bank
accounting literature, the signal-jamming literature via a discussion of Scharfsteim and
Stein’s (1990) herd behavior model, and the disclosure—equity market response literature.
This discussion focuses on existing theory and empirical evidence relating to how and why
bank managers exercise accounting discretion over loan loss recognition. In particular,
this discussion introduces signal-jamming to the accounting literatrue as a plausible use of
discretion over loan loss provisions (in equilibrium). Finally, the accmmting disclosure—
equitymarketresponse literatureisdiscussedinrelationto noisetradingmrodelsinthe
ﬁnancial economics literature, and the joint irnplicatioms of these literatures with respect to
this study are discussed.

3.1 Commercial bank accounting literature

The commercial bank accounting literature has focused primarily on two areas of inquiry:
the pricing of expected and unexpected components of loan loss provisions, and the
determinants of loan loss provision levels. Although several empirical regularities have
been demonstrated by these studies (e.g., a positive association between increases in
recognized loan losses and equity returns), this literature has shown that empirical
associations between loan loss provisions and equity market data are highly conditional.
In this connection, this section concludes by summarizing the implications of the
commemalbankaccoummghteraturewithrespecttohowandwhybankmanagers

exercise accounting discretion over loan loss provisions.

10

3.1.1 Loonlossdisclosmpricingstudia
MgenemLtheemphicalmsuhsofbmbssdiscbmmepﬁcmgstudiessuggestthmllp
components contain pricing-relevant information, but that this information content is
(perhaps highly) conditional on many ﬁrm-exogenous and ﬁrm-endogenous variables.
Madura and McDaniel (1989) and Elliott, Hanna, and Shaw (1991) ﬁnd a positive
association between short-window unexpected equity returns and Alla announcements for
large money center banks; however, Elliott, Hanna, and Shaw (1991) ﬁnd tlat this
association does not hold for non-money center banks and is not robust to further
conditioning on loan and Ila level disclosures for certain classes of risky loans, regulatory
capital ratios, and market-to-book ratios.

In longer-window studies, Beaver and Engel (1996) ﬁnd tlat there is a greater
negative association between equity prices and expected Ila components than for
rmexpected Ila components. Liu and Ryan (1995) ﬁnd that the information content of Ilp
is preempted by nonperformirrg loan disclosures of banks with loan portfolios
predominated by loan types which are more ﬁequently negotiated, but not by such
disclosures of other banks. Beaver, Eger, Ryan, and Wilson (1989) ﬁnd a positive
association between equity prices and Na levels, and negative associations between equity
pﬁcesandnpllevelsandloanmatmitydisclosmes;however,thisstudyalso ﬁndstlatthe
association between prices and Ila levels is not robust to conditioning on earnings-to-book
ratios, book equity growth rates, and CAPM beta.

Otler recent studies have shown tlat lagged unexpected Ilp components (as
proxies for discretionary components) are positively associated with both pre-loan-loss
earnings (plle) and equity returns, and therefore suggest tlat discretiorary Ilp components

11

represent pricing-relevant informative signals (Wahlen, 1994; and Liu, Ryan, and Wahlem,
1997).

3.1.2 Loan loss disclosure discretion studia
Emphicalmsuhsofbmbssdiscbsumdiscmﬁonstudiesgenmﬂysuggestthmbank
managers exercise discretion over llp components jointly with other discretionary
accounting variables to achieve multiple ﬁnancial reporting objectives. Greenawalt and
Sinkey (1988) ﬁnd evidence consistent with the hypothesis that only non-money-cemter
banks exercise discretion over llp levels to smooth earnings to both time-series and cross-
sectional means. Moyer (1990) ﬁnds evidence consistent with the hypothesis that banks
exercise discretion over llp, nco, and securities gains and losses to increase regulatory
capital to minimum required levels and, thereby, reduce regulatory costs. Beatty,
Chamberlain, and Magliolo (1995) ﬁnd evidence consistent with the hypothesis that banks
exercise discretion simultaneously over llp, nco and ﬁnancing transactions to manage
regulatory capital ratios. Collins, Shackelford, and Wahlen (1995) ﬁnd evidence
consistent with the hypothesis tlat bank managers exercise discretion over Ilp to smooth
earnings to a time-series mean, and over nco to increase regulatory capital ratios.

3.1.3 Implications ofloan loss disclosure studies

Loan loss disclosure pricing studies provide evidence that the unique pricing-relevant
information of loan loss disclosures is contained in the unexpected components of such
variables. However, results of these studies also suggest that such information contained
in llp is highly conditional: Beaver, Eger, et. al (1989) ﬁnd the price—Ila association
nonrobust to conditioning on more fundamental variables; Elliott, Hanna, and Shaw
(1991) ﬁnd the equity return-Alla association similarly nonrobust; Walllen (1994) ﬁnds

12

the return—unexpected Ilp association nonrobust to omission ofthe upper and lower 1%
of loan loss disclosure sample distributiora; and Liu, Ryan, and Wahlen (1997) show that
the sign of the return—unexpected Ilp association is conditioral on reguhtory capital levels
and interim-versus-year end reporting environment.

The loan loss disclosure discretion studies collectively provide evidence that bank
managers exercise discretion over loan loss disclosures (in certain cases, jointly with other
discretionary variables) in order to reduce intertemporal and cross-sectional variation in
reported earnings, and to manage regulatory capital ratios. However, this stream of
literature has focused largely on identifying determinants of loan loss provision levels and
isgenemﬂysiWonhowbankmamgersmayuseaccountmgdiscretiontomﬂuence
equity trader risk—retum inferences.

Theseresults,incombiration,suggestthattleerdstingcommrercialbank
accounting literatrne las not converged to a general explaration of how and why bank
managers use accounting discretion over Ilp, and of how and why equity traders respond
to discretionary Ilp components.

3.2 Signal-jamming equilibrium

Scharfstein and Stein (1990) investigate conditions tlat can lead to herd behavior in a
model characterized by multilateral uncertainty over both expected states of nature and
maragers’ ability to predict investment outcomes, and by multilateral information
asymmetry over the quality of the informatiOm set (i.e., informative versus purely noisy
signals) available to each manager. In their modeL the labor market can learn about a
narager’s ability by observing realizations of ex ante uncertain investrnemt outcomes, and
whether tlat manager’s investment decision was similar to decisions of other managers. It

13

isshownthatherdbehavioropﬁmaﬂyaﬁsesimthiscomenmewhenmanagers’
predictionerrorsareatleastpartiallycorrelatedwitheachother. Inthissetting,this
condition can lead managers to optimally “jam” the labor market’s inferences with respect
to their (perhaps poor) prediction ability through matching the investment decisions of
other managers regardless of their respective beliefs about expected investment outcomes.

To see Scharfstein and Stein’s (1990) result more clearly, consider the basic
assumptions of their model:

(1) Multilateral mnem' over expected states of nature and manager
investment outcome prediction ability implies tlat investment outcomes
andmanagers’abilitiesofpredictingthoseoutcomesareuncertainand
neither (individual) managers nor the labor market has superior infomnation
about these sources of uncertainty.

(2) Multilateral information am over managers’ infonration set quality
implies that neither managers themselves nor the labor market know
whether the information sets used in making investment decisions provides
individual managers with informative or purely noisy signals of expected
outcomes.

(3) Partiaﬂy' —correlated m1 ion errors imply that managers’ predictions of
investment outcomes tend to be related and that managers’ information sets

have a common component leading them to similar, incorrect inferences.

Irrtuitively, multilateral information asymmetry is necessary for Scharfsteirr and Stein’s

(1990) result since under perfect irrformatiom managers’ actions become observable to the

14

labor market. Similarly, without multilateral uncertainty over states of nature and manager
prediction ability, the labor market’s inference problem degenerates to a perfect
information setting for at least one manager thus allowing the labor market to observe or
infer nanagers’ (suboptimal) actions. Partially-correlated manager prediction errors are
necessary for Scharfsteirr and Stein’s (1990) result since without this condition prediction
errors become orthogonal; thus allowing the labor market to correctly infer individual
managers’ actions over time.

Itisnotclearwhethertheconditionsfortheopthnalityofsignabjammhrg identiﬁed
by Scharfstein and Stein (1990) hold—on average—in the commercial bank loan loss
provision setting considered in this study. However, the basic assumptions central to their
result (discussed above) represent conditions that seem suﬂiciemtly analogous to this
senmgtosuggestthatdismfomativesignalsemhtedbybankmanagemcanmtbe
immediately observed with certainty by equity traders.

Importantly, Scharfstein and Stein (1990) derive conditions under which
discretionary actions can result in disinformative signals that persist in a general
equihhium In the context of this study, their model simply suggests that under certain
conditions equity traders are mable to determine whether a signal emitted by a single ﬁrm
in a single time period represents an informative “non-jamming” signal, or a disinformative
“jamming” signal. The market may, however, learn over time that signal-jamming is
occurring—on average—by observing signals and subsequent realizations for a number of
ﬁrms. As a result of these inferences, equity prices for all such ﬁrms are discounted by

traders since they are only able to infer average signal-jamming behavior using this

15

information, notwhetherasingleobservedsignalrepresentsanon-jannnimg orajarmmimg
signal]
Itcanbeseenthatnoﬁonsofequﬂrbrimnherdbehaviorandsignal—jamnning
underlying Scharfstein and Stein (1990)—where it becomes optimal for managers to
choose otherwise suboptimal actions, and the managerial labor market to price rranagerial
labor based on average, expected suboptimal actions of managers—are similar to notions
of equilibrium “price protection” in Jensen and Meckling (1976) where traders optimally
set a ﬁrm’s equity price based on the average, expected unobservable agency costs, and
managers optimally impose such unobservable agency costs on the ﬁrm.
3.3 Disclosure and equity market responses
A number of theoretical models have been developed in the accounting literature that
examine the relationship between accounting disclosure characteristics and equity market
responses. Holthausen and Verrecchia (1988) develop a two-period, multi-asset model of
the relationship between equity prices and sequential disclosures. It is shown under
general assumptions tlat increases in the variance of sequential, pricing-relevant
disclosures result in nonincreasimg equity return variance over periods spanning sequential
disclosure dates. Kim and Verrecchia (1994) develop an atemporal, single-asset model of

equity market responses to ﬁnancial accounting disclosures which carry rmique

 

7 A simple model of incomplete learning is presented in Appendix 3 that shows a set of
sufﬁcient conditions for noninfonnative and disinformative discretionary accounting
signals to persist indeﬁnitely over time. Further, Appendix 5 presents a brief discussion of
the ﬁnancial economics and accounting literature suggesting that disinformative signals are
impounded in data generated by otherwise infonrationally eﬂicient capital markets.

16

mformationtonadersandamsubjecttovarymghnerpretaﬁonswithrespectto ﬁrms’
ﬁnancial performance (i.e., unique brrt noisy signals). This model shows that information
pmcessmgacthdﬁesofemutyuademwhhmspemmsuchdiscbmuesresuhmmcreased
madermformationasymnmtﬁeswhichcanEadtomcreasedequhymnnnvarameand
trading volume around disclosure dates.8

Holtlausen and Vemecchia (1990) develop an atemporal model of informative
disclosures and rational equity trader responses, and show that trader informedness and
consensus occur jointly as a result of such disclosures.9 They further show that:

(1) equity return variance and share voltme are increasing in trader
information precision since trader belief revisions are generally greater
when information is more precise and such belief revisions result in

increasedtrading activity;

 

8 Sequential increases in the variance of disclosures and, assuring rational expectations,
related increases ill information asymmetry both correspond to the notion of a
disinformative signal. Information releases in Holthausen and Verrecchia (1988) represent
noisy signals of (future) liquidating dividends which are analogous to accounting
disclosures examined in this study: loan loss provisions as signals of changes in expected
loan principal realizations. In Kim and Verrecchia (1994), higher levels of variance in
accounting signals similarly represents less informative disclosures.

9 In Holthausen and Verrecchia (1990), informedness refers to the level of precision (i.e.,
inverse variance) in a trader’s probability distribution over some pricing-relevant
disclosure; consensus refers to the level of trader agreement (i.e., the level of correlation
of traders beliefs) over some pricing-relevant disclosure.

17

(2) equity return variance is increasing in trader belief comelation levels since
“less uncertainty [is] resolved through the market [information]
aggregation process” (p. 203) when traders beliefs are more highly
correlated; and

(3) equity share volume is decreasing in trader belief comelation levels since

simﬁlmityinmaderbehefsresrﬂtsmsimilaritybenveemthenvaluations.

Holthausen and Verrecchia’s (1990) results on clanges in trader belief heterogeneity are
not of primary importance to this study since only the (dis)informativeness of discretiorary
accounting variables is examined. The empirical propositions underlying the main
hypotheses developed in this study are derived primarily ﬁ'om Holthausen and Verrecchia
(1988) and Kim and Vemecchia (1994). Rather, the positive relationship Holthausen and
Vemecchia (1990) demonstrate between the variance of trader belief distributions and
trader belief heterogeneity is used here to develop the maintaimd hypothesis—consistent
withtheemmmicalresuhsomeron(l995)—thatanmcreasemthevaﬁameofan
accounting signal is negatively related to equity slare volume over disclosure-spanning
time periods.

Empirical evidence is generally consistent with the referenced, theoretical
accounting literature on disclosrme and equity market response in suggesting that
infonrative pricing-relevant disclosures result in increased equity return variance (e.g.,
Beaver, Clarke, and Wright, 1979; McNichols and Manegold, 1983; and, Morse and
Uslman, 1983) and increased share transaction volurme around disclosure dates (e.g.,

Beaver, 1968). Several recent empirical studies however ﬁnd that equity share transaction

18

vohrrne is negatively related to the convergence of analyst beliefs in both short- and long-
windows (Ziebart, 1990; and Barron, 1995) suggesting that higher levels of accounting
sigmlmfommiomcomemmsuhmdecreasedmformationasymmemiesanengmademmd
decreased share volrnne.10

Based on Holthausen and Vemecchia’s (1990) ﬁamework of the relationships
betweeninformedness, comsensusandequitymarketresponses, Table l summarizesthe
referenced accounting literature on disclosureand equity market response using increased
signal variance and increased trader belief diversity as inversions of informedness and
consensus.

Interestingly, although the theoretical results of Holthausen and Vemecchia (1988,
1990), and Kim and Verrecchia (1994), are derived under the assumption of‘rational
trader expectations, these results are not inconsistent with noise trading models developed
in the ﬁnancial economics literature which relax the ratioral trader expectations
assumption. Black (1986) characterizes moise traders” as traders who revise beliefs and
trade on the basis of noise as if they were acting on information, while “information
traders” trade only on the basis of information (although due to the inherent limitations of

econormetric methods in the presence of nonstatiorary stochastic processes, among other

 

‘° Barron and Karpoir(1998) present a theoretical mrodel showing that increases in the
precision of accounting signals can lead to this result under conditions of nonzero market
transaction costs. That study suggests that these conditions can lead to problematic
inference in accounting studies based on samples which include substantial numbers of
ﬁrms with thinly-traded securities. Sensitivity tests (discussed in Chapter 6) suggest that
thinly-traded ﬁrm year observations do not drive the results presented in this study.

19'

factors, equitytradersoﬁendo not kmowwhethertheyaretradingonimfonrationor
noise). While the models developed in Holtlausen and Verrecchia (1988, 1990), and Kim
and Vemecchia (1994), permit accounting signals to be more and less informative, their
underlying assumption of rational trader expectations implicitly constrains equity traders
to rmb'asedly, but imperfectly, observe pricing-relevant factors which map through a
ﬁrm’s accounting system. Alternatively stated, the ratioral expectations assumption
requirestraderstoformbelieﬁandactonlyonthebasisofinformativesignalsirrthesense
tlat traders observe only sigrals drawn ﬁom actual conditional probability distributiora:
traders beliefs are consistent with actual conditional probability distributions.

Thus, under conditions where the rational expectations assumption holds, equity
traders are able to observe and distinguish between informative, noninformative, and
disinformative accounting sigrals. However, herd behavior and no'ae trading models
referencedinthisstudy suggest conditionsunderwhichthisassumptiomdoesnot hold in
the sense that equity prices do not fully aggregate all available pricing-relevant
information

Kyle (1985) presents a model where an informed trader trades with noise traders
(who may also trade among themselves) such that expected proﬁts are maximized and
“private information is incorporated into prices gradually” (p. 1316). Although exogenous
in Kyle’s model, the existence of noise trading activity both allows the informed trader to
proﬁt from having private information and prevents market makers ﬁom observing
information trading. In turn, this allows the infomned trader to choose an optimal price
pathovertime conditioralontledemand ofmoise traders suchtlatreturnsto private
information are maximized. Since the informed trader’s private information becomes

20

impoundedmpricemthelhnit,pricerevisionsandmadmgvohmneresulﬁngﬁom
information trading must also converge to zero in the limit.

Shleifer and Summers (1990) discuss a setting consisting of both information and
noisetraderswhereinformationtradersdo motdriveequitypricesto theirrationalvalues
due to the absence of riskless arbitrage opportunities. Moreover, the notion is presented
thusystemaﬁcovemeaaiombymiseuadasmmformﬁon—whichtaatopasistsmce
noiseuadersobtainahigherretmnﬁ'omanmmpﬁcitlyhigherriskportfolio
strategy—makes it optimal for information traders to condition their trading strategies on
noisetradingstrategies. Thissuggeststhatundercertaimconditionsitbecomesoptimal
for infomnationtradersto inanipulatemadingactivityandprices; temporarilydrivirig prices
furtherﬁ'omtheirratiomal valuesandincreasing slaretramsactionvolume.

The results of Kyle (1985), and Shleifer and Summers (1990), suggest that the
combination ofboth information and noise mading activity tends to result in (1) increased
equity return variance and share volume in shorter time periods around (information and
disinformation) disclosure dates where the eﬁ‘ects of noise trading strategies likely
dominatemarketdataamd(2)decreasedequﬁyretumvarameandshmevohmnem
longer time periods spamming disclosure dates where the eﬂ'ects of infomnation trading
strategies likely domirate market data.

Itcanbeseenthattheaccounting disclostme-equitymarketresponse literatureand
noise trading literature discussed here are consistent and jointly suggest tlat noisy
accounting signals generallyleadto: (1) increased equity returnvariance and slare volume
in short-windows around disclosure dates where such data is largely generated by the
actions ofnoise traders (who trade on noise as ifit were information); and, (2) decreased

21

equityretumvmiameandslarevohummbng-wmdowsspammgdiscbsmedmeswhem
such data is—on average—largely generated by the actiora of information traders (who
do not revise beliefs or trade on noise).
3.4 Implications of related research
Although considerable empirical research has been conducted on commercial bank loan
loss provisions in the accormting literature, the highly-conditional empirical results suggest
that the accounting literature has not converged to a robust explaration ofhow and why
bank managers exercise accounting discretion over loan loss recognition. Consequently, it
is not clear whether equity traders price information contained in loan loss disclosures
about future loan loss realizations per se, or whether they price other factors associated
with such disclosures. For example, it is not clear whether the widely-documented
positive association between equity returns and unexpected loan loss provisions is due to
infomnation about the credit risk inherent in banks’ loan portfolios and expected loan loss
realizations, or is due to information about some other factor inﬂuencing banks’ risk or
expected returns.

To provide a theoretical ﬁ'amework for developing hypotheses that might provide
a more adequate explanation of how and why commercial bank maragers use discretion
over loan loss provisions, and so gain insights into the equity pricing and information
content of loan loss disclosures, Scharfstein and Stein’s (1990) herd behavior model and
several noise trading models are discussed. Consistent with the commercial bank
institutional literature (discussed in Chapter 2, Section 2.1), the results of Scharfstein and
Stein (1990) suggest that it is optimal for commercial banks to use accounting discretion
to jam otherwise pricing-relevant information contained in loan loss disclosures.

22

Moreover, noise trading models developed in the ﬁnancial economics literatrme suggest
that traders with private information (including managers) have incentives to exploit
information asymmetries between themselves and noise traders. Therefore, both the
commercial bank institutional literature and ﬁnancial economics literature suggest that the
discretionary components of commerc'al bank loan loss provisions can be either
noninfonnative or disinformative. Finally, the referenced accounting literature on
disclosure and equity market response suggests observable equity market-based measures

of the (dis)information content of discretionary accounting sigrals. l

23

CHAPTER 4

HYPOTHESES

4.1 Informational characteristics of discretionary accounting signals

This study characterizes alternative explanations of the use of accounting discretion over
Ilp within a fundamental framework providing a link to theory developed in the ﬁrancial
and information economics literatures. Consistent with notions of information in Beaver
(1968, p. 69m.8), Lev (1969), and Theil (1967), it can be shown under reasonable
assumptions that accounting signals can either be informative, noninformative, or
disinformative (see Appendix 3). Table 2 presents deﬁnitions of these three possible
accormting sigral types as well as deﬁnitions of signaling and signal-jamming based on
the information economics literature. Signaling and signal-jamming behavior represent
two prominent uses of discretionary diclosure in the information and ﬁnancial economics
literature.

The ﬁamework spanned by the signaling and signal-jamming uses of discretionary
disclosure has irnportamt theoretical properties. As shown in Table 3, these two types of
discretionary disclosure behavior result in accounting signals with observable
informational characteristics that are both mutually-exclusive and exhaustive with respect
to accounting signal types. Further, Table 3 summarizes the necessary conditions for
observing sigraling and signal-jamming behavior in equity market data conditional on tle
assumption that the accounting variable (component) is discretionary.

It is also evident ﬁom Table 3 ﬂat the hypotheses developed in this study

effectively contrast the signaling and signal-jamming uses of discretion over commercial

24

bank loan loss provisions: A positive empirical association between capital market-based
measures of accounting signal informational claracteristics and the discretionary
components of Ilp is consistent (only) with signaling behavior, while a negative association
is consistent (only) with signal-jamming behavior. It should be noted that there are two
characterizations of signal-jamming in tle information economics literature: in one case,
signal-jamming results solely in tle addition of white-noise to signals (i.e., garbling) (see,
e.g., Creane, 1995); more commonly in the literature, signal-jamming results in the
distortion of other sigrals (i.e., belief manipulation) (see, e.g., Holrnstrom 1982). If bank
managers use Ilp discretion to engage in white-noise signal-jamming, then it is reasonable
that no (measurable) association between measures of information content and
discretionary Ilp components would exist in equity markets dominated by infomnation
traders.ll However, while this study does not attempt to distinguish conditions under
which white-noise signal-jamming occurs from conditions under which belief-manipulation
signal-jamming occurs, it is generally assumd that bank managers use Ilp discretion to

manipulate equity. trader inferences.

 

” Thisirmpliesthatinferencesmadeinthisstudyaredependent ontheassunrptionofthe
relative proportion of information traders to noise traders. Consistent with Kyle (1985),
inferences in this study are based on the maintained hypothesis tlat equity market data
generated in longer, disclosure-spanning time periods is dominated by information trader
activity, while such data generated in shorter periods around disclosure dates is dominated
by noise trader activity.

25

4.2 Informative loan loss provisions signak

RecemloanlossdisclosrmeMstudiesexammmgtheassocatiomsbetween
discretionary le components, pre—loan-loss earnings (plle), and equity returns (Wahlen,
1994; and Liu, Ryan, and Wahlen, 1997) do not explicitly examine the mechanisrm by
which Ilp andplle are reated; nor are these studies entirely clear as to why equity traders
would interpret discretionary components of Ilp as being predictive of plle. While nco
represents clarge-oﬁs of interest-bearing loan assets and is a relatively unambiguous
predictor of decreases in future loan interest revenue (a component of plle), Alla
npresemSWgers’beﬁeﬁovertheclamgmgcreditﬁsksmhereminbankban
portfolios—marryofwhichmaynotberealizedinlossesofloanprincipalordecreasesin
loan interest revenues for at least several years—and is consequently substantially more
ambiguous in its relationship to plle than is nco.

In this connection, two associations which could provide explanations of the
observed association between lagged discretionary Ilp components and both plle and
equity returns are: (1) a positive association between lagged discretionary Ilp components
and loan interest revenue; and (2) a negative association between lagged discretionary Ilp
components and nco (or Ilp in general). However, any positive association between
lagged discretionary Ilp components and loan interest revenue is likely spurious since net

interest revenue is decreasing in actual loan loss realizations nco, and is only related to

26

Alla indirectly through expected nco.12 Consequently, a negative association between
lagged discretionary Ilp components and nco is a more plausible explanation of the
anomalous positive association between such llp components and equity returns.

This discussion suggests that it is necessary to test for any (non-zero) association
between lagged discretionary Ilp components and both plle and nco since such an
association would provide (I) evidence of the inadequacy of the Ilp components
erpectations model used in this study, and (2) evidence complementary to formal tests of
the disinformation content of discretionary Ilp components (Hypotheses 2.1-2.4).
Accordingly, since this study hypothesizes that bank managers generally use accounting
discretion over Ilp components to jam otherwise pricing-relevant signals, it is hypothesized
(in alterrative form) tlat such Ilp components are not infomnative with respect to expected

"CO:

 

'2 To see this mrore clearly, let loan interest revenue, y, for a given time period be deﬁned
as a linear function of daily-weighted-average loan interest yield r and daily weighted-
average loan principal balance outstanding f: y(r,f) a r ~J? . Decomposing the end-of-
period balance for loan principal outstanding using its basic accounting identity and ﬁnding
the daily weighted-average of those components results in: Z=§+E—a—n—c-o
where adv, cal, and nco denote loan principal advances, collections, and net charge-oﬁ‘s
for the period, respectively; and x»: denotes the exogenous component of ending loan
principal. Using this decomposition of loan principal outstanding, the loan interest
revenue function can be written as y(r,m,ea,;c_o;i;)=r-(;;+E-a--n_c_o).

Noting that in general r > 0, it follows that loan interest revenue is decreasing in nco since
m.)/aE:—o=—r <0 foralliE>0.

27

H1: Lagged discretionary nco and lagged discretionary Alla are not associated
with net loan charge-oﬁ‘s conditional on other loan loss disclosure
information available at time t-l.

Althoughﬂeacmalhgsmuctmeofanyrehtionshipbetweenaggeddiscretiomry Ilp
components and nco is unknown, a rejection of this hypothesis in its null form would
suggest that discretionary Ilp components are not informative with respect to the loan loss
realization expectations of either bank managers or equity traders as proxied for by the llp
expectations model used in this study.

4.3 Disinformative loan loss provision signals

Since the assumptions and conditions studied in Scharfstein and Stein’s (1990) model
closely correspond to those of the commercial bank institutional setting, it is reasonable
tlat bank managers use loan loss disclosure discretion to jam pricing-relevant sigrals of
expected earnings and expected loan loss realizations, ceteris paribus. Moreover, this
proposition is reasonable since it also corresponds well with the suggestion in the
institutional literature that banks generally exhibit herd behavior with respect to
investment, ﬁnancing and accounting policy.

Thus, both the signal-jamming and commercial bank institutional literatures
suggest that bank managers lacing uncertainty (over credit-, interest-, and liquidity-risk)
use accormting discretion to inﬂuence the perceptions of investors with respect to
managerspredictiveabilitiesandthecreditriskinherentinbanks’ loanportfolios;and,

thereby, to maintain or increase information asymmetries between themselves and

28

suppliersofﬁmdssuchthatproﬁtsaremaximized.” Thissuggeststhatbankmanagers
use accormting discretion over Ilp components to emit disinformative disclosures.
Inparﬁcuhr,itisreasombletohypothesizebankmanagersemhsignakjammmg
disclosureswiththe objective ofminimizing or reducing capital costs since bank ﬁrancial
statements are used largely by investors in evaluating the risk-return characteristics of

bank debt and equity securities.""’ Based on the disclosure and equity market response

 

'3 There exist striking historical examples of ﬁrancial disintermediation in the commercial
ngdusmyresuhmgﬁomthecoﬂapseofinformaﬁonasymmemiesbetweennet
sellers and met buyers of ﬁmds; e.g., the recent growth of the “junk bond” market and
diversiﬁed investment funds which allow investors to diversify ﬁrm-idiosyncratic
information risk has reduced the need for net sellers-to place their funds with commercial
banks in their role as information-processors and asset risk transformers. This suggests
that banks derive economic rents precisely as a result of such information asymmetries.

" Here, investors includes all funding sources (including interbank placements) except for
depositors insmed by the FDIC. Although, a bank’s cost of capital includes interest costs
ondeposits, commercialpaper,andotherdebtsecurities, itisassumedthatthesecapital
costs are effectively impounded in cost of equity capital.

29

literature, if discretiorary Ilp componems represent disinformative, signal-jamming
discbamesbybankmmgersﬂenmosesigmlswouldresuhmademeasemmformation
(ie.,anincreaseinthetmcenaintyofasignal)availabletoequityuaders,andwouldbe
observabk:(l)asanmcreasemumrpeaedequhymmmvarameandmcxpectedshare
transaction volume in a short-window around a disclosure date, and (2) as a decrease in
unexpected equityretmnvarianceandrmexpectedsharetransaction volumeinalonger,

wquential disclosure date spanning period. However, given the likely differences in the

 

‘5 SignaLjamming in its most general form involves the addition ofmean-zero noise to an
existing sigral (cf. Creane, 1995). Accordingly, if bank managers’ discretionary Ilp
disclosuresresult intheadditionofmean-zero noise, thenit followsthat onlythe variance
of pricing-relevant signals will change as a result. Beaver, Kettler, and Scholes (1970) and
Beaver and Manegold (1975) ﬁnd a positive association between accounting earnings
volatility and equity market-based measures of (systematic and nonsystematic) risk.

These ﬁndings, in conjrmction with the results of Scharfstein and Stein (1990), suggest
that bank maragers may also use Ilp discretion to manipulate accounting-based measures
of systematic and nonsystematic risk to match a risk proﬁle similar to other “peer group”
banks. In so doing, 5' -jamming banks would realize lower capital costs relative to
non- ° -jamrning banks since tle market would be unable to detemnire whetler any
differential loan loss or earnings volatility observed in an individual bank is due to
differences in actual risk or to diﬁ‘erences in sigral—jamming behavior. If excess loan loss
or earnings volatility is interpreted as differences in actual risk, a bank would then be
“trapped” into engaging in signal-jamming behavior in order to avoid potentially emitting
(pemapsfalse)signalsofmfeﬁormanageralabMyandcrednqualmymhtiveto other
banks. This intuitive argument loosely follows the more formal equilibrium arguments in
the signal-jamming literature including Fudenberg and Tirole (1986), and Holmatrorn
(1982).

30

relative levels of available discretion over nco and Alla, it is not clear ex ante whether the
discretionary components of either nco or Alla (or both) are likely to be informative,
noninformative, or disinformative. Thus, more reﬁned hypotheses addressing the
relationships between discretionary components of nco and Alla , individually, and both
unexpected equity return variance and unexpected share transaction volume are not
presented here."5 Accordingly, it is hypothesized (in alternative form) that:

am rettmn variance hymtheses

Hm: Discretionary components of nco and Alla are negatively associated with

unexpected equity return variance in longer time-windows spanning
disclosure dates.

Hm: Discretionary components of nco and Alla are posiﬁvely associated with
unexpected equity return variance in short time-windows aroimd disclosure
dates.

Egm' share volume hymtheses

113.1: Discretionary components of nco and Alla are negatively associated with
unexpected share volume in a longer time-windows spanning disclosure
dates.

H33: Discretionary components of nco and Alla are positively associated with
unexpected share volume in short time-windows around disclosure dates.

A rejection of these hypotheses in their null form would suggest that llp discretion is used

to reduce pricing-relevant irrfomation available to equity traders. I

 

'6 However, this study explores empirically the relative informational characteristics of
discretionary Ilp components by estimating and testing empirical models which decompose
Ilp imto nondiscretionary and discretionary nco and Alla components.

31

ELM—w

RESEARCH DESIGN

Thischapterdescribesthepopulation, sample,anddatasetusedinthisstudy;presentsthe
expectatiora models used in estimating the expected and unexpected components of
depmdemmmdependemvmabes;presemstheempmicalmodelsusedmtestmgme
hypotheses developed in Chapter 4; and, formally restates those hypotleses in (statistical)
terms relating to such empirical models.

5.] Population, sample, and data set

This study uses equity market data available ﬁom the Center for Research on Securities
Prices (CRSP) database, and ﬁnancial reporting data available ﬁ'om the Standard & Poor’s
Compustat Disclosure database, forthe threeyearperiodended December 31,1996 for all
domestic U. S. commercial banks with over three billion dollars in total assets at tlat date.
This initial sample is comprised of1021 commercial banks that represent a substantial
portion of the total assets held in the U. S. commercial banking system (approximately
73%) at December 31, 1996. Certain data for eight banks in the initial sample were
missingineithertheCRSP orCompustatdatabasesthusreducingthe sample to 96banks.
Thisremainingsampleisassumedtoberepresentativeofthepopulationofbankswith
suﬁciemt equity market and money market access to exhibit the hypothesized
discretionary disclosure behavior.

5.2 Unexpected return variance and share transaction volume

Consistent with the referenced accounting literature on disclosure and equity market

response—and with Bernard’s (1987) suggestion that cross-sectional correlations in

32

caphalmarkddﬂacaneadtomferemepmbemsmemphicalwcoummgresearch—ahis
study focuses on two forms of market resporae to discretiorary Ilp components:
umwecteddaﬂyequhymtmnvarhmeandumxpededdailyshamﬂansactionvohme.
Unexpected components are derived ﬁom market models of returns and volume estimated
usingonlydatarelatingtothe96commercialbanksinchrdedmtlesample. Thismethod
of estirnatimg these unexpected components controls for common factors inﬂuencing
equity returns and volume in the population of larger commercial banks, thus mitigating
certain types of cross-sectional correlation problems in this study. In particular, this
method provides estimates of ﬁrm-idiosyncratic equity returns and volume conditional on
all common factors inﬂuencing average retlmns and vohrne in the sample of 96
commerc'al banks.
Formally,dailymexpectedequityrenmnvarianceismeasmedasthesquared
unexpected equity returns derived ﬁom the following model of daily equity returns for
bank i, day t as a linear function of the equally-weighted, daily average market return for

the 96 sample banks:

rn=ﬁo+ﬂ,-[{;Zrﬁ]+u“ n=96; t=1,---,T [3]
['81

wheretistheindexfortletimeperiodbegirmingontheﬁrstmarkettradingdayaﬂer
October l4thandendingonthelastmarkettradingdaybeforeMarch l6th;atimeperiod
centered approximately on December 31 (the ﬁscal year end for all U. S. comrmercial
banks). Consistent with the suggestion of Cohen, Hawawini, et. al (1980) tlat capital

marketsaregemraﬂycharacteﬁzedbymadmgﬁiaiomthmmmseﬁalwmeatiomm

33

returns and transaction volume, Prais—Wimsten transformed FGLS pmameter estimates are
obtaired for equation [3] to provide for consistent parameter estirration in the presence of
AR(1) process ser'ally-comelated error terms. (Although the actual structure of
autoregressive processes in commercial bank equity returns and volume is unknown, most
banks in the sample are actively traded suggesting that any trading ﬁictions clear quickly
and that the assumption ofan AR(1) process is reasonable.) Residuals obtained ﬁom

estimating equation [3] are then squared to obtain equity retlmn variance for bank i, day t:

I"

[542]] [41

where 3, , ,3, denote the Prais—Winsten transformed FGLS parameter estirmates.

Similarly, the second market response variable, unexpected daily equity share
transaction volume (13v, ), is measured as the lmexpected equity share transaction volume
derived ﬁom a model of daily equity share transaction volume esvi, (scaled by outstanding

shares) for bank i, day t as a linear function of tle equally-weighted, daily market average

share transaction vohrme forthe96sample banks:
rivi, =esvn—fo-f,-[%Zesvﬂ) n=96; t=1,---,T [5]

I"

where (770, 77,) denote the Prais—Winsten transformed FGLS parameter estirmates.

34

5.3 Unexpected loan loss provision components
Discretiorary components of Ilp are modeled as the difference between observed Ilp for
bank i, time t and the industry-expected Ilp derived from a pooled regression of Ilp
armounts at time t on lagged loan and loan loss disclosure variables, and contemporaneous
plle levels. The Ilp expectations model presented in equation [6] corresponds to a
conditional expectation function where the three primary loan loss disclosures—— Anpl, nco
andAlla—are assumedto be linear flmctions ofthe conditioning variables shown intheir
respective column vector in the matrix of independent variables. If there exist other
variables on which bank managers’ nco and Alla choice is conditioned, then the resulting
coeﬂiciemt estimates obtained for such mrodels will be biased and inconsistent.17

Loam loss provision emtations. The conditioning variables in [6] are
approximately consistent with Ilp expectations models in the referenced loan loss
disclosure pricing studies. The expectations model shown in [6] also incorporates
ﬁndings of the referenced loan loss disclosure discretion studies which suggest that llp and
nco are chosen jointly, conditional on plle. In this connection, the system of equations

represented in [6] is estimated using SUR (seemingly unrelated regression) FGLS

 

'7 With respect to the conditioning variables in equation [6], Sinkey and Greenawalt
(1991) examine the determinants ofcomrrercial bank nco and ﬁnds that bank geographic
region, loan portfolio growth and loan interest yield are associated with loan loss
realizations. This suggests that both discretionary and nondiscretionary components of
nco are inﬂuenced by these unmodeled ﬁictors. Further, to the extent tlat these factors
are not already irrpounded in the other conditioning variables in equation [6], it is likely
tlat equity traders’ loan loss disclosure expectations diﬂ‘er ﬁom those represented here.

35

estirmation which provides asymptotically-efﬁcient parameter estimates in the presence of

cross-equation correlation of dependent variables:

F111“

loans“ loansH loans“

Anpl" Ila“ Ila“ Ila“ BM uWJ,
nco, = anlt-I "plat-l "pie-l ' Burro + uncut [6]
Alla, O nco“ nco“ BM, um“,

0 Alla,H Allow
0 plle, plle, _

 

 

To partially mitigate potential estimation and inference problems resulting ﬁ'om
heteroscedasticity, all loan loss-related variables at time t are scaled by total loans
outstanding at that date. Sirmilarly, total loans and plle for period t are scaled by total
assets at that date resulting in total loans as a percent of total assets and pre-loan-loss
return on assets, respectively.

Table 3 presents FGLS estimates and standard errors for the parameters of
equation [6]. Although the results of this study are potentially sensitive to tle loan loss
expectations! model shown in equation [6], sensitivity analyses discussed in Chapter 6
suggest that tle results are robust to alternative speciﬁcations of this expectatiora model.

m tiom loan loss provision comments. Estimated unexpected Ilp
components, which are used to proxy for discretionary Ilp components, are measrmed as
the difference between bank i, year t reported Ilp components and the bank-speciﬁc

conditional prediction obtained ﬁom estinatirrg equation [6]:

36

17m, _ nco, -Bnco, [7]
22m, Alla, — sure,

where the expected and unexpected components of near and Allan are denoted

A

(E,_lnco,, BHAIIaJ and ( rim“, duh“), respectively.

5.4 Empirical modeh and hypothesis tests

Hymthesis 1 states in alternative form that discretionary components of nco,“ and Alla,“
do not contain sigrals with respect to future neon levels controlling for other loan loss-
related information available at tirme t—l. Based on the referenced commercial bank
accounting literature and on the Ilp expectatiora model presented above, nco expectations
are conditional on lagged loan and loan loss disclosure variables, and on contemporaneous

Alla and plle levels. However, it is assumed that only expectations of nco and Alla for
time t (denoted Bano, and fiHAlla, , respectively) are available to the equity market at
t—l. Accordingly, this expectation replaces the actual lagged observation of nco and Alla.
To test this hypothesis, the residuals from a regression of nco" on the conditioning
variables shown in the bracketed terms of the right-hand side of equation [8] (which omit

the unexpected cornpoments of nco “-1 and Alla as) are obtained as:

37

nco

J, = nco, -

 

(ll

loans
Ila

it-l
"Fla-l

A”Pllt—l
Piles-l

d-l

 

k plle. J
L.

 

[3]

 

where ([3,?) denote Prais-Winsten transformed FGLS parameter estimates ﬁom a

regression of nco“ on the conditioning variables shown in the bracketed, right-hand side

term. Then, using a Lagrange Multiplier test approach (Eagle, 1982), tle formal test of

HypothesislcanbestatedinnullformaszTheelementsof 5inequation[9] equalzero.

N)

mat——

' l

Ila,H
"P’s—l
Aanm-l
Piles-l

 

loans,_,,

L plle, ‘

 

I I

A. . t? .-
5+ 1E"-'"""" 7+ 3”“ 5+v, [9]
ElHAIIae uNlaJt-l

A rejection of this hypothesis implies ﬂat the lagged discretionary components of nco and

Alla (tim_,, rim-) are associated with the residuals obtained ﬁom estimating equation

[6]. Since this result would imply that lagged discretionary Ilp components explain a

signiﬁcant amount of variation in near not explained by the Ilp expectations model shown

in equation [6], a rejection of this hypothesis would be consistent with either the

38

misspeciﬁcatiom of equity trader expectations or the hypothesis that discretionary Ilp

components are predictive of nco.
Em retmn m’ and share vohime hmtleses. These hypotheses state in

alternative form that the discretionary components of nco and Alla are negatively
(positively) associated with both equity return variance and urexpected share volume in
long-windows (short-windows). Similar to McNichols and Manegold (1983), and Morse
and Ushman (1983), an 11 day event window centered on the disclosure date is used for
the short-window hypotheses tests. The long-window tests correspond to time periods
beginningontleﬁrstmarkettradingdayaﬁer October 14andendingonthe last market
tradingdaybeforeMarch 16 ofeachyear(recallingthatDecember31 istheﬁscalyearend
forallcormmercialbanks). Thefommaltestsoftle equityreturnvarianceand share volume
hypotheses can then be stated (in alternative form) with respect to both equations [10] and

[11]as:Theelementsofyarelessthanzero;and,Theelenentsof6aregreaterthanzero.

 

 

 

 

 

 

_ 1 _
dPe’a
plle, I '
P113: [amour “ rdperi't .ﬁAllaJt-
An I. :72 . d r {22 .
“r3: 1”; 5+ Am 7+ ”6" 1”“ 5w, [10]
Mplit uAllaJt dperlt ' uncth
opera - plle, ﬂing.“ J Ldperi, 42;” A
dper, - plle:
dper, -Anpl,
_dpera -Anpl§_

39

 

 

 

 

 

 

, 1 -
dperr
plle,If ' '
plle: ’13,“, _ Pdper, - 13A,,” -
I 122 . r. 422 .
av“: Amp; [5+ f” 1+ dpe, fa“ 6+v‘, [11]
Anpll‘t "Alla! dperi’t ' “noon
dper, - plle, fling,“ bdper, - 17,2.” J, _
dper, - plle:
dper, -Anpl,
_dpere ' Mp4:

Conditioning variables show in equations [10] and [11] are approximately consistent with
recentloanlossdisclosurepricing studies. Thevariabledperaisabinaryindieatorvariable
withavalueofoneiftheobservationofdrf (liv,)fallswithinthe 11 daydisclosure
period and zero otherwise. Ratio scale conditioning variables in equations [10] and [11]
include quadratic terms of each such variable to control for nonlinearities in the data, and
to give additional insights into the response surface characteristics of the associations
between discretionary Ilp components and both unexpected equity return variance and

unexpected share volume. I

40

w

EMPIRICAL RESULTS AND SENSITIVITY ANALYSES

Thachaptadacumestheemphicdmsuhsofmisstudymdmesemsﬁmofﬂpsemsuhs
to various assumptions used in this study. In particular, this chapter discusses quantitative
resultsintheformofparameterestirnatesandstandarderrorsformodelspresemtedin
Chapter 5; estinated marginal effects and the results of hypotheses tests; and, analyses of
the sensitivity of results to estimation criterion, inﬂuential observations, and loan loss
expectations model speciﬁcation. ‘ This chapter further explores the convexity and
concavity of nonlinearities found in the associations between estimated discretionary Ilp
compomemsandequitymarketmsponsesandmterpretsthemmthecomextofthe
hypotheses developed in this study.

Details of model parameter estimates and standard errors, hypotleses tests, and
sensitivity analyses are presented prirmarily in Appendix 1, Tables 4-9.3. Descriptive
statistics showing the basic distributional characteristics of tle variables used in estimating
equations [3]—[1 1] are presented in Table 10. Details underlying the qualitative discussion
of the relationships between discretionary loan loss provision components and equity
market responses are presented primarily in Appendix 2; such details being comprised of
plots ofequity return variance and unexpected share volume in the space ofestirnated
marginal effects of loan loss provision discretion.

6.1 Informative loan loss provision discretion results
Fundamentally, Hypothesis 1 states that if discretionary Ilp components are informative to

equity traders, then those components must be associated with future loan loss

41

realimtions—ie, future met loan charge-oil‘s (nco). Although the commercial bank
accounting literature has often suggested that the informativeness of discretionary Ilp
components results from bank managers signaling private infomnation about future
earnings,itisshowninChapter4(ﬁr. ll)thattleempiricalresultsofthisliteratureare
generally inconsistent with plausible explanations of tle relationship between discretionary
Ilp components and future plle. Further, the development of Hypotheses 2.1—3.2 suggests
that any observed association between discretiorary Ilp components and future plle is
likely spurious. For these reasons, Hypothesis 1 is developed as a more direct test of the
informativeress of discretionary Ilp components, and—consistent with a plausible
explanation of the widely-documented positive empirical association between discretionary
Ilp components and equity returns—states in alternative form that discretionary Ilp
components are negatively associated with future nco. This implies that if discretionary
Ilp components are informative to equity traders, then those components are predictive of
future decreases in nco on average.

Fﬂ mph results. Results for tle flill sample ofbanks, shown in Table 5.1,
indicate no signiﬁcant association between either of the two estimated discretionary Ilp
components (ﬁnbn 12%.“) and ﬁlture loan loss realizations nco,. Although
inconsistent with Hypothesis 1 per se, this result is generally consistent with Hypotheses
2.1—3.2 which state that discretionary Ilp components are either noninformative or
disinformative to equity traders on average. Thus, this result provides additional evidence

consistent with the results of the tests of Hypotleses 2.1-3.2 discussed below.

42

Reduced mph m. Results for a reduced sample based on observations for

the central 95% of the rim“ and 17M,”H sample distributions, shown in Table 5.2,
indicate that of the two discretionary Ilp components only the less discretionary rim.“ is

signiﬁcantly associated with near. The positive association found between ti and near

ncth-l
inthereducedsamplesuggeststhattheesthnateddiscretionarycomponem ofncois
predictive of increases future loan loss realizations, and is therefore inconsistent with
Hypothesis 1. Interestingly, however, this result also is inconsistent with results of other
loan loss disclosure pricing studies showing that estimated discretionary llp components
are positively associated with equity returns: If estimated discretionary components of
nco are predictive of increases future loan loss realizations (and discretionary components
of Alla are not predictive of loan loss realizations), them it is plausible tlat the observed
positive association between equity retlmns and discretionary Ilp components results ﬁom
correlated, omitted variables rather than pricing-relevant information contained in such
discretionary accounting variables per se.

Results shown ill Table 5.2 are also consistent with the hypothesis that discretion
over nco is substantially constrained relative to Alla such tlat it contains substantially
more information with respect to future loan realizations than does Alla. This evidence is

consistent with the notion that the relatively more discretionary 13%,,4 is less informative

than is the relatively less discretionary ti and is therefore not inconsistent with the

noth-l ’

hypothesis that bank managers use available accounting discretion over Ilp to jam

otlerwise pricing-relevant signals (i.e., Hypotheses 2.1—3.2).

43

Table 5.2 shows that the error term of the Ilp expectations model represented by
Equation [6] is ser'ally-correlated for a subset of the observations in this study. This
suggeststhatthellp expectationsmodelusedinthisstudymaybemisspeciﬁed forbanks
with certain characteristics. However, preliminary sensitivity analyses discussed later in
this chapter suggest that this potential erpectation model misspeciﬁcation does not
seriouslyaltermemfemmesdrawnwnhrespeatoeithertheequmymnmnvarance
hypotheses or the equity share volume hypotheses.

6.2 Disinformative loan loss provision dacretion results

Hypotheses 2.1—3.2 are linear hypotheses in the sense that discretionary Ilp components
are expected to be monotonically associated with equity return variance and unexpected
share volume. This implies that all levels of discretionary Ilp components have
qualitatively similar informational characteristics; e.g., all levels of discretionary Alla are
disinformative. Although these hypotheses are consistent with underlying theory
referenced in Chapter 3, intuition suggests that tlese hypotheses cannot hold in general
empirical settings. To see this more clearly, consider an extreme case where a
discretionary Alla increase was equal to 50% of a bank’s outstanding loan portfolio at
time t. Intuition suggests that equity traders would interpret this increase as indicative of
severe credit quality problems which are likely to be realized as large loan losses (nco) in
subsequent periods. Thus, intuition suggests that the linear hypotheses developed in this
study reasonably hold only on average, and not under extreme conditions.

As is common in empirical accounting research, the incompleteness of existing
theory to explain and predict empirical phenomena necessarily results in the estimation of
models that do not comfomn precisely to underlying theory. In this study, this necessitates

44

the use of empirical models that include quadratic terms to control for basic nonlinearities
ill the association between discretionary Ilp components and equity market responses.
Consequently, the estimated marginal effects of discretionary Ilp components on equity
return variance and unexpected share volume, and the inferences about the informational
claracteristics of those components, are necessarily conditional. Nonetheless, estimating
and testing models that allow for nonlinearities provides valuable insights into the limits of
thetheoryandhypothesesdiscussedirrthisstudymnd, aswillbeshown, allowstlreresults
ofthis studyto bereconciledwithexisting commnercialbankaccounting literature.

It is necessary to specify conditions under which tle linear hypotheses of this study
are predicted to hold since the estimated relationships are not constrained to be monotonic
or linear. Since most empirical accounting research and economic theory involves
explanations and predictions of central tendencies of economic behavior, the empirical
results relating to Hypotheses 2.1—3.2 are evaluated using the central 95% of the sampling
distributions of the estimated discretionary Ilp components. Thus, the empirical results of
this study can be interpreted as evidence pertaining to the central tendencies (e.g., mean,
median, etc.) ofthe informational characteristics of discretionary Ilp components.

Parameter estimates and stande errors for both the equity return variance and
unexpected share volume models shown in equations [10] and [11] are obtained using
FGLS estimation with heteroscedasticity-robust standard errors. To evaluate the
robustness of these results to alternative estimation criteria and potential violations of
assumptions underlying FGLS estimation, least absolute deviation (LAD) estimates with
bootstrap-resampling estimated standard errors, and Prais—Winsten transformation F GLS
estimates, are also obtained and discussed ill Section 6.5, “Sensitivity analyses.”

45

6.2.1 HWZIm12:Equityreturnvaﬁancemulm

Empiricalresultsare generally consistent witthpotheses 2.1 and 2.2 asevidencedbythe
signsandstatisticalsigniﬁcanceoftheesthmtedmargmaleﬁ‘ectsofﬁm andtlwaon
unexpectedequityreturnvariancewrz)shownimtheﬁrstcolumnofTable6.l. Thistable

shows tlat the signs of the estimated joint margiral effects of rim and rim, (for the central
95% of those sample distributions) on unerpected equity return variance are negative at
conventional signiﬁcance levels in long time-windows spanning disclosure dates
suggesting that—on average—equity traders ﬁnd these signals disinformative. The signs
of the estimated joint margiral effect of these variables are positive but not signiﬁcant at
conventional levels in the short time-window around disclosure dates suggesting that-—on
average—equity traders ﬁnd these signals noninformative. Importantly, the pattern of
stmisﬁcalsigmﬁcmceofmeesthmtedmargmaleﬂecwisalmwmistemwnhseveral
intuitively plausible interpretations:
(1) Bank managers have relatively less discretion over nco than over Alla, and
equity traders consequently respond to pricing-relevant sigrals contained in
nco as ifthese signals are less ambiguous than those contained in Alla
(since the higher levels of statistical signiﬁcance of the nco marginal effects
suggestthatmoreofthevarianceinequitytraderresponsesisexplainedby
n60); and,
(2) Increased levels of both noise trading activity and information trading

activity around disclosure dates results in a noisier data environment that

46

partiallyobscuresinferencesofequitymaders(andpotentiallytestsof

statisticalsigniﬁcanceimthisstudy).

Thus, both the long— and short-window results are not inconsistent with the signal—
jamming hypothesis developed in this study since jamming signals can result in either
noninformative or disirrformrative signals (see Table 3). Moreover, these results suggest
that equity traders do not ﬁnd discretionary Ilp components to be informative—on
average. Sensitivity alalyses (discussed below) corroborate these results.

6.2.2 Hypothm 3.1 and 3.2: Equity share volume malts

Although more ambiguous than results for the equity return variance hypotheses (2.1 and
2.2), empirical results are also generally consistent with Hypotheses 3.1 and 3.2 as
evidenced by the signs ofthe estimated marginal eﬁ‘ects of rim and rim, on unexpected
share volume (riv) shown inthe ﬁrst cohimn ofTable 7.1. Thistable showsthat only a
marginally signiﬁcant, positive association between rim and 12v is evident in the data set
and model used in this study. Similar to the nonsigniﬁcant short-window, equity return
variance results discussed above, the results presented in Table 7.1 are not inconsistent
with the signal-jamming hypothesis and suggest tlat equity traders do not ﬁnd
discretionary Ilp components to be infomnative—on average. The similarity between the
signs of the estimated marginal effects, and their relative statistical signiﬁcance, in both the
equity return variance and equity share volume hypotheses tests are suggestive of mean-
zero noise obscuring inference on Hypotheses 3.1 and 3.2. Alternatively stated, when
(margirally) statistically signiﬁcant, the results of tle equity share volume tests are

consistent with the equity return variance hypotheses test results.

47

Also similartotheequityreturnvarianceresultstheequitysharevollmne statistical
results are consistent with several intuitively plausible interpretations:

(1) Inference on Hypotheses 3.1 and 3.2 is obscured since equity share volume
isanoisiermeasureofinformationcontentthanisequityreme
because it is inﬂuenced by a number of random factors other tlan pricing-
relevant information (consider, e.g., liquidity trading); and

(2) Marginally-sigmiﬁcant results are obtained (only) for nco in Hypotlesis 3.2%
since (as discussed previously) equity traders respond to pricing-relevant
signals contained in nco as if these signals are less ambiguous than those
contained in Alla due to differences in levels of available accounting

discretion

Again, although the empirical results on Hypotheses 3.1 and 3.2 are somewhat ambiguous,
they are not inconsistent with the hypothesis that discretionary Ilp components are used to
jam equity trader inferences—on average. Sensitivity analyses (discussed beloyv) also
corroborate these equity share volume results. i

6.5 sensitivity analyses

The empirical results of this study were analyzed for robustness to estimation criterion,
error term assumption violations, inﬂuential observations, and alternative expectation
model speciﬁcation. These aralyses suggest tlat the results of this study are not
substantively inﬂuenced by econometric problems. A general discussion of non-signiﬁcant

results is included in Section 6.6, “Qualitative analysis of observed associations.”

48

Estm ion criterion. A well-known property of least squares estimation methods
isMestmatesmeheavﬂymﬂlemedbyobservmiomwhkbmwbstamaﬂydistamﬁom
sample means of dependent variables and independent variables; alternatively referred to
as inﬂuential observations, extreme observations, or outlying observations depending on
the particular location of the observations relative to the multivariate sarrple mean. Since
this study focuses on (robust) central tendencies of the reationship between discretiorary
Ilp components and equity market responses, it is meaningful to consider whether mean
marginal effects found using FGLS estimation are substantively similar to median marginal
effects formd using least absolute deviation (LAD) estimation.

Medianeﬁ‘ectsarecomsideredsmcethesamplemedianisambustesthmtorof
central tendency for a nlmnber of families of probability distributions (DeGroot, 1986).
Thus, equations [10] and [l l] were estimated and tested using LAD (median) estimation
with bootstrap-estimated standard errors to analyze tle robustness of results to potential
econometric problems caused by heavy-tailed and heteroscedastic, among other, error
term structures. The results of these sensitivity analyses are shown primarily in Tables 6.2
and 7.2 where long- and short-window LAD estimated marginal effects and related
hypotheses tests are presented.

TleﬁiﬂdatasetmsuhsmderLADesthnaﬁomwhenstatisticaﬂysigniﬁcaanere
qualitatively similar to the primary FGLS margiral effects and hypotleses test results
presented in Tables 6.1 and 7.1. Only one diﬁ‘erence between significant full data set

results under both FGLS and LAD estirration was found:

The short period marginal effect of limon r'ir2 (Tables 6.1 and 6.2) found

to be nonsigniﬁcant and monotonic under FGLS estimation was found to

49

be signiﬁcant (p; .028) and nommonotonic lmder LAD estimation. This
differing result suggests that inﬂuential observations obscure estimation

and inference under FGLS with respect to a nomlinearity between 13A,,“ on

in2 . This type ofnonlirearity is plausible since inspection ofthe concavity
of this margiral effect (shown geometrically in Figures 1.2 and 1.4)
suggests that the more extreme values of ii”, are more disinformative to
equity traders consistent with the hypothesized sigral-jamming use of

accounting discretion over Ilp components.

Error temn structure. The suggestion of Cohen, Hawawini, et. al (1980) that
capnalmarketsaregeneraﬂycharacteﬁzedbymadmgﬁicﬁonsresuhmgmserial
correlations in returns and transaction volume implies the possibility that the results of this
study are sensitive to assumptions about the autoregressive structtme of the error terms in
equations [10] and [11]. In particular, noise added to the equity pricing information
environment by discretionary Ilp components potentially results in lengthened equity
trader response times. To test the sensitivity of the results under FGLS estimation to
potential AR(1) process error temns, Prais—Winsten AR(1) transformed FGLS parameter
estimates and standard errors are obtained for equations [10] and [11]. (Although higher-
ordcr AR processes error terms could be considered, tle lack of any clear theoretical
guidanceintheaccounting literaturewithrespecttothelengthoftimerequired for capital
markets to adjust to new information would preclude meaningful inference in such an

analysis.)

50

Thereaﬂtsofthisemortermsmuctlmesemsiﬁvityanalysismeshownprhmrﬂym
Tables 6.3 and 7.3 where long- and short-window Prais-Winsten FGLS estimated
marginaleﬁ‘ectsandrelatedhypothesestestsarepresented. TheresultsunderPrais—
Wimsten FGLS estirratiom were qualitatively similar to the primary FGLS marginal esects
and hypotheses test results presented in Tables 6.1 and 7.1, and no differences were found
between significant results under FGLS and Prais-Winsten FGLS estimation. Thus, tlese
sensitivityanalysessuggestthattheresultsofthis studyarenot sensitive to assrmrptions
aboutthestructureofthe errortermsimequatiora [10] and [11].

Inﬂuential dMent variable omuons. The comnnercial bank accounting
literature has shown that associations between llp components and equity returns are
sensitive to omission of inﬂuential (i.e., extreme or outlying) observations. As an
example, Wahlen (1994) ﬁnds that a positive association between unexpected Ilp and
equity returns is not robust to the omission ofthe upper and lower 1% ofthe unexpected
Ilp sample distribution. These ﬁndings suggest that results ofthis study are potentially
sensitive to inﬂuential observations which are distant ﬁom the multivariate sample mean.

However, theory underlying this study suggests that more extreme independent
variable observations are associated with the hypothesized signal-jamming behavior. To
see this, recall that higher levels of discretion over Ilp components are necessary to
generate such extreme observations—assuming adequacy of the loan loss expectations
model in equation [6]. Tin-hing to optimal disclosure behavior, the institutional
characteristics of commercial banks including uncertainty over both exogenous factors
inﬂuencing loan loss realizations and credit risk characteristics of bank loan portfolios,
result in incentives for bank managers to maintain or increase information asymmetries

51

(i.e., signal-jamming). Thus, higher levels of llp discretion associated with more extreme
observationsmthesampledatasetamreasomblymomambiguousand,madymmm
setting, disinforrmative. It follows that the more extreme observations in the data set used
in this study are encompassed by that theory and the resultant hypotleses. Accordingly,
thefulldatasetresultsarecomsideredtobemostinformativewithrespecttothe
hypotheses of this study.

Notwithstanding the foregoing discussion, sensitivity of results to inﬂuential
obsewmiomamanalyzedmroughreesthnmbnandtmwmargmaleﬁecwtested
omitting separately the upper and lower 2.5% of the sample distributions of dependent
variables( u‘rzand xiv),andofindependent variables( rim and limb). Theseanalysesare
primarily conducted to gain additional insights into the robustness and generalizability of
results in this study. Accordingly, FGLS, LAD, and Prais-Winsten FGLS estirration are
again used to reestimate equations [10] and [11] using the reduced data sets.

Reduced data set analyses based on omission of upper and lower 2.5% of
dependent variable sample distributions are presented in the second columns of Tables 6.1
through 7.3; similar analyses based on omission of upper and lower 2.5% of independent
variable sample distributions are presented in the third columns of Tables 6.1 through 7.3.

As shown in Tables 6.1 through 7.3, the omission of larger dependent variable
observations generally results in either nommonotonic estimated margiral effects of
discretionary llp components, or increased statistical signiﬁcance of those margiral effects.
The tests of the signiﬁcance of margiral effects take the fomn of (mom-directional) Wald F-
tests which indicate whether estimated marginal eﬂ‘ects explain a signiﬁcant portion of the

variation in the dependent variables ( ﬁr2 and llv ). Consequently, it is not surprising that
52

omittingmoreexmemedependemvaﬁableobsewatiomsoﬁenresuhsinmcreased
statistical signiﬁcance of the estimated marginal effects. It follows that exploration of
estimated nonmonotonicity, and convexity/concavity, of signiﬁcant margiral effects when
larger dependent variable observations are omitted is of greater relevance to assessing the
mbustnessandgeneralizabilityofresultsmthisstudythanstatistical signiﬁcanceperse.

In the exploration of nonmonotonicity the association between discretionary Ilp
components and equity market responses, the convexity and concavity of ﬂat association
canbeinterpretedintermsofthehypothesesofthisstudy. Speciﬁcally,giventhe
hypothesis development in Chapter 4, the following signs of partial derivatives of the
associations estimated in equatiora [10] and [11] are consistent with the hypotheses that

discretionary Ilp components are disinformative in longer, disclosure-spanning periods:

 

(amen) azur’c)

A 2 o a A A
. ,. , . . <0 n ur isconcavem(um,u~,a).
airman,” aumauw]

 

( aztvt) azrivc)

< O a liv is concave in (ii u" ).
A A 9 A A nco’ Alla

Similarly, the following signs ofpartial derivatives ofthese associations are consistent with
the hypotheses that discretionary Ilp components are disinformative in shorter periods

around disclosure dates:

 

63rlr2(.) o’er (.)
adperaztlm ’6dper62rlwa

]>0 4: rir2 is convex in (limﬁma).

 

( 63M.) 631M.)

, A >0 c: 13v is convex in 13mm} 0 .
atlperaztlm adperazum] ( A” )

53

Thesederivativesarenot shownexplicitlyhereorimtleappemdicessincethehighestorder
terms included in equations [10] and [11] are quadratic; thus, convexity (concavity) can be
easily seen geometrically as positive (negative) slopes in plots of margiral effects shown ill
Figures 1.1 through 2.6.
Differences between full data set results and signiﬁcant margiral effects estimated
using a reduced data set of the central 95% of sample dependent variable observations are:
(1) The long-window nommonotonic marginal effect of rim, on unexpected
share volume becomes signiﬁcant when reestimated using a reduced
dependent variable observation data set as shown in Table 7.1. Consistent
with the signal-jamming hypothesis, Figlme 2.1 shows that unexpected
share volume is concave in rim suggesting that the more extreme the
discretion exercised over Alla components, the more disinformative such
signals are to equity traders; in particular, to information traders which
likely dominate market activity over longer periods; and
(2) Similarly, the short-window nommonotonic margiral eﬁ‘ect of 12m on
unexpected slare volume becomes signiﬁcant wlen reestimated using a
reduced dependent variable observation data set as shown in Table 7.1.
Again consistent with the sigral-jamming hypothesis, Figure 2.2 shows tlat
unexpected share volume is convex in rim, suggesting that the more
extreme the discretion exercised over Alla components, the more

disinformative such sigrals are to equity traders since noise traders, which

54

likely dominate market activity in shorter periods around disclosure dates,

react to disinformative signals as if they were infomative.

As shown in Figures 1.1 through 2.6, in certain cases the convexity or concavity of
associations between discretionary Ilp components and equity market responses lmder
LAD (median) estimation is inconsistent with the hypotheses developed in this study. As
an example, Figure 2.3 shows that unexpected share volume is convex in 13W in a longer
disclosure-spanning period suggesting that the more extreme the discretion exercised over
Alla components, the more informative such signals are to equity traders in longer
disclosure-spanning periods. However, this interpretation relies on the assumption that
market activity is dominated by information traders in these longer periods. If noise trader
activity generates suﬁciently extreme observations, them this result potentially represents
the measurement of signal disinfomnativeress under FGLS estirration.

Given the irmplicit linearity of theory underlying the hypotleses of this study, the
implications of these alternative results under LAD estimation are not clear and should be
explored in future extensions of this study. In some respects, this is an epistemological
issue. In contrast to the mean marginal eﬁ'ects of discretionary Ilp components on equity
market responses estimated under FGLS estimation, measures of central tendency under
LAD estimation are median effects. Since both measures of marginal effects are
“correct,” the appropriate measure of central tendency for margiral effects is necessarily
contextual. Because this study seeks to contribute to the ﬁnancial accounting literature,
FGLS estimation of mean marginal effects is considered most appropriate since this

criterion is most common in the accounting literature. In this connection, results under

55

LADestirnationareperhapsmostappropriatelyinterpreted simplyastestsofrobustress
and generalizability.

Inﬂuential indgmdent variable oﬂions. Similar to the discussion of potential
inﬂuential dependent variable observations, loan loss disclosure pricing studies in the
comnnercial bank accounting literature (e.g., Wahlen, 1994) suggest that the general full
sampleresultsofthisstudyarepotentiallynotrobusttotheomissionoflarger
independent variable observations. Reduced data set analyses based on omission of upper
and lower 2.5% of independent variable sample distributions are presented in the third
columns of Tables 6.1 through 7.3.

As shown in Tables 6.1 through 7.3, tle omission of larger independent variable
observations often results in large (positive and negative) changes in the signiﬁcance levels
of marginal effects, and often ﬁom nonsigniﬁcant monotonic margiral effects to signiﬁcant
nommonotonic marginal effects. These general results suggest that the essentially linear
tleory and hypotheses of this study potentially represent an inadequate explanation of use
of accounting discretion over Ilp components.

Speciﬁc differences between fllll sample results and signiﬁcant results obtained
when larger independent variable observations are omitted are:

(l) The long-window marginal effect of rim on equity return variance becomes
nommonotonic when reestimated using a reduced independent variable
observation data set as shown in Table 6.1. Consistent with the notion tlat
pricing-relevant signals contained in nco are less ambiguous since bank
maragers have relatively less accounting discretion over nco than over
Alla, Figure 1.1 shows that unexpected share volume is convex in rim

56

(2)

(3)

suggestingthatmoreextremenco observationsinthereduceddatasetare
informative to equity traders in long-windows.

Interestingly, since this result is derived ﬁ'om reestimating equation
[11] using areduced independent variable observation data set, it is also
consistent with the signal-jamming hypothesis: Since the reestimated
marginal effect of rim on equity return variance suggests that the
remaining less discretionary observations of rim are generally more
informative, this diﬁering result suggests that the more discretionary
(extreme) observations of rim are disinformative.
The long-window marginal effect of um, on equity return variance becomes
signiﬁcant and nommonotonic when reestimated using a reduced
independent variable observation data set and LAD estimation as shown in
Table 6.2. Consistent with the signal-jamming hypothesis, Figure 1.3 shows
that equity return variance is concave in um suggesting that more extreme
Alla observations are disinformative to equity traders in long-windows
(also consistent with the notion that higher levels of available discretion
over lIa result in more ambiguous pricing-relevant signals).
The short-window marginal effect of rim on equity return variance becomes
nommonotonic when reestimated using a reduced independent variable
observation data set and LAD estimation as shown in Table 6.2. Figure 1.4
shows tlat equity return variance is concave in rim suggesting that more

extreme nco observations in the reduced data set are disinfomnative to

57

equity traders in short-windows. Viewed in relation to the monsigniﬁcant
flrllsampleresult,thisresultsuggeststhatthesemoreexmemenco
observations are for some reason more ambiguous to equity traders.

(4) The long-window marginal eﬁ‘ect of rim on unexpected share volume
becomes nommonotonic when reestimated using a reduced independent
variable observation data set and LAD estimation as shown in Table 7.2.
Figure 2.3 shows that equity return variance is convex in rim suggesting
tlatmoreextrernencoobservationsirrthereduceddatasetaremrore
informative to equity traders in long-windows. Viewed in relation to the
monotonic ﬁrll sample result, this result suggests that these more extreme

nco observations are for some reason less ambiguous to equity traders.

AhhoughthediﬁermgmsuhsobtamedmderLADestmmionusmgmereduceddataset
omitting observations with larger values of rim and rim, are not entirely consistent with
the hypotleses developed in this study, the appropriate interpretation of these results is
not entirely clear.

As discussed, results under LAD estimation are perhaps most appropriately
interpreted as tests of robustness and gemeralizability. In this regard, these sensitivity
analysessuggestthattheprirnaryresultsofthis studyarenot entirelyrobust, sirmilartothe
ﬁndings of other studies in the commercial bank accounting literature. However, as also

discussed, the more extreme observations of rim and rim, are encompassed by the

theory underlying the hypotheses of this study. Accordingly, the ﬁrll data set results under

58

FGLS estimationareconsideredmost informativewithrespecttothehypothesesofthis
study.

Loan lpss mpvision allegations Mel mi cation. The commercial bank
accounting literature has shown that associations between loan loss disclosures and equity
market responses is often highly conditional (e.g., Beaver, Eger, Ryan, and Wilson, 1989;
Elliott, Hanna, and Slaw, 1991; Liu and Ryan, 1995; and Lili, Ryan and Wahlen, 1997)
suggesting that the results of this study are potentially sensitive to expectations model
speciﬁcation. To test the sensitivity of results to alternative expectations model
speciﬁcations, equations [10] and [l l] are reestimated with additional conditioning on the
expected nco and Alla components (Enco and EAlla ).

Results shown in Tables 10.1—11.2 suggest that the empirical results with respect
to Hypotheses 2.1—3.2 are robust to potential misspeciﬁcations (i.e., alternative
partitionings of expected and unexpected components) of the Ilp expectations model
shown in equation [6]. Speciﬁcally, where signiﬁcant the results shown ill Tables 10.1 and

10.2 are entirely similar to the results obtained when equations [10] and [l 1] are estimated

without additional conditioning on Enco and EAlla; differing only in the levels of
signiﬁcance of the estimated marginal effects.

W In aggregate, sensitivity analyses suggest that
econometric problems do not substantively inﬂuence estimation or inference in this study.
Inparticular,thesearalysesshowthattheempilicalresultsare quiterobustinthesense
that the hypothesized signal-jamming use of accounting discretion over Ilp components is

not rejected under: (1) an alternative estimation criterion, (2) an alternative error term

59

structure assumption, (3) omission of potential inﬂuential observations in the extreme
2.5% of the sample distributions of dependent and independent variables in equations [10]
and [11], and (4) alternative partitionings of Ilp into expected and unexpected
components. Moreover, these analyses provide evidence corroborating the primary results
of this study showing that discretionary Ilp components are generally disinformative to
equity traders consistent with the hypothesized signal-jamming use of accounting

discretion in commercial banks. I

60

CHAPTER 7

SUMMARY AND CONCLUSIONS

This study provides both theory and evidence suggesting that discretionary earnings
components can contain disinformative signals that result in systematic changes in equity
return variability and share volume. In contrast to prior loan loss disclosure pricing
studies, this study provides evidence consistent with the hypothesis that the discretionary
components of commercial bank loan loss provisions do not contain pricing-relevant
infomnation on average. Moreover, some evidence is presented suggesting that greater
use of accounting discretion over Ilp components results in more disinformative pricing-
relevant signals to equity traders.

This study makes several contributions to the ﬁnancial accounting literature. The
notion of a disinformative accounting signal is developed and linked with existing
theoretical models in the accounting and economics literatures. An alternative explanation
for the use of accounting discretion and, relatedly, herd belmvior and noise trading models
from the ﬁnancial economics literature are introduced. Empirical evidence consistent with
the hypothesized signal-jamming use of discretion over accounting variables subject to
uncertainty and infomnation asymmetry is presented, and the second-order informational
characteristics of discretionary accounting variables are explored. In particular, results
obtained ﬁom the exploration of nonlinearities, including convexity and concavity of
associations between discretionary Ilp components and equity market responses,
emphasize the limitations of the implicitly linear theory underlying this and other ﬁnancial

accounting studies. In aggregate, these contributions suggest that use of theoretical

61

models to guide empirical research, and the estimation of higher—order associations, can
lead to meaningful, new insights into the relationships between accounting variables and
equity rmrket data

With respect to identiﬁed nonlinearities, estimated parameters for the quadratic
terms in equations [10] and [11] and shown in Tables 6.1 and 7.1 suggests that the
second-order informational characteristics of discretionary Ilp components (i.e.,
convexity/concavity in equity return variance and share volume) differ under certain
conditions. This, and the nonsigniﬁcant short-window and equity share volume results,
suggest that more reﬁned hypotheses and empirical tests would be necessary to obtain a
more complete understanding of the conditions under which discretionary Ilp components
are disinformative.

Future extensions of this study appear worthwhile since theory that explains and
predicts when discretionary accounting variables and other disclosures are noninfonnative
or disinformative has important implications. Speciﬁcally, the notion that accounting
signals can be disinformative, and the conditions under which accounting signals are
noninfonnative or disinformative, has clear implications for accounting education, ﬁnancial
analysts, portfolio managers, and accounting standard-setters. Future extensions of this
study should examine potential sources of nonlinearities in the relationship between
discretionary Ilp components and equity market responses including constrained discretion
over Ilp components and the related effects on equity trader inferences, equity return
variance and share volume to gain further insights into the conditions under which

discretionary Ilp components are noninfonnative or disinformative. I

62

APPENDICES

63

APPENDIX 1

 

Table 1 Disclosure and equity market response

 

 

 

 

 

 

Equity market response
Return Share
variance volume
In long-windows spanning disclosure dates
Increased signal variance NegativeA
Increasedtrader beliefheterogeneity Negative”
In short-windows around disclosure dates
Increased signal variance PositiveB Positive'
lnereasedtraderheliefheterogeneity Positive' Positive“

 

" theoretical result ofHolthausen and Verrecchia (I988).
' Theoretical result of Kim and Verrecchia (1994).

C Empirical result of Ziebart (1990).

D Empirical result of Barron (1995).

 

65

 

Table 2 Deﬁnitions of signal types

Term

Deﬁnition

 

Informative signal

Noninformative signal

Disinformative signal

Signaling

Signal-jamming

Any data resulting in the revision of decision-makers’ beliefs
over the distribution of some information var'mble such that
expectations with respect to that variable become more
precise (cf Theil, 1967; Hirshleifer, 1973; Holthausen and
Verrecchia, 1988; and, Kim and Verrecchia, 1994).

Any data not resulting in a revision of decision-mnkers’
beliefs over the distribution of some inforlmtion variable (of.
Theil, 1967; and Hirshleifer, 1973).

Any data resulting in the revision of decision-makers’ beliefs
over the distribution of some infommtion variable such that
expectations with respect to that variable become less precise
(cf. Theil, 1967; Holthausen and Vemecchia, 1988; and, Kim
and Verrecchia, 1994).

An observable, discretionary informative signal emitted by an
agent with private information for the purpose of conveying
such inforrmtion where that signal cannot reasonably be
irnitatedbyotheragentsduetotheirhighercostofemitting
that signal (cf. Spence, 1974; Rothschild and Stiglitz. 1976;
Beaver, 1981).

An unobservable, discretionary noninformative or
disinformative signal emitted by an agent resulting in a
decrease in the level of information contained in some other
signal (cf. Holrnstrom, 1982; Fudenberg and Tirole, 1986;
Stein, 1989; and Creme, 1995).

 

 

Table 3 Necessary conditions for disclosure type observability

 

Observable signal type‘
List—0W W W

Disclosure goo"

Nondiscretionary ....... Increased equity Nonincreased and Decreased equity
returnvarianceor nondecreased equity returnvarianceor
share transaction return variance and share transaction

volume, and share transaction volume, and
observable volume, and observable
nondiscretion. observable nondiscretion.
nondiscretion.
Discretionary:
Signaling ............... Informative signal (Not applicable by (Not applicable by
conditions (above), deﬁnition) deﬁnition.)
and observable
discretion and
private
information.
Signal-jamming ..... (Not applicable by Noninformative Disinformative
deﬁnition.) signal conditions signal conditions
(above) and (above) and
observable observable
discretion. discretion.

 

' Signal type is observable since under an assumption of semi-strong form infommtionally
eﬁcient equity markets, the type of market response defines signal type.

b In general, disclosure type is unobservable for various reasons; see Wilson (1996) and
DeAngelo (1988) for discussions of the problems associated with observing discretionary
accounting-related behavior.

 

67

 

Table 4 Loan loss expectations model SUR estimation results

 

 

 

 

 

Dependent variables
Change in Change in
nomperforming loans Net loan chargeﬂﬁ loan loss allowance
MP1: "CO: Alla!
Independent
and lagged
dependent Parameter Standard Parameter Standard Parameter Standard
variables estimate error estimate error estimate error
Intercept .0020 .0021 -.0058 .0016‘“ .0036 .0007‘"
leans-n —.0024 .0028 .0022 .0022 —.0025 .0010"
Ilan .0669 .0410 .0150 .0315 —.1150 .0146'“
nab-l —.41 15 .0321‘“ .1290 .0260'“ -0312 .0120‘“
plle: .4097 .0587’“ .0134 .0271
nco... .0439 .0502 .1650 .0232'“
Alla... .2443 0608'“ .0897 .0281'“
n=281 n=281 n=281
122: .4929'“ in: .3253'“ i2: .4560‘“

It. 0. t

, , denote signiﬁcantly diﬂ‘erent ﬁ'om zero (two-tail test for parameter
coeﬂicients) at p S .01, p S .05, and p S .10, respectively.

1&2 denotes asyrnptotically-consistent estimates of individual equation R2 statistics.

 

68

 

Table 5.1 Expectations model residual regression results and hypothesis test of
lagged loan loss provision residuals (Full data set)

 

 

 

Residual regression [5.1.2] Lagrange Multiplier tar of an», and ﬁmw

Pug, > (13,3, = "R2 = 188-0055 4,, )1 e .5963

',° Prais-W'msten FGLS and OLS parameter estimates, respectively.

Dependent variable
Residuals from [5.1.1]
Net loan charge-offs estimation Net loan charge-oil‘s
nco, é”, "cor
[5.1.1] [5.1.2] [5.1.3]
lndependalt
and lagged
dependent Parameter Standard Parameter Standard Paramaer Standard
variables estimate‘ aror estimateb em: estimate' em:
10 (en) .0769 .0731 -.0100 .0733
Intercept -.0115 .0037'“ -.0012 .0040 -—.0127 .0040‘“
pIIet .4130 .0855'“ —.0121 .0866 .3992 .0865‘“
plle.-. .0549 .1697 .0268 .1727 .0805 .1723
[mt-1 .0070 .0033“ .0013 .0035 .0082 .0035“
”an .1327 .“0660 .0217 .0727 .1533 .0727“
ann .2507 .0617'“ .0058 .0621 .2558 .0620'“
Anpl... .0277 .0676 —.0134 .0696 .0155 .0694
Ema. -.3042 .3763 -.0768 .3882 -.3749 .3874
é.-.AIIa,, 1.3107 .4324'" .1359 .4617 1.4391 .4611'"
tel... .0072 .0719 .0074 .0718
"inn—i -.1642 .1776 -.1615 .1775
n=188 n=188 n=188
R2 = .3863‘“ R1 = .0055 R2 = .3882'"

, , denote signiﬁcantly diﬁ‘erent from zero (two-tail test for parameter estimates) at
p S .01,p S .05, andp S .10, respectively.

 

69

 

Table 5.2 Expectations model residual regression results and hypothesis test of
lagged loan loss provision residuals (Reduced data set)

 

 

 

Residual regression [5.1.2] Lagrange Multiplier test 0] aw, and 17A,“.-.

Pug/,3, > ( 13:, = "R2 = 153-.55304.=,)] s .000

',' Prais-Winsten FGLS and OLS parameter estimates, respectively.

..0 O. .

Dependent variable
Residuals from [5.2.1]
Net loan clarge-oﬂ's estimation Net loan charge-offs
nco, é”, nco,
[5.2.1] [5.2.2] [5.2.3]
Independent
and lagged
dependent Parameter Standard Parameter Standard Parameter Standard
variables estimate' error estimate. error estimate' ems
p(é,-.) —.0067 .0816 .1511 .0816“
Intercept —.0152 .0033‘“ .0133 .0025‘“ -.0008 .0023
plle: .1959 .0485‘“ —.0983 .0340’“ .1071 .0335‘“
pliant .5954 .1750‘“ —.5365 .1244'“ .0146 .1160
loans” .0067 .0024'“ —.0055 .0017'“ .0003 .0016
11am .2895 .0629'“ —.2390 .0490'“ .0367 .0471
"plot .2178 .0601‘“ -.2328 .0446'“ -.0191 .0423
Anpln -.1544 .0673“ .1011 .0460“—.0471 .0438
I3.-.nco.~. -l.4377 .3790'“ 1.9590 .2970‘" .5816 .2742“
Elma. 1.3319 .4000'“ -1.2131 .2981'“ .0724 .2890
rim.-. .9004 .0766'“ .8929 .0755'“
in.-. .0286 .0980 .0088 .0988
n=153 n=153 n=153
R2 = .3465‘“ R’ = .5530‘“ R’ = .7174‘“

, , denote signiﬁcantly different ﬁom zero (two-tail test for parameter estimates) at

p .<_ .01,p S .05, andp s .10, respectively.

 

70

 

Table 6.1 Equity return variance (an?) hypotheses tests:
FGLS estimated marginal effects and related signiﬁcance tests

Marginal
eﬂ'ect Sign of estimated margiral eﬁ‘ectu'z’ based on parameter estimates ﬁom

Reduceddatasetbased Reduceddatasetbased
on central 95% of on central 95% of

dependent variable independent variable
Full data set sample distribution sample distributions

Hmthesg‘ 2.1: Full period marginal effect on equity return variance < 0

 

 

aﬁrz < 0 < 0 NW.
612,“ P > H128866) z .000 P > R127692) s .000 P > R126570) .=. .000
6&2 < 0 < 0 < 0

612m, P>F(l,28866)§ .024 P> “127692); .023 P>F(1,26570)._= .991

Hypothesis 2.2: Disclosure period marginal effect on equity return variance > 0

J3”:— > 0 < 0 Nonmonotonic
aﬁmadper P>F(1,28866)s .109 P>F(l,27692)s .234 P>R1.26570)s.l81

azﬁrz > 0 Nonnonotonlc > 0
aﬁubadper P > H128866) a .801 P > H127692) s .229 P > F(1,26570)5 .876

m Tests ofthe signiﬁcance ofmarginal eﬁ‘ects, e.g., 7i...+7.-.3,= 0, 6mgw+ (SW, = 0
based on the notation in equations [10] and [11], take the form of a Wald F—test:
P(Fl,...l > Fifty.)-

(2) Sign of estinated marginal eﬂ‘ectbased on applicable parameter estimates in Table 8.1
for equation [10] evaluated on central 95% of the rim and lim, sample distributions:
any”, a [—.0059, .0053] and an”... 5 [-.0031, .0032 ]. “Nonmonotonic”
denotes nommonotonic estimated marginal eﬁ'ect evaluated using the central 95% of
the rim and 1?”, sample distributions; e.g., earl/art” >0 for some ﬁwﬂm.

 

71

 

Table 6.2 Equity return variance (iii-,2) hypotheses tests:
LAD estimated marginal eﬂ’ects and related signiﬁcance tests

Marginal
eﬂ‘ect Sign of estimated marginal eﬁect‘m based on parameter estimates ﬁom
Reduced data set based Reduced data set based
on central 95% of on central 95% of
dependent variable independent variable
Full data set samrple distribution sample distributions

Hmthesis 2.1: Full period marginal eﬂ'ect on equity return variance < 0

< 0 NW

6&2 < 0
P > P1126570); .030

 

 

612m P> P1128866); .ooo P> F(1,27692) a; .042
6&2 < 0 < O Nonmonotonic
612,”, P > P1128866) ._-= .535 P > F(1.27692) e .346 P > P1126570) s .003

Hmthesis 2.2: Disclosure period marginal eﬂ’ect on equity return variance > 0

£12,2—- < 0 Nonmotonic Nonmonotnnle
aﬁmadper P > 1511 ,28866) g _433 P > “1,27692) s .193 P > I-‘(l,26570) _=. .002
6212’ 2 NW NW Nonmonotonle
P > R126570) a .591

aﬁmadper P>F(l,28866)§.028 P> 11127692); .135

11) Tests ofthe signiﬁcance of narginal effects, e.g., 7k+7iia= 0, 5wa_.+ w§3~= 0

based on the notation in equations [10] and [11], take the form of a Wald F-test:
P(Fl,n-r > Fir-k):

‘2) Sign of estimated marginal eﬁ'ect based on applicable parameter estinates in Table 8.2
for equation [10] evaluated on central 95% of the rim and 17“,, sample distributions:

12mm, §[-.0059, .0053] and 13“,, MM 5[—.003l, .0032]. “Nonmonotonic”

denotes nomnonotonic estimated marginal effect evaluated using the central 95% of
the rim and rim sample distributions; e.g., dart/612,, > 0 for some 13”“.

72

 

Table 6.3 Equity return variance (ﬁr-,2) hypotheses tests:
Prais-Winsten estimated marginal eﬂects and related signiﬁcance tests
. l
eﬁ‘ect Sign of estimated marginal eﬂ‘ect‘ '2) based on parameter estimates from
Reduceddatasetbased Reduceddatasetbased
on central 95% of on central 95% of

dependent variable independent variable
Full data set sample distribution sample distributions

Hymthesis 2.1: Full period marginal effect on equity return variance < 0

 

 

6&2 . < 0 < 0 Nonmonotonic
all... P > P1128866) .=. .000 P > P1127692) 5 .000 P > P1126570) s .000
612,2 < 0 < 0 < 0

622A”, P > P1128866) g .128 P > P1127692) e .020 P > P1126570) e .995

Hyuthesis 2.2: Disclosure period marginal effect on equity return variance > 0

iii— > 0 < O Nonmonotonic
aﬁmadper P> P1128866); .231 P> P1127692); .153 P>F(l.26570)s .316

_6_2_iir2_ > 0 Nonmonotonic > 0
aﬁmaoper P > P1128866) e .901 P > “1276932284 P > P1126570) e .928

11) Tests ofthe signiﬁcance ofmargiral eﬁ‘ects, e.g., 7i...+7.i3,= 0, 5wat ”a”: 0

based onthe notation in equations [10] and [11], take the form of a Wald F-test:
P(FL,,_, > F531,) .

‘2’ Sign of estimated marginal eﬁ‘ect based on applicable parameter estimates in Table 8.3
for equation [10] evaluated on central 95% of the rim and lim, sample distributions:
12mm, 5 {—.0059, .0053] and amwm s {—.003 1, .0032 ]. “Nonmonotonic”
denotes nomnonotonic estinated marginal eﬁ‘ect evaluated using the central 95% of
the 13m and rim, sample distributions; e.g., aurZ/arzm > 0 for some'r'imm.

 

73

 

Table 7.1 Equity share volume (1311,) hypotheses tests:
FGLS estimated marginal eﬂects and related significance tests

Marginal
effect Sigﬂfestimated marj'gmal effect“) based on parameter estinates ﬁom
Reduceddatasetbased Reduceddatasetbased
on central 95% of on central 95% of

dependent variable independent variable
Full data set sample distribution sample distributions

Hymthesis 3.1: Full period marginal eﬂ'ect on unexpected share volume < 0

 

if?"— < 0 < O Noninonotonic
a“... P>F(1,29066)5 .618 15151137592); .123 P>F(l,26753)5 .936
617v Non-mic Nonmonotonlc Nonmonotonic
all”, P > P1129066) 5 .576 P > P1127692) s .001 P > P1126753) 5 .987

Hymthesis 3.2: Disclosure period marginal eﬂect on unexpected share volume > 0

i > 0 > 0 Nonmonotonic
aamaaper P > P1129066) -:-. .106 P > P1127692) 5 .122 P > R126753)s.788

i Nonnunotunic Nonmonotonic Nonmotonic
51381an P > I”(139066) E -I76 P > P1127692) s .075 P > P1126753) 5 .830

(1) Tests ofthe signiﬁcance ofmarginal effects, e.g., yk+yﬁ~=0, 6wi~+ 5M, = 0
based on the notation in equations [10] and [11], take the form of a Wald F-test:
P(Fi.n-k > Fisk) °

‘2’ Sign of estimated marginal effect based on applicable parameter estimates in Table 9.1
for equation [11] evaluated on central 95% ofthe rim and rim samrple distributions:
umwm 5 {-.0059, .0053] and 9mm,“ §[—.0031,.0032]. “Nonmonotonic”
denotes nonmonotonic estimated margiral eﬂ‘ect evaluated using the central 95% of
the rim and rim, sample distributions; e.g., adv/613m > 0 for some 13,“ ”95%.

 

74

 

Table 7.2 Equity share volume (1%,) hypotheses tests:
LAD estimated marginal effects and related signiﬁcance tests

. l
eﬁ‘ect Signofestimatedmargin;aleﬂ‘ect‘ 'z’basedonparameter estimates ﬁom

Reduceddatasetbased Reduceddatasetbased
on central 95% of on central 95% of

dependent variable independent variable
Full data set sample distribution sample distributions

Hymthesis 3.1: Full period marginal eﬂ'ect on unexpected share volume < 0

 

i < 0 < O Non-onetime
a"... P>F(l,29066); .000 1511137592); .000 P>F(l,26753)§ .010
617v Non-motuic Nonmonotonic Nonrnonotonic
622,”, P > P1129066) s .006 P > P1127692) a .000 P > P1126753) s .322

Hyﬂthesis 3.2: Disclosure period marginal eﬂ'ect on unexpected share volume > 0

J??— > 0 > O Nonmonotonic
aﬁmadper P>R1,29066)§.236 P>F(1,27692)5 .106 P>F(l.26753).=. .416

liv— > 0 Nannie-(mule Nonmonotonic
aﬁmadper P>R1,29066)§ 301 P> 151127692); .000 P>F(l,26753)§ .425

11) Tests ofthe signiﬁcance ofmarginal eﬁ‘ects, e.g., yk+7ﬂ=0, awaﬂ' 15¢“, =0
based on the notation in equations [10] and [11], take the form of a Wald F-test:
P(Fl,n—t > Flﬁk) '

‘2) Sign of estimated marginal eﬂ‘ect based on applicable parameter estimates in Table 9.2
for equation [11] evaluated on central 95% ofthe rim and rim sample distributions:
12mm, 5 [-.0059, .0053] and 12“,, M3,, 5 [-.0031, .0032 ]. “Nonmonotonic”
denotes nonmonotonic estimated marginal eﬂ'ect evaluated using the central 95% of
the rim and lim sample distributions; e.g., adv/612m > 0 for some 13,“, ”95% .

 

75

 

Table 7.3 Equity share volume ( 1211,) hypotheses tests:
Prais-Winsten estimated marginal eﬁects and related signiﬁcance tests

Marginal
eﬂ‘ect Sign of estimated marginal eﬁ‘ect("2’ based on parameter estimates from

Reduceddatasetbased Reduceddatasetbased
on central 95% of on central 95% of

dependent variable independent variable
Full data set sample distribution sample distributions

Hymthesis 3.1: Full period marginal effect on unexpected share volume < 0

 

i < 0 < O Nonmonotunic
a"... P> P1129066) s .652 P> P1127692) .2: .154 P> P1126753) a .913
613v Non-onetime Nonmonotonic Non-moronic
612,”, P > P1129066) s .398 P > P1127692) s .000 P > P1126753) 5 .984

Hyggthesis 3.2: Disclosure period marginal eﬂect on unexpected share volume > 0

ﬂ— ) 0 > O Nonmonotonic
aﬁmadper P>P1129066)s .131 P> P11 371592)E .139 P>P1126753).=_ .768
am" Nonmonotnnic Nonmonotonic NW];

aﬁwaadper P > 51129066) 5 .020 P > F(l,27692) a .009 P > P1126753); .846

11) Tests ofthe signiﬁcance of marginal effects, e.g., 71L..+7.:3,=0’ awaww, =0
based on the notation in equations [10] and [11], take the fomn of a Wald F-test:
P(17l.n-k > Risk) '

‘2’ Sign of estimated marginal eﬁ‘ect based on applicable parameter estimates in Table 9.3
for equation [11] evaluated on central 95% of the 12m and lim, sample distributions:
1?,“ ”95% 5 [-.0059, .0053] and 13”,“ 3111939. 5 {—.003 1, .0032 ]. “Nomnonotonic”

denotes nomnonotonic estimated marginal eﬂ‘ect evaluated using the central 95% of
the rim and 1?“, sample distributions; e.g., adv/613mo > 0 for some 13,,” “95%.

 

76

 

Table 8.] Equity return variance (1%,?) model FGLS estimation results

Reduceddatasetbased Reduceddatasetbased

 

 

 

on central 95% of on central 95% of
dependent variable independent variable
Full data set sample distribution sample distributions
Independent Parameter Standard Parameter Standard Parameter Standard
variable estimate error estirrate error estimate error
Intercept .0003 .0000'“ .0002 .“0000 .0006 .“‘0000
plle —.0094 .0012'“ —.0027 .'“0006 -.0400 .0037'"
plle’ .1530 .0400“ .0963 .0172'“ .8733 .0862'“
Anpl .0071 .0025'“ .0006 .0004' .0101 .0033'“
Anpf .1191 0566'“ .0233 .0093“ .3333 .1436“
ti... —.0189 .0021‘“ -.0050 .0007‘“ —.0287 .0040'”
iii... .6102 .0650‘“ .1490 0209‘“ 5.7503 1.1571'“
till. -.0098 .0023‘“ -.0029 .0009‘" —.0043 .0038
13211.. -.7664 .3435“ —.3079 .1362" .0360 2.6527
dper -.0000 .0000 .0000 .0000' —.0000 .0001
dper 'lee —.0005 .0037 —.0014 .0016 —.0020 .0110
dper 'plle’ .1531 .1371 .0142 .0508 .1936 .3016
dper ~21an —.0058 .0036 .0006 .0013 —.0069 .0043
dper 75in -.0561 .0751 .0288 p .0328 .0357 .2161
dPer‘ ti... .0069 .0055 —.0012 .0019 .0185 .0086"
(WW 135.. —.2473 .1548 .0764 .0645 —3.6S91 2.7223
dper till. .0064 .0055 .0013 .0026 .0093 .0087 -
dper' rife. —.2028 .7788 —.4360 .3603 -.9962 6.3419
n = 28884 n = 27710 n = 26588 .
P’ = .‘0044‘ P2 = .0073'“ R’ = .0073'“

0.. O. Q

, , Signiﬁcantly diﬁemnt from zero at pS.01, pS..05, pS.10, respectively. Parameter

tests are two-tailed and based on heteroscedasticity-robust standard errors.

 

77

 

Table 8.2 Equity return variance (ﬁr-,2) model LAD regression estimation results

Reduced data set based Reduced data set based
on central 95% of on central 95% of
dependent variable independent variable
Full data set sample distribution sample distributions

Independent Parameter Standard Parameter Standard Parameter Standard
variables estimates errors estimates errors estimates errors

 

 

 

.0. .0. .0.

' Intercept .0001 .0000 .0001 .0000 .0001 .0000
plle -.0015 .“‘0006 —.0009 .0005‘ -.0084 .0015‘“
pllez .0583 .0180" .0461 .0172‘“ .2390 .0434‘“
Anpl .0007 .0003" .0003 .0004 .0007 .0002'“
Anpl’ .0219 .0077'“ .0110 .0080 .0443 .0129‘“

11m -.0026 .“0006 -.0015 .0004‘“ —.0015 .0009‘
a; .1199 .0274'“ .0520 .0250“ .3706 .1707“
11A”, —.0015.“0006 —.0011 .0005“ .0005 .0009
11;”, -.0720 .1184 -.0973 .1043 -1.3480 .4607‘“
dper .0000 .0000 .0000 .0000 .0001 .0000‘
dper 'plle -.0019 .0020 -.0019 .0019 -.0062 .0038
dper ‘pllez .0365 .0688 .0265 .0552 .1915 .1204
dperAnpl -.0013 .0010 -.0006 .0008 -.0009 .0011
dperAnpl’ .0033 .0434 .0098 .0285 .1151 .0682‘
dper' 11m -.0008 .0014 —.0013 .0013 .0003 .0014
dper “300 .0733 .1054 .1370 .1046 —1.5136 .4881'“
dper- 12“,, .0000 .0029 —.0001 .0015 .0017 .0022
dper' 12;, -.5198 .2363“ -.3734 .2506 —.7745 1.4391

n = 28884 n = 27710 n = 26588

Pseudo-RE .0018 pseudo-P2= .0018 Pseudo-P2= .0023

it. C. O

, , Signiﬁcantly different ﬁ'om zero at p501, p305, p310, respectively. Parameter
tests are two-tailed and based on bootstrap-resampling estimated standard errors.

 

78

 

Table 8.3 Equity return variance (1%,?) model Praia-Winston estimation results

 

 

Reduced data set based Reduced data set based
on central 95% of on central 95% of
dependent variable independent variable
Full data set sample distribution sample distributions
Independent Parameter Standard Parameter Standard Parameter Standard
variables estimates errors estinates errors estimates errors
p .0020 .0059 .0337 .“0060 .0078 .0061
Intercept .0003 .0000” .0002 .'“0000 .0006 .“‘0000
plle —.0094 .0021‘“ —.0027 .0005'“ —.0401 .0046'"
pllez .1528 .0597“ .0952 .0150‘“ .8756 .1192‘“
Anpl .0071 .0013'“ .0006 .0003“ .0100 .0015'“
Anplz .1191 .0338'“ .0223 0085'“ .3330 0717‘“
ti... -.0189 .0023'“ —.0050 .“0006 —.0288 .0036'"
iii... ' .6101 .0670‘“ .1497 0172'” 5.7840 1.2083‘“
till. —.0098 .0034'” —.0029 .0008'“ —.0043 .0055
till. -.7657 .5082 -.2968 .1284’“ -.0163 3.0841
dper -.0000 .0001 .0000 .0000' —.0000 .0001
dper 'plle —.0005 .0065 —.0015 .0016 -.0020 .0143
dper 'pllez .1533 .1843 .0167 .0461 .1963 .3677
dperAnpl -.0058 .0041 .0006 .0010 —.0069 .0046
dperAnplz —.0564 .1043 .0300 .0259 .0373 .2203
dper' 13.... .0069 .0072 —.0011 .0018 .0183 .0111“
dper' 133.. -.2484 .2072 .0743 0527 —3.7474 3.7208
dper' tin. .0064 .0105 .0014 .0026 .0095 .0171
dper' iii”. -.2031 1.5708 —.4265 .3960 —.8731 9.5099
n = 28884 n = 27710 n = 26588
R2= 0.0044“ R2= 0.0072'“ R’= 0.0073'“

*0. O. O

, , Signiﬁcantly diﬂerent ﬁ'om zero at p301, p305, p$.10, respectively. Parameter
tests are two-tailed and based on Prais-W'msten FGLS estimated standard errors.

 

79

 

Table 9.1 Equity share volume (1211,) model FGLS estimation results

 

 

Reduceddatasetbased Reduceddatasetbased
oncentral95% of oncelrmal95% of
dependent variable independent variable

Full data set sample distribution sample distributions
Independent Parameter Standard Paramaer Standard Parameter Standard
variable estimate error estimate error estinate error
Intercept .0512 .0709 -2974 .0500‘“ .0850 .1741
plle -5.5551 6.9402 9.6933 52664‘ —9.0050 18.5798
plle2 109.5146 172.4685 -58.4197 138.5031 195.0603 432.4086
Anpl -.8225 5.6415 -3.9126 2.5512 -1.8990 72402
Anplz -6.1293 136.9504 -86.8973 67.4794 433.9542 346.1376
13... -3.6542 7.0077 -5.3851 4.5863 1.6930 82981
133... 83.3542 166.4177 169.9128 111.0722 -328.0400 40522540
17111.. -3.8446 11.0495 —1.9402 72029 .5172 11.9282
12:”, -1141.084 2045.599 4283212 1288.579‘“ -131.5254 8054.2790
dper -.4995 .1773“ -.2328 .1446 -.8597 .3944“
dper ’plle 522018 17.2061“ 35.5323 15.0489“ 89.0850 41.2717“
dper 'plle -1015.576 447.0096“ -995.4857 3860642“ -1923.771 967.0371“
dper ‘Anpl -1.5925 11.01 19 13.7927 8.3836‘ 4.3338 122374
dper 'Anpt’ -153.6676 255.7221 173.4291 200.4841 637.0107 652.1034
dper' 17.... 36.3998 21.6999“ 29.1025 14.5982“ -15.0889 29.0713
dper' 121,, -828.9889 512.1087 —551.1934 351.9137 2720,4700 10077.77
ape, aw 28.4797 40.4329 12.6574 21.3302 -6.5728 33.8381
dper - 123,0 9425.5860 6965.6750 7083.0460 3990.972‘ 4545.9330 21199.16
n=29084 n=27710 n=26771
R2 = .0006 R2 = .0030'“ 112 = .0004

it. Q. I

, , Signiﬁcantly diﬁemm ﬁom zero at p301, p305, p310, respectively. Parameter
tests are two-tailed and based on heteroscedasticity-robust standard errors.

 

80

 

Table 9.2 Equity share volume (1%,) model LAD regression estimation results

 

 

Reduced datasetbased Reduced datasetbased
on central 95% of on central 95% of
dependent variable independent variable
Full data set sample distribution sample distributions
Independent Parameter Standard Parameter Standard Parameter Standard
variables estimates errors estimates errors estimates errors
Intercept -.4049 .0442‘“ -.4482 .0430‘“ -.4359 .0569“
plle 13.8479 5.2815‘“ 15.1617 4.6539‘“ 15.3013 6.4549“
plle2 —238.7819 148.5350 —248.7474 126.0201“ -299.7498 183.7157
Mp1 4.9128 2.1297“ 32777 22774 -1.3307 2.4008
Mp1? 43.5951 5.8461 6.2695 70.3514 —592.8600 156.5212“
13..., —13.8917 1.3104‘“ -14.7730 22484‘“ -23.7757 4.8231“
123“, 410.1298 40.1045” 427.3518 56.8285“" 3564.555 1329.451“
13,01, -3 .0494 4.3403 -—2.2821 6.6906 —9.4921 7.6849
1330,. -3589.942 1292.74‘“ -4507.475 1191.052“ 4475.782 3562.089
dper -. 1990 .0805“ -.1821 .1 142 -2932 .3276
dpe, 7,119 29.2582 9.4877‘“ 28.4503 9.7359‘“ 38.1042 31.4534
ape, pug -910.7148 406.774“ -888.8962 349.1630“ -1091.865 852.8507
dperAan 4.5174 6.8527 6.1078 6.1998 15.0654 21.6215
apermpf 14.7956 174256 67.1311 158.9010 1391.620 880.9906
dper' 12,,” 16.0926 12.5537 20.7500 30.3331 —3.9819 47.4513
dper' 133..., —287.7700 324.7623 —390.7037 697.495 3865241 18607.17
dper’ 12 1111.. 14.2585 25.6545 22.4755 38.5729 -l.6383 29.4970
dper - 122,1. 1066.624 6112.594 1393.776 6388.413 40202.82 24714.97
n=29084 n=27710 n=26771

Pseudo-R2 = 0.0027

Pseudo-R2 = 0.0036

1361:0064?2 = 0.0031

, , Signiﬁcantly different from zero at p$.01, pS.05, pS.10, respectively. Parameter
tests are two-tailed and based on bootstrap-resampling estirmted standard errors.

 

81

 

Table 9.3 Equity share volume (1%,) model Prais-Winsten estimation results

 

 

Reduced data set based Reduced data set based
on central 95% of on central 95% of
dependent variable independent variable
Full data set sample distribution sample distributions
Independent Parameter Standard Parameter Standard Parameter Standard
variables estimates errors estirmtes errors estimates errors
p -.0184 —.0008 .0060 -.0042 .0061
.0059‘“
Intercept .0514 .0533 -2974 .0357‘“ .0854 .1042
plle -5.5903 5.4481 9.6973 3.6390‘“ -9.0414 11.3662
pIIeZ 1 10.1214 154.2623 —58.5648 102.9188 195.6442 292.7288
MP] -.7370 3.3943 —3.9160 22730' -1.9198 3.6794
Mp1: —6.1549 87.3798 -87.0204 58.3305 -l34.8521 175.8357
12,,“ ‘ -3.6280 5.9901 -5.3871 4.0209 1.6710 8.8808
12,3“, 1 79.6817 173.3257 170.0085 118.4645 -—326.3606 2967233
17101.. -3.6836 8.7615 —1.9470 5.8207 .5540 13.5279
13:”. —1107.425 1312.320 4283.602 881.7140‘“ -156.0391 7577.348
dper -.5032 .1653‘“ -2330 .1084“ -.8588 .3227‘“
(1pc, “plle 52.6157 16.9157‘“ 35.5301 11.0482‘“ 88.9916 352024“
ape, 7,119 -1026.236 478.0977“ —995.2702 316.7511‘“ —1921.675 905.6496“
dper‘Aan -1.8321 10.5197 13.7892 7.0062“ 4.4381 1 1.4000
dper‘Aanz —157.83 16 270.3536 173.5742 177.9597 640.6496 542.8893
dper ' 12,“, 36.1458 18.5783‘ 29.1131 12.4322“ -l4.9894 27.3658
dper' 123“, —825.6404 537.2879 -551.1440 362.4471 2712.945 9167.700
dper 12M. 28.3577 27.1862 12.6662 ' 18.0006 -6.3437 41.9472
dper' 122,,” 9501.947 4071.591“ 7080.305 2718.483‘“ 4555.929 23420.18
n=29084 n=27710 n=26771
R2 = .0006 R’ = 0.0030'“ R2 = 0.0004

ﬁt. .0 O

, , Signiﬁcantly different from zero at p301, p$.05, pS.lO, respectively. Parameter

tests are two-tailed and based on Prais-W'msten FGLS estimated standard errors.

 

82

 

Table 10.1 Expectations model sensitivity analysis of iirﬂ,2 hypotheses tests:
FGLS estimated marginal effects and related signiﬁcance tests

 

Marginal
effect Sign of estimated margin] eﬂ‘ect‘m based on parameter estinates ﬁ'om
Reduced data set based Reduced data set based
on central 95% of on central 95% of
dependent variable independent variable
Full data set sample distribution sample distributions

 

 

Hmthesis 2.1: Full period marginal eﬂ'ect on equity return variance < 0

 

 

51272 < 0 < 0 NW
612m P > H128858) _=. .000 P > 51127684) 2 .000 P > P1126562) a .000
5,2,2 < 0 Noumouotouic < 0

612m P > P1128858) a .034 P > P1127684) s .022 P > F(l,26562) s .778

Hyp_othesis 2.2: Disclosure period marginal effect on equity return variance > 0
__a:&L2_ > O < O Noumouotouic
aﬁmadper P > F(l,28858) 5 .029 P > F(1,27684) s .357 P > H126562) s .362

EL > 0 Noumouotouic Noumouotouic
azimadper p > 1411333511) 5 .325 P > F(l,27684) s .500 P > F(1,26562) s .742

“’ Tests ofthe signiﬁcance ofmarginal effects, e.g., 7i~+7az.=O’ 5wen+ 6waL=0
based on the notation in equations [10] and [11], take the form of a Wald F-test:
P(E.n—k > Flatt) '

‘2) Sign of estimated marginal eﬁect based on applicable parameter estimates in Table 8.1
for equation [10] evaluated on central 95% of the 12m and rim, sample distributions:
12mm,“ 5 {—.0059, .0053] and ﬁmmwx s {-.0031, .0032 ]. “Nonmonotonic”
denotes nonmonotonic estimated marginal eﬁ‘ect evaluated using the central 95% of
the rim and 13”,, sample distributions; e.g., ar'irz/arim >0 for some rimmx.

 

83

 

Table 10.2 Expectations model sensitivity analysis of ﬁv, hypotheses tests:
FGLS estimated marginal eﬂ'ects and related signiﬁcance tests

 

Marginal
eﬂ‘ect Sign of estimated marginal eﬂ‘ectm’ based on parameter estimates from
Reduceddatasetbased Reduceddatasetbased
on central 95% of on central 95% of
dependent variable independent variable
Full data set sample distribution sample distributions

 

Hmthesis 3.1: Full period marginal eﬂect on unexpected share volume < 0

 

 

612,2 < 0 < 0 Nonmouotouic
613...... P > P1129058) a .805 P > 111137634) 5 .113 P > P1126745) a .932
azir2 . ,

- < 0 Noumouotonrc Noumouotoruc
61?“), P > P1129058) s .939 P > P1127684) .=. .110 P > P1126745) s .931

Hymthesis 3.2: Disclosure period marginal eﬂ’ect on unexpected share volume > 0

£2— > 0 > O Nonmouotouic
aﬁmadper P > P1129058) ; .320 P > P1127684) s .214 P > P1126745) a .823
__62_’2’:_ > 0 Noumouotonic Noumouotouic
aﬁubadper p > 51139053) 2 .731 P > P1127684) s .523 P > P1126745) s .939
“’ Tests ofthe signiﬁcance ofmarginal eﬂ‘ects, e.g., 7i...+7.2;,=0’ JMR+5W530= 0

based on the notation in equations [10] and [11], take the form of a Wald F-test:
Pm.” > mitt).

0’ Sign of estimated marginal effect based on applicable parameter estimates in Table 8.1
for equation [10] evaluated on central 95% of the 12m and 12m, sample distributions:
13mm”: 5 [- .0059, .0053] and 1311222954 5 [- .0031, .0032 ]. “Nomnonotonic”

denotes nomnonotonic estinated marginal eﬂect evaluated using the central 95% of
the rim and 13“,” sample distributions; e.g., aarz/azzm > 0 for some ﬁmwgm.

 

84

 

Table 11.1 Equity return variance ( 1243) model FGLS estimation results with

additional conditioning on expected Ilp components (Enco and ﬁAlla)

 

 

Reduced data set based Reduced data set based
on central 95% of on central 95% of
dependent variable independent variable
Full data set sample distribution sample distributions
Independent Parameter Standard Parameter Standard Parameter Standard
variable estimate error estimate error estimate error
Intercept .0003 .0000‘“ .0001 .0000“‘ .0006 .0001‘“
plle —.0002 .0041 .0004 .0012 -.0335 .0081‘“
plle2 ~ -.5153 1352‘“ —.0985 .0397“ .3220 2471
Anpl .0091 .0028‘“ .0010 .‘“0004 .0140 .0032‘“
Anpl2 .0323 0492 —.0001 .0101 .3822 .1333“‘
17m -.0154 .0025‘“ -.0037 .0007“‘ -.0274 .“0040‘
a; .4797 0769‘“ .1063 .0224‘“ 4.9156 1.1929‘“
17111., -.0084 .0024“‘ -.0021.“0009 —.0079 .0037“
:2 211.. -12228 5803“ —.3879 .1698“ .7728 2.7098
dper -.0001 .0001 .0000 .0000 -.0001 .0001
dper "plle .0062 .0084 .0002 .0034 .0137 .0210
dper ‘pllez -.1613 .3425 -.0334 .1204 -.3138 .6815
dper 'Aan -.0070 .0036 .0005 .0013 -.0082 .0049‘
dper 'Aan’ -.0639 0790 .0275 .0325 .1149 2569
dper' am .0122 .0057“ -.0008 .0020 .0152 .0088‘
dper' 123m -.3848 1761“ .0633 .0693 -2.6656 2.9090
dper 17111.. .0116 .0058“ .0018 .0027 .0123 .0088
dper - 123% 1.0916 1.1195 -.3294 .4843 2.1289 6.5122
n = 28884 n = 27710 n = 26588
R2 = .0007‘“ R2 = .0108‘“ R2 = .0095‘“

9.. ﬁt

, ,' Signiﬁcantly different from zero at p301, pS.05, pSJO, respectively. Parameter
tests are two-tailed and based on heteroscedasticity-robust standard errors.

(Parameter estimates and standard errors for Enco and EAIla are not shown.)

 

85

 

Table 11.2 Equity share volume (121;?) model FGLS estimation results with

additional conditioning on expected Ilp components (Enco and éNla)

 

 

0.. O. 0

Reduced data set based Reduced data set based
on central 95% of on central 95% of
dependent variable independent variable
Full data set sample distribution sample distributions
Independent Parameter Standard Parameter Standard Parameter Standard
variable estimate error estimate error estimate error

Intercept .0565 .0997 —2847 .0640“ .1373 .2592

plle —6. 1603 13.5333 5.1439 9.0966 -17.4095 35.1819

plle2 102.0267 392.6803 278.5092 289.6346 353.5080 933.6975

Anpl -1.4989 6.2752 -6. 1860 2.6654“ -1.3329 6.0090

Anpl2 9.8526 12.6756 -11.2330 70.0853 -99.8478 341.0789

1?” -2.2474 7.6890 -5.0651 4.8766 22543 8.4760

' 12;, 46.4738 186.6758 184.4598 119.4560 -356.1642 4146.3760

12m, -2.6205 11.4947 —.6074 7.4249 .4864 12.3686

1712111., -195.5291 2577.084 -2393.429 1494.7060 6662982 7687.4240
dper -.6114 2910“ -.3641 .1992‘ -1.4105 .6172“
dper “plle 69.5015 42.3954 57.7359 29.1805“ 183.6198 85.1982“

dper 'pllez -1271.775 1132.62 —1543.834 899.1 143‘ -3690.436 2341.3670

dper ' Anpl 4.4447 12.2316 18.1346 9.0818“ 5.1767 13.5263

dper 'Anpt’ —278.1751 274.5694 77.0140 215.6372 860.4665 1176.7520

dper' am 26.2479 24.1597 25.4303 15.6783 —24.4201 29.4760

dper‘ 123“, -578.8285 579.0215 —479.9551 380.8089 2336.752 10343.730

dper 12% 19.4398 41.9075 8.7763 21.6655 4.4441 34.8962

dper' 12;,“ 2204.881 7963.404 2884.027 4532.6740 —1617.991 21081.060

n=29084 n=27710 n=26‘77l
R2 = .0012 R2 = .0042“‘ R2 = .0007

, , Signiﬁcantly diﬁ‘erent from zero at p301, p$.05, pSJO, respectively. Parameter
tests are two-tailed and based on heteroscedasticity-robust standard errors.
(Estimated parameters and standard errors for Erica and EAlla are not shown.)

 

86

 

Table 12 Descriptive statistics

 

 

Percentiles

Standard
Variable Cormt Minimrnn 2.5% 50% 97.5% Maximum Mean deviation
Alla 29821 —.0206 -.0058 .0003 .0033 .0100 .0001 .0025
,5an 29401 -.0537 -.0250 -.0017 .0048 .0231 —.0035 .0075
Ila 29821 .0102 .01 17 .0170 .0488 .1002 .0199 .0099
Ilp 29821 -.0256 -.0021 .0030 .0121 .0598 .0034 .0051
loan 29821 .1215 .1495 .6573 .7561 .8284 .6203 1267
nco 29821 -.0152 -.0014 .0026 .0110 .0592 .0034 .0048
npl 29401 .0000 .0025 .0077 .0306 .1141 .0101 0105
plle 29821 -.0190 .0069 .0135 .021 1 .0388 .0138 .0047
r,, 30018 —.1630 -.0308 .0000 .0341 .3091 .0010 0162
r... 30332 -.0280 -.0131 .0012 .0131 .0193 .0010 .0061
it Mr. 29506 -.0117 -.0031 —.0001 .0032 .0082 .0000 .0018
I3...» 29506 -.0148 -.0059 -.0003 .0053 .0473 .0000 .0039
ﬁr" 29824 —.1571 -.0274 -.0004 .0300 2992 .0000 .0145
ﬁr: 29824 .0000 .0000 .0001 .0013 .0896 .0002 .0008
13v“ 30031 -144101 —2.7098 -2785 4.5887 76.7362 —.0002 2.1432

 

87

APPENDIX 2

88

 

”fall“ nco’dpe’}l .-'

 

I I \
ur rd. 1 i" nco ,dperﬁ, . 1 1
- . ﬁr I

”drill" nco’dpe’) .

0..
I
’7 .
I

1"75.21“ dlla’dpe'}
-e-

"" r1121" dlla’dpe')
~9-

Ur' ﬁ.2(u dIIa,dper/ ...aa

 

I
.L

11 new” new" new" dlla'” dlla’" dlla

 

 

. 2
urg,(um,dper) a a: (') = -.0189+1,.2204-12m +.0069~dper-.4946-dper~1im

ur;,(um,dper)ea—;——’ ( l: 0—.050+2980 um -.0012-dper+.1528-dper-rim

nco

- 2
urr'“(um,dper).=s 6‘6”“ (°) =-.0287+11.5006-1im +.Ol85-dper—7.3182-dper-1im

unoo

 

ur;2(uw,dper)=%12= —-.-0098 1.5328 u~b+.0064 dper-4056-dper-17Ma

Ana

ur,;.,rz(u..,.,dpe r)=—= L—g; ( )= -.0029—.6158-12~,a +.0013-dper-.8720-dper-ﬁ~a
Alla

ur,',2(ua,a,dper)=a—gi2= —.0043+ .0072 u~b+ .0093 elm—1.9924 dper um,

“Alla

fr,rd,ri demtesmargmaleﬁ‘ectbasedonparmneterestimatesofequnyretmnvaﬁance
model using full data set, central 95% of dependent variable sample distribution,
and central 95% of independent variable sample distribution, respectively.

 

Fm re 1.1 Plot of FGLS estimated long-window marginal effects of loan loss
provision discretion (13m, 13“,) on equity return variance (ﬁr’).

 

89

 

”’"frJ3'1" nco f 5'...

”'"rd13iuncoi

"
ur ri.l3‘." nco} o..
.0. .qr

W" fit. 23‘., " dlla ,1
@-

 

    
 
 
  

A
W -A. ~ -
-.———-- .‘vvv-

‘- - ~‘ 0.5' H a .9
via-L3 _ :3; sh- - .v - .sv

  

 
  
  
 
 

 
     

‘
“r" r1123” dlla} ” ‘ " "

W" ri.23 I." dlla )1 ..

 

11 new” new“ new" dlla’“ dlla’“ dlla

 

. 2
14021414”) 5 $1)— = .0069 - .4946- 13m
' Buma dper

A 2
mg” um)e—a—2'%d;):=—.0012+.1528oam
um r .
e 2
urr'ri13(um) E "é—Er—(‘L
Bumadper

,, 6&r2( .) ,.
urle (udb) E W = .0064- .4056' “Alla

=.0185-7.3l82-1im

A 2
1153231114,“) 5 gig—(1; = .0013 — .8720- 13111..
Alla
,, Brir2 . .
arm-B “anlEW;=-OO93‘1-9924’uma
Alla

f8, rd, ri denotes marginal effect based on parameter estimates of equity return variance
model using full data set, central 95% of dependent variable sample distnbution,
and central 95% of independent variable sample distribution, respectively.

 

Figure 1.2 Plot of FGLS estimated short-window marginal effects of loan loss
provision discretion (1’)”, 12%) on equity return variance (tir’).

 

90

 

“r'frJi” nco"lp"”jI

ur' rd.1i"‘ nco’dperl

ur' "11111 nco’dpe’j

 

 

 

 

1'" fr.2(_" (ﬁla’dpe’l _- _ -_
'9' , ‘ Q
w'rd.2'\u dlla’dpe') 7 .........- (Db
“"ri.2'\" dlla'dpe’i “ QO
'0

l.

 

11 new" new“ nco" rﬂIa’“ dlla’“ dlla

 

 

. 2
urj'3_,(um,dper)a :30: (') =—.0026+.2398-rim-.0008-dper+.l466-dper-13m

nco

urm(um,dper)=——— a ur2( )= -..0015+ 1040 um—.0013-dper+.274O-dper-1im

101,,(um,aper)a i—E’ ( )=— .0015+.7412-12m +.0003-aper-3.0272-dper-1im

. 2
ur,’§_2(uwa,dper)=a—— “"( ——)-= -..0015— 1440 rim—l. 0396 dper um,

513m.

. 2
ur,;,_2(uawa,dper) a Za'LL-z = -.0011-.1946-13Ma -.0001odper-.7468odper-17M0

“Alla

 

. 2
11¢, (udua,dper) e a: U = .0005— 2.696124% +.0017-dper-1.549-dper-1iMa

“Ma

fs, rd, ri denotes rmrginal eﬁ'ect based on parameter estimates of equity return variance
model using full data set, central 95% of dependent variable sample distribution,
and central 95% of independent variable sample distribution, respectively.

 

Figure 1.3 Plot of LAD estimated long-window marginal eﬂ'ects of loan loss
prov'uion discretion (1')”, rim) on equity return variance (ﬁr2 ).

 

91

 

"'"fsJ3l" nco} "..

"rurd.l3(" nco,3 ’ '0003

“'"riJ3iuncol

 

 

 

urn/3.23“! dlla) + .0006:—‘-
-e-

W" rd 23 1" dlla ,1

W" r1231" dlla)
.0 C

 

la

11 new” new" new“ ﬁlm" dlla’“ dlla

 

a12r’( .)
aﬁmadper
6&r2( .)
aﬁmadper
aar’c)
aﬁmadper
612r2( .)
aﬁmadper
613r2(.)
aﬁmadper
atria)
aﬁmadper

=-—.0008+.1466-1im

”r1113 (um) 5

= -.0013+.2740.12m

urrii.13(um)£

= .0003- 3.027242”

Wilda”) ’

ragga“) -=- = 4.039643%

= -.0001- .7468-12Ma

W325 (“41.) 5

ur,',f23(ud,b)z 10017-154943”,

fardri demtesnnrgnnleﬂ‘ectbasedonpammeterestinntesofequityremmvariance
model using full data set, central 95% ofdependent variable sample distribution,
and central 95% of independent variable sample distribution, respectively.

 

Fgg' are 1.4 Plot of LAD estimated short-window marginal effects of loan loss
provision discretion (12m, 12“,) on equity return variance (iir2 ).

 

92

 

ur'ﬂ.‘ 1(11 nco’dpe')

 

w'rdJi” nco'dpe'l

""r'i.l("nco’dpe')

""1321” dlla JP")
-e-

 

 

11r' r1121" dlla’dpe') _.~°

ur' ﬁ.2(u dlla’dper/ 0..

 

db

11 new" new” nco" tﬂla" rﬂla’" dla

 

Blitz-=0

ur];1(um,dper)= a -.0189+1.2202o on“ + .0069 dper- .4968-dper11im

nco

. 2
ur;,_l(um,dper) .-—.- 3249—) = —.0050+.2994.12m -.0011.dper+.1486.dper.12m

 

 

urr'i‘r,(um,dpe r)=::; ( )=—.0288+11.568.12m+.0183-dper-7.4948-dper.12m
1. 2
urfsl(uma,dper)=a a ""( )=—.0098- 1.5314 uMa+.0064 dper— .4062-dper-riwa
“Alta

 

ur;.2(ud,a,dper)=a an ur'2.( )= — .-0029 .5936 um + .0014- -dper-. 8530 o-dper um,
Alla

6_u___r(.)_

ur;,(u,,,,dper)=—— a —.-0043 .0326 um, + .0095 dper— 1.7462 dper um

“Ma

f5, rd,ri demtesmarginaleﬁ’ectbasedonpamneterestnnatesofequityremmvariance
model using full data set, central 95% of dependent variable sample distribution,
and central 95% of independent variable sample distribution, respectively.

 

Figure 1.5 Plot of Prais-Winsten estimated long-window marginal effects of loan
loss provision discretion (13m, 12”,) on equity return variance (ﬁrz).

 

93

 

“"7813” nco; O" 7‘

"’"rd.l31” nco; "-.. «-

Wu ri.l3"-1" nco: '-..
..." . .ﬁ.
31s. 2311" dlla ,1 3

 
  
 
  

 

     
 
 

" ' i 3.:t73‘3
W "1231“ dlla)

H.—.-— ' ;-v;-:; _
‘c‘r‘q‘a’.- .ﬁsf
- , J

  
 

\

 

""3131" 11111:} ~- -

 

11 new" new" new" ﬁlm" ﬂla'" dlla

 

aar’(.)
aﬁmadper
6&r2(.)
aﬁmadper
~ 2
Wilda”) 5 w
6 madper
613r2(.)
aﬁwadper
. 2
1153231114,“) 5 W = .0014 —.8530«12A,,a
613r2(.)
aﬁmadper

= .0069 -.4968-12m

ur;.13(”m) E

=-—.0011+.1486-1'im

W3. 13 (u...) a

= .0183 - 7.4948- 13...
= .0064- .4062- 12A”,

ur 12.3 (”111111) E

= .0095 — 1.7462 . 12M,

urr'1'23(udlla)5

fs, rd, ri denotes marginal eﬂ‘ect based on parameter estimates ofequity return variance
model using ﬁrll data set, central 95% of dependent variable sample distribution,
and central 95% of independent variable sample distribution, respectively.

 

Figure 1.6 Plot of Prais-Winsten estimated short-window marginal eﬂ'ects of loan
loss provision discretion (12m, 12”,) on equity return variance (rir’).

 

94

 

W'fr.1("nco’dp"l

11v' rdlij" nco’dp")

"V'riJi" nco’dp”) .

 

 

”91121“ dlla’dp")
'0-

W'n:21" dlla'dpe'}

 

 

11 new“ new” nco”l dlla" dlla’“ dlla

 

 

 

 

 

 

 

w;_,(um,dper) 2 ‘36"1‘ ') = -3.654+166.708-1’im + 36.400- dper-1657.978-dper- 13....
um
avg.l(um,dper) 5 :"Il ') = —5.385+ 339326-12,“ + 29.103-dper —1102.387-dper~1'im
um
uv;_,(um,dper) e 56“ ') =1.693- 656.0804?” - 15.089- dper+ 5440.940-dper-1'im
um
av' (11 dper)5 aM') —-3 845-2282168-12 +28 480-dper+1885117-dper-1i
153 dla’ at?” — ' ' Ana ' ’ Alla
uv,'ﬂ(udh,dper) 2 66% °) = -1.940-8566.424~17m +12.657~dper+14166.09-dper-13Ma
11M, . '
uv' (u dper)az 6M.) - 517—263 051-13 -6573-dper+9091866-dper-13
"'2 an, all“ -' ' Alla ’ ' Alla

f8,rd,ri demtesmarginaleﬁ‘ectbasedonparameteresﬁmtesofequityremmvariame
mdelusingﬁrlldataset,centml95%ofdependentvariablesample distribution,
and central 95% of independent variable sample distribution, respectively.

 

Frg' are 2.1 Plot of FGLS estimated long-window marginal eﬁects of loan loss
provision discretion (13m, 13“,) on unexpected share volume (ﬁv).

 

95

 

"$131“ nco)

“311131” nco)

-- k

 

M 1
"V ri.l3(" nco,l ““----—-__
.0.

gnaw dlla ) '

 

“#11231" dllalr ' ° -' '
'0- y

W" #231” dlla) .
8

11 new" new" new” ﬁlm" rﬂla’“ rﬂla

 

w; .30....) as M: 36.400-1657978-12”,
' Bumadper
uv" (n )=—aﬂ‘)—- 29103-1102387-12
mama”) 3M: —15.089+ 544094012”,
' Bumaérer
H a A ' A
uvﬁ,,(u,h)sm“%;:= 28.480+18851.17-u~,,
N a a ') A
wd.n(uw)smii3(a-;;=12.657+14166.09-u~,a
" 6“.) A
. —_ = —6.573+9091.866-
"v“ (14.1...) 5 aawa dper “Ma

ﬁ,rd,ri demtesnmginaleﬂ'ectbasedonpmameterestinmtesofequitymmmvarimce
model using full data set, central 95% ofdependent variable sample distribution,
and central 95% of independent variable sample distribution, respectively.

 

Frg' ure 2.2 Plot of FGLS estimated short-window marginal eﬁects of loan loss
provision discretion (13”, 13”,.) on unexpected share volume (13v).

 

 

  
 

”In!“ nco’dp")

 

"V'rdJi‘l nco’dpe'} P

In"rill" nco'dpe’)

"V3821" draw")
'6' .
"V' r1121“ dua~dW)

W'riliu dawdper) . ...- ..

 

db

11 new” new" new" ﬁlm" dlla’" (ﬁlo

 

 

uvL§_,(um,dper) .=. as?" ') = -13.892+820.260.12,,, +16.093~ dper—575.540.dper-12,,,

um

ude_,(um,dper) a 6;wa ') = ~14.773+ 854.7041?” +12.554~dper+649.525~dper~ rim

 

uvL,,(um,dper)§ 3M "3=_23. 776+7129. 110~ ~14 m-3.982~dper+7730.482~aper~1im

 

 

5 "m
uv'f,2(udh,dper) a 66 )= —3.049-7l79.88~1im +14.259~dper+ 2133.248-dper-13Ma
“811a
w1,(u,,,,dper)=—— 6““ ) :4. 282— 9014. 95 um, +25. 655 dper+12225. 19 dper 12“,,
“Ma

uv,,.2(ua,dper)£—— auv(. =) —9.492+8951.56~13Ma -l.638~dper—20405.64~dper~13~,a

aunlla

f5, rd,ri demtesnnrgmaleﬁ’ectbasedonpamneterestunatesofequityretumvariance
model using full data set, central 95% of dependent variable sample distn‘bution,
and central 95% of independent variable sample distribution, respectively.

 

Fgg' ure 2.3 Plot of LAD estimated long-window marginal effects of loan loss
provision discretion (12m, 13”,) on unexpected share volume (13v).

 

97

 

W _fs."131 nco)

Wurd. I31" nco)

 

Wurlil3iu n00) ----

.0. l J

 

 

 

 

 

glam" a1.)
. - .e'.... a
$1,423” dug) ......... QB
W" r1231" dlla) Ge
11 new” nco" new" ﬁle" tﬂla’“ tﬂla
,, 611v"( .) ,
Wﬁ,[3(um) E W = 16.093 - 575.540~ um
av;1,,(a,,, )a 2M=12.554+649.525.am
6 umadper
av,,. ",,,,,(a 13% = -3.9819+ 7730.482 . a”,
a umadper
5M.) ..
———= l4.259+ 213324814
Wﬁzswana)‘ 6 2T6¢er Alla
n 51M -) ..
—— = 25.655 + 12225.19 ~
Wmmwaa)‘ aﬁmadper ”Alla
n 6M .) A
, —— = -1.638- 20405.64-
uvrrﬂo‘tﬂla)! a “we”? ”Ana

fr,rd,ri demtesnnrgmaleﬂ‘ectbasedonpammeterestnmtesofequityremmvariance
modelusingﬁrﬂdatasencennal95%ofdependemwﬁablesampledisuibmion,
and central 95% of independent variable sample distribution, respectively.

 

Fgg' ure 2.4 Plot of LAD estimated short-window marginal eﬂ'ects of loan loss
provision discretion (13m, 12”,) on unexpected share volume (ﬁv).

 

98

 

4. Q
, _ (9
ifs-.11” ncotheU .. 9'6 .- .
2,111.11" nco’dpe') 99 ... ......

 

 
  

I 1
"V 11111" nco~dPe’,:

$11.21" andp") .r

 

“ nco’" nco" nco’” dlla'“ tﬂla’” cﬂla

 

 

 

 

 

uv},_,(um,dper) s 66“ ') = —3.628+ 36.146-dper+159.363~1im -1651.281~ dper-rim
”nco
, 612v(.) . ..
uvm(um,dper) a 6 ,1 = -5.387+29.l l3~ dper+340.017~um -1102.288~dper~um
um
.. 61M.) . .
uv 1,“ (ummper) 5 a ,1 = 8.881 + 27.366-dper+ 5934.466~um +18335.40~ dper- um
uvL,‘2 (navdper) E 2621—)- = -3.684+ 28.358~ dper- 2214.850~ 13M, +19003.89~ dper- 13“,,
“Ma
ude.2(u,,b,dper) a 63%; = —1.947+12.666~ dper-8567.204~13N,a +14l60.61~dper~1i~,a
“Ma
uvL,2(uM,aper)=.= 66% ')=13.528+41.947~aper+1515470-13“, +46840.36~dper~13~,a
“Ma

f8,rd,ri demtesnnrgmaleﬂ‘ectbasedonparaneteresﬁnntesofequityretmnvariance
model using full data set, central 95% ofdependent variable sample distribution,
and central 95% of independent variable sample distribution, respectively.

 

Fgg' ure 2.5 Plot of Prais-Winsten estimated long-window marginal eﬁ'ects of loan
loss provision discretion (13m, 37.5111.) on unexpected share volume (13v ).

 

 

171.131" nco) 6

W" rd I31" nco)

“V"ri.l3(," nco}

 

    
 

 

 

""11231" dlla) ,. , ‘

'9 ...... f

11v" rd.231“ dlla) "O. (‘5

.0. O ..

”31.231,“ dlla)

 

11

11 new" new" new" dlla’" dlla’" dlla

 

auv"( .)
613,006 dper
,, auv"( .) a
1mm, um) :- W =12.554—1102.288~ um

811v"( .)
613ml? dper

11 _ 6M~) .
Wﬁﬁolw) = W = 28.358+19003.89°ll~b

uvLL,23(ud,a) a 3%: = 12.666+ 14160.61- 13”,,
Ma

av;;_,, (11“,) a 53% = 41.947 + 46840.36- aw,
Alla

av;1,,(a,,,) a =36.146-1651.281-a,,,

= 27.366 + 18335.40 ~ 13",,

UV: 13 (um) E

13*, rd, ri denotes marginal eﬁ‘ect based on parameter estimates of equity return variance
model using full data set, central 95% of dependent variable sample distribution,
and central 95% of independent variable sample distribution, respectively.

 

Figure 2.6 Plot of Prais-Winsten estimated short-window marginal eﬂ'ects of loan
loss provision discretion (1')”, 12”,“) on unexpected share volume (12v).

 

100

APPENDIX 3

Informative, noninformative, and disinformative signals

The notions of informative and noninfonnative signals are well-developed in the
accounting literature. However, since the notion of disinformative signals is not as
common in the accounting literature,l it is useful to compare notions of infor'rmtion
content found in the accounting literature with the formal foundations of the information
content of signals developed in the economics literature. While this discussion focuses on
a deﬁnition for disinformative sigmls and the conditions under which such signals exist,
thewndniomunderwhkhdismfornntivesignalscanbehnpoundedmpricessetm
informationallyeﬂicientmarketsareconsideredinAppendices3and4.

Informa_tion gcontent , in the accountmg' literature. In the ﬁnancial accounting
literature, an accounting signal is generally said to have pricing-relevant information
comemifthatsigmlresuhsinachangeinthebelieiSOfnaderssuchthattheyengagein

observable equity unrket activity on the basis ofthat signal (cf. Beaver, 1968).2 As an

 

' No references to “disinformation” or “disinformative” were found in a keyword search
of major accounting research journals for the period 1970 through 1995.

2 With respect to other deﬁnitions of information content, Beaver (1968) comments that
“reduction of uncertainty was not one of the deﬁnitions chosen” (p. 69, fn. 8) in his study
of the infornmtion content of accounting earnings. However, given the operational
deﬁnition of infornntion content commonly used in ﬁnancial accounting research, it is
diﬁcult to distinguish between trading activity resulting ﬁom changes in traders’
assessments of uncertainty over expectations, and that resulting from changes in traders’
expectations per se. Presmnably, the “reduction of uncertainty” deﬁnition referred to by

101

example, aconnnonmaintainedhypothesisinﬁnancialaccountingresearchisthat changes
maggregmennrketbehefsresuhmgﬁomsomewcomdiscbauemeobservedwhen
there exists a significant association between unexpected equity returns and the relevant
unexpected accounting signal; alternatively stated, an accounting signal is said to have
inforrmtion content if there exists a signiﬁcant association between unexpected equity
returns and the unexpected component ofthat accounting signal. Formally, this test of

information content commonly takes the form of a hypothesis test of a parameter in a

regression equationsuchas:
127}, =ﬂ0+ﬂl.fad+zﬂ.pz+uﬂ [A1]
where
ﬁrnEra‘yoa'l'fu'ru) [A2]
12!, E101 "x1181: ‘21 = (19x119x211"'1xt,11) [A3]

rir theunexpectedreturnforﬁrmi,timet

1271,, the unexpected component of the accounting signal

)3,”— return expectation model parameter estimates

r." theactualretrunforthe(equity)market,timet

xo,a the observed value of the accounting variable under study
z,,x,, vectors of various other conditioning variables

is.

accounting variable expectation model parameter estimtes

 

Beaver (1968) was not considered relevant since there existed few theoretical models of
equity market responses to noisy accounting signals at that time. Holthausen and
Verrecchia (1988) presents such a model. Comider the following statement made in Kim
and Verrecchia (1994, pp. 57-58): “The informativeness of price at the time of an earnings
announcement can be manned by the reduction of uncertainty due to the price”
[emphasis added].

102

Givenﬂreforegoingnotaﬁomifthenullhypothesisl-Iozﬂl =0,isrejected,thenitis
usuaﬂycomludedthmmeaccounﬁngvanableorsignalhassigmﬁcammformation
content. Imponantly,mferencesdrawnﬁomsuchhypothesestestsareusuallyﬁamed
such that the measme of information content is eﬁecﬁvely bimry. Speciﬁcally, the
information content (ic) of the unexpected component of an accounting variable, denoted
fix in equation [A3], is usually measured as:
{exists if ,6, =1: 0.
ic(iix) = [A4]
does not exist otherwise.

Inferences drawn from other somewhat less common measures of information content in
the accounting literature, share transaction volume, equity return variance, and bid-ask
spreadsmegeneraﬂyﬁamedinasimilarmarmer. Therefore, underoperationaldeﬁnitions
of information content commonly used in the ﬁnancial accomting literature, an accounting
disclosure may either be informative or noninfonnative: a signiﬁcant association between

unexpected retmns and accounting variables either exists (ﬂl $0) or does not exist

(,6, = 0) with some probability.
Informgipn content in the economics literature. In a summary of the economic
theory of information, Hirshleifer (1973, p. 31) states:

The microeconomics of inforrmtion . . . is an outgrowth of the economic theory of
uncertainty. Uncertainty is summarized by the dispersion of individuals’ subjective
probability (or belief) distributions over possible states of the world. Information,
for our purposes, consists of events tending to change these probability
distributions . . . it is changes in belief distributions—a process not a
condition—that constitutes here the essense of information.

103

Thisclnracteﬁmtionhnplhsthﬂmevemremhmgmaclnngemmewmmicagent’s
belief distribution is infornntive. Thus, Hirshleifer’s (1973) notion of information is
closely analogous to the notion of information content in the ﬁnancial accormting
literatme.

Underlying Hirshleifer’s (1973) characterization of informtion and uncertainty is
the assumption of ‘ratioml expectations” that underlies many theoretical models in the
economics literature, as well as my theoretical models in the accounting literature; in
particular, Holthausen and Verrecchia (1988), and Kim and Verrecchia (1994), referenced
in this study. This assumption, often termed the rational expectations lopothesis,
generally states that the beliefs (and belief distributions) of economic agents are equivalent
to the actual probability distributions over the random variables on which economic
decisions are made; less formally, agents’ beliefs about decision variables correspond to
the actual realizations of those variables on average. Thus, in a rational expectations
world all events (signals) are either informative or noninformative since they must, by
assumption, represent observations of either actual changes in the economic environment,
or actual realizations ﬁom a stationary economic environment.

At least three related classes of theoretical models in the economics literature
relax, in a certain sense, the rational expectations assumption in order to explain market
eﬂiciency anomalies and explicitly model learning processes of agents with incorrect prior
beliefs: learning models (e.g., Hohnstrom, 1982), herd behavior models (e.g., Scharfstein
and Stein, 1990), and noise trading models (e.g., Kyle, 1985). Similarly, this study relaxes
the rational expectations assumption in order to examine how accounting discretion aﬁ‘ects

the ability ofequity traders to make inferences over time. Ifequity traders do not have

104

(fully) rational expectations, then a deﬁnition of infomntion content that explicitly allows
foraccounting signalsto inﬂuenceequitytraders’ learningprocessesisnecessary.
In the econometrics literature, Theil (1967, p. 3) deﬁnes information content of a,

“deﬁnite and reliable message” that some event i has occurred in a manner equivalent to:

h(x.>sln[-:—]=1n(1)-1n(x.) [AS]

I

wherex, istheexanteprobabilityofeventioccurring, andthereforeO <x,- S 1. Equation
[A5]canbeseentorepresemmeexpostchangemthepmbabﬂityassessmemofeventi
occurring given the message. Here the meaning of Theil’s reference to a “deﬁnite and
reliable message” is that the message represents event i with probability equal to one (i.e.,
it is a perfect signal).

Similar to Hirshleifer’s (1973) characterimtion of information and uncertainty, this
deﬁnition of information content shown in equation [A5] corresponds closely to the
general notion of the information content in the empirical ﬁnancial accounting literature.
This can been seen by observing that equation [A5] is always non-negative for all ex ante
probability assessments, implying that the inforrmtion content of a peJect signal is always
non-negative. Thus, under both the common operational deﬁnition of information content
in the ﬁnancial accounting literature, and under the deﬁnition of the information content of
a perfect signal in the economics literature presented in equation [A5], signals must
always have non-negative information content.

The information content of M ect s;gna_ls‘ . The concept of information content

corresponding to accounting signals as “perfect” signals (i.e., equation [A5]) is inadequate

105

mthewmemofdiscraionmymcoummgwﬁablesmpresemmgestnmtessuchasllaand
Ilpsincesuchvariablesdonotgenerallyrepresentnoiselessortmbiasedsignalsofrealized
facts. That is, equation [A5] is not an appropriate deﬁnition of infomration content for
discretbmryacthgvaﬁabkssmcesmhvaﬁabksdomtmgwerﬂremesentsigmls
ofarealizedeventwithaprobabilityequalto one.

Thiscanbeseenmoreclearly followingTheil(1967) deﬁningy,astheprobability
thatsignalinoiselesslyandunbiasedlyrepresentssome eventl;then,substitutingy, into

equation [A5] to obtain:
h(y,.,x,)£ln(y,)-ln(x,) [A6]

it canbe seenthat equation [A6] is equivalent to equation [A5] wheny, = 1. However, in
general accounting signals do not noiselessly and unbiasedly represent economic events,
irnplyingthat,ingeneral,y,:1vt1.3 Nowconsideringthethreeexhaustivegeneralcasesof

therelationshipbetweenthecurrent signaly,versusthepriorsignalx,,itcanbeshowntlmt

y,>x, c: h(y,.,x,.)>0
y1=x1 Q h012x1)=0 [A7]

y,<x, c: h(y,.,x,.)<0

It follows from the more general deﬁnition of information content in equation [A6], and

the relations shown in [A7], that an accounting signal may result in either an increase, no

 

3 Equation [6] is equivalent to the general deﬁnition of the inforrmtion content of a signal
presented in Theil (1967) and introduced to the accounting literature by Lev (1969).

106

change, or a decrease in information available to decision-makers. Thus, in general,
accounting signals may be either informative, noninfonnative, or disinformative.
Persistence of noninfornntive and disinformative ggnal_s.' It is not immediately
clear from the preceding discussion whether noninformative and disinformative signals can
persist in infornntion environments similar to that of bank loan loss provisions. For
example,acommnnmgumemmtheﬁnmcialaccounﬁnglneratmestm$thmmional
equity traders can infer the disinformative or noninformative component of an accounting
variable and are thus able to adjust for that component in their decision-making processes.
To explore the notion that rational equity traders can infer whether a sigml is
noninfonnative or disinformative, it is necessary to examine how equity traders learn ﬁom
observing time series of pricing relevant variables. The model considered here is closely
analogous to the incomplete learning model presented in Hohnstrom (1982). Let n30;
denote bank i, time t reported net loan charge-oil‘s, and Il,’ denote the exogenous
economic factors inﬂuencing actual loan losses for bank i. Here the asterisk “ ° ” denotes
thatthesevaﬁablesareobservablebybothbankmamgersandequityﬁaders. Assume

that the conditional expectation of n50; for bank i, time t is:
E(nEo; Ill: ,17,) = II,’ + 5,. [A8]

where I]: is nonrandom, and 17,. represents unobservable accounting discretion exercised
over 1150; by the bank manager with expectation E07,) = 11,, . Equation [A8] says that
the expectation of observable net loan charge-offs (n'E'o,’,) is conditional on both an

observable factor (II: ) and on the manager’s unobservable accounting discretion (5, ).

107

Inordertoexamhearationalbarnhgproeesanisassunedthatequnynaders
know the form of this conditional expectation ﬁmction [A8] and are interested in
estimating its parameters. The equity trader’s problem of inference reduces to estinmting
5,. since ll,’ is nomandom and stationary; with the objective of rationally inferring and
pricing both the nondiscretionary and discretionary components of nE'oL. Note that, by
assumption, 17,. is not conditional on time; that is, E(17,) = E07,. It) for all t. Thus, [A8]
implies that in choosing 17,. the bank manager responds to a large number of unrelated
mndomfactomeachpeﬁodbmﬂmtthesefactorsamunpmdicmbkandmdependent of
17,. Thisassumptioncanbemadewithout lossofgeneralitysinceitisunnecessarytouse
(in this case, stronger) assumptions of nonstationary or nonindependent accounting
discretion to obtain the result presented here.

Consider how an equity trader might estirmte 17,. from observing a time series of
n30; and 11: . Equation [A8] can be rewritten in estimation form as:

1130; = ll,’ + 17,. +2”, ; E(E’,, | t) = 13(12): 0 [A9]
which says that n30; is comprised of a nonrandom component, a random discretionary
component, and another independent random source of mean-zero noise. Given the
simple, stationary form of the conditional expectation function [A8], the sample mean
based on a series of n observations over time can be used to estimate of [A9]. Moreover,

ncanbeshownthmforﬂrecondhionalexpecmtionﬁmctionconsideredhem,thesample

meanisanunbiasedestimatorofthepopulationmean,suggestingthatarationalequity

108

traderwouldusethismethodtoestimatethemeanofiir Thus,theestirmteofthemean

of 17,. denoted 17,. can be formd (omitting ~) as:

Raﬁinco; =%:(Il’ +12, +e,)=ll’ +;:+e—,
t-l tn]

1?, = nco: —ll° -e,..

lim 13,. = nco; —ll° [A10]

This result says tlm given [A9], equity traders’ inferences about accounting discretion are
limited to observing (only) the average accounting discretion exercised by managers over
time. That is, equity traders’ learning over accounting discretion 17, is incomplete—even
asymptotically. Thus, this result suggests that equity traders cannot infer the discretionary
component of accounting variables with certainty and, therefore, that noninfonnative and

disinformative signals often cannot be observed by equity traders. I

109

APPENDIX 4

Discretionary and nondiscretionary accounting disclosure

The three possible signal types shown in [A7] represent an exhaustive listing of possible
states resulting ﬁom accounting disclosures. However, since the focus of this study is the
empirical examination of pricing-relevant signals contained in discretionary accounting
disclosuresnisnecessarytoreﬁnethisﬁamework. Accountingdisclosurecanbe
decomposed along at least two dimensions: (1) discretionary versus nondiscretionary
disclosure; and (2) observable versus nonobservable disclosure behavior. It is diﬁcult to
observe these categories of accounting disclosure for at least two reasons. Many
accounting variables effectively have both a discretionary and a nondiscretiomry
component, and discretionary accounting behavior is in general unobservable since
accountingvariablessubjecttodiscretionamoﬁenbasedontheumbsewable
expectations of mamgers. In particular, loan loss provision (Ilp) can be decomposed into
a relatively less discretionary component, net loan charge-offs (nco), which is based on
observable events suggesting declines in the net realizable value of loans, and a relatively
more discretionary component, change in loan loss allowance (Alla), based largely on

managers unobservable expectations over ﬁrture loan loss realizations where:
Ilp, = nco, + Alla, = nco, — (Ila, - lla,_.)

Based on deﬁnitions presented in Table 1, a cross-tabulation of accounting disclosure and
signal types is presented in Table 2 to explicate the necessary conditions for the

observability of disclosure types. The observability of inforrmtive, noninformative, and

110

disinformative signals is essentially tautological: these signal types are operationally
deﬁned by their respective equity market response. Necessary conditions for the
observability of disclosure type shown in Table 2 which are substantially unobservable are
shown in bold and relate to amnagers’ private information and disclosure behavior. As
suggested by Table 2, disclosure type (nondiscretionary versus discretionary) is
ﬁmdamentally unobservable since both managers’ private information and, therefore,
disclosure actions are unobservable. To see this more clearly, consider the alternative
extreme case where a manager’s private information is perfectly observable: if equity
traders can perfectly observe the manager’s private information, then it is straightforward
that traders can observe whether the public disclosure is equivalent to the manager’s
private information and whether the manager has exercised accounting discretion.
Although disclosure type (i.e., nondiscretionary versus discretionary disclosure) is
substantially unobservable, signaling disclosure belmvior must result in informative signals,
and signal-jamming disclosure behavior must either result in noninformative or
disinformative signals, by deﬁnition (see Table 1). Thus, conditional on the assumption
that an accounting variable (or component of an accounting variable) is discretionary, it
follows that informative signals are consistent with signaling disclosure behavior, and
noninformative and disinformative signals are consistent with signal~jamming disclosure

behavior. I

111

APPENDIX 5

Disinformative signals, no'ue traders, and equity prices

The notion that disinformation (or disinformative signals) can be impounded in equity
prices set in otherwise informationally eﬁcient markets is not new to either the ﬁnancial
economics or accounting literatmes. In a discussion of the relative roles of infommtion
and noise in ﬁnancial markets, Black (1986) summarizes a number of theoretical studies
suggesting that the existence of“noise traders” who revise beliefs on the basis ofnoise as
1fthey were acting on information is weessary for the existence ofliquid capital markets.
Thisimpliesthat,ingeneral,“noise”isimpom1dedinequitypricessetinliquid capital
markets such as the NYSE, AMEX, and NASDAQ markets commonly used in examining
the information content of accounting variables. Grossman and Stiglitz (1980) show
under general assumptions that markets cannot be completely informationally emcient (in
the conventional sense) in equih'brium when information is costly. Verrecchia (1980)
deﬁnes market emciency as the condition where the market price ofa security is equal to
thatprice setinamarketwhereeverytraderhasthesameinformationasthatrepresented
by the union of all traders’ information sets. Under this “consensus belief’ price deﬁnition
of market efﬁciency, Verrecchia (1980) shows that an informationally eﬂicient equilibrium
price can result under conditions of costly information acquisition and heterogeneous
beliefs over risk-return distributions. Importantly, these models of mket inforrmtion
efﬁciency do not preclude the existence of equih’brium prices set based on incomplete
information (e.g., prices set Imder persistent information asymmetry between nmnagers

and equity traders). This suggests that the rnanager-trader inforrmtion asymmetries

112

implicit in disinformative accounting signals allow such signals to be impounded in
equilibrium equity prices set in otherwise informationally eﬂicient markets.

From another perspective, it is intuitive that a sufﬁcient condition for
disinformative signals to be imrpounded in equity prices is that managers with superior,
private information relative to those disinformative disclosrues maximize their wealth by
nottradingonthatinformation. Itisreasonablethatsincemamgersinadynamicsettmg
oﬁen have an incentive to maximize the price of their respective ﬁrm’s equity without
simultaneously trading on their private information (e.g., SEC law and regulation prohibit
managers and other insiders ﬁ'orn trading on “insider”——i.e., private—information), it is
plausrhle that disinformative disclosures emitted by managers can be impormded in equity
prices set in informationally eﬂicient capital markets; particularly over time periods
ordinarily spanned by periodic ﬁnancial and accounting disclosures. In this connection,
Kyle (1985) presents a model where an informed trader trades with noise traders such that
expected proﬁts are maximized and “private information is incorporated into prices
gradually” (p. 1316). Relatedly, Fischer and Verrecchia (1998) presents an equilibrium
model in an incomplete information setting where rational traders are unable to adjust
perfectly for manager induced biases in ﬁnancial reporting (i.e., disinformative signals).

113

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