Asymmetry in earnings timeliness and persistence: a
simultaneous equations approach
William H. Beaver · Wayne R. Landsman · Edward L. Owens
Abstract
This study addresses simultaneity bias in piecewise linear forms of
the earnings-return relation. We specify an overidentified system of simultaneous
equations that incorporates both asymmetric earnings timeliness and asymmetric
earnings persistence specifications, and implement two-stage least squares for this
piecewise linear system. Estimation of such a system that is piecewise linear in
endogenous variables presents several distinctive issues for which there exists no
precedent in the accounting literature. Findings provide evidence that the
asymmetric timeliness specification is particularly affected by simultaneity, and
that failing to correct for simultaneity results in coefficient estimates that
potentially understate the degree of asymmetric earnings timeliness. Moreover,
inferences regarding how conditional conservatism has evolved over time are
sensitive to whether OLS or 2SLS coefficients are used as the basis of
comparison.
Keywords
Asymmetric timeliness · Asymmetric persistence · Simultaneity ·
Earnings-return relation · Accounting conservatism
JEL Classification
C33 · G14 · M41 · M44
__________________________________________
W. H. Beaver
Stanford Graduate School of Business, Stanford University, Stanford, CA 94305, USA
e-mail: fbeaver@stanford.edu
W. R. Landsman
Kenan-Flagler Business School, University of North Carolina, Chapel Hill, NC 27599, USA
E. L. Owens
Simon Graduate School of Business, University of Rochester, Rochester, NY 14627, USA
1
1
Introduction
Beaver et al. (1980) observe that prices and earnings can be characterized as joint
signals from a larger set of publicly available information regarding the economic
state of a firm. More recently, Ball et al. (2009) find that the common factors of
earnings and returns are highly correlated, and interpret this as evidence that
earnings and returns are jointly determined. Consistent with these observations,
Beaver et al. (1997) (hereafter, BMS) suggest a simultaneous equations approach
to investigations of the earnings-return relation. Using linear specifications, BMS
find empirical evidence consistent with simultaneity bias affecting both the
coefficient from a return-on-earnings model (i.e., the earnings response
coefficient) and the coefficient from an earnings-on-return model (i.e., the return
response coefficient), with the return response coefficient being particularly
affected.
Beginning with Hayn (1995) and Basu (1997), the accounting literature has
commonly modeled the earnings-return relation as if it is piecewise linear. In an
earnings-on-return specification, Basu (1997) provides evidence of conditional
conservatism, i.e., “asymmetric timeliness,” by documenting a larger return
response coefficient for negative return than for positive return. In a return-onearnings specification, Hayn (1995) provides evidence of asymmetric persistence
by documenting a larger earnings response coefficient for profits than for losses
based on separate estimations for positive and negative earnings. Subsequent
research explicitly uses the Basu (1997) model when drawing inferences
regarding the extent of asymmetric timeliness, and relies on the Hayn (1995)
result to justify inclusion of controls for loss observations when drawing
inferences based on earnings response coefficients. However, no study has yet
examined how corrections for simultaneity bias affect estimated coefficients from
the piecewise linear earnings-return relation.1 The purpose of this study is to fill
this gap by exploring a correction for potential simultaneity bias and
underidentification in piecewise linear formulations of the earnings-return relation
using two-stage least squares (2SLS). The results of the study not only provide a
richer view of the return-earnings simultaneity bias first documented in BMS, but
also speak to whether fundamental conclusions regarding asymmetric timeliness
and asymmetric persistence hold after correction for such bias.
We first estimate ordinary least squares (OLS) and 2SLS models using a
linear earnings-return specification, where we obtain a set of instrumental
variables from prior literature. Because the simultaneous equations approach is
necessary only if earnings and return are each endogenous, we test for
1
Although Dietrich et al. (2007) raise concerns about coefficient estimates from the Basu (1997)
specification that derive from the endogenous nature of return, that study does not pursue a
correction for this endogeneity.
2
endogeneity of earnings and return directly based on the linear models using
Hausman (1978) tests for endogeneity. Findings confirm that earnings and return
are indeed endogenous, which implies that simultaneity will need to be considered
in the piecewise linear specification. In addition, comparisons of OLS and 2SLS
coefficients indicate that the return response coefficient is more affected by
simultaneity bias than is the earnings response coefficient, which is consistent
with the inference drawn in BMS.
We investigate our primary research question by specifying an overidentified
system of simultaneous equations that incorporates the Basu (1997) specification
(i.e., earnings expressed as a linear function of return, an indicator variable for
negative return, and their interaction) and a formulation of the Hayn (1995)
specification that makes piecewise linearity explicit (i.e., return expressed as a
linear function of earnings, an indicator variable for negative earnings, and their
interaction), and perform 2SLS estimation to mitigate potential simultaneity bias.
Whereas estimation of a system of equations that is linear in endogenous variables
is relatively straightforward, estimation of a system that is piecewise linear in the
endogenous variables presents several distinctive issues for which there exists no
precedent in the accounting literature. Because findings from the linear
specification indicate that earnings and return are endogenous, functions of
earnings and return, i.e., their indicator and interaction functions, also are
endogenous by definition. Therefore, as the piecewise linear system of equations
includes six endogenous variables—earnings, return, and indicator and interaction
functions of each—we implement 2SLS by estimating six first-stage equations
which require the formation of additional instruments that capture the system's
nonlinearity.
Regarding the piecewise linear earnings-on-return model, findings from OLS
estimation based on a sample period corresponding to that used in Basu (1997)
and Hayn (1995) provide evidence consistent with the findings in Basu (1997)
that the incremental coefficient on negative return over positive return, i.e., “the
asymmetric timeliness coefficient,” is positive and significant. When we extend
the sample period to include more recent sample years, OLS findings indicate that
the asymmetric timeliness coefficient increases over time. Findings from 2SLS
estimation provide evidence that coefficients on both positive and negative return
are affected by simultaneity bias. In particular, the asymmetric timeliness
coefficients estimated via 2SLS are substantially larger than the corresponding
OLS coefficients for both sample periods. This finding suggests that studies using
the OLS asymmetric timeliness coefficient as a measure of conditional
conservatism potentially understate the degree of conservatism. In addition, in
contrast to the OLS results, the 2SLS findings indicate that the asymmetric
timeliness coefficient declines when the sample period is extended to more recent
3
years. Thus, inferences regarding how conservatism has evolved over time are
sensitive to whether OLS or 2SLS coefficients are used as a basis of comparison.
Regarding the piecewise linear return-on-earnings model, findings from OLS
estimations using both sample periods are broadly consistent with results
documented in Hayn (1995) in that the earnings response coefficient for losses is
substantially smaller than the earnings response coefficient for profits, i.e., there
is a significantly negative “asymmetric persistence coefficient.” Findings from the
2SLS estimations indicate that earnings response coefficients are similar in
magnitude to the corresponding OLS coefficients. This finding is consistent with
the relatively minor influence of simultaneity bias on earnings response
coefficients documented both in BMS and our linear specification. Thus, both
OLS and 2SLS estimation approaches provide evidence that profits have
substantially higher pricing multiples than losses. In addition, the response
differential between profits and losses is of similar magnitude across estimation
techniques based on either sample period.
A key methodological point in this study is that we necessarily instrument the
endogenous indicator and interaction variables using separate first-stage
estimations. The extant accounting and finance literatures include studies wherein
a function of an endogenous variable is instrumented not via a separate first-stage,
but by direct substitution of the fitted value of the endogenous variable into its
function. This approach, often referred to as a “forbidden regression” in the
economics literature, generally results in biased and inconsistent coefficient
estimates because of its failure to take into account the full system of endogeneity.
To assess whether this approach affects inferences in our setting, we present
findings from an implementation of 2SLS in which fitted values of indicator and
interaction variables are constructed directly from the fitted values of return and
earnings. Findings for the earnings-on-return model based on the forbidden
regression approach suggest that conditional conservatism is absent during the
early sample period, but manifests only when later sample years are considered.
These findings contrast sharply with those based on the correct 2SLS
implementation. Consistent with earnings response coefficients being relatively
unaffected by simultaneity bias, inferences from the return-on-earnings
specification are unaltered based on the forbidden regression approach.
The remainder of the paper is organized as follows. Section 2 provides
background and motivation for simultaneous equation estimation. Section 3
presents the research methodology. Section 4 discusses the sample selection
procedure and descriptive statistics. Section 5 presents our results, and Section 6
concludes.
4
2
Background and Motivation
Beaver et al. (1980) characterize the earnings-return relation as percentage change
in price expressed as a linear function of percentage change in earnings:
Pi ,t
Ei ,t
(1)
  0  1
 ei ,t ,
Pi ,t 1
Ei ,t 1
where the coefficient δ1 is often referred to as the earnings response coefficient.
Beaver et al. (1987) reverse this regression as follows:
Ei ,t
P
(2)
  0  1 i ,t  ui ,t ,
Ei ,t 1
Pi ,t 1
where the coefficient θ1 is often referred to as the return response coefficient.
Beaver et al. (1987) introduce this specification to address measurement error in
earnings, which induces correlation between ΔEi,t/Ei,t-1 and ei,t.
However, measurement error in earnings is not the only source of the
residuals in the system represented by Eqs. (1) and (2). BMS and, more recently,
Ball et al. (2009) observe that prices and earnings can be viewed as being jointly
determined by a larger set of publicly available information. BMS note that if this
is the case, then estimation of Eqs. (1) or (2) separately without taking account of
simultaneity can induce bias when estimating either δ1 or θ1. BMS document
empirically that simultaneity bias exists in the earnings-return relation, and
concludes that this bias is particularly acute with respect to the regression
coefficient in the earnings-on-return specification (i.e., Eq. 2). Although BMS are
aware of the existence of non-linearity in the earnings-return relation, that study
focuses on establishing how simultaneity bias affects returns and earnings
coefficients in the context of a linear specification.
Basu (1997) and Hayn (1995) explore nonlinearities in the earnings-return
relation in a reverse and traditional regression framework, respectively, without
considering simultaneity bias. Hayn (1995) estimates separate return-on-earnings
models based on the sign of earnings and finds a larger earnings response
coefficient for profits than for losses. The basis for that study’s tests is the
suggestion that losses are less persistent than profits and therefore are expected to
be associated with a smaller earnings response coefficient.2 Basu (1997) estimates
a piecewise linear earnings-on-return model that allows different return response
coefficients for positive and negative return. Basu (1997) finds that the coefficient
on negative return exceeds that on positive return, which is consistent with that
study’s conjecture that, because of conditional conservatism, accounting earnings
will reflect bad news more quickly than good news.
2
This suggestion is consistent with the Ohlson (1995) and Feltham-Ohlson (1995) frameworks
where the value of the firm is a function of the persistence of abnormal earnings.
5
Subsequent research explicitly uses the Basu (1997) model when drawing
inferences regarding the extent of asymmetric timeliness. For example, the
incremental slope coefficient on negative return has been used extensively in the
accounting literature to infer conservatism in accounting across countries and
legal regimes (Pope and Walker 1999; Bushman and Piotroski 2006), over time
(Givoly and Hayn 2000; Holthausen and Watts 2001), in relation to equity cost of
capital (Francis et al. 2004), and in relation to debt (Ball et al. 2008). Likewise,
subsequent research relies on the Hayn (1995) result to motivate inclusion of
controls for losses when drawing inferences based on earnings response
coefficients. For example, when examining the properties of earnings and equity
book value coefficients in relation to financial distress, Barth et al. (1998) include
controls for losses. Similarly, Wilson (2008) includes controls for losses when
examining earnings response coefficients following earnings restatements. In light
of the ubiquity of nonlinear earnings-return relations in accounting research, it is
surprising that there is little evidence regarding the extent to which such relations
are affected by simultaneity.
Dietrich et al. (2007) suggest that there is endogeneity bias in the Basu (1997)
coefficient estimates because of an errors-in-variables problem. Dietrich et al.
(2007) point out the potential for endogeneity bias to be a contributing factor to
the empirical manifestation of conditional conservatism, but make no attempt to
econometrically correct the bias.3 Although Dietrich et al. (2007) focus
exclusively on bias in return response coefficients, based on the insights in BMS,
that study’s critique can be viewed as also applying to earnings response
coefficients.
3 Research Design and Methodology
3.1 Linear specification
Although our primary interest is in the effect of simultaneity in a piecewise linear
system of earnings and return, we first estimate a linear system using OLS and
2SLS to establish whether earnings and return are indeed simultaneously
determined. We formally test for simultaneity bias in the system using a Hausman
(1978) test for endogeneity. We cannot strictly rely on the findings in BMS to
justify simultaneous estimation. Whereas BMS document simultaneity between
return and percentage change in earnings using a sample of banks, our focus is on
the relation between return and the level of earnings across a broad industry cross3
Other studies raise concerns about measuring conditional conservatism using coefficients from
the piecewise linear earnings-on-return model that are not directly related to endogeneity (e.g.,
Givoly et al. 2007; Patatoukas and Thomas 2011). The extent to which these other concerns
remain after consideration of simultaneity is beyond the scope of our study.
6
section. Thus, both the variables in our linear system and our sample differ from
those in BMS.
The linear OLS system is given by Eqs. (3) and (4):
X i ,t  0   2 Ri ,t   i ,t
(3)
Ri,t   0   2 X i,t   i,t ,
(4)
where X is annual earnings per share divided by opening price, and R is
contemporaneous annual stock return. We obtain 2SLS coefficient estimates by
estimating the following two second-stage regressions:4
 i ,t  
X   R
(5)
i ,t
0
2
i ,t
Ri ,t   0   2 
X i ,t   i ,t ,
(6)
 i ,t and 
X i ,t are fitted values from the following two first-stage equations:
where R
15
Ri ,t   0    j Z j  iR,t
(7)
j 1
15
X i ,t   0    j Z j  iX,t .
(8)
j 1
Z j is a vector of fifteen instruments we obtain from prior literature, which we
describe more fully in Section 3.3. Note that we do not include any of the fifteen
instruments in the second-stage regression Eqs. (5) and (6).5
3.2
Piecewise linear specification
Moving to the core of our study, we estimate using OLS and 2SLS the piecewise
linear earnings-on-return model as specified by Basu (1997) and a corresponding
piecewise linear return-on-earnings model, which can be viewed as an alternate
specification of the analysis conducted in Hayn (1995). The OLS estimations are
given by the following equations:
X i ,t  0  1 DRi ,t   2 Ri ,t  3 DRRi ,t   i ,t
(9)
Ri ,t   0  1 DX i ,t   2 X i ,t  3 DXX i ,t  i ,t ,
4
(10)
For ease of exposition, throughout we use the same notation for coefficients and error terms in
the OLS and corresponding 2SLS equations. In all likelihood they differ. Throughout the paper,
variable subscripts i and t refer to firm i and fiscal year t, respectively.
5
We thank an anonymous referee for pointing out that inclusion of exogenous variables in the
second-stage equations, as is done in BMS, is econometrically unnecessary for the purpose of
identification. As long as the number of excluded instruments from an equation meets or exceeds
the number of endogenous variables in the equation, identification is achieved. This point applies
both to the linear and piecewise linear systems.
7
where DRi,t is an indicator variable that equals one if Ri,t is less than zero and
equals zero otherwise, DRRi,t is an interaction variable that equals DRi,t*Ri,t, DXi,t
is an indicator variable that equals one if Xi,t is less than zero and equals zero
otherwise, and DXXi,t is an interaction variable that equals DXi,t*Xi,t. Following
Basu (1997) and Hayn (1995), we predict a positive asymmetric timeliness
coefficient, i.e., β3 > 0, and a negative asymmetric persistence coefficient, i.e., α3
< 0.
Estimation of a system of equations that is linear in endogenous variables is
relatively straightforward. However, estimation of a system that is piecewise
linear in the endogenous variables presents several distinctive issues for which
there exists no precedent in the accounting literature. Whereas the linear
specification includes two endogenous variables, R and X, the non-linear system
includes six endogenous variables, R, X, DR, DRR, DX, and DXX.6 Thus, 2SLS
estimation for the piecewise linear system requires estimating first-stage
regressions separately for each of the six endogenous variables. Moreover,
relative to the vector of fifteen instruments used in the first-stage regressions for
the linear system, the instrument set for the piecewise linear system must include
additional instruments that account for the non-linearity. Although this can be
done directly by adding indicator and interaction functions of each of the fifteen
exogenous variables to the instrument set, the resulting first-stage equations can
suffer from loss of efficiency because of the large number of additional variables.
Accordingly, we use an alternative approach suggested in Wooldridge (2002, pp.
235-237) that requires only four additional instruments. That is, to the instrument
 , where R and X
 are
set we add indicator and interaction functions of R and X
obtained from regressing R and X on the original fifteen instruments, i.e., as is
done in Eqs. (7) and (8). Specifically, the four additional instruments are
constructed as follows:
 i ,t  I ( R
 i ,t )
DR
(11a)
 i ,t  I ( 
DX
X i ,t )
(11b)
 i ,t  DR
 i ,t * R
 i ,t
DRR
 i ,t  DX
 i ,t * 
DXX
X i ,t ,
(11c)
(11d)
where I(*) is the indicator function, which assigns a value of one if the function’s
argument is negative, and assigns a value of zero otherwise.
We obtain 2SLS coefficient estimates by separately estimating the following
two second-stage regressions:



 i ,t   R
 i ,t   DRR
 i ,t  
X     DR
(12)
i ,t
0
1
2
6
3
i ,t
Because R and X are endogenous, their indicator and interaction functions are endogenous by
definition.
8


 i ,t   


Ri ,t   0  1 DX
(13)
2 X i ,t   3 DXX i ,t  i ,t .



 






DR
i ,t , R i ,t , DRR i , t , DX i , t , X i ,t , and DXX i ,t are fitted values from the following six
first-stage equations, estimated using OLS:
15
4
j 1
k 1
15
4
j 1
k 1
15
4
j 1
k 1
DRi ,t  0    j Z j   kWi ,kt  iDR
,t
Ri ,t  0    j Z j   kWi ,kt  iR,t
DRRi ,t  0   j Z j  kWi ,kt  iDRR
,t
(14a)
(14b)
(14c)
and
15
4
j 1
k 1
15
4
j 1
k 1
15
4
j 1
k 1
DX i ,t  0    j Z j   kWi ,kt  iDX
,t
X i ,t  0    j Z j   kWi ,kt  iX,t
DXX i ,t  0   j Z j  kWi ,kt  iDXX
.
,t
(15a)
(15b)
(15c)
W is a vector of the four additional instruments constructed based on Eqs. (11a)(11d), and Z is the original vector of fifteen instruments, as described below.
Although DR and DX are binary variables, and DRR and DXX are truncated
with mass points at zero, it is important to note that estimating first-stage models
for these variables using probit and Tobit regression, respectively, is inadvisable,
and generally introduces specification error that can generate inconsistent secondstage coefficient estimates (Angrist and Kruger 2001). Using OLS in the first
stage generates consistent second-stage coefficient estimates regardless of the
functional form of the dependent variables in the first stage (Kelejian 1971).
Separate instrumentation of the indicator and interaction variables, as in Eqs.
(14a), (14c), (15a), and (15c), has two noteworthy features. First, whereas the


indicator variables DR and DX are binary by construction, their fitted values, DR

 , are not. Second, the values (or signs) of the fitted values for the
and DX




interaction variables, DRR
and DXX
, need not correspond to the values (or



 * R and DX
 *X
 . However, as is standard with 2SLS, the coefficients
signs) of DR
obtained from estimating Eqs. (12) and (13) retain the interpretation of the
structural equation coefficients when applied to actual values of the regressors
(Wooldridge 2002).
9
From a methodological perspective, it is important to stress that correct 2SLS
estimation requires that the indicator and interaction variables be instrumented
separately, rather than constructing their fitted values directly from the fitted
values of return and earnings. The latter approach appeared with sufficient
frequency in the early economics literature to receive a special name–the
“forbidden regression” (Wooldridge 2002).7 Specifically, Wooldridge (2002)
defines the forbidden regression as “replacing a nonlinear function of an
endogenous explanatory variable with the same nonlinear function of fitted values
from a first-stage estimation" (p. 236). Doing so generally results in biased and
inconsistent coefficient estimates, with t-statistics that are invalid, even
asymptotically. Bias and inconsistency in resulting estimators arise because
neither the conditional expectation nor the linear projection operator passes
through nonlinear functions (e.g., generally E(Y )2  E(Y 2 ) ). In the context of
this study, the forbidden regression approach involves estimating the following
two second-stage models:
 i ,t   R
 i ,t   DRR
 i ,t  
X     DR
(16)
i ,t
0
1
2
3
i ,t
 i ,t   

Ri ,t   0  1 DX
2 X i ,t   3 DXX i ,t  i ,t ,
(17)
 i ,t and 
 i ,t , DX
 i ,t ,
X i ,t are the fitted values from Eqs. (7) and (8), and DR
where R
 i ,t , and DXX
 i ,t are the constructed values from Eqs. (11a), (11b), (11c), and
DRR
(11d), respectively.8 Below, we present results from estimations that apply the
forbidden regression approach and assess the extent of coefficient bias by
comparing such coefficients to those obtained from estimations using the correct
2SLS approach, i.e., Eqs. (12) and (13).
3.3
Instrumental variables
A key challenge in implementing the 2SLS procedure is the identification of a set
of exogenous instruments that are highly correlated with the endogenous variables
but uncorrelated with the disturbances. Misspecification of the set of instruments
reduces the potential benefits of the simultaneous equations approach. Prior
research motivates our use of the following variables as proxies for economic
earnings, expected returns, or both: total debt per common share outstanding
(DEBTi,t) (Miller and Modigliani 1966), dividends per common share outstanding
7
The forbidden regression is not without precedent in the accounting and finance literatures (e.g.,
Hanlon et al. 2003; Johnson 2003).
8
Note that we use the fitted values from Eqs. (11a), (11b), (11c), and (11d) as additional
instruments in the first-stage regressions under the correct 2SLS approach. That is not the same as
the forbidden regression, where these fitted values are substituted directly into the second-stage
equations.
10
(DIVi,t) (Miller and Modigliani 1966), percentage change in total assets (PCTAi,t)
(Ou and Penman 1989; BMS), percentage change in total liabilities (PCTLi,t) (Ou
and Penman 1989; BMS), percentage change in revenue (PCREVi,t) (Ou and
Penman 1989; BMS), percentage change in employees (PCEMPi,t) (BMS), lagged
book-to-market ratio (BTMi,t-1) (Fama 1991; BMS), lagged return (Ri,t-1) (BMS),
lagged dividend yield (DIVYDi,t-1) (Ou and Penman 1989), lagged earnings-toprice ratio (EPi,t-1) (Fama 1991; BMS), percentage change in dividends per share
(PCDPSi,t) (Ou and Penman 1989), and the firm-year coefficients on the market
risk premium (CERMi,t), small-minus-big (CSMBi,t) and high-minus-low factors
(CHMLi,t) from a Fama-French three-factor regression (Fama and French 1993).9
Additionally, we include as an instrument for firm i in year t the average return in
year t of all other firms in firm i’s two-digit SIC (INDRETi,t).10 Using the industry
level return as an instrument for a particular firm follows Lev and Sougiannis
(1996), who use industry level R&D expenditure as an instrument for firm R&D
expenditure, and is based on the reasoning that industry level return is obviously
unaffected by firm idiosyncratic shocks, thereby considerably limiting its
correlation with the original regression residuals. We provide detailed definitions
of all instruments, as well as all other variables used in this study, in the
Appendix.
4
Data
4.1 Sample selection
For initial inclusion in the sample, firm-years must be available on the Compustat
Xpressfeed database for fiscal years ending during the period 1963-2008, and
must have non-missing values for earnings before extraordinary items, positive
fiscal year-end closing stock price, and positive common shares outstanding.
Next, we match these observations to annual returns compounded from the CRSP
monthly returns file, imposing the requirement that a firm-year must have twelve
monthly return observations available in CRSP. We calculate annual returns, R,
commencing in the fourth month of a firm’s fiscal year, and ending three months
after fiscal year-end. We measure earnings, X, as earnings before extraordinary
items per share deflated by opening fiscal year stock price. Following Basu
(1997), we exclude firm-year observations falling in the top or bottom 1% of
opening price-deflated earnings and returns in each year.
9
We estimate ERM, SMB and HML firm-year coefficients using daily CRSP returns and daily
factor returns from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. 10
Following Lev and Sougiannis (1996), we require at least four other firms in the two-digit SIC
group.
11
Table 1 Descriptive statistics
Mean
Std. Dev.
P1
P25
P50
P75
P99
Sample period 1963-1990; n = 35,541 firm-year observations
R
0.166
0.388
0.539
0.083
0.112
0.348
1.447

R


R
0.166
0.202
0.224
0.023
0.142
0.292
0.707
0.166
0.202
0.213
0.024
0.143
0.293
0.707
X
0.108
0.100
0.190
0.060
0.098
0.152
0.382

X


X
0.108
0.068
0.050
0.065
0.101
0.148
0.290
0.108
0.068
0.040
0.063
0.101
0.148
0.295
Sample period 1963-2008, n = 62,991 firm-year observations
R
0.143
0.384
0.636
0.091
0.103
0.327
1.385

R


R
0.143
0.197
0.312
0.022
0.128
0.251
0.711
0.143
0.199
0.389
0.047
0.143
0.254
0.667
X
0.083
0.097
0.222
0.047
0.076
0.119
0.341

X


X
0.083
0.061
0.063
0.049
0.076
0.115
0.248
0.083
0.061
0.053
0.047
0.077
0.116
0.256
Table 1 presents descriptive statistics of return and earnings, and their fitted values from firststage estimation of both the linear and piecewise linear 2SLS models. R is firm i's stock return
from 9 months before fiscal year-end to 3 months after fiscal year-end. X is earnings before
 (
extraordinary items per common share, scaled by beginning of year stock price. R
X ) is the
 


first-stage fitted value of R (X) from a linear 2SLS model. R ( X ) is the first-stage fitted value of
R (X) from a piecewise linear 2SLS model.
Our sample is further constrained to those firm-year observations with nonmissing data for all instruments. As demanded by our industry return (INDRETi,t)
calculation, we delete firm-year observations where there are less than four other
firms in a two-digit SIC industry-fiscal year grouping. Finally, to minimize the
effects of outliers on the fit of our first-stage regressions, we exclude firm-year
observations falling in the top or bottom 1% of all non-return-based instruments
(DEBTi,t, PCTAi,t, PCTLi,t, PCREVi,t, PCEMPi,t, BTMi,t-1, DIVYDi,t-1, EPi,t-1, DIVi,t,
and PCDPSi,t) in each year.11 Our final sample consists of 62,991 firm-year
observations.
11
The percentage change in dividends variable, PCDPS, is assigned a value of zero for those firmyears wherein a firm did not pay dividends in both the current and prior year.
12
4.2
Descriptive statistics
Table 1 presents descriptive statistics for earnings and return, and their first-stage
fitted values under both the linear and piecewise linear 2SLS estimations. We
present statistics for the full sample period 1963-2008, as well as for the period
1963-1990, which corresponds to the sample period used by both Basu (1997) and
Hayn (1995). Two observations are noteworthy. First, instrumentation results in a
tighter distribution relative to that relating to the actual values of each variable.
For example, the standard deviation of the two fitted return variables in the 19632008 period, 0.197 and 0.199, is approximately half of that of actual return, 0.384.
This is not surprising given that, by design, instrumentation tends to result in
fewer extremes in the fitted values. Second, the distribution of the fitted values of
X and R are essentially the same for the linear and piecewise linear systems. This
also is not surprising because the first-stage regressions for X and R differ only to
the extent that the piecewise linear first-stage includes the four additional
instruments as estimated in Eqs. (11a), (11b), (11c), and (11d).
5 Results
5.1
Structural overview
Table 2 presents results from estimating linear specifications of the earningsreturn relation using both OLS (i.e., Eqs. 3 and 4) and 2SLS (i.e., Eqs. 5 and 6).
Table 3 presents results from the 2SLS first-stage regressions for both the linear
(i.e., Eqs. 7 and 8) and piecewise linear (i.e., Eqs. 14 and 15) specifications. Table
4 presents results from estimating the piecewise linear specification of the
earnings-on-return model using both OLS and 2SLS, as in Eqs. (9) and (12),
respectively. Table 5 presents results from estimating the piecewise linear
specification of the return-on-earnings model using both OLS and 2SLS, as in
Eqs. (10) and (13), respectively. Table 6 presents results from estimating the
piecewise linear specifications of the earnings-return relation using the forbidden
regression approach to 2SLS (i.e., Eqs. 16 and 17).
In addition to presenting results for the full sample period 1963-2008, in each
Table we present results separately using the sub-period 1963-1990, which
corresponds to the sample period used in both Basu (1997) and Hayn (1995). In
all cases, reported t-statistics are based on heteroskedasticity robust (White 1980)
two-way clustered standard errors (Petersen 2009) along the industry and fiscal
year dimensions. We do not report adjusted-R2 for our 2SLS estimations, because
the meaning of R2 is ambiguous for 2SLS results (e.g., Godfrey 1999).12
12
Also, refer to http://www.stata.com/support/faqs/stat/2sls.html for additional discussion
concerning the lack of statistical meaning of R2 in the context of 2SLS.
13
Table 2
Linear specifications of the earnings-return relation
Sample Period:
1963-1990
1963-2008
Methodology:
OLS
2SLS
OLS
2SLS
Column:
(1)
(2)
(3)
(4)
Panel A Earnings-on-return
 
OLS: X   0   2 R   ; 2SLS: X   0   2 R
Intercept
R
Firm-year obs.
2
Adjusted-R
0.094***
0.082***
0.072***
0.063***
(11.30)
(8.69)
(11.03)
(10.55)
0.084***
0.152***
0.081***
0.143***
(5.73)
(3.90)
(6.85)
(4.66)
35,541
35,541
62,991
62,991
0.108
0.101
Panel B Return-on-earnings
 
OLS: R   0   2 X   ; 2SLS: R   0   2 X
Intercept
X
Firm-year obs.
2
Adjusted-R
0.028
0.019
0.038
0.018
(0.84)
(0.54)
(1.30)
(0.53)
1.279***
1.361***
1.260***
1.505***
(9.75)
(5.60)
(8.42)
(5.42)
35,541
35,541
62,991
62,991
0.108
0.101
Table 2, Panel A (Panel B) reports OLS and 2SLS regression results for an earnings-on-return
(return-on-earnings) model using firm-year observations. Columns (1) and (2) utilize the sample
period 1963-1990, and columns (3) and (4) utilize the sample period 1963-2008. X is earnings
before extraordinary items per share scaled by beginning of year stock price. R is firm i's stock
 (
return beginning 9 months before fiscal year-end to 3 months after fiscal year-end. R
X ) is the
first-stage fitted value of R (X) from a linear 2SLS model. Robust t-statistics based on two-way
clustered standard errors at the industry and fiscal year levels are reported in parentheses. ***, **,
and * indicate statistical significance (two-sided) at the 1%, 5%, and 10% levels, respectively.
5.2 Linear specification
5.2.1 Ordinary least squares
In Panel A of Table 2, columns (1) and (3) present results from OLS estimation of
the linear earnings-on-return model of Eq. (3) for the 1963-1990 and 1963-2008
sample periods, respectively. As documented in extant literature, there exists a
14
positive and significant return response coefficient, β2, in both sample periods,
which is consistent with news in return being partially reflected in
contemporaneous accounting earnings. Specifically, columns (1) and (3) reveal
return response coefficients of 0.084 and 0.081, with t-statistics of 5.73 and 6.85,
respectively. These coefficient magnitudes, as well as the model R2s of 0.11 and
0.10, are comparable to those reported in prior literature. For example, Basu
(1997) reports an analogous return response coefficient of 0.11, with an
associated R2 of 0.11 (see that study’s Table 1, p. 13).
In Panel B of Table 2, columns (1) and (3) present results from OLS
estimation of the linear return-on-earnings model of Eq. (4) for the 1963-1990 and
1963-2008 sample periods, respectively. As documented in extant literature, there
exists a positive and significant earnings response coefficient, α2, in both sample
periods, which is consistent with earnings information being impounded into
contemporaneous return. Specifically, columns (1) and (3) reveal earnings
response coefficients of 1.279 and 1.260, with t-statistics of 9.75 and 8.42,
respectively. These coefficient magnitudes, as well as the model R2s of 0.11 and
0.10, are similar to those reported in prior literature. For example, Hayn (1995)
reports an analogous earnings response coefficient of 0.95, with an associated R2
of 0.09 (see that study's Table 4, p. 135).
5.2.2
Two-stage least squares
We begin our simultaneous equations approach by testing for the presence of
simultaneity in the system represented by Eqs. (3) and (4) using Hausman (1978)
tests for endogeneity separately for each equation.13 Untabulated χ2 statistics reject
both null hypotheses that earnings and return are exogenous variables, at less than
the 0.001 level, for both sample periods. Thus, the OLS coefficients in Eqs. (3)
and (4) are subject to simultaneity bias. Columns (1) and (2) (9 and 10) of Table 3
present results from estimating our first-stage Eqs. (7) and (8) for the sample
period 1963-1990 (1963-2008).14 The adjusted-R2 from the first-stage estimations
for return and earnings exceed 26% and 39%, respectively. These
13
Larcker and Rusticus (2010) point out the importance of the over-identifying restrictions test
before conducting the Hausman (1978) test for endogeneity. The over-identifying restrictions test
is a test of the joint null that the instruments used in the first-stage regression are exogenous and
that the exclusion restriction is appropriate (i.e., appropriate omission of the instruments from the
second-stage equation). Untabulated findings indicate joint rejection of the null. However,
additional untabulated findings from specifications in which we include 13 of our 15 exogenous
variables in the second-stage model indicate the null cannot be rejected at the 0.05 level. This
latter finding suggests that the rejection of the null in which all fifteen instruments are excluded is
attributable to our exclusion restrictions rather than lack of exogeneity of the instruments.
14
We do not specifically discuss estimated coefficients from the first-stage models. In general,
inferences are similar across the 1963-1990 and 1963-2008 sample periods.
15
Table 3 2SLS first-stage regression results for both the linear and piecewise linear models
Sample:
1963-1990; n = 35,541 firm-year observations
1963-2008; n = 62,991 firm-year observations
Model:
Linear
Piecewise linear
Linear
Piecewise linear
Dep.Var:
R
X
DR
R
DRR
DX
X
DXX
R
X
DR
R
DRR
DX
X
Column:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
Intercept -0.105a -0.021a 0.518a -0.104a -0.084a 0.075a -0.020a -0.004a -0.071a -0.014a 0.451a -0.037a -0.064a 0.071a -0.012a
a
a
INDRET 0.752a 0.011a -0.531a 0.749a 0.102a 0.007 0.003 -0.002 0.656 0.019 -0.439a 0.585a 0.084a 0.003 0.006a
CERM
3.344a -0.301a 0.819 3.336a -1.748a 1.395a -0.362a -0.330a 2.498 -0.058 1.135a 2.355a -2.082a 1.737a -0.149b
a
a
CHML
-1.726a 0.009
0.651c -1.738a 0.592a -0.404b 0.021 0.031 -1.619 -0.134 -0.330 -1.250a 0.504a -0.157 -0.060
b
a
a
a
a
a
CSMB
0.520 0.222
1.549 0.508 -0.734 0.452 0.215 0.042 -0.953 -0.040 2.926a -0.755a -0.912a 0.616a -0.047
a
a
a
a
a
Rt-1
-0.050a 0.015a 0.020a -0.051a 0.001 -0.026 0.015 0.003 -0.018 0.021 0.013a -0.023a 0.003b -0.046a 0.020a
a
a
a
a
a
DEBT
-0.001a -0.000a 0.001a -0.001a -0.000a 0.001 -0.000 -0.000 -0.001 -0.000 0.000a -0.001a -0.000a 0.001a -0.000a
a
a
a
a
b
a
a
b
a
DIV
0.009 0.008
-0.048 0.009 0.024 -0.040 0.009 0.005 0.002 0.008 -0.038a 0.001 0.023a -0.043a 0.008a
a
a
a
a
a
PCTA
0.418a 0.148a -0.262a 0.420a 0.060a -0.293 0.150 0.049 0.306 0.112 -0.155a 0.265a 0.024a -0.213a 0.109a
a
a
a
a
a
a
a
a
a
a
PCTL
-0.184 -0.075 0.100 -0.187 -0.023 0.123 -0.078 -0.021 -0.146 -0.061 0.074a -0.126a -0.004c 0.100a -0.062a
a
a
a
a
a
PCREV 0.162a 0.089a -0.089a 0.163a 0.006 -0.077 0.091 0.006 0.152 0.065 -0.089a 0.135a 0.003 -0.075a 0.066a
a
a
a
a
PCEMP 0.112a -0.001 -0.068a 0.112a 0.024a -0.026 -0.001 0.007 0.056 -0.006 -0.036a 0.053a 0.004 -0.014b -0.005b
a
a
a
a
a
a
a
a
a
a
BTMt-1
0.060 0.030
-0.027 0.059 0.010 0.034 0.027 -0.009 0.069 0.024 -0.013a 0.057a 0.004a 0.057a 0.017a
a
a
a
DIVYDt-1 0.500a 0.538a -1.121a 0.477a 0.152a 0.009 0.504 0.017 0.429 0.422 -0.826a 0.285a 0.025 0.224a 0.353a
a
a
a
a
a
EPt-1
0.093a 0.450a -0.021 0.118a -0.035a -0.256 0.498 0.030 0.119 0.472 -0.114a 0.211a -0.008 -0.472a 0.578a
a
a
a
a
a
a
a
a
b
a
PCDPS 0.019 0.094
-0.043 0.017 0.012 -0.070 0.095 0.014 0.026 0.073 -0.039a 0.020a 0.016a -0.068a 0.073a
a
a
a

0.181a -0.026a -0.022a -0.004 0.004a
0.153a -0.012c -0.027a 0.020 -0.005 -0.003
DR
a
a
c
a

-0.473a 0.377a 0.822a -0.292a 0.118a
-0.386 -0.104 0.471 0.102 0.005 -0.008
DRR
a
a

0.002 -0.020b -0.029a 0.223a -0.006a
0.019 -0.027b -0.026a 0.234 -0.004 -0.018
DX
a
a
a
b
a

0.546a -0.759a -0.081b 0.462a -0.688a
0.558 -0.482 -0.060 -0.376 -0.507 0.550
DXX
2
Adj.-R
0.272 0.461
0.185 0.272 0.223 0.187 0.464 0.152 0.264 0.391 0.192 0.268 0.307 0.181 0.402
CD F-stat 885.1 2025.6
18.2
44.3
1506.7 2699.5
76.9
77.1
KP F-stat 565.4 869.4
13.1
6.5
886.1 920.8
64.6
7.0
16
DXX
(16)
-0.001b
-0.000
-0.371a
0.014
-0.073b
0.006a
-0.000a
0.005a
0.043a
-0.018a
0.006a
0.002
-0.016a
-0.002
0.064a
0.013a
0.004a
0.075a
-0.019a
0.409a
0.155
Table 3 reports first-stage regression statistics and coefficient estimates for the endogenous return and earnings variables estimated using OLS
with firm-year observations. Columns (1) and (2) (9 and 10) report first-stage results for the linear system estimated using the following models
for the sample period 1963-1990 (1963-2008):
15
R
, X i ,t    0    j Z j  i ,t .
i ,t
j 1
Columns (3)-(8) (11-16) report first-stage results for the piecewise linear system estimated using the following models for the sample period
1963-1990 (1963-2008):
DR
i ,t
15
 i ,t   DRR
 i ,t   DX
 i ,t   DXX
 i ,t   .
, Ri ,t , DRRi ,t , DX i ,t , X i ,t , DXX i ,t   0    j Z j  16 DR
i ,t
17
18
19
j 1
X is earnings before extraordinary items per share scaled by beginning of year stock price. R is firm i's stock return from 9 months before fiscal
year-end to 3 months after fiscal year-end. DR is an indicator variable = 1 if R < 0 and = 0 otherwise. DRR is an interaction variable = DR*R.
DX is an indicator variable = 1 if X < 0 and = 0 otherwise. DXX is an interaction variable = DX*X. Z is a vector of the following fifteen
instruments: industry return (INDRETi,t); sensitivity of firm i's return to the Fama-French market return factor (CERMi,t), HML factor
(CHMLi,t), and SMB factor (CSMBi,t); lagged firm return (Ri,t-1), total debt per common share outstanding (DEBTi,t); dividends per common
share outstanding (DIVi,t); percentage change in total assets (PCTAi,t); percentage change in total liabilities (PCTLi,t); percentage change in
revenue (PCREVi,t); percentage change in number of employees (PCEMPi,t); lagged book-to-market ratio (BTMi,t-1); lagged dividend yield
 is an
(DIVYDi,t-1); lagged earnings-to-price ratio (EPi,t-1); percentage change in dividends per common share outstanding (PCDPSi,t). DR
 < 0 and = 0 otherwise, where R
 is the first-stage fitted value from the linear system. DRR
 = DR
 *R
 . DX
 is an
indicator variable = 1 if R





indicator variable = 1 if X < 0 and = 0 otherwise, where X is the first-stage fitted value from the linear system. DXX = DX * X .
"CD F-stat" is the F-statistic from the Cragg-Donald test of weak instruments (Cragg and Donald 1993). "KP F-stat" is the F-statistic from the
Kleibergen-Paap test of weak instruments (Kleibergen and Paap 2006). Superscripts "a", "b", and "c" denote statistical significance (two-sided)
at the 1%, 5%, and 10% levels, respectively.
17
model fit statistics suggest that we have identified instruments that are moderately
to highly correlated with both endogenous variables. As a further check, we
conduct an F-test on the first-stage regressions to assess whether the instrument
coefficients are jointly zero.15 If the F-statistic is “low”, the selected instruments
are weak. For both first-stage equations, Cragg-Donald F-statistics (Cragg and
Donald 1993) and Kleibergen-Paap F-statistics (Kleibergen and Paap 2006) are
well in excess of the suggested critical F-values (Stock et al. 2002).
In Panel A of Table 2, columns (2) and (4) present results from estimation of
the second-stage linear earnings-on-return model of Eq. (5) for the 1963-1990 and
1963-2008 sample periods, respectively. In comparison to the OLS coefficient
estimates from Eq. (3), the estimated second-stage return response coefficients,
β2, are substantially larger for both sample periods. Specifically, columns (2) and
(4) reveal return response coefficients of 0.152 and 0.143, with associated tstatistics of 3.90 and 4.66, respectively. These coefficient estimates are 81% and
77% larger than the respective coefficients estimated under OLS, which is
consistent with removal of endogeneity bias in moving from OLS to 2SLS
estimation.
In Panel B of Table 2, columns (2) and (4) present results from estimation of
the second-stage linear return-on-earnings model of Eq. (6) for the 1963-1990 and
1963-2008 sample periods, respectively. In comparison to the OLS coefficient
estimates from Eq. (4), the estimated second-stage earnings response coefficients,
α2, are of similar magnitude for both sample periods. Specifically, columns (2)
and (4) reveal earnings response coefficients of 1.361 and 1.505, with associated
t-statistics of 5.60 and 5.42, respectively. These coefficient estimates are 6% and
19% larger than the respective coefficients estimated under OLS, suggesting that
there is little endogeneity bias in the OLS coefficients. Taken together, the
findings in Panels A and B of Table 2 suggest that the return response coefficients
are more affected by endogeneity bias than are the earnings response coefficients.
This inference is consistent with inferences BMS draw when comparing that
study’s OLS and 2SLS price and earnings response coefficients.
5.3
Piecewise linear specification
5.3.1 Ordinary least squares
Columns (1) and (3) of Table 4 present results from estimation of Eq. (9) for
the 1963-1990 and 1963-2008 sample periods, respectively. As documented in
extant conditional conservatism literature, there is an asymmetric response
coefficient across positive and negative return observations, where negative return
15
We do not consider a partial-R2 or partial F-test, as we do not have non-instrument control
variables in our system.
18
Table 4
Piecewise linear earnings-on-return regression specification



   R   DRR
 
OLS: X   0  1 DR   2 R   3 DRR   ; 2SLS: X   0  1 DR
2
3
Sample Period:
1963-1990
1963-2008
Methodology:
OLS
2SLS
OLS
2SLS
Column:
(1)
(2)
(3)
(4)
Intercept
0.108***
0.089**
0.085***
0.067**

(2.47)
(12.38)
(2.50)
0.001
0.117
0.007
0.052
(0.18)
(1.23)
(1.53)
(0.85)
0.056***
0.116*
0.049***
0.113*
(3.41)
(1.66)
(3.97)
(1.78)
0.136***
0.638***
0.152***
0.256**
(4.08)
(3.09)
(6.72)
(2.48)
Firm-year obs.
35,541
35,541
62,991
62,991
Adjusted-R2
0.126
DR
R
DRR
0.126
Table 4 reports OLS and 2SLS regression results for a piecewise linear earnings-on-return model
using firm-year observations. Columns (1) and (2) utilize the sample period 1963-1990, and
columns (3) and (4) utilize the sample period 1963-2008. X is earnings before extraordinary items
per share scaled by beginning of year stock price. R is firm i's stock return from 9 months before
fiscal year-end to 3 months after fiscal year-end. DR is an indicator variable = 1 if R < 0 and = 0



, R
 , and DRR
 are first-stage fitted values
otherwise. DRR is an interaction variable = DR*R. DR
of DR, R, and DRR, respectively, from a piecewise linear 2SLS model. Robust t-statistics based on
two-way clustered standard errors at the industry and fiscal year levels are reported in parentheses.
***, **, and * indicate statistical significance (two-sided) at the 1%, 5%, and 10% levels,
respectively.
has a significantly larger response coefficient. Specifically, columns (1) and (3)
reveal asymmetric timeliness coefficients, β3, of 0.136 and 0.152, with t-statistics
of 4.08 and 6.72, respectively. Further, the ratio of total negative return response
to positive return response, (β3 + β2)/β2, is 3.43 and 4.10 in the 1963-1990 and
1963-2008 sample periods, respectively. Together, these findings support the
inference in extant literature that conditional conservatism has increased in years
subsequent to the sample period used in Basu (1997) (e.g., Givoly and Hayn
2000; Watts 2003).
Columns (1) and (3) of Table 5 present results from estimation of Eq. (10) for
the 1963-1990 and 1963-2008 sample periods, respectively. Columns (1) and (3)
19
Table 5
Piecewise linear return-on-earnings regression specification



   X   DXX
 
OLS: R   0  1 DX   2 X   3 DXX   ; 2SLS: R   0  1 DX
2
3
Sample Period:
1963-1990
1963-2008
Methodology:
OLS
2SLS
OLS
2SLS
Column:
(1)
(2)
(3)
(4)
Intercept
0.012
0.011
0.001
0.030

(0.25)
(0.03)
(0.83)
0.052*
0.127
0.089***
0.340**
(1.80)
(0.56)
(3.92)
(2.18)
1.597***
1.412***
1.664***
1.446***
(7.75)
(4.31)
(6.95)
(3.95)
1.412***
1.432**
1.396***
1.808***
(5.97)
(2.34)
(5.69)
(3.11)
Firm-year obs.
35,541
35,541
62,991
62,991
Adjusted-R2
P-value for test
of X + DXX = 0
0.122
DX
X
DXX
0.023
0.120
0.977
0.027
0.593
Table 5 reports OLS and 2SLS regression results for a piecewise linear return-on-earnings model
using firm-year observations. Columns (1) and (2) utilize the sample period 1963-1990, and
columns (3) and (4) utilize the sample period 1963-2008. X is earnings before extraordinary items
per share scaled by beginning of year stock price. R is firm i's stock return from 9 months before
fiscal year-end to 3 months after fiscal year-end. DX is an indicator variable = 1 if X < 0 and = 0
 




, X , and DXX
are first-stage fitted values
otherwise. DXX is an interaction variable = DX*X. DX
of DX, X, and DXX, respectively, from a piecewise linear 2SLS model. Robust t-statistics based on
two-way clustered standard errors at the industry and fiscal year levels are reported in parentheses.
***, **, and * indicate statistical significance (two-sided) at the 1%, 5%, and 10% levels,
respectively.
reveal earnings response coefficients on positive earnings, α2, of 1.597 and 1.664,
with t-statistics of 7.75 and 6.95, respectively. The significantly negative
asymmetric persistence coefficients, α3, are consistent with results documented in
Hayn (1995) that the response coefficient on negative earnings is significantly
smaller than the response coefficient on positive earnings. Specifically, α3 is
1.412 and 1.396 with t-statistics of 5.97 and5.69 in the 1963-1990 and
1963-2008 sample periods, respectively. The total response coefficient on
negative earnings, α2 + α3, is relatively small (0.185 and 0.268 in columns 1 and
3, respectively) but statistically greater than zero in both sample periods.
20
5.3.2
Two-stage least squares
Columns (3)-(8) (11-16) in Table 3 present results from estimation of the firststage Eqs. (14) and (15) using the sample period 1963-1990 (1963-2008). The
adjusted-R2 from the return and earnings first-stage regression models exceed
26% and 40%, respectively, which are comparable to the first-stage model fit
statistics corresponding to the linear specification.16 The adjusted-R2 for the
indicator and interaction variables range from 15% to 30%. As with the linear
specification, first-stage Cragg-Donald F-statistics and Kleibergen-Paap Fstatistics exceed the suggested critical F-values.
Columns (2) and (4) of Table 4 present results from estimation of the secondstage piecewise linear earnings-on-return model of Eq. (12) for the 1963-1990 and
1963-2008 sample periods, respectively. In comparison to the OLS coefficient
estimates from Eq. (9), both the second-stage response coefficients on positive
return and asymmetric timeliness coefficients, β2 and β3, respectively, are
substantially larger for both sample periods. Specifically, columns (2) and (4)
reveal response coefficients on positive return of 0.116 and 0.113, with associated
t-statistics of 1.66 and 1.78, respectively. These coefficient estimates are 107%
and 131% larger than the respective coefficients estimated under OLS. Columns
(2) and (4) reveal asymmetric timeliness coefficients of 0.638 and 0.256, with tstatistics of 3.09 and 2.48, respectively. These coefficients are 369% and 69%
larger than the respective coefficients estimated under OLS. Collectively, these
second-stage results are consistent with endogeneity bias causing substantial
attenuation of OLS return response coefficients for both positive and negative
return.
In the context of the conservatism literature, two additional observations are
noteworthy. First, our finding that the asymmetric timeliness coefficients are
larger under 2SLS than OLS suggests that studies using the OLS coefficient as a
measure of conditional conservatism potentially understate the degree of
conditional conservatism. Second, inferences regarding how conditional
conservatism has changed over time are sensitive to whether OLS or 2SLS
coefficients are used as the basis of comparison. Extant literature provides
evidence that conditional conservatism increases in the years subsequent to the
Basu (1997) sample period (e.g., Givoly and Hayn 2000; Watts 2003). The Table
16
The similarity in first-stage model fit between the linear and piecewise linear specifications for
return and earnings is expected. The instrumentation across specifications differs only by the four
additional instruments from Eq. (11), the primary role of which is to facilitate instrumentation of
the indicator and interaction functions of return and earnings in the piecewise linear specification.
Accordingly, these additional four variables have little effect on the instrumentation of return and
earnings themselves.
21
4 OLS findings are consistent with this evidence, as β3 increases from 0.136 to
0.152 when the sample period is extended to include 1990-2008. In contrast, the
2SLS findings are inconsistent with this evidence, as β3 decreases from 0.638 to
0.256 when the sample period is extended to include 1990-2008. However, we are
hesitant to infer that conditional conservatism has decreased in the more recent
sample period, as we cannot rule out the possibility that this apparent decrease in
conditional conservatism is affected by differential explanatory power of our
exogenous variables in the first-stage models across the two sample periods.
Columns (2) and (4) of Table 5 present results from estimation of the secondstage piecewise linear return-on-earnings model of Eq. (13) for the 1963-1990 and
1963-2008 sample periods, respectively. Columns (2) and (4) reveal response
coefficients on positive earnings, α2, of 1.412 and 1.446, with associated tstatistics of 4.31 and 3.95, respectively. These coefficient estimates are 12% and
13% smaller than the respective coefficients estimated under OLS. Columns (2)
and (4) reveal asymmetric persistence coefficients, α3, of 1.432 and 1.808, with
t-statistics of 2.34 and 3.11, respectively. These coefficients are 1% and 29%
larger in magnitude than the respective coefficients estimated under OLS. The
total response coefficient on negative earnings, α2 + α3, is not statistically
different from zero in either sample period. The magnitudes of the percentage
changes in earnings response coefficient estimates under 2SLS relative to OLS
are substantially smaller than the corresponding percentage changes in return
response coefficients reported above. These findings are again consistent with
simultaneity bias having less of an impact on OLS earnings response coefficients
than on OLS return response coefficients.
Inferences concerning the asymmetric persistence of profits and losses are
essentially the same across OLS and 2SLS estimation. In particular, both
estimation approaches provide evidence that profits have substantially higher
pricing multiples than losses. Moreover, this asymmetric earnings persistence is
of similar magnitude across estimation techniques based on either sample period.
5.4
Forbidden regression
As noted above in Section 3, constructing fitted values for indicator and
interaction variables directly from the fitted values of return and earnings, i.e., the
forbidden regression approach, generally results in biased and inconsistent
coefficient estimates. In the context of this study, the forbidden regression
approach involves estimating fitted values for indicator and interaction variables
using Eqs. (11), rather than Eqs. (14a), (14c), (15a) and (15c).17 Here we provide
17
The forbidden regression approach also involves estimating fitted values for return and earnings
using Eqs. (7) and (8), rather than Eqs. (14b) and (15b), respectively. However, there is little
22
evidence on the extent to which inferences obtained using the forbidden
regression approach differ from those obtained under the correct 2SLS approach.
Columns (1) and (3) of Table 6 present results from estimation of the secondstage piecewise linear earnings-on-return model of Eq. (16) for the 1963-1990 and
1963-2008 sample periods, respectively. The forbidden regression second-stage
response coefficients on positive return, β2, are of comparable magnitude to those
obtained from correct 2SLS estimation using Eq. (12). Specifically, columns (1)
and (3) reveal response coefficients on positive return of 0.132 and 0.113, with
associated t-statistics of 2.85 and 2.34, respectively. These coefficient estimates
are 14% and 0% larger than the respective coefficients estimated under the correct
2SLS approach. In contrast, the forbidden regression second-stage asymmetric
timeliness coefficients, β3, are substantially smaller than those obtained using the
correct 2SLS approach. Specifically, columns (1) and (3) reveal asymmetric
timeliness coefficients of 0.060 and 0.140, with associated t-statistics of 0.86 and
2.27, respectively. These coefficient estimates are 91% and 45% smaller than the
respective coefficients estimated under correct 2SLS estimation.
In the context of the conditional conservatism literature, the forbidden
regression approach to 2SLS leads to the following inferences: 1) there was no
statistically significant asymmetric timeliness (i.e., no evidence of conditional
conservatism) during the Basu (1997) sample period; 2) OLS estimation
overstates the degree of conditional conservatism; 3) conditional conservatism has
increased in the period subsequent to the Basu (1997) sample period. These
inferences contrast sharply with those obtained using the correct 2SLS approach.
This contrast provides evidence that the forbidden regression approach does
indeed introduce substantial coefficient bias in the piecewise linear earnings-onreturn model.
Columns (2) and (4) of Table 6 present results from estimation of the secondstage piecewise linear return-on-earnings model of Eq. (17) for the 1963-1990 and
1963-2008 sample periods, respectively. Both the forbidden regression secondstage response coefficients on positive earnings, α2, and asymmetric persistence
coefficients, α3, are of comparable magnitude to those obtained from correct 2SLS
estimation using Eq. (13). Specifically, columns (2) and (4) reveal response
coefficients on positive earnings of 1.485 and 1.746, with associated t-statistics of
5.50 and 5.44, respectively. These coefficient estimates are 5% and 21% larger
than the respective coefficients estimated under the correct 2SLS approach.
Columns (2) and (4) further reveal asymmetric persistence coefficients of 1.729
and 2.066, with associated t-statistics of 4.24 and 5.88. These asymmetric
persistence coefficients are 21% and 14% larger in magnitude than the respective
coefficients from the correct 2SLS approach.
effective difference in the resulting fitted values for return and earnings across these alternatives,
as discussed in footnote 16.
23
Table 6
Forbidden regression approach to 2SLS
   R   DRR
   ; R     DX
  

X   0  1 DR
0
1
2 X   3 DXX  
2
3
Sample period:
1963-1990
1963-2008
Dependent var.:
X
R
X
R
Column:
(1)
(2)
(3)
(4)
Intercept
0.089***
0.004
0.071***
0.005

(0.10)
(7.82)
(0.16)

DR

R

DRR
0.009
0.002
(1.05)
(0.23)
0.132***
0.113**
(2.85)
(2.34)
0.060
0.140**
(0.86)
(2.27)

DX

X

DXX
Firm-year obs.
35,541
0.014
0.032
(0.53)
(1.07)
1.485***
1.746***
(5.50)
(5.44)
1.729***
2.066***
(4.24)
(5.88)
35,541
62,991
62,991
Table 6 reports 2SLS regression results for piecewise linear earnings-on-return and return-onearnings models using firm-year observations and the forbidden regression approach to 2SLS.
Columns (1) and (2) utilize the sample period 1963-1990, and columns (3) and (4) utilize the
sample period 1963-2008. X is earnings before extraordinary items per share scaled by beginning
of year stock price. R is firm i's stock return from 9 months before fiscal year-end to 3 months
 (
after fiscal year-end. R
X ) is the first-stage fitted value of R (X) from a linear 2SLS model.
 is an indicator variable = 1 if R
 < 0 and = 0 otherwise. DRR
 = DR
 *R
 . DX
 is an indicator
DR




variable = 1 if X < 0 and = 0 otherwise. DXX = DX * X . Robust t-statistics based on two-way
clustered standard errors at the industry and fiscal year levels are reported in parentheses. ***, **,
and * indicate statistical significance (two-sided) at the 1%, 5%, and 10% levels, respectively.
Inferences concerning asymmetric persistence of earnings across profits and
losses are not particularly sensitive to the use of the forbidden regression
approach to 2SLS. In particular, profits have substantially higher pricing multiples
24
than losses, where the estimated asymmetric persistence has comparable
magnitudes across OLS, correct 2SLS, and forbidden regression approaches.
6
Conclusion
This study addresses simultaneity bias in piecewise linear forms of the earningsreturn relation by estimating return and earnings models within a simultaneous
equations framework. To do so, we specify an overidentified system of
simultaneous equations that incorporates both asymmetric earnings timeliness and
asymmetric earnings persistence specifications, and implement two-stage least
squares for this piecewise linear system. Whereas estimation of a system of
equations that is linear in endogenous variables is relatively straightforward,
estimation of a system that is piecewise linear in the endogenous variables raises
several issues for which there exists no precedent in the accounting literature.
The results of the study not only provide a richer view of the earnings-return
simultaneity bias first documented in BMS, but also speak to whether
fundamental conclusions regarding asymmetric timeliness and asymmetric
persistence hold after correction for such bias.
Regarding the piecewise linear earnings-on-return model, findings indicate
that the 2SLS coefficients are substantially larger than the corresponding OLS
coefficients. This suggests that studies using the OLS coefficients as a measure of
conditional conservatism potentially understate the degree of conservatism.
Moreover, in contrast to both our OLS results and inferences drawn in extant
literature, the 2SLS findings suggest that asymmetric earnings timeliness may
have decreased over time. Thus, inferences regarding how conditional
conservatism has evolved over time are sensitive to whether OLS or 2SLS
coefficients are used as the basis of comparison. Regarding the piecewise linear
return-on-earnings model, findings from 2SLS estimation indicate that earnings
response coefficients are similar in magnitude to the corresponding OLS
coefficients. Thus, both OLS and 2SLS estimation approaches provide evidence
that profits have substantially higher pricing multiples than losses. In addition,
the response differential between profits and losses is of similar magnitude across
estimation techniques.
Two caveats are important to consider when interpreting our study’s findings.
First, as with any study that addresses endogeneity or simultaneity, identification
of appropriate instrumental variables for returns and earnings is a major
challenge. Second, the quality of instrumentation of a piecewise linear
endogenous variable may suffer if there is misspecification within the structural
model. We therefore acknowledge the always present possibility that our findings
could be attributable to instrumentation misspecification, rather than to removal
of coefficient bias. Moreover, any inferences related to how 2SLS coefficients
25
change over time may be affected by differential explanatory power of the
exogenous variables in first-stage models estimated using different sample
periods. Subject to these caveats, our findings suggest that it is important to
consider simultaneity bias in piecewise linear specifications of the earnings-return
relation, and that such consideration is particularly important for earnings-onreturn models.
Acknowledgements
We appreciate the helpful comments of Stephen Ryan (editor), two
anonymous referees, John Abowd, Tom Mroz, Daniel Taylor, Tim Vogelsang, and seminar
participants at the University of North Carolina at Chapel Hill. We acknowledge funding from the
KPMG research fund at the University of North Carolina. Edward Owens gratefully acknowledges
funding from the Deloitte Doctoral Fellowship.
Appendix
Variable definitions
BTMi,t-1
book-to-market ratio, computed as (XPF-CEQ)/(XPF-CSHO*XPF-PRCC_F)
CERMi,t
sensitivity of firm i's return to the Fama-French excess market return factor,
measured as the coefficient on the excess market return factor from a daily FamaFrench three-factor model, estimated over the twelve months ending on firm i's
fiscal year t end date. We obtain daily firm return from CRSP, and the daily
Fama-French factor returns from
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
CHMLi,t
sensitivity of firm i's return to the Fama-French HML factor, measured as the
coefficient on the HML factor from a daily Fama-French three-factor model,
estimated over the twelve months ending on firm i's fiscal year t end date. We
obtain daily firm return from CRSP, and the daily Fama-French factor returns
from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
CSMBi,t
sensitivity of firm i's return to the Fama-French SMB factor, measured as the
coefficient on the SMB factor from a daily Fama-French three-factor model,
estimated over the twelve months ending on firm i's fiscal year t end date. We
obtain daily firm return from CRSP, and the daily Fama-French factor returns
from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
DEBTi,t
total debt per common share outstanding, computed as (XPF-DLTT + XPFDLC)/(XPF-CSHO)
DIVi,t
dividends per common share outstanding, computed as XPF-DVC/XPF-CSHO
DIVYDi,t-1
dividend yield, computed as DIV/XPF-PRCC_F
DRi,t
an indicator variable = 1 if Ri,t < 0 and = 0 otherwise
 i ,t
DR
 i ,t < 0 and = 0 otherwise
an indicator variable = 1 if R
26

 i ,t
DR
the fitted value from a first-stage regression of DRi,t on the following nineteen
instruments: BTMi,t-1 , CERMi,t, CHMLi,t, CSMBi,t, DEBTi,t, DIVi,t, DIVYDi,t-1,
EPi,t-1, INDRETi,t, PCDPSi,t, PCEMPi,t, PCREVi,t, PCTAi,t, PCTLi,t, Ri,t-1,
 i ,t , DX
 i ,t , DRR
 i ,t , DXX
 i ,t
DR
DRRi,t
an interaction variable = DR*R
 i ,t
DRR
 i ,t * R i ,t
an interaction variable = DR

the fitted value from a first-stage regression of DRRi,t on the following nineteen
instruments: BTMi,t-1 , CERMi,t, CHMLi,t, CSMBi,t, DEBTi,t, DIVi,t, DIVYDi,t-1,
EPi,t-1, INDRETi,t, PCDPSi,t, PCEMPi,t, PCREVi,t, PCTAi,t, PCTLi,t, Ri,t-1,
 i ,t
DRR
 i ,t , DX
 i ,t , DRR
 i ,t , DXX
 i ,t
DR
DXi,t
an indicator variable = 1 if Xi,t < 0 and = 0 otherwise
 i ,t
DX
 i ,t < 0 and = 0 otherwise
an indicator variable = 1 if X

the fitted value from a first-stage regression of DXi,t on the following nineteen
instruments: BTMi,t-1 , CERMi,t, CHMLi,t, CSMBi,t, DEBTi,t, DIVi,t, DIVYDi,t-1,
EPi,t-1, INDRETi,t, PCDPSi,t, PCEMPi,t, PCREVi,t, PCTAi,t, PCTLi,t, Ri,t-1,
 i ,t
DX
 i ,t , DX
 i ,t , DRR
 i ,t , DXX
 i ,t
DR
DXXi,t
an interaction variable = DX*X
 i ,t
DXX
 i ,t * X i ,t
an interaction variable = DX

the fitted value from a first-stage regression of DXXi,t on the following nineteen
instruments: BTMi,t-1 , CERMi,t, CHMLi,t, CSMBi,t, DEBTi,t, DIVi,t, DIVYDi,t-1,
EPi,t-1, INDRETi,t, PCDPSi,t, PCEMPi,t, PCREVi,t, PCTAi,t, PCTLi,t, Ri,t-1,
 i ,t
DXX
 i ,t , DX
 i ,t , DRR
 i ,t , DXX
 i ,t
DR
EPi,t-1
earnings-to-price ratio, computed as (XPF-IB/XPF-CSHO)/XPF-PRCC_F
INDRETi,t
industry return, measured as the average annual return (R) in fiscal year t for all
other firms in firm i's two-digit SIC
PCDPSi,t
percentage change in DIV from fiscal year t-1 to t
PCEMPi,t
percentage change in employees from fiscal year t-1 to t (XPF-EMP)
PCREVi,t
percentage change in revenue from fiscal year t-1 to t (XPF-SALE)
PCTAi,t
percentage change in total assets from fiscal year t-1 to t (XPF-AT)
PCTLi,t
percentage change in total liabilities from fiscal year t-1 to t (XPF-LT)
27
Ri,t
buy-and-hold annual return, commencing in the fourth month of fiscal year t and
ending in the third month of fiscal year t+1, using return data from the monthly
CRSP file
 i ,t
R
the fitted value from a first-stage regression of Ri,t on the following fifteen
instruments: BTMi,t-1 , CERMi,t, CHMLi,t, CSMBi,t, DEBTi,t, DIVi,t, DIVYDi,t-1,
EPi,t-1, INDRETi,t, PCDPSi,t, PCEMPi,t, PCREVi,t, PCTAi,t, PCTLi,t, Ri,t-1

the fitted value from a first-stage regression of Ri,t on the following nineteen
instruments: BTMi,t-1 , CERMi,t, CHMLi,t, CSMBi,t, DEBTi,t, DIVi,t, DIVYDi,t-1,
EPi,t-1, INDRETi,t, PCDPSi,t, PCEMPi,t, PCREVi,t, PCTAi,t, PCTLi,t, Ri,t-1,
 i ,t
R
 i ,t , DX
 i ,t , DRR
 i ,t , DXX
 i ,t
DR
Xi,t
earnings before extraordinary items (XPF-IB) divided by number of common
shares outstanding (XPF-CSHO), scaled by firm i's stock price at the beginning of
fiscal year t (XPF-PRCC_F)
 i ,t
X
the fitted value from a first-stage regression of Xi,t on the following fifteen
instruments: BTMi,t-1 , CERMi,t, CHMLi,t, CSMBi,t, DEBTi,t, DIVi,t, DIVYDi,t-1,
EPi,t-1, INDRETi,t, PCDPSi,t, PCEMPi,t, PCREVi,t, PCTAi,t, PCTLi,t, Ri,t-1

the fitted value from a first-stage regression of Xi,t on the following nineteen
instruments: BTMi,t-1 , CERMi,t, CHMLi,t, CSMBi,t, DEBTi,t, DIVi,t, DIVYDi,t-1,
EPi,t-1, INDRETi,t, PCDPSi,t, PCEMPi,t, PCREVi,t, PCTAi,t, PCTLi,t, Ri,t-1,
 i ,t
X
 i ,t , DX
 i ,t , DRR
 i ,t , DXX
 i ,t
DR
Note: Variables prefixed by "XPF-" are the mnemonic identifiers of raw data items obtained from
the annual file in Compustat Xpressfeed. Subscripts i and t refer to firm and fiscal year,
respectively.
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