Description
Range forecasts have evolved to be the most common form of management forecasts. Prior
studies typically use the midpoint to evaluate analyst reaction to range forecasts, implicitly
assuming that analysts place equal weights on the upper and the lower bounds of management
range forecasts. We empirically test this restrictive assumption and provide strong
evidence of unequal weights – analysts place significantly more (less) weight on the lower
(upper) bound of forecast ranges.
How do analysts interpret management range forecasts?
q
Michael Tang
a,?
, Paul Zarowin
a
, Li Zhang
b
a
Stern School of Business, New York University, United States
b
Rutgers Business School, Rutgers University, United States
a r t i c l e i n f o
Article history:
Available online 19 February 2015
a b s t r a c t
Range forecasts have evolved to be the most common form of management forecasts. Prior
studies typically use the midpoint to evaluate analyst reaction to range forecasts, implicitly
assuming that analysts place equal weights on the upper and the lower bounds of manage-
ment range forecasts. We empirically test this restrictive assumption and provide strong
evidence of unequal weights – analysts place signi?cantly more (less) weight on the lower
(upper) bound of forecast ranges. Moreover, such overweight on the lower bound is more
pronounced when analysts face higher ambiguity, consistent with the ‘‘max–min’’ axiom,
which predicts that decision-makers tend to assign higher probability to the worst-case
scenario when facing ambiguity. Further tests show that ‘‘optimal revisions’’ with perfect
foresight of actual earnings also overweight the lower bound.
Ó 2015 Elsevier Ltd. All rights reserved.
Introduction
Management earnings forecasts, also known as earnings
guidance, play a signi?cant role in capital markets (Ball &
Shivakumar, 2008; Beyer, Cohen, Lys, & Walther, 2010;
Hirst, Koonce, & Venkataraman, 2008) that affects stock
prices and bid-ask spreads (Coller & Yohn, 1997; Pownall,
Wasley, & Waymire, 1993). In particular, a growing lit-
erature on ‘‘expectation management’’ examines howman-
agement forecasts establish and alter analyst earnings
expectations (e.g., Ajinkya & Gift, 1984; Baginski &
Hassell, 1990; Waymire, 1986; Williams, 1996; Cotter,
Tuna, & Wysocki, 2006; Kross & Suk, 2012; Matsumoto,
2002; Rogers & Van Buskirk, 2013). These studies usually
regress analyst forecast revisions around a management
forecast on the news conveyed from the management fore-
cast. However, measuring forecast news can be dif?cult for
range forecasts where managers provide both an upper
bound and a lower bound of their earnings expectations.
This issue becomes more important because range fore-
casts recently emerge as the most popular type of forecasts,
accounting for around 80% of all management forecasts
issued in the last decade (Ciconte, Kirk, & Tucker, 2014), a
sharp increase from under 20% in samples used in earlier
studies (e.g., Pownall et al., 1993). This paper examines
how analysts interpret management range forecasts.
Most of the prior studies typically use the mid-point to
calculate forecast news, implicitly assuming that users of
range forecasts such as analysts place equal ‘‘weights’’ on
the upper and lower bounds of management range fore-
casts (Baginski, Conrad, & Hassell, 1993).
1
A recent study
by Ciconte et al. (2014) challenges this convention andhttp://dx.doi.org/10.1016/j.aos.2014.12.005
0361-3682/Ó 2015 Elsevier Ltd. All rights reserved.
q
We thank Lisa Koonce (editor) and two anonymous reviewers for
comments and suggestions that signi?cantly improved the manuscript.
We are grateful for helpful comments from Phil Berger (discussant), Jenny
Tucker, Shankar Venkataraman (discussant), Jian Xue (discussant), Jerry
Zimmerman, and workshop participants at 2014 AAA Annual Meeting,
Accounting Conference at Temple University, 2014 CAPANA Conference,
New York University, the Ohio State University, and PwC Young Scholar
Symposium at the University of Illinois at Urbana Champaign. All errors
and omissions are our own.
?
Corresponding author.
E-mail addresses: [email protected] (M. Tang), pzarowin@stern.
nyu.edu (P. Zarowin), [email protected] (L. Zhang).
1
In this paper, by ‘‘equal weights,’’ we mean that the empirical
sensitivity of analyst revision to the upper and lower bounds of manage-
ment forecast ranges is ‘‘equal.’’ Most prior empirical studies on expecta-
tion management regress analyst revisions on management forecast news,
which relates to analysts’ ‘‘weight’’ (i.e. the coef?cient) on the news.
Accounting, Organizations and Society 42 (2015) 48–66
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examines whether the midpoint represents managers’ true
expectation – a question that is related to but different from
ours. Finding the distribution of actual reported earnings to
be more concentrated around the upper bound of manage-
ment range forecasts, they conclude that the upper bound
is more representative of managers’ expectations than the
midpoint. Although it is easy and natural to interpret range
signals such as management range forecasts at a single point
(either the midpoint or the upper bound) based on some
convenient ‘‘rule of thumb’’ (Tversky & Kahneman, 1982),
such interpretation imposes a restrictive assumption, that
is, 100% weight must be placed on a single point of the
range, thus ignoring information conveyed by the entire
forecast range. In this study we relax this restrictive
assumption and empirically investigate whether analysts
place equal weights on the upper and lower bounds of range
forecasts.
We evaluate the weights that analysts place on the
upper and the lower bounds of range forecasts by regress-
ing analyst forecast revisions on management forecast
news conveyed from both the upper and the lower bounds
of forecast ranges. The coef?cient on each news measure
re?ects the relative weight that analysts place on the cor-
responding bound of the range. Because the upper and
lower bounds are highly correlated (Pearson correla-
tion = 0.8 in our sample), to mitigate the concern of multi-
collinearity, we modify our main empirical model by
replacing the news from the upper bound (the lower
bound) with the news from the midpoint plus (minus) half
of the range width, measured as the distance between the
upper and lower bounds of the range forecast. After this
modi?cation, the coef?cient on the range width captures
the differences in the weights that analysts place on the
upper and lower bounds of the forecast range. Under
the null hypothesis implied in the extant studies that use
the midpoint to compute management forecast news, we
would expect the coef?cient on the range width to be zero.
Contrary to this conventional implication, we predict
that analysts place unequal weights, and that they are like-
ly to place more weight on the lower bound of manage-
ment range forecasts. Theories of decision-making predict
that ambiguity-averse agents tend to assign high probabil-
ity to the worst-case scenario when facing ambiguity
(Epstein & Schneider, 2008). Therefore, such decision-mak-
ers choose to maximize their expected utility assuming the
worst scenario, so called ‘‘max–min’’ axiom proposed by
Gilboa and Schmeidler (1989). Prior literature documents
that analysts are less likely to cover ?rms in more uncer-
tain environments or with less transparent disclosure
(e.g., Lang & Lundholm, 1996; O’Brien & Bhushan, 1990),
consistent with analysts being ambiguity-averse. By indi-
cating a range of possible future outcomes, management
range forecasts deliver ambiguous signals to analysts.
Therefore, we expect ambiguity-averse analysts to treat
the worst-case scenario (i.e., the lower bound) as more
likely than the best-case scenario (i.e., the upper bound),
and hence weight the lower bound more heavily. More-
over, we expect such overweight on the lower bound to
be more pronounced as the degree of ambiguity increases.
Consistent with our expectations, we ?nd that analysts
place an average of 73–77% weight on the lower bound of
management ranges forecasts, signi?cantly more weight
than on the upper bound. This effect is distinct from that
of managers using range forecasts to ‘‘walk down’’ analyst
expectations (e.g., Cotter et al., 2006) and also from the
optimistic-to-pessimistic patterns observed in analyst
forecasts as horizon decreases (e.g., Ke & Yu, 2006). Results
from various robustness tests further suggest that this
effect is not driven by ‘‘bundled forecasts’’ – management
forecasts that are simultaneously released with earnings
announcements (Rogers & Van Buskirk, 2013). Moreover,
such overweight on the lower bound is more pronounced
in scenarios where ambiguity or uncertainty is known to
be higher, including when management forecasts are (a)
issued earlier in the year, (b) issued with wider ranges,
(c) issued by ?rms with higher analyst forecast dispersion,
and (d) issued by ?rms with more volatile stock returns.
In supplemental tests, we ?nd evidence that analysts
adjust their weights based on the outcome of past range
forecasts, consistent with the conjecture that analysts are
‘‘Bayesian’’ and learn from the past (Hillary et al., 2013).
However, analysts’ overweight on the lower bound of man-
agement range forecasts does not seem to be driven by
their incentives to ‘‘lowball’’ their forecasts (Hilary & Hsu,
2013; Ke & Yu, 2006). Finally, using actual reported earn-
ings to impute the ‘‘optimal’’ forecast revision by a hypo-
thetical analyst with perfect foresight, we ?nd that the
‘‘optimal’’ weight also lies more on the lower bound than
on the upper bound. Hence analysts’ overweight on the
lower bound is indeed conducive to accurate prediction
relative to equal weighting. But unlike weights from ana-
lyst forecasts, the ‘‘optimal’’ weight does not shift further
to the lower bound in situations of heightened uncertainty,
consistent with analysts acting according to the ‘‘max–
min’’ axiom but inconsistent with them anticipating the
‘‘optimal’’ weight.
We caution readers to distinguish the ‘‘weight’’ from
the ‘‘distance’’, which is examined by Ciconte et al.
(2014). After showing that the actual earnings are more
likely to be around the upper bound rather than the mid-
point of managers’ range forecasts, they investigate and
?nd that analysts’ revised forecasts are, on average, slightly
above the midpoint but well below the upper bound, sug-
gesting that analysts barely unravel the pessimistic bias in
managers’ range forecasts. Our evidence of analysts’ ‘‘over-
weight’’ on the lower bound does not contradict their ?nd-
ing of analysts’ revised forecasts being slightly ‘‘closer’’ to
the upper bound. This is because analysts not only respond
to management forecast news but also to managers’ provi-
sion of the forecast, which is captured by the intercept in
our model of analyst forecast revision. Existing theoretical
(e.g., Grossman & Hart, 1980) and empirical (e.g., Clement,
Frankel, & Miller, 2003) studies suggest that managers’ vol-
untary provision of earnings forecast is perceived as a
desirable action. Consistent with this prediction, we ?nd
a signi?cantly positive intercept when we allow analysts
to place unequal weights on the upper and lower bounds
of range forecasts. However, the intercept turns sig-
ni?cantly negative when we follow the conventional
design and force the weights to be equal. This ?nding
demonstrates the importance of allowing analysts to place
unequal weights on the upper and the lower bounds of
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 49
management range forecasts. The positive intercept we
?nd also explains why, in terms of ‘‘distance’’, analysts’
revised forecasts are on average slightly ‘‘closer’’ to the
upper bound, even though analysts place more ‘‘weight’’
on the lower bound.
2
This study makes at least two contributions to the lit-
erature. First, it cautions researchers about the convention-
al practice of using the midpoint to interpret management
range forecasts – an increasingly predominant form of
management forecasts. This practice implicitly assumes
that users of range forecasts place equal weights on both
endpoints. We offer a simple and intuitive approach to
assessing the relative weights on the endpoints of range
forecasts, in the setting of analyst forecast revisions. Our
?ndings reject the null hypothesis implied by the conven-
tional approach and show that analysts place signi?cantly
more weight on the lower bound than on the upper bound
of range forecasts. To the best of our knowledge, the differ-
ential weights on the endpoints of range forecasts have
never been investigated before in the literature. However,
we emphasize that our approach is developed to examine
how analysts interpret range forecasts and may not be
appropriate or desirable in all range-forecast-related set-
tings.
3
Nonetheless, future research on analyst reaction to
management forecasts can follow this study and simply
include the forecast range width to relax the assumption
of equal weights that is refuted by our ?ndings.
Second, this study deepens our understanding of the
growing literature on ‘‘expectation management’’, which
focuses on the average effect of managers ‘‘walking down’’
analysts’ expectations with management forecasts (e.g.,
Cotter et al., 2006; Kross & Suk, 2012). These studies, how-
ever, ignore the differential effect of the upper and lower
bounds of range forecasts on analyst expectations, as well
as any cross-sectional variations in such differential effect.
We document that analysts place more weight on the low-
er bound than on the upper bound, and this differential
reaction is more pronounced when ambiguity is higher,
consistent with the ‘‘max–min’’ axiom proposed in the
decision-making literature (Epstein & Schneider, 2008;
Gilboa & Schmeidler, 1989). Therefore, our paper con-
tributes to the expectation management literature by
introducing a new factor (ambiguity) through a new chan-
nel (analysts’ differential weights on the upper and lower
bounds of management range forecasts). This new channel
is also relevant to managers who provide range forecasts,
to analysts who use managers’ range forecasts, and to mar-
ket participants who use managers’ or analysts’ forecasts.
Section ‘Related research and hypothesis development’
reviews related research and develops our hypotheses. In
Section ‘Sample selection’ we describe our sample. Sec-
tion ‘Empirical research design’ describes our empirical
research design. We present our empirical results in Sec-
tion ‘Empirical results’, and Section ‘Conclusion’ concludes.
Related research and hypothesis development
Management earnings forecasts typically take four
forms – points, (closed-ended) ranges, maximums and
minimums (also referred to as open-ended ranges), or
qualitative forecasts – in decreasing order of precision. Ear-
lier studies ?nd mixed evidence on the effect of forecast
form on market reaction (Baginski et al., 1993; Pownall
et al., 1993). Notably, range forecasts have emerged as
the predominant form of management forecasts from
6.8% in the 1980s (Pownall et al., 1993) to over 80% in
recent years (Choi, Myers, Zang, & Ziebart, 2011; Ciconte
et al., 2014). Despite its popularity, little research exists
on how analysts interpret range forecasts. Most studies
treat range forecasts as equivalent to point forecasts at
the midpoints (e.g., Ajinkya, Bhojraj, & Sengupta, 2005;
Feng & Koch, 2010; Gong et al., 2011; Rogers & Stocken,
2005).
When managers issue a point forecast, only one number
can serve as the benchmark against which analyst expecta-
tions can be measured. In contrast, a range forecast from
managers expresses expectations in terms of both an upper
and a lower limit, each of which can serve as a benchmark
(Libby, Tan, & Hunton, 2006). Psychology research suggests
that users of range estimates typically apply a simple ‘‘rule
of thumb’’ and use the midpoint to interpret range esti-
mates (Tversky & Kahneman, 1982). Earlier empirical evi-
dence also supports the use of midpoint to interpret
management range forecasts because investors appear to
respond most strongly to the midpoint of range forecasts
(Baginski et al., 1993). Following this convention, most
accounting studies use the midpoint to measure manage-
ment forecast news in evaluating analysts’ revisions in
response to management forecasts (e.g., Feng & McVay,
2010; Gong et al., 2011).
Ciconte et al. (2014) challenge this convention and seek
to explore which point of the forecast range best repre-
sents managers’ true expectations. Relative to the mid-
point, they ?nd the upper bound is more representative
of managers’ ex ante true beliefs, proxied by the ex post
reported earnings. Their analysis of stock price reaction
and analyst revision suggests that while investors’ reaction
is consistent with interpreting range forecasts near the
upper bound, analysts seem to respond to the midpoint.
Unlike this study, they use ‘‘distance’’ to evaluate which
point of the range forecast is ‘‘closer’’ to analysts’ revised
forecasts, and do not consider the ‘‘weights’’ that analysts
place on the endpoints of range forecasts, because their
main focus is not on analysts’ interpretation of manage-
ment range forecasts.
Regardless of whether the upper bound or midpoint is
more representative of managers’ true expectations, we
argue that analysts are unlikely to anchor on only a single
point of a range forecast. An extensive body of psychology
literature suggests that evaluations are made by
2
In cross-sectional tests, all of our indicators of high-uncertainty
scenarios load signi?cantly positive, suggesting that high uncertainty shifts
analysts’ revisions ‘‘closer’’ (in distance) to the upper bound. This ?nding
contrasts from more ‘‘weight’’ on the lower bound in high-uncertainty
scenarios and highlights that the ‘‘max–min’’ axiom applies only to the
‘‘weight’’ but not to the ‘‘distance’’ of analyst forecasts. We discuss this
further in the results section.
3
In particular, we do not speak to whether the midpoint of management
range forecasts should be used to measure forecast errors or forecast biases
(Gong, Li, & Wang, 2011; Rogers & Stocken, 2005), or whether the midpoint
represents managers’ true expectations (Ciconte et al., 2014).
50 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
comparisons to one or more reference points or standards
(e.g., Helson, 1964; Kahneman & Tversky, 1979; Kida &
Smith, 1995; Thaler, 1999; Thibaut & Kelley, 1959). Follow-
ing this literature, Libby et al. (2006) suggest that analysts
use both the upper bound and the lower bound of manage-
ment range forecasts as benchmarks to evaluate reported
earnings, so-called the ‘‘benchmark effect.’’ Responses
from their analyst subjects are consistent with the ‘‘bench-
mark effect’’ of management range forecasts.
Building upon the ‘‘benchmark effect,’’ we argue that
analysts reacting to a management range forecast consider
both the upper bound and the lower bound instead of a sin-
gle point.
4
Therefore, both the upper and lower bounds of a
management forecast convey news to the market relative to
the preexisting expectations, which we refer to as ‘‘news
upper’’ and ‘‘news lower’’ respectively. Moreover, analysts
can respond to both news by assigning to them equal or
unequal weights. If analysts place equal weights, then it is
equivalent to them reacting to the midpoint of range fore-
casts, as is commonly used in prior studies. If analysts put
all weight on ‘‘news upper (lower)’’ and zero weight on
‘‘news lower (upper),’’ then it is equivalent to them reacting
just to the upper (lower) bound. Unlike these approaches,
which restrict the weights to be zero or ?fty percent on
the endpoints, we allow these weights to be determined
empirically and to vary with economic determinants. There-
fore our new approach is a more generalized framework
which encompasses the existing approaches in the literature
as its special cases.
Although the extant literature implicitly assumes that
investors and analysts place equal weights on ‘‘news
upper’’ and ‘‘news lower’’ (with the exception of Ciconte
et al., 2014), we expect such weights to differ, with ‘‘news
lower’’ being overweighed by analysts. Theories in the
decision-making literature predict that ambiguity-averse
agents are more likely to assign high probability to the
worst scenario when they face ambiguity (Epstein &
Schneider, 2008). Hence such agents make choices that
maximize their expected utility under the worst scenario,
so called ‘‘max–min’’ axiom proposed by Gilboa and
Schmeidler (1989). Prior studies ?nd that analysts are less
likely to cover ?rms in more volatile environments and
with less transparent disclosure (Lang & Lundholm, 1996;
O’Brien & Bhushan, 1990), consistent with analysts being
ambiguity-averse. Management range forecasts deliver
ambiguous signals to analysts, in the sense that a range
of possible outcomes could be deemed as consistent with
their forecasts. If analysts are ambiguity-averse on average,
they will give more consideration to the worst-case sce-
nario (e.g., the lower bound) than to the best-case scenario
(e.g., the upper bound).
5
H1. Ceteris paribus, when analysts revise earnings forecasts
in response to management range forecasts, they place
more weight on the news conveyed from the lower bound
(‘‘news lower’’) than on the news conveyed from the upper
bound (‘‘news upper’’).
Extending the ‘‘max–min’’ axiom, we expect analysts’
relative overweight on the lower bound to be more pro-
nounced when more ambiguity is present (Gilboa &
Schmeidler, 1989). Ambiguity can be manifested both in
the properties of the management forecast itself and in
the information environment. Speci?cally, forecasts issued
earlier or with wider ranges are viewed as more ambigu-
ous (Libby et al., 2006). Moreover, under heightened uncer-
tainty, analysts tend to disagree with each other to a
greater extent and hence analyst forecast dispersion is
larger (Diether, Malloy, & Scherbina, 2002). Finally, stock
price becomes more volatile when uncertainty is high
(Bloom, 2009).
6
This leads to our second set of empirical
predictions.
H2. Ceteris paribus, when analysts revise earnings forecasts
in response to a management range forecast, their over-
weight on the lower bound relative to the upper bound is
more pronounced in the following scenarios:
(H2a) when the management forecast is provided ear-
lier during the period;
(H2b) when the management forecast contains a wider
range;
(H2c) when the dispersion of the preexisting analyst
forecasts is larger; and
(H2d) when stock return volatility is higher.
Sample selection
We use First Call Company Issued Guideline (CIG) data-
base to identify all management forecasts of annual earn-
ings per share issued by U.S. ?rms between 1996 and
2011. We choose annual forecasts instead of quarterly
forecasts for three reasons. First, the economic signi?cance
of differentiating between equal and unequal weights is
greater for annual forecasts because their ranges are con-
siderably wider than quarterly range forecasts.
7
Second,
annual forecasts recently overtook quarterly forecasts in
popularity due to both criticisms of quarterly forecasts
(Chen et al., 2011; Houston et al., 2010) and increased fre-
quency of updates of annual forecasts (Tang, Yao, &
Zarowin, 2014). Third, despite many recent papers that
study management quarterly forecasts (e.g., Ciconte et al.,
2014; Kross, Ro, & Suk, 2011), annual forecasts remain an
4
Although analysts may form expectations over the entire range,
unfortunately the distribution of their expectations is unobservable to
researchers. Hence, we leave it to future research and focus only on the
endpoints in this paper.
5
It is certainly possible that the worst (best) scenario could be some
point below (above) the lower (upper) bound, but under the max–min
framework, the same prediction would result about the unequal weights on
the upper and lower bounds of management forecast range, that is, more
weight would be placed on the lower bound, regardless of which two points
outside of the range are selected to represent the best and worst scenarios.
6
It is also possible that analysts are ‘‘Bayesian’’ and hence adjust their
weights on the upper and lower bounds of the management forecast range
based on their previous experience. We defer this discussion to our
empirical tests.
7
The median (mode) range width is $0.08 ($0.10) for annual forecasts,
compared with $0.03 ($0.02) for quarterly forecasts. Hence for an average
quarterly range forecast, there is only about $0.01 difference between the
midpoint and the endpoint, rendering the equal/unequal weight a trivial
issue in the setting of quarterly forecasts.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 51
important setting in the management forecast literature
(e.g., Ajinkya et al., 2005; Gong et al., 2011; Rogers &
Stocken, 2005; Hutton et al., 2012). Hence we focus on annu-
al range forecasts. Following the literature, we exclude fore-
casts issued either before the previous year’s earnings
announcement (‘‘long horizon forecasts’’) or after the end
of the current ?scal year (‘‘preannouncements’’). We obtain
non-split-adjusted actual earnings and analyst earnings
forecasts from I/B/E/S. After eliminating duplicate forecasts
and forecasts without valid identi?ers or corresponding
actual earnings, we arrive at a sample of 47,436 manage-
ment annual earnings forecasts, which include revisions
within the ?scal year.
To assess the prevalence of range forecasts, we classify
all forecasts into four types: point, range, max or min
(open-range), and qualitative forecasts. Panel A of Table 1
reports the yearly distribution by forecast types. The share
of range forecasts increases from 36.5% in 1996 to a pre-
dominant 92.1% in 2011. Accordingly, the share of point
forecasts decreases from 47.5% in 1996 to only 5.5% in
2011. Moreover, the percentages of the other two types
of forecasts also decline steadily over time, although a por-
tion of this trend could be attributed to expansion of First
Call’s coverage of quantitative forecasts through time
(Chuk, Matsumoto, & Miller, 2013). Nonetheless these
trends highlight the importance of analyzing range fore-
casts. The emergence of range forecasts as the pre-
dominant form of management forecasts starts around
the passage of Regulation Fair Disclosure (Reg FD) in late
2000, but the mean (median) range width remains roughly
constant until 2007 when the ?nancial crisis started,
increasing from around $0.08 to $0.10 ($0.05–$0.06) before
the crisis to $0.11 ($0.09) and higher. As we explain later,
in our empirical analysis, we require analyst forecasts to
be non-missing within 30 days before and after manage-
ment range forecasts, which reduces our sample size to
10,989.
8
Panel B of Table 1 presents the distribution of this
sample by whether there is one or more annual forecast
within the year and by whether or not the forecast is bun-
dled with an earnings announcement. As shown, the major-
ity of the ?rms issue more than one annual forecast (96.3%)
and bundle them with earnings announcements (82.5%),
consistent with prior research (Rogers & Van Buskirk,
2013; Tang et al., 2014).
Table 1
Sample composition.
All annual management forecasts Range forecast width
Year N Point (%) Range (%) Open (%) Qualitative (%) Mean Median Std. dev.
Panel A: broad sample distribution by year and by forecast form
1996 301 47.5 36.5 10.3 5.6 0.085 0.060 0.076
1997 453 46.6 30.0 12.8 10.6 0.103 0.060 0.126
1998 814 45.7 28.0 7.1 19.2 0.087 0.050 0.084
1999 1,126 32.8 30.0 12.1 25.1 0.092 0.050 0.165
2000 1,166 33.5 40.2 8.3 17.9 0.079 0.050 0.153
2001 2,659 21.4 66.7 5.1 6.8 0.088 0.050 0.083
2002 3,582 17.5 75.5 4.0 3.0 0.087 0.050 0.085
2003 3,954 13.4 79.2 4.6 2.9 0.093 0.060 0.101
2004 4,630 10.4 83.2 3.8 2.6 0.096 0.060 0.109
2005 4,539 9.2 87.9 2.4 0.5 0.097 0.060 0.105
2006 4,861 9.4 88.0 1.6 0.9 0.104 0.080 0.106
2007 4,508 10.2 87.6 1.6 0.6 0.108 0.090 0.105
2008 4,491 10.6 86.8 2.6 0.0 0.121 0.100 0.111
2009 3,498 8.9 89.1 2.0 0.0 0.149 0.100 0.142
2010 3,955 7.1 90.5 2.4 0.0 0.133 0.100 0.122
2011 2,899 5.5 92.1 2.5 0.0 0.144 0.100 0.132
Total 47,436 13.2 80.6 3.4 2.8 0.110 0.080 0.114
Unbundled Bundled Total
Panel B: regression sample distribution by forecast frequency and by bundling with quarterly earnings announcement news
Only one management forecast during the year 101 (0.9%) 303 (2.8%) 404 (3.7%)
Multiple management forecasts during the year 1,826 (16.6%) 8,759 (79.7%) 10,585 (96.3%)
Total 1,927 (17.5%) 9,062 (82.5%) 10,989 (100.0%)
Bundled forecasts with positive earnings news 6,966 (76.9%)
Bundled forecasts with negative earnings news 2,096 (23.1%)
Total 9,062 (100.0%)
Note: This table presents the composition of our sample. Panel A presents the distribution by year and by forecast form of the broader sample before we
focus on the subset of range forecasts. The sample is constructed based on the First Call Company Issued Guideline (CIG) database and contains man-
agement forecasts for annual earnings of ?scal years between 1996 and 2011. Forecasts are classi?ed into four forms: point, range, open-ended range (max/
min), and qualitative. For all range forecasts in each year, we also report the distribution of range widths, measured as the distance (in dollar amount)
between the upper bound and the lower bound of management range forecasts. Panel B presents the distribution by forecast frequency during the year and
by bundling with quarterly earnings announcement news of the sample of 10,989 range forecasts in our analysis, after requiring suf?cient data to calculate
our base line regression model.
8
The requirement of the [À30, +30] window is to ensure that analysts’
revisions are driven by management forecasts. Results are qualitatively the
same if we relax the window to [À60, +60] to obtain a bigger sample size of
15,122.
52 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
Table 2 presents the distribution of analyst consensus
forecasts before management range forecasts (Panel A)
and after management forecasts (Panel B), over ?ve mutu-
ally exclusive cases with respect to the corresponding fore-
cast ranges (Columns (a) through (e)): (À1, Low), [Low,
Mid), {Mid}, (Mid, High], and (High, +1), where ‘‘Low,’’
‘‘Mid,’’ and ‘‘High’’ indicate the lower bound, midpoint,
and upper bound of management range forecasts, respec-
tively. We present the distribution for the full sample as
well as separately for each ?scal quarter. Prior to manage-
ment forecasts (see Panel A), 29.4% (28.8%) of all analyst
consensus forecasts are below (above) the entire forecast
range, resulting in an asymmetry ratio of 1.021 around
the entire forecast range. Similarly, within the range,
19.9% (18.8%) of all analyst consensus forecasts are below
(above) the midpoint, leading to an asymmetry ratio of
1.036 around the midpoint.
9
While the asymmetry ratios
are below one in the ?rst quarter (Fq1) and above one in
the remaining quarters (Fq2, Fq3, and Fq4), the overall ratios
are close to one, suggesting that managers issue range fore-
casts roughly symmetrically around the prevailing analyst
forecasts, with 41.8% of all management range forecasts con-
taining the prevailing analyst consensus. Although only
34.1% of analysts’ consensus forecasts in the fourth quarter
(Fq4) are within management forecast ranges, this is partly
because the forecast ranges are also narrower in the fourth
quarter than in other quarters.
After management forecasts (Panel B of Table 2), the dis-
tribution of analyst consensus forecasts is notably different.
13.2% (20.4%) of all analyst consensus forecasts are below
(above) the entire forecast range, resulting in an asymmet-
ric ratio of 0.647 around the forecast range. Also within the
range, 25.5% (33.8%) of all analyst consensus forecasts are
below (above) the midpoint, leading to an asymmetry ratio
of 0.714 around the midpoint. Both asymmetry ratios
remain below one across all ?scal quarters, suggesting that
analysts more often revise their forecasts above the mid-
point, consistent with the ?nding in Ciconte et al. (2014).
Overall 66.4% of all analysts’ revised consensus forecasts
are within the management forecast range, with over half
of them (33.8% of total) in the upper half of managers’ fore-
cast range (Column (d)). The apparently different distribu-
tions of analyst consensus forecasts before and after
management forecasts suggest that analysts indeed react
to management forecasts. The wide distribution of analyst
revised forecasts over management forecast ranges implies
that analysts respond not just to the midpoint. Below we
develop our formal empirical design to investigate how
analysts interpret management range forecasts.
Empirical research design
Assume that h is the hypothetical weight that an analyst
places on the upper bound of a management range forecast
and hence 1 À h is the weight placed on the lower bound.
10
Thus the news conveyed by a management range forecast
can be expressed as h ? Upper Bound
i,t
+ (1 À h) ? Lower
Bound
i,t
À AF
i,tÀ1
, where Upper Bound and Lower Bound are
the upper and lower bounds of management forecast ranges,
and AF is the prevailing analyst consensus forecast prior to
the management forecast.
11
For each management forecast,
Table 2
The location of analyst consensus forecasts with regard to management forecast ranges.
Quarter N (À1, Low) [Low, Mid) {Mid} (Mid, High] (High, +1) Asymmetry % In range Range width
(a) (%) (b) (%) (c) (%) (d) (%) (e) (%) (a)/(e) (a + b)/(d + e) (b + c + d) (%) Mean Median Std. dev.
Panel A: analyst consensus forecasts issued prior to management forecasts by ?scal quarters
Fq1 2,765 23.9 18.7 2.6 20.8 34.0 0.703 0.777 42.1 0.141 0.100 0.115
Fq2 2,709 29.3 23.5 2.8 21.0 23.4 1.252 1.189 47.3 0.136 0.100 0.112
Fq3 2,803 28.8 21.2 3.3 19.1 27.6 1.043 1.071 43.6 0.117 0.100 0.101
Fq4 2,712 35.7 16.0 3.8 14.3 30.2 1.182 1.162 34.1 0.075 0.050 0.073
Total 10,989 29.4 19.9 3.1 18.8 28.8 1.021 1.036 41.8 0.117 0.100 0.105
Panel B: revised analyst consensus forecasts post management forecasts by ?scal quarters
Fq1 2,765 14.4 27.5 7.0 34.3 16.8 0.857 0.820 68.8 0.141 0.100 0.115
Fq2 2,709 14.8 24.1 5.6 32.6 22.9 0.646 0.701 62.3 0.136 0.100 0.112
Fq3 2,803 12.3 26.2 6.5 33.9 21.1 0.583 0.700 66.6 0.117 0.100 0.101
Fq4 2,712 11.4 24.0 9.4 34.2 21.0 0.543 0.641 67.6 0.075 0.050 0.073
Total 10,989 13.2 25.5 7.1 33.8 20.4 0.647 0.714 66.4 0.117 0.100 0.105
This table presents the distribution of the median analyst forecasts that are issued prior to and after the management forecasts with reference to
management forecast ranges, partitioned into ?ve mutually exclusive cases (columns (a) through (e)): (À1, Low), [Low, Mid), {Mid}, (Mid, High], and
(High,+1), where ‘‘Low,’’ ‘‘Mid,’’ and ‘‘High’’ indicates the lower bound, midpoint, and upper bound of management forecasts, respectively. The sample
includes 10,989 management range forecasts of annual earnings of ?scal years between 1996 and 2011. Two measures of asymmetry are de?ned as ratios of
the total number of observations to the left versus to the right of the range (or of the middle point). Fq1 (Fq2, Fq3, or Fq4) indicates that the management
annual forecast is issued during the ?rst (second, third, or fourth) ?scal quarter of the year. ‘‘Range Width’’ is measured as the distance (in dollar amount)
between the upper bound and the lower bound of management range forecasts.
9
This ratio should equal one for a symmetric distribution. A ratio smaller
(greater) than one indicates that fewer (more) observations are below
rather than above the range or the midpoint.
10
In our baseline model, we parsimoniously treat h as a constant, but in
later analyses, we allow h to be a function of various economic factors,
including historical outcomes to allow analysts to be ‘‘Bayesian.’’
11
Because in this paper we are interested in understanding the average
analysts’ interpretation of management range forecasts, we focus on the
consensus of analyst forecasts and ignore individual analysts’ forecasts,
which also form a range that represents analysts’ different beliefs.
However, in our robustness test section, we repeat our analyses using
individual analysts’ forecasts and obtain similar results.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 53
we collect analysts’ last forecasts issued within 30 days
before the management forecast date and use the median
analyst forecast as the consensus analyst forecast. To exam-
ine the relative weights that analysts place on the upper and
lower bounds of management range forecasts in revising
their own forecasts, we estimate the following model using
ordinary least squares (OLS) regression.
Revision
i;t
¼ a þ b½h à Upper Bound
i;t
þ ð1 À hÞ
à Lower Bound
i;t
À AF
i;tÀ1
? þe ð1Þ
where Revision is mean analyst forecast revision around a
management forecast, calculated as analysts’ ?rst forecasts
within 30 days after the management forecast minus their
last forecasts within 30 days before the management
forecast, scaled by the closing price at the end of the prior
year.
12
Accordingly we also scale forecast news by the clos-
ing price at the end of the prior year.
13
Observations are
deleted if the stock price is less than $1 to mitigate small
denominator problems.
Our focus in Model (1) above is whether h is less than
0.5, as our H1 predicts analysts to underweight the upper
bound of range forecasts. Note that if we force h to be
0.5, then Model (1) degenerates into a model using the
midpoint of management forecast to calculate manage-
ment forecast news, as is commonly used in the existing
literature (e.g., Ajinkya et al., 2005; Gong et al., 2011;
Rogers & Stocken, 2005; Rogers & Van Buskirk, 2013). By
allowing h to be estimated from the regression, we can sta-
tistically validate the assumption that h = 0.5. However,
because in a panel sample, the upper and lower bounds
of range forecasts are highly correlated, directly estimating
Model (1) suffers from severe multi-collinearity problem
(Wooldridge, 2002). To circumvent the problem we rear-
range the right-hand side of Model (1) by considering the
fact that Upper/Lower Bound = Midpoint ± 0.5 ? Width,
where Width is width of management range forecast and
Midpoint is the midpoint of management range forecast.
After rearrangement, we obtain the following model
14
:
Revision
i;t
¼ a þ bðNews Mid
i;t
Þ þ bðh À0:5Þ
à Width
i;t
þe ð1MÞ
where News_Mid is management forecast news calculated
as the midpoint minus the prevailing analyst consensus
before management forecast, scaled by the closing price
at the end of the prior year. Our empirical model of Model
(1M) can be easily adapted to consider three points of the
range forecast – the upper and lower bounds, and the mid-
point. Appendix A provides the details.
Our baseline approach is the following. Because the
ratio of the coef?cient on Width divided by the coef?cient
on News_Mid is a univariate function of h, we can infer h
from the coef?cient estimates from the regression results
of Model (1M). If analysts place equal weights on the upper
and lower bounds (h = 0.5), the ratio of the coef?cient on
Width divided by the coef?cient on News_Mid in Model
(1M) should be statistically indifferent from zero.
To examine cross-sectional variations in the relative
weights analysts place on the upper and lower bounds of
management forecasts, we interact forecast width (Width)
with variables that capture ?rm characteristics and the
properties of management forecasts. By doing so, we allow
h to be a function of these variables. If analysts adjust their
weights on the upper and lower bounds according to these
variables, these interaction terms should be signi?cant in
explaining analyst forecast revisions. Our H2 predicts that
such variables include the ?scal quarter in which the man-
agement forecast occurs (Fq1, Fq2, and Fq3), forecast range
width of the management forecast (Range), analyst forecast
dispersion (Dispersion), and stock return volatility (RetVol).
More detailed de?nitions are elaborated in the Appendix B.
In our additional analysis, we evaluate the ‘‘optimal’’
weights on the upper and lower bounds of forecast ranges
that lead to the perfect prediction of actual reported earn-
ings. To do so, we compute the ‘‘optimal revision’’ as the
actual earnings minus the prevailing analyst consensus
forecast prior to the management forecast, scaled by the
closing price at the end of the prior year, which is labeled
as AFE_PRE. We replace the dependent variable in Model
(1) with AFE_PRE to assess the optimal weights that ana-
lysts would place on the upper and lower bounds if their
revisions can perfectly predict actual earnings.
Empirical results
Descriptive statistics
Table 3 Panel A presents the descriptive statistics of the
variables used in our empirical models. The mean (median)
of Revision is À0.053% (0.039%) of the share price, suggest-
ing that analysts more often revise their forecasts upward
than downward after management range forecasts, but the
average magnitude of downward revisions exceeds that of
upward revisions (t = À8.67, untabulated). In contrast, the
magnitude of AFE_PRE (our measure of the optimal revi-
sion) is greater than that of Revision, suggesting that ana-
lysts on average only partially correct their initial
forecast errors. This partial correction, however, should
not affect the relative weights analysts place on the end-
points of management range forecasts, for the reasons we
explained earlier. The median of News_Mid is 0, consistent
with our results in Table 2 Panel A that the prevailing
analyst consensus forecasts is nearly symmetric around
the midpoint of management range forecasts. The mean
12
Our results are robust to using either the mean or the median analyst
forecasts for AF and Revision. Scaling these variables by the absolute value
of the forecasted earnings (instead of by stock price) or extending the
revision window to ±60 days also does not change our inferences.
13
We follow prior studies to price-de?ate our regression variables (e.g.,
Gong et al., 2011), but our results are robust to using the magnitude of
forecasted earnings as an alternative de?ator, or to de?ating the intercept
in the regression model.
14
Note that from Model (1) to Model (1M) is pure algebra rearrangement,
and hence the coef?cient b and parameter h should remain the same.
However, this equality and hence the relation between b and h implied
from the ratio of the regression coef?cients will no longer hold if we also
include an interaction term News_Mid  Width as in prior studies (e.g.,
Baginski, Hassell, & Wieland, 2011). To see this, consider the coef?cient b in
Model (1M) as analysts’ reaction to the midpoint of any range forecast.
However, once the interaction term News_Mid  Width is included in the
model, the coef?cient on News_Mid becomes analysts’ reaction to the
midpoint of range forecasts with a zero width.
54 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
Table 3
Descriptive statistics.
Variables N Mean Std. dev. 25% Median 75%
Panel A: summary statistics
Revision (%) 10,989 À0.053 0.644 À0.177 0.039 0.193
AFE_PRE (%) 10,989 À0.274 1.877 À0.532 0.058 0.462
News_Mid (%) 10,989 À0.048 0.642 À0.193 0.000 0.179
Width (%) 10,989 0.406 0.411 0.154 0.279 0.490
Bundle_Eanews (%) 9,062 0.082 0.340 0.000 0.062 0.180
Fq1 10,989 0.252 0.434 0.000 0.000 1.000
Fq2 10,989 0.247 0.431 0.000 0.000 0.000
Fq3 10,989 0.255 0.436 0.000 0.000 1.000
Dispersion 10,599 0.003 0.004 0.001 0.002 0.003
RetVol 10,983 0.024 0.013 0.015 0.021 0.030
D_LastActualClosertoUpper 7,617 0.626 0.484 0.000 1.000 1.000
D_WiderThanLast 7,660 0.521 0.450 0.000 1.000 1.000
D_MeetAF 9,730 0.787 0.409 1.000 1.000 1.000
D_GuideDown 10,989 0.276 0.447 0.000 0.000 1.000
Revision AFE_PRE News_Mid Width Bundle_Eanews Fq1 Fq2 Fq3 D_Dispersion D_Ret-Vol D_Last-Actual-
Closer-toUpper
D_Wider-Than-Last D_Meet-AF D_Guide-Down
Panel B: correlation matrix
Revision 1.000
AFE_PRE 0.517 1.000
News_Mid 0.785 0.390 1.000
Width À0.201 À0.156 À0.114 1.000
Bundle_Eanews 0.421 0.318 0.308 0.038 1.000
Fq1 À0.090 À0.075 À0.075 0.115 À0.025 1.000
Fq2 0.034 À0.022 0.042 0.096 0.012 À0.332 1.000
Fq3 0.020 0.019 0.012 À0.018 0.005 À0.339 À0.335 1.000
D_Dispersion À0.089 À0.097 À0.045 0.417 0.011 0.145 0.029 À0.033 1.000
D_RetVol À0.088 À0.091 À0.032 0.229 0.022 À0.006 À0.033 À0.008 0.222 1.000
D_LastActual-ClosertoUpper 0.128 0.124 0.061 À0.222 0.062 À0.091 À0.021 0.009 À0.146 À0.109 1.000
D_WiderThan-Last À0.125 À0.118 À0.047 0.276 À0.017 0.000 À0.005 0.013 0.124 0.170 À0.151 1.000
D_MeetAF 0.109 0.115 0.071 À0.119 0.157 À0.019 0.000 0.013 À0.074 À0.005 0.251 À0.071 1.000
D_GuideDown À0.489 À0.238 À0.603 0.001 À0.198 0.064 À0.067 À0.013 0.073 0.037 À0.049 0.022 À0.062 1.000
The sample includes 10,989 management range forecasts of annual earnings of ?scal years between 1996 and 2011. All continuous variables are winsorized at the 1st and 99th percentiles. Revision is the mean revision of all analysts that issue
forecasts both before and after a management forecast, de?ated by the stock price at the beginning of the year. AFE_PRE is the difference between the actual earnings and the median analyst earnings forecast prior to a management range forecast,
de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast minus the prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance
between the upper bound and the lower bound of a management range forecast, de?ated by the stock price at the beginning of the year. Bundle_Eanews is the actual earnings announced along with a management range forecast minus the median
analyst forecast for the actual earnings, de?atedby the stock price at the beginning of the year. Fq1(Fq2, Fq3) is an indicator variable set to one if a management forecast is issued inthe ?rst (second, third) ?scal quarter, andzero otherwise. Dispersion
is the standard deviation of analyst forecasts issued within 90 days before the management forecast announcement, de?ated by the stock price at the beginning of the year. RetVol is the stock return volatility measured as the standard deviation of
daily stock returns from day À120 to day À1 relative to the management forecast date. D_LastActualClosertoUpper is an indicator variable set to one if the previous year’s actual earnings are closer to the upper bound of the management forecast
issued in the same quarter of the previous year, and zero otherwise. D_WiderThanLast is an indicator variable set to one if the current range forecast width is wider than the range width of the management forecast issued in the same quarter of the
previous year, and zero otherwise. D_MeetAF is an indicator variable set to one if a company’s actual earnings meet analysts’ consensus in the previous year, and zero otherwise. D_GuideDown is an indicator variable set to one if the upper bound of a
management range forecast is lower than the prevailing analyst consensus, and zero otherwise.
This table presents the Pearson pairwise correlation coef?cients. Correlations in bold are signi?cantly different from zero at the 1% level. All continuous variables are winsorized at the 1st and 99th percentiles.
Revision is the mean revision of all analysts that issue forecasts both before and after a management forecast, de?ated by the stock price at the beginning of the year. AFE_PRE is the difference between the actual
earnings and the median analyst earnings forecast prior to a management range forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast minus the
prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance between the upper bound and the lower bound of a management range forecast, de?ated by the
stock price at the beginning of the year. Bundle_Eanews is the actual earnings announced along with a management range forecast minus the median analyst forecast for the actual earnings, de?ated by the stock
price at the beginning of the year. Fq1(Fq2, Fq3) is an indicator variable set to one if a management forecast is issued in the ?rst (second, third) ?scal quarter, and zero otherwise. D_Dispersion is an indicator variable
set to one if Dispersion is higher than the median, and zero otherwise, where Dispersion is the standard deviation of analyst forecasts issued within 90 days before the management forecast announcement, de?ated
by the stock price at the beginning of the year. D_RetVol is an indicator variable set to one if RetVol is higher than the median, and zero otherwise, where RetVol is the stock return volatility measured as the standard
deviation of daily stock returns fromday À120 to day À1 relative to the management forecast date. D_LastActualClosertoUpper is an indicator variable set to one if the previous year’s actual earnings are closer to the
upper bound of the management forecast issued in the same quarter of the previous year, and zero otherwise. D_WiderThanLast is an indicator variable set to one if the current range forecast width is wider than the
range width of the management forecast issued in the same quarter of the previous year, and zero otherwise. D_MeetAF is an indicator variable set to one if a company’s actual earnings meet analysts’ consensus in
the previous year, and zero otherwise. D_GuideDown is an indicator variable set to one if the upper bound of a management range forecast is lower than the prevailing analyst consensus, and zero otherwise.
M
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4
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1
5
)
4
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–
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6
5
5
(median) Width is 0.406% (0.279%) of the share price. For
the 9062 management range forecasts that are bundled
with earnings announcements, the bundled earnings news
(Bundle_Eanews) has a mean (median) of 0.082% (0.062%).
Table 3 Panel B presents the univariate Pearson correla-
tions among the variables. Values in boldface are sig-
ni?cant at the 1% level. Revision is positively correlated
with News_Mid (q = 0.785), suggesting that management
forecasts affect analyst revisions (e.g., Cotter et al., 2006).
Upper Bound and Lower Bound are highly correlated
(q = 0.803 untabulated), which con?rms our concern of
multi-collinearity if both these variables are included in
the same regression. Width is only moderately correlated
with News_Mid (q = À0.114), thus mitigating multi-
collinearity when it is used in place of both Upper Bound
and Lower Bound.
Analysts’ weights on the upper and lower bounds of
management range forecasts (H1)
Table 4 presents our primary results. The standard
errors are robust and clustered by ?rm. In Column (1),
we follow prior literature and measure management fore-
cast news using the midpoint (News_Mid), which implicitly
forces analysts’ weights to be equal on the upper bound
and lower bound of management forecast ranges. Consis-
tent with prior literature, News_Mid is signi?cantly posi-
tive (t = 55.05), suggesting that analysts react strongly to
management forecast news. Note that the intercept in Col-
umn (1) is signi?cantly negative (t = À3.25), which implies
that analysts on average react negatively to the action of
management forecasts. This suggests that analysts would
revise forecasts downward even when the midpoint of a
management forecast coincides with their prevailing con-
sensus (i.e., News_Mid = 0), which contradicts the notion
that voluntary disclosure of con?rming forecasts is typical-
ly viewed positively because it reduces uncertainty about
future earnings (Clement et al., 2003), and is also inconsis-
tent with the prior ?ndings that investors and analysts on
average prefer more management disclosures (Bushee &
Noe, 2000; Lang & Lundholm, 1993).
15
Importantly, the negative intercept reverses to positive
once we allow analysts to place unequal weights on the
upper and lower bounds of management forecast ranges
by including forecast width (Width) in Model (1M), as the
intercept in Column (2) is signi?cantly positive (t = 8.00),
suggesting that analysts positively perceive managers’
action of providing forecasts, consistent with analysts
favoring more disclosure (Lang & Lundholm, 1993). There-
fore, the puzzling result in Column (1) is likely due to the
empirical design that fails to allow analysts to place
unequal weights on the upper and lower bounds of man-
agement range forecasts.
Results in Column (2) provide evidence that the weights
are indeed unequal. Recall that h is the hypothetical weight
that analysts place on the upper bound when revising fore-
casts. If analysts weigh the upper and lower bounds equal-
ly (h = 0.5), the coef?cient on Width divided by the
coef?cient on News_Mid, which is expected to equal
h À 0.5, should be statistically indifferent from zero. Con-
trary to this prediction, the estimated coef?cient ratio is
signi?cantly negative at À0.229 (t = À8.24), rejecting the
null hypothesis that analysts place equal weights on the
upper and lower bounds of management forecast ranges
when revising their own forecasts. Our regression coef?-
cients imply that analysts place 0.271 weight on the upper
bound of management forecasts, thus 0.729 (=1–0.271)
weight on the lower bound, when responding to range
forecasts.
16
Next in Columns (3) and (4), we follow Gong et al.
(2011) and include industry and year ?xed effects in our
Base Model and Model (1M), to account for industry-
speci?c effects and any temporal trend.
17
The inclusion of
?xed effects renders the intercept uninformative of analysts’
response to managers’ action of providing forecasts. The
coef?cient ratio in Column (4) implies that analysts place a
weight of 0.244 on the upper bound, signi?cantly less than
0.5 (t = À8.71), consistent with our hypothesis H1 that ana-
lysts respond to a management range forecast (a signal of
ambiguity) by overweighting the lower bound (treating
the worst scenario as more likely than the best scenario).
The strong and consistent evidence that analysts place
unequal weight on the upper and the lower bounds of man-
agement range forecasts is important to researchers, given
its sharp contrast from the implicit assumption of ‘‘equal
weights’’ from the conventional research design that uses
the midpoint to measure forecast news in studying analyst
reaction to management forecasts (e.g. Ajinkya et al., 2005;
Gong et al., 2011; Rogers & Stocken, 2005; Rogers & Van
Buskirk, 2013). To relax the ‘‘equal weight’’ assumption,
which is refuted by our evidence, future studies should at
least include Width in the analyst revision model to allow
analysts to place unequal weights on the endpoints of
management range forecasts.
We also emphasize and caution readers to distinguish
the ‘‘weight’’ from the ‘‘distance.’’ Analysts’ overweight on
the lower bound does not con?ict with our previous result
in Table 2 that analysts’ revised forecasts are actually ‘‘clo-
ser’’ to the upper bound (also see Ciconte et al., 2014).
Recall that the ‘‘weight’’ is the empirical sensitivity of ana-
lyst forecast revision to the forecast news conveyed from
management forecast endpoints. Therefore, even though
analyst forecast revision is more sensitive to the lower
bound of management range forecasts, analysts respond
positively to managers’ action of providing forecasts (evi-
denced by a positive intercept in Column (2)), resulting in
the revised forecasts actually above the midpoint.
Overall, the results in Table 4 provide strong evidence
that analysts place unequal weight on the upper and lower
15
The positive effect of the mere act of providing voluntary disclosure is
twofold. First, investors will only dismiss the belief that the ?rm is hiding
the worst news when they receive a disclosure, regardless of the content
(Grossman & Hart, 1980). Second, the disclosure itself reduces uncertainty
about the future (Clement et al., 2003).
16
Despite concerns of multi-collinearity, in an untabulated test, we
regress Revision on news measured from both the Upper Bound and Lower
Bound, and we continue to ?nd a positive intercept (t = 7.02) and h À 0.5
signi?cantly negative (t = À7.44).
17
For the same reason, we include industry and year ?xed effects in all
our remaining analyses.
56 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
bounds of management range forecasts, with signi?cantly
more weight placed on the lower bound than on the upper
bound, consistent with the prediction of H1.
Addressing concerns of management forecasts bundled with
earnings announcements
Because our dependent variable – analysts forecast
revision – can be affected also by any concurrent release
of information with management forecasts, we conduct a
battery of analyses to mitigate the impact of the most com-
mon concurrent information – bundled earnings news
(e.g., Rogers & Van Buskirk, 2013). The results are present-
ed in Table 5.
In Column (1), we directly control for the bundled earn-
ings news. The implied h is 0.197 and remains signi?cantly
less than 0.5 (t = À9.72). In Column(2), we exclude all ‘‘bun-
dled’’ management forecasts and retain only ‘‘stand-alone’’
forecasts, reducing the sample size to 1927. The implied h is
0.060 and remains signi?cantly less than 0.5 (t = À4.91). In
Column (3), we restrict the sample to only bundled fore-
casts, and the implied h is 0.217 and remains signi?cantly
less than 0.5 (t = À8.90). Next we separate forecasts bun-
dled with positive earnings news (Bundle_Eanews P0 in
Column (4)) from forecasts bundled with negative earnings
news (Bundle_Eanews < 0 in Column (5)). In both cases, the
implied h remains signi?cantly less than 0.5 (t = À7.85 and
À5.57). In Column (6), we follow the procedure described
in Rogers and Van Buskirk (2013) to calculate analysts’ pre-
dicted revision in response to bundled earnings news, and
measure management forecast news against this predicted
analysts’ revised forecasts. The implied h is 0.218 and
remains signi?cantly less than 0.5 (t = À3.15). However,
the sample size is substantially reduced due to the require-
ment of additional variables, limiting the testing power.
Therefore, we choose to directly control for bundled earn-
ings news in our remaining analyses.
Overall, our ?nding that analysts overweight the lower
bound of management forecasts is robust to a battery of
tests that mitigate the confounding effect of ‘‘bundled’’
earnings news.
Cross-sectional variations in analysts’ weights on
management forecast bounds (H2)
Results in Tables 3 and 4 suggest that, on average, ana-
lysts place more weight on the lower bound than on the
upper bound of management range forecasts. However,
we expect the degree of such unequal weight to differ
across subsamples. Speci?cally, if analysts’ overweight on
the lower bound is a result of following the ‘‘max–min’’
axiom of decision making behavior, then we expect their
overweight on the lower bound to be more pronounced
when uncertainty is higher, predicted in our H2. To exam-
ine this prediction, we re-estimate Model (1M), interacting
Width with different measures of uncertainty, in the fol-
lowing form.
18
Revision
i;t
¼ b
0
þ b
1
ðNews Mid
i;t
Þ þ b
2
Width
i;t
þ b
3
ðWidth
i;t
à X
i;t
Þ þ b
4
X
i;t
þ b
5
Bundle Eanews þe ð2Þ
where X is the variable that we expect to change analysts’
relative weights on the upper and the lower bounds of
management forecast ranges.
Table 4
Analysts’ weights on the upper and lower bounds of management range forecasts.
Revision
i;t
¼ a þ bðNews Mid
i;t
Þ þ bðh À 0:5Þ Ã Width
i;t
þ
Base Model Model (1M) Base Model Model (1M)
(1) (2) (3) (4)
Intercept À0.0002
***
0.001
***
À0.001 À0.001
(À3.25) (8.00) (À0.79) (À0.46)
News_Mid 0.788
***
0.775
***
0.785
***
0.771
***
(55.05) (55.06) (54.58) (54.38)
Width À0.177
***
À0.198
***
(À8.56) (À9.09)
h À 0.5 À0.229
***
À0.256
***
(t-stat) (À8.24) (À8.71)
Implied h 0.271
***
0.244
***
(t-stat) (9.75) (8.29)
Industry Fixed Effect No No Yes Yes
Year Fixed Effect No No Yes Yes
No of OBS 10,989 10,989 10,989 10,989
Adjusted R-Squared 61.6% 62.9% 62.5% 63.8%
This table presents results from OLS regressions of analyst forecast revisions on management forecast news and range widths. The sample includes 10,989
management range forecasts of annual earnings of ?scal years between 1996 and 2011. Revision is the mean revision of all analysts that issue forecasts both
before and after a management forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast
minus the prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance between the upper bound and
the lower bound of a management range forecast, de?ated by the stock price at the beginning of the year. t-Stats are based on standard errors clustered on
the ?rm level. h is the hypothetical weight that analysts place on the upper bound of management forecast ranges when revising their own forecasts. t-Stats
about h are calculated using the delta method (Rao, 1965).
?
Signi?cance level lower than 10%.
??
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
18
Although we do not expect the coef?cient on News_Mid to vary with X,
nevertheless, in untabulated tests, we also control for the interaction of X
with News_Mid and obtain qualitatively similar results.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 57
If analysts increase (decrease) their relative overweight
on the lower bound when X takes a higher value, we expect
the coef?cient on the corresponding interaction term to be
signi?cantly negative (positive).
19
For ease of interpreting
the results, we transform continuous variables into indicator
variables that are set to one for observations above sample
medians and zero otherwise. Hence the coef?cient on Width
in Model (2) is (b
2
+ b
3
X), which should be equal to
b ? (h À 0.5) as in Model (1M). Drawing from Model (1M),
the coef?cient ratio of (b
2
+ b
3
X)/b
1
in Model (2) should be
equal to h À 0.5, which allows h to be a function of X. For
observations where X = 0, the implied h
X=0
= b
2
/b
1
+ 0.5,
whereas for observations where X = 1, the implied h
X=1
=
(b
2
+ b
3
)/b
1
+ 0.5; the difference in the implied Dh = h
X=1
À
h
X=0
= b
3
/b
1
.
The results are reported in Table 6. In Column (1), we
test our H2a and examine whether analysts increase their
weight on the lower bound of forecasts issued in earlier
quarters, indicated by three dummy variables for the ?rst,
second, and third quarter (Fq1, Fq2, and Fq3), using the
fourth quarter as the benchmark. The coef?cient on the
interaction term Width ? Fq1 is negative and signi?cant at
À0.144 (t = À3.03), suggesting that analysts overweight
the lower bound to a larger extent in the ?rst quarter than
in the fourth quarter. Using the coef?cients to infer ana-
lysts’ weight on the lower bound (h), analysts add another
0.204 weight on the lower bound in the ?rst quarter than
in the fourth quarter. Because earlier management fore-
casts tend to contain higher uncertainty, this ?nding is
consistent with analysts shifting more weight to the worse
scenario as they face more uncertainty, which is consistent
with the ‘‘max–min’’ axiom (Gilboa & Schmeidler, 1989).
The interaction terms Width ? Fq2 and Width ? Fq3 are
negative but not signi?cant (t = À1.26 and À0.36), but
the standalone term Width is signi?cantly negative
(t = À4.19), suggesting that analysts still overweight the
lower bound even when management forecast is issued
in the fourth quarter, when uncertainty about the annual
earnings is the lowest.
20
In Column (2), we test our H2b and examine whether
analysts increase their weight on the lower bound of fore-
casts with wider ranges (D_WideRange is set to one if Width
is larger than the median). Consistent with this prediction,
the coef?cient on the interaction term Width ? X is nega-
tive and signi?cant at À0.110 (t = À2.02). The coef?cients
imply that analysts shift additional weight of 0.155 from
the upper bound to the lower bound when management
range forecasts are wider, even though the weight is
already signi?cantly less than 0.5 on the upper bound
(t = À2.31) for narrow ranges. This ?nding is consistent
with analysts viewing wider range forecasts as more
uncertain and shift even more weight on the lower bound,
consistent with the ‘‘max–min’’ axiom (Gilboa &
Schmeidler, 1989).
Both Columns (1) and (2) of Table 6 examine the uncer-
tainty conveyed by the properties of management fore-
casts, that is, the timing and the range width. Next we
examine whether uncertainty re?ected in the ?rm’s infor-
mation environment also affects analysts’ weight on the
endpoints of management range forecasts. We use analyst
forecast dispersion and return volatility as measures of
information uncertainty following prior literature (e.g.,
Feng & Koch, 2010; Chen et al., 2011) and report the results
in Columns (3) and (4). Consistent with our H2c and H2d,
we ?nd that analysts further reduce weights on the upper
bound when facing higher uncertainty as the interaction
terms are signi?cantly negative (t = À3.99 and À4.53).
Moreover, the coef?cient on Width remains signi?cantly
negative (t = À3.41 and À1.85), suggesting that even when
the information environment contains relatively little
uncertainty, analysts still view range forecasts from man-
agers as ambiguous signals and overweight the lower
bound, consistent with the ‘‘max–min’’ axiom.
While analysts shift more ‘‘weight’’ to the lower bound
as uncertainty increases, their revised forecasts do not nec-
essarily get ‘‘closer’’ to the lower bound, echoing our earlier
caveat on the distinction between the ‘‘weight’’ and the
‘‘distance’’.
21
The max–min axiom applies when a decision-
maker faces a set of possibility distributions and makes
choices by weighing different possible scenarios (e.g., weigh-
ing the upper and lower bounds of management range fore-
casts) (Epstein & Schneider, 2008), but the resulting decision
might not necessarily be pessimistic. Consistent with this, in
Table 6, while we ?nd that analysts overweight the lower
bound more when uncertainty is higher, most of the
stand-alone indicators of high uncertainty (Fq1, Fq2, and
Fq3 in Column (1), and X in Columns (2) to (4)) are sig-
ni?cantly positive (e.g., t = 2.90 for Fq1 in Column (1)), which
echoes our ?nding of a positive intercept in Model (1M) and
suggests that analysts actually value managers’ provision of
forecasts even more in face of more uncertainty. Therefore,
our results suggest that the max–min axiom applies only to
the ‘‘weight’’ that analysts choose but not to the ‘‘distance’’
of their revised forecasts from managers’ range forecasts.
In summary, the results in Table 6 are consistent with
our H2 cross-sectional predictions of the ‘‘max–min’’
axiom. We ?nd that analysts shift more ‘‘weight’’ to the
lower bound when uncertainty is higher.
Are analysts ‘‘Bayesian’’ and learn from the past?
We next investigate whether analysts are ‘‘Bayesian’’ in
the sense that they adjust their weights on management
forecast bounds based on past experience. Two reasons
19
Note that we are comparing the weight analysts put on the lower
bound in the cross-sectional analyses, although on average analysts still
place less weight on the upper bound than on the lower bound (i.e., h < 0.5)
in most cases.
20
These results are similar in the subsample of bundled forecasts.
However, all three interaction terms (Width ? Fq1, Width ? Fq2, and
Width ? Fq3) are insigni?cant in the subsample of unbundled forecasts
(untabulated t-stats = À0.55, 0.87, and 0.96, respectively). One possible
explanation is the smaller sample size (only 1927 unbundled compared
with 9062 bundled). Another explanation is that the timing of unbundled
forecasts is unpredictable by their nature, regardless of when they are
provided. Hence, analysts’ weights do not vary signi?cantly with their
forecast timing.
21
Indeed, analysts’ revised forecasts, on average, shift ‘‘closer’’ to the
upper bound (see Table 2). The ‘‘distance’’ of analysts’ revised forecasts to
managers’ range forecasts depend on both their ‘‘weight’’ on the end-points
and their reaction to managers’ provision of the range forecasts.
58 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
motivate this analysis. First, many managers provide earn-
ings forecasts regularly (e.g., Rogers, Skinner, & Van
Buskirk, 2009; Tang, 2013), thus providing the opportunity
for analysts to learn from past management forecasts
(Hilary & Shen, 2013). Second, prior literature also provides
evidence consistent with analysts facing parameter uncer-
tainty and learning rationally about the parameters over
time (Markov & Tamayo, 2006). Table 7 presents the
results from this analysis.
First, if actual earnings were closer to the upper bound
than to the lower bound of management forecast in the
previous year (D_LastActualCloserToUpper = 1), a ‘‘Baye-
sian’’ analyst is likely to shift more weight from the lower
bound to the upper bound. To ensure that the current man-
agement forecast is comparable to that in the previous
year, we require them to be issued in the same quarter,
which reduces the sample size to 7617. In Column (1),
we ?nd a marginally signi?cant and positive coef?cient
on the interaction term (t = 1.73), providing some evidence
that analysts place more weight on the range endpoint that
was previously proven to be more accurate. Importantly,
the coef?cients continue to imply a weight of less than
0.5 on the upper bound (0.170 + 0.113 = 0.283) even when
the actual earnings were closer to the upper bound in the
previous year, consistent with our main hypothesis.
Next, in Column (2), we examine whether analysts
compare the range width with past forecasts and adjust
their weights accordingly. If the current forecast is wider
than that in the same quarter in the previous year
(D_WiderThanLast = 1), we ?nd that analysts shift sig-
ni?cantly more weight from the upper bound to the lower
bound, as the interaction term is signi?cantly negative
(t = À7.95). This result shows that as uncertainty increases,
the weight on the lower bound increases. This is consistent
with the results in Table 6, where uncertainty is measured
in the cross section, whereas in Table 7 uncertainty is mea-
sured with respect to each ?rm’s own time series, both of
which are consistent with the max–min axiom.
Taken together, Columns (1) and (2) in Table 7 provide
evidence that analysts are Bayesian and learn from past
experience. While we ?nd some evidence that analysts
adjust their weights based on whether actual earnings
were closer to the upper or lower bound, we ?nd strong
evidence that their overweight on the lower bound is more
pronounced when the current forecast range is wider than
before, consistent with the ‘‘max–min’’ explanation.
22
Table 5
Accounting for earnings news bundled with management range forecasts.
Revision
i;t
¼ a þ bðNews Mid
i;t
Þ þ bðh À 0:5Þ Ã Width
i;t
þ c Bundle Earnews þe
All
management
forecasts
Stand-alone
management
forecasts
Bundled
management
forecasts
Bundled management
forecasts with positive
earnings news
Bundled management
forecasts with negative
earnings news
Bundled
management
forecasts
a
(1) (2) (3) (4) (5) (6)
Intercept À0.001 0.003
**
À0.001 À0.001 À0.001 0.003
***
(À0.57) (2.11) (À0.73) (À0.61) (À0.52) (7.94)
News_Mid 0.709
***
0.710
***
0.704
***
0.703
***
0.698
***
0.549
***
(45.83) (17.30) (40.04) (32.53) (24.26) (6.95)
Width À0.215
***
À0.312
***
À0.199
***
À0.175
***
À0.242
***
À0.155
***
(À10.35) (À5.53) (À9.42) (À8.02) (À6.08) (À3.03)
Bundle_Eanews 0.422
***
0.422
***
0.399
***
0.321
***
(15.81) (14.67) (10.82) (5.58)
h À 0.5 À0.303
***
À0.440
***
À0.283
***
À0.249
***
À0.346
***
À0.282
***
(t-stat) (À9.72) (À4.91) (À8.90) (À7.85) (À5.57) (À3.15)
Implied h 0.197
***
0.060 0.217
***
0.251
***
0.154
**
0.218
**
(t-stat) (6.30) (0.67) (6.81) (7.88) (2.47) (2.43)
Industry Fixed
Effect
Yes Yes Yes Yes Yes Yes
Year Fixed
Effect
Yes Yes Yes Yes Yes Yes
No of OBS 10,989 1,927 9,062 6,966 2,096 4,874
Adjusted R-
Squared
67.4% 57.7% 69.7% 65.5% 66.9% 55.9%
This table presents results from OLS regressions of analyst forecast revisions on management forecast news and range widths, controlling bundled earnings
announcement news. The sample includes 10,989 management range forecasts of annual earnings of ?scal years between 1996 and 2011, of which 9062
management forecasts are bundled with quarterly earnings announcements. Revision is the mean revision of all analysts that issue forecasts both before and
after a management forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast minus the
prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance between the upper bound and the lower
bound of a management range forecast, de?ated by the stock price at the beginning of the year. Bundle_Eanews is the actual earnings announced along with
a management range forecast minus the median analyst forecast for the actual earnings, de?ated by the stock price at the beginning of the year. t-Stats are
based on standard errors clustered on the ?rm level. h is the hypothetical weight that analysts place on the upper bound of management forecast ranges
when revising their own forecasts. t-Stats about h are calculated using the delta method (Rao, 1965).
?
Signi?cance level lower than 10%.
**
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
a
This column uses conditional expectations to calculate analyst forecast revisions and management forecast news, following the method described in
Rogers and Van Buskirk (2013).
22
In untabulated analysis, we ?nd the ‘‘Bayesian’’ results to be slightly
more signi?cant (slightly less signi?cant) in the subsample of bundled
(unbundled) forecasts, possibly due to a larger (smaller) sample size.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 59
Does ‘‘Lowballing’’ explain analysts’ overweight on the lower
bound?
Prior research suggests that analysts have incentives to
‘‘lowball’’ their forecasts so that managers could meet or
beat their forecasts more easily and possibly return the
favor with more private communication (Hilary & Hsu,
2013; Ke & Yu, 2006). However, analysts also want to avoid
issuing forecasts that are too gloomy because poor
expectations could hurt the ?rm’s stock price and anger
managers to limit the analysts’ access to management
(Brown, Call, Clement, & Sharp, 2013). It is possible that
management range forecasts offer the lower bound as an
apparent target for analysts to ‘‘lowball’’ their forecasts.
To evaluate this explanation, we examine whether ana-
lysts’ overweight on the lower bound becomes more pro-
nounced when ‘‘meeting and beating’’ analysts’ forecasts
is more important to managers, who therefore are more
Table 6
Cross-sectional analysis of analysts’ weights on range forecast bounds.
Revision
i;t
¼ b
0
þ b
1
ðNews Mid
i;t
Þ þ b
2
Width
i;t
þ b
3
ðWidth
i;t
à X
i;t
Þ þ b
4
X
i;t
þ b
5
Bundle Eanews
i;t
þe
X As D_WideRange D_Dispersion D_RetVol
(1) (2) (3) (4)
Intercept À0.001 À0.001 À0.001 À0.001
(À0.78) (À0.74) (À0.77) (À0.90)
News_Mid 0.706
***
0.709
***
0.716
***
0.708
***
(45.43) (45.83) (47.34) (46.11)
Width À0.147
***
À0.115
**
À0.098
***
À0.066
*
(À4.19) (À2.32) (À3.41) (À1.85)
Width ? Fq1 À0.144
***
(À3.03)
Width ? Fq2 À0.062
(À1.26)
Width ? Fq3 À0.018
(À0.36)
Width ? X À0.110
**
À0.139
***
À0.182
***
(À2.02) (À3.99) (À4.53)
Fq1 0.001
***
(2.90)
Fq2 0.0004
**
(2.43)
Fq3 0.0002
(1.07)
X 0.0003
*
0.0003
**
0.0003
**
(1.71) (2.29) (2.23)
Bundle_Eanews 0.420
***
0.421
***
0.412
***
0.420
***
(15.80) (15.77) (14.97) (15.74)
Implied h When X = 0 0.292
***
0.338
***
0.363
***
0.407
***
(t-stat) (5.78) (4.84) (8.98) (8.05)
h À 0.5 When X = 0 À0.208
***
À0.162
**
À0.137
***
À0.093
*
(t-stat) (À4.13) (À2.31) (À3.37) (À1.84)
Difference in Implied h À0.204
*** a
À0.155
**
À0.195
***
À0.258
***
(t-stat) (À3.00) (À2.02) (À3.96) (À4.50)
Industry Fixed Effect Yes Yes Yes Yes
Year Fixed Effect Yes Yes Yes Yes
No of OBS 10,989 10,989 10,599 10,983
Adjusted R-Squared 67.6% 67.4% 68.3% 67.7%
This table reports results from OLS regressions to examine the cross-sectional variations in the weight analysts place on the upper and lower bounds of
management range forecasts. The sample includes 10,989 management range forecasts of annual earnings of ?scal years between 1996 and 2011. The
actual sample size varies due to the unavailability of independent variables. The dependent variable is Revision. Revision is the mean revision of all analysts
that issue forecasts both before and after a management forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a
management range forecast minus the prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance
between the upper bound and the lower bound of a management range forecast, de?ated by the stock price at the beginning of the year. Fq1(Fq2, Fq3) is an
indicator variable set to one if a management forecast is issued in the ?rst (second, third) ?scal quarter, and zero otherwise. D_WideRange is an indicator
variable set to one if the width of management forecast range is higher than the sample median, and zero otherwise. D_Dispersion is an indicator variable set
to one if Dispersion is higher than the median, and zero otherwise, where Dispersion is the standard deviation of analyst forecasts issued within 90 days
before the management forecast announcement, de?ated by the stock price at the beginning of the year. D_RetVol is an indicator variable set to one if RetVol
is higher than the median, and zero otherwise, where RetVol is the stock return volatility measured as the standard deviation of daily stock returns from day
À120 to day À1 relative to the management forecast date. Bundle_Eanews is the actual earnings announced along with a management range forecast minus
the median analyst forecast for the actual earnings, de?ated by the stock price at the beginning of the year. t-Stats are based on standard errors clustered on
the ?rm level. h is the hypothetical weight that analysts place on the upper bound of management forecast ranges when revising their own forecasts. t-Stats
about h are calculated using the delta method (Rao, 1965).
*
Signi?cance level lower than 10%.
**
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
a
The difference in implied h in this case is between Fq1 and Fq4.
60 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
likely to favor analysts issuing ‘‘low ball’’ forecasts (Hilary
& Hsu, 2013). Prior literature suggests that managers have
stronger incentives to meet and beat analyst forecasts if
they have done so in the recent past (Kross et al., 2011).
Therefore, if the actual earnings met or beat analyst con-
sensus forecasts in the previous year (D_MeetAF = 1), we
would expect analysts to overweight the lower bound to
a greater extent if ‘‘low balling’’ is the primary reason for
them to overweight the lower bound. We report the results
in Column (3) of Table 7 and the interaction term is insig-
ni?cant (t = 0.13).
23
Hence, we do not ?nd evidence that
they overweight the lower bound more when the incentive
to ‘‘low ball’’ forecasts is stronger.
Related to analysts’ incentives to ‘‘lowball’’ their fore-
casts, it has been documented that managers often use
earnings forecasts to ‘‘walk down’’ analyst forecasts (e.g.,
Cotter et al., 2006; Matsumoto, 2002). To examine whether
our result of analysts’ overweight on the lower bound is
driven by managers ‘‘walking down’’ analyst expectation,
we de?ne a dummy variable for ‘‘guide-down’’ guidance
(D_GuideDown), which is set equal to one if the entire
range of management forecasts falls below the prevailing
analyst consensus, and zero otherwise.
24
If our result is dri-
ven by managers’ guiding down analyst forecasts, then we
would expect the overweight on the lower bound to be more
pronounced for ‘‘guide-down’’ forecasts and hence the inter-
action term of D_Guidedown ? Width should be negative. The
result, reported in Column (4) in Table 7, shows that this
interaction term is insigni?cant (t = À0.85). Therefore, we
do not ?nd evidence that analysts’ overweight on the lower
Table 7
Additional cross-sectional analysis of analysts’ weights on forecast bounds.
Revision
i;t
¼ b
0
þ b
1
ðNews Mid
i;t
Þ þ b
2
Width
i;t
þ b
3
ðWidth
i;t
à X
i;t
Þ þ b
4
X
i;t
þ b
5
Bundle Eanews
i;t
þe
X As Are analysts ‘‘Bayesian’’? Is ‘‘Lowballing’’ the explanation?
D_LastActualCloser-toUpper D_WiderThanLast D_MeetAF D_GuideDown
(1) (2) (3) (4)
Intercept À0.001
**
À0.003
***
À0.001 À0.001
(À2.54) (À5.23) (À0.81) (À0.50)
News_Mid 0.724
***
0.726
***
0.709
***
0.682
***
(36.51) (38.13) (43.85) (33.66)
Width À0.239
***
0.062
*
À0.215
***
À0.209
***
(À7.60) (1.79) (À4.88) (À9.16)
Width ? X 0.082
*
À0.323
***
0.006 À0.037
(1.73) (À7.95) (0.13) (À0.85)
X 0.0001 0.001
***
0.0001 À0.0004
***
(0.53) (4.06) (0.71) (À2.68)
Bundle_Eanews 0.387
***
0.387 0.418
***
0.422
***
(12.29) (12.26) (14.55) (15.86)
Implied h When X = 0 0.170
***
0.586
***
0.197
***
0.193
***
(t-stat) (3.75) (12.21) (3.09) (5.57)
h À 0.5 When X = 0 À0.330
***
0.086
*
À0.303
***
À0.307
***
(t-stat) (À7.31) (1.79) (À4.76) (À8.84)
Difference in Implied h 0.113
*
À0.445
***
0.009 À0.054
(t-stat) (1.73) (À7.64) (0.13) (À0.85)
Industry Fixed Effect Yes Yes Yes Yes
Year Fixed Effect Yes Yes Yes Yes
No of OBS 7,617 7,660 9,730 10,989
Adjusted R-Squared 68.0% 68.7% 67.8% 67.5%
This table reports results from OLS regressions to examine: (a) whether analysts are ‘‘Bayesian’’ and learn from their past experience, and (b) whether
analysts’ overweight on the lower bound of management range forecast can be explained by their incentives of ‘‘lowballing.’’ The sample is based on 10,989
management range forecasts of annual earnings between 1996 and 2011. The actual sample size varies due to the unavailability of independent variables.
The dependent variable is Revision. Revision is the mean revision of all analysts that issue forecasts both before and after a management forecast, de?ated by
the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast minus the prevailing consensus analyst forecast,
de?ated by the stock price at the beginning of the year. Width is the distance between the upper bound and the lower bound of a management range
forecast, de?ated by the stock price at the beginning of the year. D_LastActualClosertoUpper is an indicator variable set to one if the previous year’s actual
earnings are closer to the upper bound of the management forecast issued in the same quarter of the previous year, and zero otherwise. D_WiderThanLast is
an indicator variable set to one if the current range forecast width is wider than the range width of the management forecast issued in the same quarter of
the previous year, and zero otherwise. D_MeetAF is an indicator variable set to one if a company’s actual earnings meet analysts’ consensus in the previous
year, and zero otherwise. D_GuideDown is an indicator variable set to one if the upper bound of a management range forecast is lower than the prevailing
analyst consensus, and zero otherwise. Bundle_Eanews is the actual earnings announced along with a management range forecast minus the median analyst
forecast for the actual earnings, de?ated by the stock price at the beginning of the year. t-Stats are based on standard errors clustered on the ?rm level. h is
the hypothetical weight that analysts place on the upper bound of management forecast ranges when revising forecasts. t-Stats about h are calculated using
the delta method (Rao, 1965).
*
Signi?cance level lower than 10%.
**
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
23
The interaction remains insigni?cant in both the bundled and unbun-
dled subsamples (t-stats = À0.01 and 0.23).
24
Our results remain qualitatively the same if we de?ne D_GuideDown as
one if the midpoint of the range forecast (rather than the entire range) is
below the prevailing analyst consensus forecast, and zero otherwise.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 61
bound is more pronounced when management forecasts
‘‘walk down’’ analyst expectations. Note that the coef?cient
on Width remains signi?cantly negative (t = À9.16), suggest-
ing that even if management forecasts do not ‘‘walk down’’
analyst expectations, analysts still overweight the lower
bound as h is signi?cantly less than 0.5 (t = À8.84).
We conduct several additional analyses (untabulated)
regarding ‘‘guide-down’’ forecasts and we ?nd mixed
results, suggesting that ‘‘low-balling’’ at best only partially
explains analysts’ over-weight on the lower bound of man-
agers’ range forecasts. First, we ?nd that the coef?cient on
Width ? D_GuideDown becomes signi?cantly negative
(marginally positive) in the subsample of bundled (unbun-
dled) forecasts with a t-stat of À2.37 (1.88), suggesting that
‘‘lowballing’’ partially explains analysts’ overweight on the
lower bound for bundled forecasts, but not for unbundled
forecasts. Second, for the subset of updated forecasts, we
de?ne ‘‘D_GuideDown’’ by comparing the current manage-
ment forecast with the previous forecast (using either the
midpoint or the upper or the lower bound for comparison),
and we ?nd the interaction term to be signi?cantly
negative (t-stats = À4.40, À4.95, and À4.54 respectively),
consistent with analysts overweighting the lower bound
for downwardly revised forecasts. Finally, when we de?ne
‘‘D_GuideDown’’ by requiring only the lower bound to be
below analysts’ preexisting consensus, we ?nd the interac-
tion to be signi?cantly positive (t-stat = 3.36), inconsistent
with ‘‘lowballing’’ explanation. Across all these speci?ca-
tions, the Width term remains signi?cantly negative (t-stat
ranging from À2.45 to À7.65), suggesting that analysts’
overweight on the lower bound of managers’ forecasts can-
not be fully explained by analysts’ incentives to ‘‘lowball’’
their forecasts.
To summarize, in Table 7 Columns (3) and (4), we do
not ?nd evidence that analysts’ overweight on the lower
bound of management range forecasts is more pronounced
when they have stronger incentives to ‘‘lowball’’ their fore-
casts, proxied by recent success of managers meeting or
beating analyst forecasts and by managers’ explicit
‘‘guide-down’’ forecasts. These results suggest that our
?nding of analysts’ overweight on the lower bound of man-
agement range forecasts is distinct from the documented
phenomena of analysts ‘‘lowballing’’ their forecasts and
managers’ ‘‘walking down’’ analyst expectations (e.g.,
Cotter et al., 2006; Hilary & Hsu, 2013; Ke & Yu, 2006;
Matsumoto, 2002). While these phenomena focus on the
‘‘distance’’ of analysts’ forecasts to management forecasts
or to actual earnings, our focus is on the ‘‘weight’’ of ana-
lyst forecast revision on the upper and lower bounds of
management range forecasts.
Table 8
Optimal weights on management range forecast bounds.
AFE PRE
i;t
¼ a þ bðNews Mid
i;t
Þ þ bðh À 0:5Þ Ã Width
i;t
þ cBundle Eanews
i;t
þe
All
management
forecasts
All
management
forecasts
Bundled
management
forecasts
Bundled
management
forecasts
Bundled management
forecasts with positive
earnings news
Bundled management
forecasts with negative
earnings news
(1) (2) (3) (4) (5) (6)
Intercept À0.001
**
À0.0004 À0.001
***
À0.002 À0.0002 À0.009
(À2.56) (À0.08) (À2.70) (À0.44) (À0.05) (À0.67)
News_Mid 0.889
***
0.867
***
0.826
***
0.819
***
0.890
***
0.711
***
(15.75) (16.07) (13.64) (14.24) (12.49) (7.37)
Width À0.592
***
À0.722
***
À0.573
***
À0.680
***
À0.502
***
À0.917
***
(À5.89) (À7.29) (À5.58) (À6.56) (À4.17) (À6.07)
Bundle_Eanews 1.391
***
1.250
***
1.426
***
1.293
***
1.065
***
1.337
***
(13.45) (12.48) (13.40) (12.46) (7.13) (6.01)
h À 0.5 À0.666
***
À0.832
***
À0.694
***
À0.830
***
À0.564
***
À1.290
***
(t-stat) (À5.31) (À6.27) (À5.02) (À5.76) (À3.82) (À4.72)
Implied h À0.166 À0.332
**
À0.194 À0.330
**
À0.064 À0.790
***
(t-stat) (À1.32) (À2.50) (À1.40) (À2.29) (À0.43) (À2.89)
Industry Fixed
Effect
No Yes No Yes Yes Yes
Year Fixed
Effect
No Yes No Yes Yes Yes
No of OBS 10,989 10,989 9,062 9,062 6,966 2,096
Adjusted R-
Squared
21.2% 26.3% 21.7% 26.8% 20.3% 27.6%
This table reports results from OLS regressions to examine the optimal weights on the upper and lower bounds of management range forecasts, assuming
that analysts possess perfect foresight of actual earnings. The full sample includes 10,989 management range forecasts of annual earnings of ?scal years
between 1996 and 2011. The actual sample size varies due to the unavailability of independent variables. The dependent variable is AFE_PRE, which re?ects
the optimal revision assuming perfect foresight of actual earnings. AFE_PRE is the difference between the actual earnings and the median analyst earnings
forecast prior to a management range forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range
forecast minus the prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance between the upper
bound and the lower bound of a management range forecast, de?ated by the stock price at the beginning of the year. Bundle_Eanews is the actual earnings
announced along with a management range forecast minus the median analyst forecast for the actual earnings, de?ated by the stock price at the beginning
of the year. t-Stats are based on standard errors clustered on the ?rm level. h is the hypothetical weight that the optimal analyst forecast revisions should
place on the upper bound of management forecast ranges. t-Stats about h are calculated using the delta method (Rao, 1965).
?
Signi?cance level lower than 10%.
**
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
62 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
Optimal weights on management forecast bounds
So far we have documented strong and robust evi-
dence that analysts place signi?cantly more weight on
the lower bound of management range forecasts and that
such overweight on the lower bound is stronger when
uncertainty is higher. However, it is unclear whether
overweighting the lower bound of management range
forecasts leads to more accurate forecast revisions. To
investigate this, we estimate the ‘‘optimal weights’’ on
the upper and lower bounds of management forecast
ranges assuming perfect foresight of the actual reported
earnings is available to analysts. Therefore, we replace
the dependent variable in the previous models with
AFE_PRE, measured as the actual earnings minus the con-
sensus analyst forecast prior to the management forecast,
de?ated by the beginning stock price. If analysts could
forecast earnings accurately with perfect foresight, then
the optimal weight they place on the lower bound should
be consistent with the h implied from the AFE_PRE regres-
sion reported in Table 8. We admit that analysts have
imperfect information about actual reported earnings;
hence we do not expect analysts’ weights in Table 4 to
be perfectly aligned with the ‘‘optimal weights’’ in Table 8.
The purpose of this analysis is rather to answer the fol-
lowing question: compared with placing equal weights
on the upper and lower bounds of management range
forecasts, as implied in the extant research, is analysts’
overweight on the lower bound qualitatively consistent
with the optimal weight implied from actual reported
earnings? If so, we expect the implied h in the AFE_PRE
regression to be signi?cantly less than 0.5.
Table 8 reports the results on ‘‘optimal weights’’ in the
same format as in Table 5, which accounts for bundled
earnings news. Across all speci?cations, the ‘‘optimal
weight’’ on the upper bound implied from actual earnings
is signi?cantly less than 0.5 with t-stats ranging from
À3.82 to À6.27, thus rejecting the null hypothesis that
equal weights on the upper and lower bounds of manage-
ment range forecasts should be the optimal weights, as
implicitly assumed in the existing research design in
empirical accounting literature.
One caveat exists about the ‘‘optimal weight’’. Although
we ?nd it to be ‘‘optimal’’ to overweigh the lower bound,
which is consistent with analysts’ weighting, analysts’
behavior is more consistent with the ‘‘max–min’’ axiom
than with them anticipating the ‘‘optimal weight’’ for
two reasons. First, while analysts shift more weight to
the lower bound for range forecasts that are issued earlier
or that have wider ranges, we ?nd that the ‘‘optimal
weight’’ does not behave in such an ‘‘ambiguity-averse’’
manner (p-value >0.10, untabulated). Second, if analysts
base their weight on their rational anticipation of the opti-
mal weight, there is no clear prediction as to how analysts’
‘‘weight’’ would vary with uncertainty, which we ?nd a
systematic correlation in Table 6. Third, while analysts
overweight the lower bound, the magnitude of their over-
weighting, still appears too small (implied h appears too
large) compared with the ‘‘optimal weight’’. If they antici-
pate the ‘‘optimal weight’’, they should overweight the
lower bound much more heavily.
In summary, using the actual reported earnings to com-
pute ‘‘optimal revisions’’, we ?nd evidence that the ‘‘opti-
mal weight’’ is also signi?cantly higher on the lower
bound. Therefore, even though as a result of their ambi-
guity-averse behavior, analysts’ overweighting on the low-
er bound of management range forecasts indeed leads to
more accurate revisions than if they place equal weights
on management forecast bounds.
Additional tests and robustness checks
Throughout the paper, we use the revision in analysts’
consensus forecasts, because we are interested in whether
the average analyst places equal weights on the upper and
lower bounds of management range forecasts. In unt-
abulated tests, we use individual analyst forecast revisions
so that the benchmark for each analyst’s revision is his or
her own forecast prior to management forecasts. The ana-
lyst-level design results in a sample of 22,407 unique ana-
lyst revisions. Using this sample, we continue to ?nd that
individual analysts’ weight on the lower bound signi?cant-
ly exceeds 0.5 (untabulated t-stat = 7.03), with no sig-
ni?cant difference in the weighting between analysts
whose preexisting forecasts are above the midpoint of
management range forecasts and those below the mid-
point (untabulated t-stat = 1.28).
25
Moreover, when we
alternatively measure revision as the highest or the lowest
analyst forecast minus the preexisting consensus, we again
obtain similar result that analysts’ weight on the lower
bound is signi?cantly more than 0.5 (t-stats = 3.94 and
12.60 respectively).
26
Another possible explanation for analysts to overweight
one endpoint over another is that they might place more
weight simply on the bound that is closer to their preexist-
ing consensus, because psychology research suggests that
people tend to interpret information in a biased way that
con?rms their existing expectations, so-called ‘‘con?rma-
tion bias’’ (e.g., Lord, Ross, & Lepper, 1979). We investigate
this explanation by estimating analysts’ weight on the low-
er bound separately for forecasts that are above the preex-
isting consensus (where the lower bound is closer to
current expectation) and for forecasts that are below the
preexisting consensus (where the upper bound is closer
to current expectation). In both cases, we continue to ?nd
that analysts’ weight on the lower bound is signi?cantly
higher than 0.5 (untabulated t-stats = 8.13 and 6.39
respectively). We extend this analysis by partitioning the
sample into four mutually exclusive cases, depending on
whether the preexisting consensus is: (a) less than or equal
to the lower bound of managers’ range forecast, (b) greater
25
To investigate whether analysts with later preexisting forecasts have
less stale benchmarks and are more likely to herd with other analysts, we
partition the sample by the median number of lead days from analysts’
preexisting forecasts to the release of management forecasts (14 days). In
both samples we ?nd similar evidence that analysts overweight the lower
bound (untabulated t-stats = 8.20 and 7.45 for earlier and later analysts,
respectively).
26
As an additional robustness check, we follow Gu and Wu (2003) and
include the skewness of earnings to account for the possibility that analysts
may aim to forecast the median rather than the mean of earnings. Our
result from this analysis is qualitatively the same as our main result.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 63
than the lower bound but less than or equal to the mid-
point of managers’ range forecast, (c) greater than the mid-
point but less than or equal to the upper bound of
managers’ range forecast, or (d) greater than the upper
bound of managers’ range forecast. Across all cases, we
continue to ?nd that analysts signi?cantly overweight
the lower bound (untabulated t-stats = 3.60, 2.90, 2.75,
and 2.19, respectively).
Next, we examine whether the weighting of analyst
revision is different when responding to ?rms issuing only
a single annual forecast versus to those issuing multiple
forecasts. Tang et al. (2014) document an increasingly large
number of ?rms that issue multiple annual forecasts with-
in the year. To the extent that an updated forecast might
offer more information on how to weight the upper and
lower bounds to analysts, we partition the sample into
three groups: (a) ?rm-years with only a single annual fore-
cast, (b) initial forecasts of those with multiple forecasts,
and (c) forecast updates. Across all three cases, we contin-
ue to ?nd that analysts put signi?cantly more weight on
the lower bound (untabulated t-stats = 3.19, 5.25, and
7.46, respectively).
Finally, we assess whether macro-economic conditions
play a role in analysts’ weights on management forecast
bounds. Following NBER’s de?nition of recessions, we ?nd
that analysts’ weight on the upper bound is lower during
recessions (h = 0.098) than during expansions (h = 0.308),
although both are signi?cantly less than 0.5 (t-
stats = À7.59 and À5.05 respectively). To the extent that
uncertainty tends to be higher during recessions, this ?nd-
ing is consistent with our H2 that heightened uncertainty
exacerbates analysts’ overweight on the lower bound.
Conclusion
Range forecasts have evolved to be the most common
form of management forecasts. Most prior studies use
the midpoint to evaluate analyst reaction to range fore-
casts, implicitly assuming that analysts place equal
weights on the upper and lower bounds of management
range forecasts. In this study, we relax this restrictive
assumption and ?nd strong empirical evidence of unequal
weights: analysts place signi?cantly more weight on the
lower bound than on the upper bound of management
range forecasts. Moreover, analysts’ overweight on the
lower bound is more pronounced when ambiguity is high-
er, consistent with the ‘‘max–min’’ axiom that decision-
makers facing ambiguity tend to assign higher probability
to the worst-case scenario.
Our results are robust to a host of tests controlling for
‘‘bundled’’ earnings news (Rogers & Van Buskirk, 2013)
and are distinct from the documented phenomena of ana-
lysts ‘‘lowballing’’ their forecasts or managers ‘‘walking
down’’ analyst expectations (Cotter et al., 2006). Analysts
also appear to be ‘‘Bayesian’’ and overweight the lower
bound to a greater extent when facing range forecasts that
are wider than previously observed. Additional analyses
show that ‘‘optimal revisions’’ with perfect foresight of
actual earnings also overweight the lower bound, suggest-
ing that analysts’ overweight on the lower bound of
management range forecasts facilitates accurate forecast-
ing compared with equal weighting on both endpoints of
management range forecasts.
Our study is of interest to managers that issue range
forecasts, to investors and analysts who use range fore-
casts, and to the growing literature on expectation man-
agement that examines analyst reactions to management
forecasts. Building upon analysts’ unequal weights placed
on the upper and lower bounds of management range fore-
casts, future studies can further explore whether the accu-
racy and credibility of management range forecasts can
affect analysts’ unequal weights on the forecast bounds.
Another promising avenue for future research is to exam-
ine the range of analyst forecasts and to explore its interac-
tion with the range of management forecasts.
Appendix A. Adapting Model (1M) to consider three
points of the range forecasts
In this appendix, we illustrate an alternative model, in
which analysts choose to allocate their weights on three
points of the management range forecasts – the upper
bound, the lower bound, and the midpoint. Assume that
h
1
and h
2
are analysts’ weights on the upper and lower
bounds respectively, then the weight on the midpoint is
(1 À h
1
À h
2
).
Following the derivation in the paper, Model (1) can be
revised as follows, in which we now allow the weight on
the mid-point to be non-zero while still allowing the
weights on the upper and lower bounds to differ:
Revision ¼ a þ b½h
1
à Upper Bound þ h
2
à Lower Bound þ ð1 À h
1
À h
2
Þ
à Mid-Point À AF? þe ðA1Þ
Subscripts are suppressed for brevity and all variables
are de?ned as the same in original Model (1), with the
additional Mid-Point equals the midpoint of management
range forecasts.
Now consider the following:
Upper Bound ¼ Mid-Point þ1=2 Width ðA2Þ
Lower Bound ¼ Mid-Point À1=2 Width ðA3Þ
Substitute (A2) and (A3) into (A1) and we arrive at the
following model:
Revision
¼ a þ b½h
1
à ðMid-Point þ1=2 WidthÞ
þ h
2
à ðMid-Point À1=2 WidthÞ
þ ð1 À h
1
À h
2
Þ Ã Mid-Point À AF?
¼ a þ b½Mid-Point À AF þ1=2ðh
1
À h
2
Þ Ã Width?
¼ a þ b News Mid þ1=2bðh
1
À h
2
Þ Ã Width ðA4Þ
Compare (A4) with equation (1M) in the paper, the
only difference is the coef?cient on Width, which is now
½b(h
1
À h
2
) instead of b(h À 0.5). Recall that our prediction
following the max–min axiom is that analysts’ weight on
the upper bound (h
1
) should be less than their weight on
64 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
the lower bound (h
2
), and hence (h
1
À h
2
) < 0, which is
equivalent to our original prediction of (h À 0.5) < 0 in
Model (1M).
As shown above, our method can be readily adapted to
a framework where analysts allocate weights over three
points of management range forecasts – the upper bound,
the lower bound, and the midpoint, without forcing the
weight on the midpoint to be zero. All inferences in our
paper remain qualitatively unchanged under this alterna-
tive framework.
Appendix B. Variable name and de?nition
Dependent variables
Revision = the mean revision of all analysts that issue
forecasts both before and after a management forecast,
de?ated by the stock price at the beginning of the year.
AFE_PRE = the difference between the actual earnings
and the median analyst earnings forecast prior to a
management range forecast, de?ated by the stock price
at the beginning of the year.
Independent variables
News_Mid = the midpoint of a management range fore-
cast minus the prevailing consensus analyst forecast,
de?ated by the stock price at the beginning of the year.
Width = the distance between the upper bound and the
lower bound of a management range forecast, de?ated
by the stock price at the beginning of the year.
Bundle_Eanews = the actual earnings announced along
with a management range forecast minus the median
analyst forecast for the actual earnings, de?ated by
the stock price at the beginning of the year.
Fq1 = an indicator variable set to one if a management
forecast is issued in the ?rst ?scal quarter, and zero
otherwise.
Fq2 = an indicator variable set to one if a management
forecast is issued in the second ?scal quarter, and zero
otherwise.
Fq3 = an indicator variable set to one if a management
forecast is issued in the third ?scal quarter, and zero
otherwise.
D_WideRange = an indicator variable set to one if the
width of management forecast range is higher than
the sample median, and zero otherwise.
D_Dispersion = an indicator variable set to one if Disper-
sion is higher than the median, and zero otherwise, Dis-
persion is the standard deviation of analyst forecasts
issued within 90 days before the management forecast
announcement, de?ated by the stock price at the begin-
ning of the year.
D_RetVol = an indicator variable set to one if RetVol is
higher than the median, and zero otherwise, where
RetVol is the stock return volatility measured as the
standard deviation of daily stock returns from day
À120 to day À1 relative to the management forecast
date.
D_LastActualClosertoUpper = an indicator variable set to
one if the previous year’s actual earnings are closer to
the upper bound of the management forecast issued
in the same quarter of the previous year, and zero
otherwise.
D_WiderThanLast = an indicator variable set to one if the
current range forecast width is wider than the range
width of the management forecast issued in the same
quarter of the previous year, and zero otherwise.
D_MeetAF = an indicator variable set to one if a compa-
ny’s actual earnings meet analysts’ consensus in the
previous year, and zero otherwise.
D_GuideDown = an indicator variable set to one if the
upper bound of a management range forecast is lower
than the prevailing analyst consensus, and zero
otherwise.
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66 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
doc_243291063.pdf
Range forecasts have evolved to be the most common form of management forecasts. Prior
studies typically use the midpoint to evaluate analyst reaction to range forecasts, implicitly
assuming that analysts place equal weights on the upper and the lower bounds of management
range forecasts. We empirically test this restrictive assumption and provide strong
evidence of unequal weights – analysts place significantly more (less) weight on the lower
(upper) bound of forecast ranges.
How do analysts interpret management range forecasts?
q
Michael Tang
a,?
, Paul Zarowin
a
, Li Zhang
b
a
Stern School of Business, New York University, United States
b
Rutgers Business School, Rutgers University, United States
a r t i c l e i n f o
Article history:
Available online 19 February 2015
a b s t r a c t
Range forecasts have evolved to be the most common form of management forecasts. Prior
studies typically use the midpoint to evaluate analyst reaction to range forecasts, implicitly
assuming that analysts place equal weights on the upper and the lower bounds of manage-
ment range forecasts. We empirically test this restrictive assumption and provide strong
evidence of unequal weights – analysts place signi?cantly more (less) weight on the lower
(upper) bound of forecast ranges. Moreover, such overweight on the lower bound is more
pronounced when analysts face higher ambiguity, consistent with the ‘‘max–min’’ axiom,
which predicts that decision-makers tend to assign higher probability to the worst-case
scenario when facing ambiguity. Further tests show that ‘‘optimal revisions’’ with perfect
foresight of actual earnings also overweight the lower bound.
Ó 2015 Elsevier Ltd. All rights reserved.
Introduction
Management earnings forecasts, also known as earnings
guidance, play a signi?cant role in capital markets (Ball &
Shivakumar, 2008; Beyer, Cohen, Lys, & Walther, 2010;
Hirst, Koonce, & Venkataraman, 2008) that affects stock
prices and bid-ask spreads (Coller & Yohn, 1997; Pownall,
Wasley, & Waymire, 1993). In particular, a growing lit-
erature on ‘‘expectation management’’ examines howman-
agement forecasts establish and alter analyst earnings
expectations (e.g., Ajinkya & Gift, 1984; Baginski &
Hassell, 1990; Waymire, 1986; Williams, 1996; Cotter,
Tuna, & Wysocki, 2006; Kross & Suk, 2012; Matsumoto,
2002; Rogers & Van Buskirk, 2013). These studies usually
regress analyst forecast revisions around a management
forecast on the news conveyed from the management fore-
cast. However, measuring forecast news can be dif?cult for
range forecasts where managers provide both an upper
bound and a lower bound of their earnings expectations.
This issue becomes more important because range fore-
casts recently emerge as the most popular type of forecasts,
accounting for around 80% of all management forecasts
issued in the last decade (Ciconte, Kirk, & Tucker, 2014), a
sharp increase from under 20% in samples used in earlier
studies (e.g., Pownall et al., 1993). This paper examines
how analysts interpret management range forecasts.
Most of the prior studies typically use the mid-point to
calculate forecast news, implicitly assuming that users of
range forecasts such as analysts place equal ‘‘weights’’ on
the upper and lower bounds of management range fore-
casts (Baginski, Conrad, & Hassell, 1993).
1
A recent study
by Ciconte et al. (2014) challenges this convention andhttp://dx.doi.org/10.1016/j.aos.2014.12.005
0361-3682/Ó 2015 Elsevier Ltd. All rights reserved.
q
We thank Lisa Koonce (editor) and two anonymous reviewers for
comments and suggestions that signi?cantly improved the manuscript.
We are grateful for helpful comments from Phil Berger (discussant), Jenny
Tucker, Shankar Venkataraman (discussant), Jian Xue (discussant), Jerry
Zimmerman, and workshop participants at 2014 AAA Annual Meeting,
Accounting Conference at Temple University, 2014 CAPANA Conference,
New York University, the Ohio State University, and PwC Young Scholar
Symposium at the University of Illinois at Urbana Champaign. All errors
and omissions are our own.
?
Corresponding author.
E-mail addresses: [email protected] (M. Tang), pzarowin@stern.
nyu.edu (P. Zarowin), [email protected] (L. Zhang).
1
In this paper, by ‘‘equal weights,’’ we mean that the empirical
sensitivity of analyst revision to the upper and lower bounds of manage-
ment forecast ranges is ‘‘equal.’’ Most prior empirical studies on expecta-
tion management regress analyst revisions on management forecast news,
which relates to analysts’ ‘‘weight’’ (i.e. the coef?cient) on the news.
Accounting, Organizations and Society 42 (2015) 48–66
Contents lists available at ScienceDirect
Accounting, Organizations and Society
j our nal homepage: www. el sevi er. com/ l ocat e/ aos
examines whether the midpoint represents managers’ true
expectation – a question that is related to but different from
ours. Finding the distribution of actual reported earnings to
be more concentrated around the upper bound of manage-
ment range forecasts, they conclude that the upper bound
is more representative of managers’ expectations than the
midpoint. Although it is easy and natural to interpret range
signals such as management range forecasts at a single point
(either the midpoint or the upper bound) based on some
convenient ‘‘rule of thumb’’ (Tversky & Kahneman, 1982),
such interpretation imposes a restrictive assumption, that
is, 100% weight must be placed on a single point of the
range, thus ignoring information conveyed by the entire
forecast range. In this study we relax this restrictive
assumption and empirically investigate whether analysts
place equal weights on the upper and lower bounds of range
forecasts.
We evaluate the weights that analysts place on the
upper and the lower bounds of range forecasts by regress-
ing analyst forecast revisions on management forecast
news conveyed from both the upper and the lower bounds
of forecast ranges. The coef?cient on each news measure
re?ects the relative weight that analysts place on the cor-
responding bound of the range. Because the upper and
lower bounds are highly correlated (Pearson correla-
tion = 0.8 in our sample), to mitigate the concern of multi-
collinearity, we modify our main empirical model by
replacing the news from the upper bound (the lower
bound) with the news from the midpoint plus (minus) half
of the range width, measured as the distance between the
upper and lower bounds of the range forecast. After this
modi?cation, the coef?cient on the range width captures
the differences in the weights that analysts place on the
upper and lower bounds of the forecast range. Under
the null hypothesis implied in the extant studies that use
the midpoint to compute management forecast news, we
would expect the coef?cient on the range width to be zero.
Contrary to this conventional implication, we predict
that analysts place unequal weights, and that they are like-
ly to place more weight on the lower bound of manage-
ment range forecasts. Theories of decision-making predict
that ambiguity-averse agents tend to assign high probabil-
ity to the worst-case scenario when facing ambiguity
(Epstein & Schneider, 2008). Therefore, such decision-mak-
ers choose to maximize their expected utility assuming the
worst scenario, so called ‘‘max–min’’ axiom proposed by
Gilboa and Schmeidler (1989). Prior literature documents
that analysts are less likely to cover ?rms in more uncer-
tain environments or with less transparent disclosure
(e.g., Lang & Lundholm, 1996; O’Brien & Bhushan, 1990),
consistent with analysts being ambiguity-averse. By indi-
cating a range of possible future outcomes, management
range forecasts deliver ambiguous signals to analysts.
Therefore, we expect ambiguity-averse analysts to treat
the worst-case scenario (i.e., the lower bound) as more
likely than the best-case scenario (i.e., the upper bound),
and hence weight the lower bound more heavily. More-
over, we expect such overweight on the lower bound to
be more pronounced as the degree of ambiguity increases.
Consistent with our expectations, we ?nd that analysts
place an average of 73–77% weight on the lower bound of
management ranges forecasts, signi?cantly more weight
than on the upper bound. This effect is distinct from that
of managers using range forecasts to ‘‘walk down’’ analyst
expectations (e.g., Cotter et al., 2006) and also from the
optimistic-to-pessimistic patterns observed in analyst
forecasts as horizon decreases (e.g., Ke & Yu, 2006). Results
from various robustness tests further suggest that this
effect is not driven by ‘‘bundled forecasts’’ – management
forecasts that are simultaneously released with earnings
announcements (Rogers & Van Buskirk, 2013). Moreover,
such overweight on the lower bound is more pronounced
in scenarios where ambiguity or uncertainty is known to
be higher, including when management forecasts are (a)
issued earlier in the year, (b) issued with wider ranges,
(c) issued by ?rms with higher analyst forecast dispersion,
and (d) issued by ?rms with more volatile stock returns.
In supplemental tests, we ?nd evidence that analysts
adjust their weights based on the outcome of past range
forecasts, consistent with the conjecture that analysts are
‘‘Bayesian’’ and learn from the past (Hillary et al., 2013).
However, analysts’ overweight on the lower bound of man-
agement range forecasts does not seem to be driven by
their incentives to ‘‘lowball’’ their forecasts (Hilary & Hsu,
2013; Ke & Yu, 2006). Finally, using actual reported earn-
ings to impute the ‘‘optimal’’ forecast revision by a hypo-
thetical analyst with perfect foresight, we ?nd that the
‘‘optimal’’ weight also lies more on the lower bound than
on the upper bound. Hence analysts’ overweight on the
lower bound is indeed conducive to accurate prediction
relative to equal weighting. But unlike weights from ana-
lyst forecasts, the ‘‘optimal’’ weight does not shift further
to the lower bound in situations of heightened uncertainty,
consistent with analysts acting according to the ‘‘max–
min’’ axiom but inconsistent with them anticipating the
‘‘optimal’’ weight.
We caution readers to distinguish the ‘‘weight’’ from
the ‘‘distance’’, which is examined by Ciconte et al.
(2014). After showing that the actual earnings are more
likely to be around the upper bound rather than the mid-
point of managers’ range forecasts, they investigate and
?nd that analysts’ revised forecasts are, on average, slightly
above the midpoint but well below the upper bound, sug-
gesting that analysts barely unravel the pessimistic bias in
managers’ range forecasts. Our evidence of analysts’ ‘‘over-
weight’’ on the lower bound does not contradict their ?nd-
ing of analysts’ revised forecasts being slightly ‘‘closer’’ to
the upper bound. This is because analysts not only respond
to management forecast news but also to managers’ provi-
sion of the forecast, which is captured by the intercept in
our model of analyst forecast revision. Existing theoretical
(e.g., Grossman & Hart, 1980) and empirical (e.g., Clement,
Frankel, & Miller, 2003) studies suggest that managers’ vol-
untary provision of earnings forecast is perceived as a
desirable action. Consistent with this prediction, we ?nd
a signi?cantly positive intercept when we allow analysts
to place unequal weights on the upper and lower bounds
of range forecasts. However, the intercept turns sig-
ni?cantly negative when we follow the conventional
design and force the weights to be equal. This ?nding
demonstrates the importance of allowing analysts to place
unequal weights on the upper and the lower bounds of
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 49
management range forecasts. The positive intercept we
?nd also explains why, in terms of ‘‘distance’’, analysts’
revised forecasts are on average slightly ‘‘closer’’ to the
upper bound, even though analysts place more ‘‘weight’’
on the lower bound.
2
This study makes at least two contributions to the lit-
erature. First, it cautions researchers about the convention-
al practice of using the midpoint to interpret management
range forecasts – an increasingly predominant form of
management forecasts. This practice implicitly assumes
that users of range forecasts place equal weights on both
endpoints. We offer a simple and intuitive approach to
assessing the relative weights on the endpoints of range
forecasts, in the setting of analyst forecast revisions. Our
?ndings reject the null hypothesis implied by the conven-
tional approach and show that analysts place signi?cantly
more weight on the lower bound than on the upper bound
of range forecasts. To the best of our knowledge, the differ-
ential weights on the endpoints of range forecasts have
never been investigated before in the literature. However,
we emphasize that our approach is developed to examine
how analysts interpret range forecasts and may not be
appropriate or desirable in all range-forecast-related set-
tings.
3
Nonetheless, future research on analyst reaction to
management forecasts can follow this study and simply
include the forecast range width to relax the assumption
of equal weights that is refuted by our ?ndings.
Second, this study deepens our understanding of the
growing literature on ‘‘expectation management’’, which
focuses on the average effect of managers ‘‘walking down’’
analysts’ expectations with management forecasts (e.g.,
Cotter et al., 2006; Kross & Suk, 2012). These studies, how-
ever, ignore the differential effect of the upper and lower
bounds of range forecasts on analyst expectations, as well
as any cross-sectional variations in such differential effect.
We document that analysts place more weight on the low-
er bound than on the upper bound, and this differential
reaction is more pronounced when ambiguity is higher,
consistent with the ‘‘max–min’’ axiom proposed in the
decision-making literature (Epstein & Schneider, 2008;
Gilboa & Schmeidler, 1989). Therefore, our paper con-
tributes to the expectation management literature by
introducing a new factor (ambiguity) through a new chan-
nel (analysts’ differential weights on the upper and lower
bounds of management range forecasts). This new channel
is also relevant to managers who provide range forecasts,
to analysts who use managers’ range forecasts, and to mar-
ket participants who use managers’ or analysts’ forecasts.
Section ‘Related research and hypothesis development’
reviews related research and develops our hypotheses. In
Section ‘Sample selection’ we describe our sample. Sec-
tion ‘Empirical research design’ describes our empirical
research design. We present our empirical results in Sec-
tion ‘Empirical results’, and Section ‘Conclusion’ concludes.
Related research and hypothesis development
Management earnings forecasts typically take four
forms – points, (closed-ended) ranges, maximums and
minimums (also referred to as open-ended ranges), or
qualitative forecasts – in decreasing order of precision. Ear-
lier studies ?nd mixed evidence on the effect of forecast
form on market reaction (Baginski et al., 1993; Pownall
et al., 1993). Notably, range forecasts have emerged as
the predominant form of management forecasts from
6.8% in the 1980s (Pownall et al., 1993) to over 80% in
recent years (Choi, Myers, Zang, & Ziebart, 2011; Ciconte
et al., 2014). Despite its popularity, little research exists
on how analysts interpret range forecasts. Most studies
treat range forecasts as equivalent to point forecasts at
the midpoints (e.g., Ajinkya, Bhojraj, & Sengupta, 2005;
Feng & Koch, 2010; Gong et al., 2011; Rogers & Stocken,
2005).
When managers issue a point forecast, only one number
can serve as the benchmark against which analyst expecta-
tions can be measured. In contrast, a range forecast from
managers expresses expectations in terms of both an upper
and a lower limit, each of which can serve as a benchmark
(Libby, Tan, & Hunton, 2006). Psychology research suggests
that users of range estimates typically apply a simple ‘‘rule
of thumb’’ and use the midpoint to interpret range esti-
mates (Tversky & Kahneman, 1982). Earlier empirical evi-
dence also supports the use of midpoint to interpret
management range forecasts because investors appear to
respond most strongly to the midpoint of range forecasts
(Baginski et al., 1993). Following this convention, most
accounting studies use the midpoint to measure manage-
ment forecast news in evaluating analysts’ revisions in
response to management forecasts (e.g., Feng & McVay,
2010; Gong et al., 2011).
Ciconte et al. (2014) challenge this convention and seek
to explore which point of the forecast range best repre-
sents managers’ true expectations. Relative to the mid-
point, they ?nd the upper bound is more representative
of managers’ ex ante true beliefs, proxied by the ex post
reported earnings. Their analysis of stock price reaction
and analyst revision suggests that while investors’ reaction
is consistent with interpreting range forecasts near the
upper bound, analysts seem to respond to the midpoint.
Unlike this study, they use ‘‘distance’’ to evaluate which
point of the range forecast is ‘‘closer’’ to analysts’ revised
forecasts, and do not consider the ‘‘weights’’ that analysts
place on the endpoints of range forecasts, because their
main focus is not on analysts’ interpretation of manage-
ment range forecasts.
Regardless of whether the upper bound or midpoint is
more representative of managers’ true expectations, we
argue that analysts are unlikely to anchor on only a single
point of a range forecast. An extensive body of psychology
literature suggests that evaluations are made by
2
In cross-sectional tests, all of our indicators of high-uncertainty
scenarios load signi?cantly positive, suggesting that high uncertainty shifts
analysts’ revisions ‘‘closer’’ (in distance) to the upper bound. This ?nding
contrasts from more ‘‘weight’’ on the lower bound in high-uncertainty
scenarios and highlights that the ‘‘max–min’’ axiom applies only to the
‘‘weight’’ but not to the ‘‘distance’’ of analyst forecasts. We discuss this
further in the results section.
3
In particular, we do not speak to whether the midpoint of management
range forecasts should be used to measure forecast errors or forecast biases
(Gong, Li, & Wang, 2011; Rogers & Stocken, 2005), or whether the midpoint
represents managers’ true expectations (Ciconte et al., 2014).
50 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
comparisons to one or more reference points or standards
(e.g., Helson, 1964; Kahneman & Tversky, 1979; Kida &
Smith, 1995; Thaler, 1999; Thibaut & Kelley, 1959). Follow-
ing this literature, Libby et al. (2006) suggest that analysts
use both the upper bound and the lower bound of manage-
ment range forecasts as benchmarks to evaluate reported
earnings, so-called the ‘‘benchmark effect.’’ Responses
from their analyst subjects are consistent with the ‘‘bench-
mark effect’’ of management range forecasts.
Building upon the ‘‘benchmark effect,’’ we argue that
analysts reacting to a management range forecast consider
both the upper bound and the lower bound instead of a sin-
gle point.
4
Therefore, both the upper and lower bounds of a
management forecast convey news to the market relative to
the preexisting expectations, which we refer to as ‘‘news
upper’’ and ‘‘news lower’’ respectively. Moreover, analysts
can respond to both news by assigning to them equal or
unequal weights. If analysts place equal weights, then it is
equivalent to them reacting to the midpoint of range fore-
casts, as is commonly used in prior studies. If analysts put
all weight on ‘‘news upper (lower)’’ and zero weight on
‘‘news lower (upper),’’ then it is equivalent to them reacting
just to the upper (lower) bound. Unlike these approaches,
which restrict the weights to be zero or ?fty percent on
the endpoints, we allow these weights to be determined
empirically and to vary with economic determinants. There-
fore our new approach is a more generalized framework
which encompasses the existing approaches in the literature
as its special cases.
Although the extant literature implicitly assumes that
investors and analysts place equal weights on ‘‘news
upper’’ and ‘‘news lower’’ (with the exception of Ciconte
et al., 2014), we expect such weights to differ, with ‘‘news
lower’’ being overweighed by analysts. Theories in the
decision-making literature predict that ambiguity-averse
agents are more likely to assign high probability to the
worst scenario when they face ambiguity (Epstein &
Schneider, 2008). Hence such agents make choices that
maximize their expected utility under the worst scenario,
so called ‘‘max–min’’ axiom proposed by Gilboa and
Schmeidler (1989). Prior studies ?nd that analysts are less
likely to cover ?rms in more volatile environments and
with less transparent disclosure (Lang & Lundholm, 1996;
O’Brien & Bhushan, 1990), consistent with analysts being
ambiguity-averse. Management range forecasts deliver
ambiguous signals to analysts, in the sense that a range
of possible outcomes could be deemed as consistent with
their forecasts. If analysts are ambiguity-averse on average,
they will give more consideration to the worst-case sce-
nario (e.g., the lower bound) than to the best-case scenario
(e.g., the upper bound).
5
H1. Ceteris paribus, when analysts revise earnings forecasts
in response to management range forecasts, they place
more weight on the news conveyed from the lower bound
(‘‘news lower’’) than on the news conveyed from the upper
bound (‘‘news upper’’).
Extending the ‘‘max–min’’ axiom, we expect analysts’
relative overweight on the lower bound to be more pro-
nounced when more ambiguity is present (Gilboa &
Schmeidler, 1989). Ambiguity can be manifested both in
the properties of the management forecast itself and in
the information environment. Speci?cally, forecasts issued
earlier or with wider ranges are viewed as more ambigu-
ous (Libby et al., 2006). Moreover, under heightened uncer-
tainty, analysts tend to disagree with each other to a
greater extent and hence analyst forecast dispersion is
larger (Diether, Malloy, & Scherbina, 2002). Finally, stock
price becomes more volatile when uncertainty is high
(Bloom, 2009).
6
This leads to our second set of empirical
predictions.
H2. Ceteris paribus, when analysts revise earnings forecasts
in response to a management range forecast, their over-
weight on the lower bound relative to the upper bound is
more pronounced in the following scenarios:
(H2a) when the management forecast is provided ear-
lier during the period;
(H2b) when the management forecast contains a wider
range;
(H2c) when the dispersion of the preexisting analyst
forecasts is larger; and
(H2d) when stock return volatility is higher.
Sample selection
We use First Call Company Issued Guideline (CIG) data-
base to identify all management forecasts of annual earn-
ings per share issued by U.S. ?rms between 1996 and
2011. We choose annual forecasts instead of quarterly
forecasts for three reasons. First, the economic signi?cance
of differentiating between equal and unequal weights is
greater for annual forecasts because their ranges are con-
siderably wider than quarterly range forecasts.
7
Second,
annual forecasts recently overtook quarterly forecasts in
popularity due to both criticisms of quarterly forecasts
(Chen et al., 2011; Houston et al., 2010) and increased fre-
quency of updates of annual forecasts (Tang, Yao, &
Zarowin, 2014). Third, despite many recent papers that
study management quarterly forecasts (e.g., Ciconte et al.,
2014; Kross, Ro, & Suk, 2011), annual forecasts remain an
4
Although analysts may form expectations over the entire range,
unfortunately the distribution of their expectations is unobservable to
researchers. Hence, we leave it to future research and focus only on the
endpoints in this paper.
5
It is certainly possible that the worst (best) scenario could be some
point below (above) the lower (upper) bound, but under the max–min
framework, the same prediction would result about the unequal weights on
the upper and lower bounds of management forecast range, that is, more
weight would be placed on the lower bound, regardless of which two points
outside of the range are selected to represent the best and worst scenarios.
6
It is also possible that analysts are ‘‘Bayesian’’ and hence adjust their
weights on the upper and lower bounds of the management forecast range
based on their previous experience. We defer this discussion to our
empirical tests.
7
The median (mode) range width is $0.08 ($0.10) for annual forecasts,
compared with $0.03 ($0.02) for quarterly forecasts. Hence for an average
quarterly range forecast, there is only about $0.01 difference between the
midpoint and the endpoint, rendering the equal/unequal weight a trivial
issue in the setting of quarterly forecasts.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 51
important setting in the management forecast literature
(e.g., Ajinkya et al., 2005; Gong et al., 2011; Rogers &
Stocken, 2005; Hutton et al., 2012). Hence we focus on annu-
al range forecasts. Following the literature, we exclude fore-
casts issued either before the previous year’s earnings
announcement (‘‘long horizon forecasts’’) or after the end
of the current ?scal year (‘‘preannouncements’’). We obtain
non-split-adjusted actual earnings and analyst earnings
forecasts from I/B/E/S. After eliminating duplicate forecasts
and forecasts without valid identi?ers or corresponding
actual earnings, we arrive at a sample of 47,436 manage-
ment annual earnings forecasts, which include revisions
within the ?scal year.
To assess the prevalence of range forecasts, we classify
all forecasts into four types: point, range, max or min
(open-range), and qualitative forecasts. Panel A of Table 1
reports the yearly distribution by forecast types. The share
of range forecasts increases from 36.5% in 1996 to a pre-
dominant 92.1% in 2011. Accordingly, the share of point
forecasts decreases from 47.5% in 1996 to only 5.5% in
2011. Moreover, the percentages of the other two types
of forecasts also decline steadily over time, although a por-
tion of this trend could be attributed to expansion of First
Call’s coverage of quantitative forecasts through time
(Chuk, Matsumoto, & Miller, 2013). Nonetheless these
trends highlight the importance of analyzing range fore-
casts. The emergence of range forecasts as the pre-
dominant form of management forecasts starts around
the passage of Regulation Fair Disclosure (Reg FD) in late
2000, but the mean (median) range width remains roughly
constant until 2007 when the ?nancial crisis started,
increasing from around $0.08 to $0.10 ($0.05–$0.06) before
the crisis to $0.11 ($0.09) and higher. As we explain later,
in our empirical analysis, we require analyst forecasts to
be non-missing within 30 days before and after manage-
ment range forecasts, which reduces our sample size to
10,989.
8
Panel B of Table 1 presents the distribution of this
sample by whether there is one or more annual forecast
within the year and by whether or not the forecast is bun-
dled with an earnings announcement. As shown, the major-
ity of the ?rms issue more than one annual forecast (96.3%)
and bundle them with earnings announcements (82.5%),
consistent with prior research (Rogers & Van Buskirk,
2013; Tang et al., 2014).
Table 1
Sample composition.
All annual management forecasts Range forecast width
Year N Point (%) Range (%) Open (%) Qualitative (%) Mean Median Std. dev.
Panel A: broad sample distribution by year and by forecast form
1996 301 47.5 36.5 10.3 5.6 0.085 0.060 0.076
1997 453 46.6 30.0 12.8 10.6 0.103 0.060 0.126
1998 814 45.7 28.0 7.1 19.2 0.087 0.050 0.084
1999 1,126 32.8 30.0 12.1 25.1 0.092 0.050 0.165
2000 1,166 33.5 40.2 8.3 17.9 0.079 0.050 0.153
2001 2,659 21.4 66.7 5.1 6.8 0.088 0.050 0.083
2002 3,582 17.5 75.5 4.0 3.0 0.087 0.050 0.085
2003 3,954 13.4 79.2 4.6 2.9 0.093 0.060 0.101
2004 4,630 10.4 83.2 3.8 2.6 0.096 0.060 0.109
2005 4,539 9.2 87.9 2.4 0.5 0.097 0.060 0.105
2006 4,861 9.4 88.0 1.6 0.9 0.104 0.080 0.106
2007 4,508 10.2 87.6 1.6 0.6 0.108 0.090 0.105
2008 4,491 10.6 86.8 2.6 0.0 0.121 0.100 0.111
2009 3,498 8.9 89.1 2.0 0.0 0.149 0.100 0.142
2010 3,955 7.1 90.5 2.4 0.0 0.133 0.100 0.122
2011 2,899 5.5 92.1 2.5 0.0 0.144 0.100 0.132
Total 47,436 13.2 80.6 3.4 2.8 0.110 0.080 0.114
Unbundled Bundled Total
Panel B: regression sample distribution by forecast frequency and by bundling with quarterly earnings announcement news
Only one management forecast during the year 101 (0.9%) 303 (2.8%) 404 (3.7%)
Multiple management forecasts during the year 1,826 (16.6%) 8,759 (79.7%) 10,585 (96.3%)
Total 1,927 (17.5%) 9,062 (82.5%) 10,989 (100.0%)
Bundled forecasts with positive earnings news 6,966 (76.9%)
Bundled forecasts with negative earnings news 2,096 (23.1%)
Total 9,062 (100.0%)
Note: This table presents the composition of our sample. Panel A presents the distribution by year and by forecast form of the broader sample before we
focus on the subset of range forecasts. The sample is constructed based on the First Call Company Issued Guideline (CIG) database and contains man-
agement forecasts for annual earnings of ?scal years between 1996 and 2011. Forecasts are classi?ed into four forms: point, range, open-ended range (max/
min), and qualitative. For all range forecasts in each year, we also report the distribution of range widths, measured as the distance (in dollar amount)
between the upper bound and the lower bound of management range forecasts. Panel B presents the distribution by forecast frequency during the year and
by bundling with quarterly earnings announcement news of the sample of 10,989 range forecasts in our analysis, after requiring suf?cient data to calculate
our base line regression model.
8
The requirement of the [À30, +30] window is to ensure that analysts’
revisions are driven by management forecasts. Results are qualitatively the
same if we relax the window to [À60, +60] to obtain a bigger sample size of
15,122.
52 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
Table 2 presents the distribution of analyst consensus
forecasts before management range forecasts (Panel A)
and after management forecasts (Panel B), over ?ve mutu-
ally exclusive cases with respect to the corresponding fore-
cast ranges (Columns (a) through (e)): (À1, Low), [Low,
Mid), {Mid}, (Mid, High], and (High, +1), where ‘‘Low,’’
‘‘Mid,’’ and ‘‘High’’ indicate the lower bound, midpoint,
and upper bound of management range forecasts, respec-
tively. We present the distribution for the full sample as
well as separately for each ?scal quarter. Prior to manage-
ment forecasts (see Panel A), 29.4% (28.8%) of all analyst
consensus forecasts are below (above) the entire forecast
range, resulting in an asymmetry ratio of 1.021 around
the entire forecast range. Similarly, within the range,
19.9% (18.8%) of all analyst consensus forecasts are below
(above) the midpoint, leading to an asymmetry ratio of
1.036 around the midpoint.
9
While the asymmetry ratios
are below one in the ?rst quarter (Fq1) and above one in
the remaining quarters (Fq2, Fq3, and Fq4), the overall ratios
are close to one, suggesting that managers issue range fore-
casts roughly symmetrically around the prevailing analyst
forecasts, with 41.8% of all management range forecasts con-
taining the prevailing analyst consensus. Although only
34.1% of analysts’ consensus forecasts in the fourth quarter
(Fq4) are within management forecast ranges, this is partly
because the forecast ranges are also narrower in the fourth
quarter than in other quarters.
After management forecasts (Panel B of Table 2), the dis-
tribution of analyst consensus forecasts is notably different.
13.2% (20.4%) of all analyst consensus forecasts are below
(above) the entire forecast range, resulting in an asymmet-
ric ratio of 0.647 around the forecast range. Also within the
range, 25.5% (33.8%) of all analyst consensus forecasts are
below (above) the midpoint, leading to an asymmetry ratio
of 0.714 around the midpoint. Both asymmetry ratios
remain below one across all ?scal quarters, suggesting that
analysts more often revise their forecasts above the mid-
point, consistent with the ?nding in Ciconte et al. (2014).
Overall 66.4% of all analysts’ revised consensus forecasts
are within the management forecast range, with over half
of them (33.8% of total) in the upper half of managers’ fore-
cast range (Column (d)). The apparently different distribu-
tions of analyst consensus forecasts before and after
management forecasts suggest that analysts indeed react
to management forecasts. The wide distribution of analyst
revised forecasts over management forecast ranges implies
that analysts respond not just to the midpoint. Below we
develop our formal empirical design to investigate how
analysts interpret management range forecasts.
Empirical research design
Assume that h is the hypothetical weight that an analyst
places on the upper bound of a management range forecast
and hence 1 À h is the weight placed on the lower bound.
10
Thus the news conveyed by a management range forecast
can be expressed as h ? Upper Bound
i,t
+ (1 À h) ? Lower
Bound
i,t
À AF
i,tÀ1
, where Upper Bound and Lower Bound are
the upper and lower bounds of management forecast ranges,
and AF is the prevailing analyst consensus forecast prior to
the management forecast.
11
For each management forecast,
Table 2
The location of analyst consensus forecasts with regard to management forecast ranges.
Quarter N (À1, Low) [Low, Mid) {Mid} (Mid, High] (High, +1) Asymmetry % In range Range width
(a) (%) (b) (%) (c) (%) (d) (%) (e) (%) (a)/(e) (a + b)/(d + e) (b + c + d) (%) Mean Median Std. dev.
Panel A: analyst consensus forecasts issued prior to management forecasts by ?scal quarters
Fq1 2,765 23.9 18.7 2.6 20.8 34.0 0.703 0.777 42.1 0.141 0.100 0.115
Fq2 2,709 29.3 23.5 2.8 21.0 23.4 1.252 1.189 47.3 0.136 0.100 0.112
Fq3 2,803 28.8 21.2 3.3 19.1 27.6 1.043 1.071 43.6 0.117 0.100 0.101
Fq4 2,712 35.7 16.0 3.8 14.3 30.2 1.182 1.162 34.1 0.075 0.050 0.073
Total 10,989 29.4 19.9 3.1 18.8 28.8 1.021 1.036 41.8 0.117 0.100 0.105
Panel B: revised analyst consensus forecasts post management forecasts by ?scal quarters
Fq1 2,765 14.4 27.5 7.0 34.3 16.8 0.857 0.820 68.8 0.141 0.100 0.115
Fq2 2,709 14.8 24.1 5.6 32.6 22.9 0.646 0.701 62.3 0.136 0.100 0.112
Fq3 2,803 12.3 26.2 6.5 33.9 21.1 0.583 0.700 66.6 0.117 0.100 0.101
Fq4 2,712 11.4 24.0 9.4 34.2 21.0 0.543 0.641 67.6 0.075 0.050 0.073
Total 10,989 13.2 25.5 7.1 33.8 20.4 0.647 0.714 66.4 0.117 0.100 0.105
This table presents the distribution of the median analyst forecasts that are issued prior to and after the management forecasts with reference to
management forecast ranges, partitioned into ?ve mutually exclusive cases (columns (a) through (e)): (À1, Low), [Low, Mid), {Mid}, (Mid, High], and
(High,+1), where ‘‘Low,’’ ‘‘Mid,’’ and ‘‘High’’ indicates the lower bound, midpoint, and upper bound of management forecasts, respectively. The sample
includes 10,989 management range forecasts of annual earnings of ?scal years between 1996 and 2011. Two measures of asymmetry are de?ned as ratios of
the total number of observations to the left versus to the right of the range (or of the middle point). Fq1 (Fq2, Fq3, or Fq4) indicates that the management
annual forecast is issued during the ?rst (second, third, or fourth) ?scal quarter of the year. ‘‘Range Width’’ is measured as the distance (in dollar amount)
between the upper bound and the lower bound of management range forecasts.
9
This ratio should equal one for a symmetric distribution. A ratio smaller
(greater) than one indicates that fewer (more) observations are below
rather than above the range or the midpoint.
10
In our baseline model, we parsimoniously treat h as a constant, but in
later analyses, we allow h to be a function of various economic factors,
including historical outcomes to allow analysts to be ‘‘Bayesian.’’
11
Because in this paper we are interested in understanding the average
analysts’ interpretation of management range forecasts, we focus on the
consensus of analyst forecasts and ignore individual analysts’ forecasts,
which also form a range that represents analysts’ different beliefs.
However, in our robustness test section, we repeat our analyses using
individual analysts’ forecasts and obtain similar results.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 53
we collect analysts’ last forecasts issued within 30 days
before the management forecast date and use the median
analyst forecast as the consensus analyst forecast. To exam-
ine the relative weights that analysts place on the upper and
lower bounds of management range forecasts in revising
their own forecasts, we estimate the following model using
ordinary least squares (OLS) regression.
Revision
i;t
¼ a þ b½h à Upper Bound
i;t
þ ð1 À hÞ
à Lower Bound
i;t
À AF
i;tÀ1
? þe ð1Þ
where Revision is mean analyst forecast revision around a
management forecast, calculated as analysts’ ?rst forecasts
within 30 days after the management forecast minus their
last forecasts within 30 days before the management
forecast, scaled by the closing price at the end of the prior
year.
12
Accordingly we also scale forecast news by the clos-
ing price at the end of the prior year.
13
Observations are
deleted if the stock price is less than $1 to mitigate small
denominator problems.
Our focus in Model (1) above is whether h is less than
0.5, as our H1 predicts analysts to underweight the upper
bound of range forecasts. Note that if we force h to be
0.5, then Model (1) degenerates into a model using the
midpoint of management forecast to calculate manage-
ment forecast news, as is commonly used in the existing
literature (e.g., Ajinkya et al., 2005; Gong et al., 2011;
Rogers & Stocken, 2005; Rogers & Van Buskirk, 2013). By
allowing h to be estimated from the regression, we can sta-
tistically validate the assumption that h = 0.5. However,
because in a panel sample, the upper and lower bounds
of range forecasts are highly correlated, directly estimating
Model (1) suffers from severe multi-collinearity problem
(Wooldridge, 2002). To circumvent the problem we rear-
range the right-hand side of Model (1) by considering the
fact that Upper/Lower Bound = Midpoint ± 0.5 ? Width,
where Width is width of management range forecast and
Midpoint is the midpoint of management range forecast.
After rearrangement, we obtain the following model
14
:
Revision
i;t
¼ a þ bðNews Mid
i;t
Þ þ bðh À0:5Þ
à Width
i;t
þe ð1MÞ
where News_Mid is management forecast news calculated
as the midpoint minus the prevailing analyst consensus
before management forecast, scaled by the closing price
at the end of the prior year. Our empirical model of Model
(1M) can be easily adapted to consider three points of the
range forecast – the upper and lower bounds, and the mid-
point. Appendix A provides the details.
Our baseline approach is the following. Because the
ratio of the coef?cient on Width divided by the coef?cient
on News_Mid is a univariate function of h, we can infer h
from the coef?cient estimates from the regression results
of Model (1M). If analysts place equal weights on the upper
and lower bounds (h = 0.5), the ratio of the coef?cient on
Width divided by the coef?cient on News_Mid in Model
(1M) should be statistically indifferent from zero.
To examine cross-sectional variations in the relative
weights analysts place on the upper and lower bounds of
management forecasts, we interact forecast width (Width)
with variables that capture ?rm characteristics and the
properties of management forecasts. By doing so, we allow
h to be a function of these variables. If analysts adjust their
weights on the upper and lower bounds according to these
variables, these interaction terms should be signi?cant in
explaining analyst forecast revisions. Our H2 predicts that
such variables include the ?scal quarter in which the man-
agement forecast occurs (Fq1, Fq2, and Fq3), forecast range
width of the management forecast (Range), analyst forecast
dispersion (Dispersion), and stock return volatility (RetVol).
More detailed de?nitions are elaborated in the Appendix B.
In our additional analysis, we evaluate the ‘‘optimal’’
weights on the upper and lower bounds of forecast ranges
that lead to the perfect prediction of actual reported earn-
ings. To do so, we compute the ‘‘optimal revision’’ as the
actual earnings minus the prevailing analyst consensus
forecast prior to the management forecast, scaled by the
closing price at the end of the prior year, which is labeled
as AFE_PRE. We replace the dependent variable in Model
(1) with AFE_PRE to assess the optimal weights that ana-
lysts would place on the upper and lower bounds if their
revisions can perfectly predict actual earnings.
Empirical results
Descriptive statistics
Table 3 Panel A presents the descriptive statistics of the
variables used in our empirical models. The mean (median)
of Revision is À0.053% (0.039%) of the share price, suggest-
ing that analysts more often revise their forecasts upward
than downward after management range forecasts, but the
average magnitude of downward revisions exceeds that of
upward revisions (t = À8.67, untabulated). In contrast, the
magnitude of AFE_PRE (our measure of the optimal revi-
sion) is greater than that of Revision, suggesting that ana-
lysts on average only partially correct their initial
forecast errors. This partial correction, however, should
not affect the relative weights analysts place on the end-
points of management range forecasts, for the reasons we
explained earlier. The median of News_Mid is 0, consistent
with our results in Table 2 Panel A that the prevailing
analyst consensus forecasts is nearly symmetric around
the midpoint of management range forecasts. The mean
12
Our results are robust to using either the mean or the median analyst
forecasts for AF and Revision. Scaling these variables by the absolute value
of the forecasted earnings (instead of by stock price) or extending the
revision window to ±60 days also does not change our inferences.
13
We follow prior studies to price-de?ate our regression variables (e.g.,
Gong et al., 2011), but our results are robust to using the magnitude of
forecasted earnings as an alternative de?ator, or to de?ating the intercept
in the regression model.
14
Note that from Model (1) to Model (1M) is pure algebra rearrangement,
and hence the coef?cient b and parameter h should remain the same.
However, this equality and hence the relation between b and h implied
from the ratio of the regression coef?cients will no longer hold if we also
include an interaction term News_Mid  Width as in prior studies (e.g.,
Baginski, Hassell, & Wieland, 2011). To see this, consider the coef?cient b in
Model (1M) as analysts’ reaction to the midpoint of any range forecast.
However, once the interaction term News_Mid  Width is included in the
model, the coef?cient on News_Mid becomes analysts’ reaction to the
midpoint of range forecasts with a zero width.
54 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
Table 3
Descriptive statistics.
Variables N Mean Std. dev. 25% Median 75%
Panel A: summary statistics
Revision (%) 10,989 À0.053 0.644 À0.177 0.039 0.193
AFE_PRE (%) 10,989 À0.274 1.877 À0.532 0.058 0.462
News_Mid (%) 10,989 À0.048 0.642 À0.193 0.000 0.179
Width (%) 10,989 0.406 0.411 0.154 0.279 0.490
Bundle_Eanews (%) 9,062 0.082 0.340 0.000 0.062 0.180
Fq1 10,989 0.252 0.434 0.000 0.000 1.000
Fq2 10,989 0.247 0.431 0.000 0.000 0.000
Fq3 10,989 0.255 0.436 0.000 0.000 1.000
Dispersion 10,599 0.003 0.004 0.001 0.002 0.003
RetVol 10,983 0.024 0.013 0.015 0.021 0.030
D_LastActualClosertoUpper 7,617 0.626 0.484 0.000 1.000 1.000
D_WiderThanLast 7,660 0.521 0.450 0.000 1.000 1.000
D_MeetAF 9,730 0.787 0.409 1.000 1.000 1.000
D_GuideDown 10,989 0.276 0.447 0.000 0.000 1.000
Revision AFE_PRE News_Mid Width Bundle_Eanews Fq1 Fq2 Fq3 D_Dispersion D_Ret-Vol D_Last-Actual-
Closer-toUpper
D_Wider-Than-Last D_Meet-AF D_Guide-Down
Panel B: correlation matrix
Revision 1.000
AFE_PRE 0.517 1.000
News_Mid 0.785 0.390 1.000
Width À0.201 À0.156 À0.114 1.000
Bundle_Eanews 0.421 0.318 0.308 0.038 1.000
Fq1 À0.090 À0.075 À0.075 0.115 À0.025 1.000
Fq2 0.034 À0.022 0.042 0.096 0.012 À0.332 1.000
Fq3 0.020 0.019 0.012 À0.018 0.005 À0.339 À0.335 1.000
D_Dispersion À0.089 À0.097 À0.045 0.417 0.011 0.145 0.029 À0.033 1.000
D_RetVol À0.088 À0.091 À0.032 0.229 0.022 À0.006 À0.033 À0.008 0.222 1.000
D_LastActual-ClosertoUpper 0.128 0.124 0.061 À0.222 0.062 À0.091 À0.021 0.009 À0.146 À0.109 1.000
D_WiderThan-Last À0.125 À0.118 À0.047 0.276 À0.017 0.000 À0.005 0.013 0.124 0.170 À0.151 1.000
D_MeetAF 0.109 0.115 0.071 À0.119 0.157 À0.019 0.000 0.013 À0.074 À0.005 0.251 À0.071 1.000
D_GuideDown À0.489 À0.238 À0.603 0.001 À0.198 0.064 À0.067 À0.013 0.073 0.037 À0.049 0.022 À0.062 1.000
The sample includes 10,989 management range forecasts of annual earnings of ?scal years between 1996 and 2011. All continuous variables are winsorized at the 1st and 99th percentiles. Revision is the mean revision of all analysts that issue
forecasts both before and after a management forecast, de?ated by the stock price at the beginning of the year. AFE_PRE is the difference between the actual earnings and the median analyst earnings forecast prior to a management range forecast,
de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast minus the prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance
between the upper bound and the lower bound of a management range forecast, de?ated by the stock price at the beginning of the year. Bundle_Eanews is the actual earnings announced along with a management range forecast minus the median
analyst forecast for the actual earnings, de?atedby the stock price at the beginning of the year. Fq1(Fq2, Fq3) is an indicator variable set to one if a management forecast is issued inthe ?rst (second, third) ?scal quarter, andzero otherwise. Dispersion
is the standard deviation of analyst forecasts issued within 90 days before the management forecast announcement, de?ated by the stock price at the beginning of the year. RetVol is the stock return volatility measured as the standard deviation of
daily stock returns from day À120 to day À1 relative to the management forecast date. D_LastActualClosertoUpper is an indicator variable set to one if the previous year’s actual earnings are closer to the upper bound of the management forecast
issued in the same quarter of the previous year, and zero otherwise. D_WiderThanLast is an indicator variable set to one if the current range forecast width is wider than the range width of the management forecast issued in the same quarter of the
previous year, and zero otherwise. D_MeetAF is an indicator variable set to one if a company’s actual earnings meet analysts’ consensus in the previous year, and zero otherwise. D_GuideDown is an indicator variable set to one if the upper bound of a
management range forecast is lower than the prevailing analyst consensus, and zero otherwise.
This table presents the Pearson pairwise correlation coef?cients. Correlations in bold are signi?cantly different from zero at the 1% level. All continuous variables are winsorized at the 1st and 99th percentiles.
Revision is the mean revision of all analysts that issue forecasts both before and after a management forecast, de?ated by the stock price at the beginning of the year. AFE_PRE is the difference between the actual
earnings and the median analyst earnings forecast prior to a management range forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast minus the
prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance between the upper bound and the lower bound of a management range forecast, de?ated by the
stock price at the beginning of the year. Bundle_Eanews is the actual earnings announced along with a management range forecast minus the median analyst forecast for the actual earnings, de?ated by the stock
price at the beginning of the year. Fq1(Fq2, Fq3) is an indicator variable set to one if a management forecast is issued in the ?rst (second, third) ?scal quarter, and zero otherwise. D_Dispersion is an indicator variable
set to one if Dispersion is higher than the median, and zero otherwise, where Dispersion is the standard deviation of analyst forecasts issued within 90 days before the management forecast announcement, de?ated
by the stock price at the beginning of the year. D_RetVol is an indicator variable set to one if RetVol is higher than the median, and zero otherwise, where RetVol is the stock return volatility measured as the standard
deviation of daily stock returns fromday À120 to day À1 relative to the management forecast date. D_LastActualClosertoUpper is an indicator variable set to one if the previous year’s actual earnings are closer to the
upper bound of the management forecast issued in the same quarter of the previous year, and zero otherwise. D_WiderThanLast is an indicator variable set to one if the current range forecast width is wider than the
range width of the management forecast issued in the same quarter of the previous year, and zero otherwise. D_MeetAF is an indicator variable set to one if a company’s actual earnings meet analysts’ consensus in
the previous year, and zero otherwise. D_GuideDown is an indicator variable set to one if the upper bound of a management range forecast is lower than the prevailing analyst consensus, and zero otherwise.
M
.
T
a
n
g
e
t
a
l
.
/
A
c
c
o
u
n
t
i
n
g
,
O
r
g
a
n
i
z
a
t
i
o
n
s
a
n
d
S
o
c
i
e
t
y
4
2
(
2
0
1
5
)
4
8
–
6
6
5
5
(median) Width is 0.406% (0.279%) of the share price. For
the 9062 management range forecasts that are bundled
with earnings announcements, the bundled earnings news
(Bundle_Eanews) has a mean (median) of 0.082% (0.062%).
Table 3 Panel B presents the univariate Pearson correla-
tions among the variables. Values in boldface are sig-
ni?cant at the 1% level. Revision is positively correlated
with News_Mid (q = 0.785), suggesting that management
forecasts affect analyst revisions (e.g., Cotter et al., 2006).
Upper Bound and Lower Bound are highly correlated
(q = 0.803 untabulated), which con?rms our concern of
multi-collinearity if both these variables are included in
the same regression. Width is only moderately correlated
with News_Mid (q = À0.114), thus mitigating multi-
collinearity when it is used in place of both Upper Bound
and Lower Bound.
Analysts’ weights on the upper and lower bounds of
management range forecasts (H1)
Table 4 presents our primary results. The standard
errors are robust and clustered by ?rm. In Column (1),
we follow prior literature and measure management fore-
cast news using the midpoint (News_Mid), which implicitly
forces analysts’ weights to be equal on the upper bound
and lower bound of management forecast ranges. Consis-
tent with prior literature, News_Mid is signi?cantly posi-
tive (t = 55.05), suggesting that analysts react strongly to
management forecast news. Note that the intercept in Col-
umn (1) is signi?cantly negative (t = À3.25), which implies
that analysts on average react negatively to the action of
management forecasts. This suggests that analysts would
revise forecasts downward even when the midpoint of a
management forecast coincides with their prevailing con-
sensus (i.e., News_Mid = 0), which contradicts the notion
that voluntary disclosure of con?rming forecasts is typical-
ly viewed positively because it reduces uncertainty about
future earnings (Clement et al., 2003), and is also inconsis-
tent with the prior ?ndings that investors and analysts on
average prefer more management disclosures (Bushee &
Noe, 2000; Lang & Lundholm, 1993).
15
Importantly, the negative intercept reverses to positive
once we allow analysts to place unequal weights on the
upper and lower bounds of management forecast ranges
by including forecast width (Width) in Model (1M), as the
intercept in Column (2) is signi?cantly positive (t = 8.00),
suggesting that analysts positively perceive managers’
action of providing forecasts, consistent with analysts
favoring more disclosure (Lang & Lundholm, 1993). There-
fore, the puzzling result in Column (1) is likely due to the
empirical design that fails to allow analysts to place
unequal weights on the upper and lower bounds of man-
agement range forecasts.
Results in Column (2) provide evidence that the weights
are indeed unequal. Recall that h is the hypothetical weight
that analysts place on the upper bound when revising fore-
casts. If analysts weigh the upper and lower bounds equal-
ly (h = 0.5), the coef?cient on Width divided by the
coef?cient on News_Mid, which is expected to equal
h À 0.5, should be statistically indifferent from zero. Con-
trary to this prediction, the estimated coef?cient ratio is
signi?cantly negative at À0.229 (t = À8.24), rejecting the
null hypothesis that analysts place equal weights on the
upper and lower bounds of management forecast ranges
when revising their own forecasts. Our regression coef?-
cients imply that analysts place 0.271 weight on the upper
bound of management forecasts, thus 0.729 (=1–0.271)
weight on the lower bound, when responding to range
forecasts.
16
Next in Columns (3) and (4), we follow Gong et al.
(2011) and include industry and year ?xed effects in our
Base Model and Model (1M), to account for industry-
speci?c effects and any temporal trend.
17
The inclusion of
?xed effects renders the intercept uninformative of analysts’
response to managers’ action of providing forecasts. The
coef?cient ratio in Column (4) implies that analysts place a
weight of 0.244 on the upper bound, signi?cantly less than
0.5 (t = À8.71), consistent with our hypothesis H1 that ana-
lysts respond to a management range forecast (a signal of
ambiguity) by overweighting the lower bound (treating
the worst scenario as more likely than the best scenario).
The strong and consistent evidence that analysts place
unequal weight on the upper and the lower bounds of man-
agement range forecasts is important to researchers, given
its sharp contrast from the implicit assumption of ‘‘equal
weights’’ from the conventional research design that uses
the midpoint to measure forecast news in studying analyst
reaction to management forecasts (e.g. Ajinkya et al., 2005;
Gong et al., 2011; Rogers & Stocken, 2005; Rogers & Van
Buskirk, 2013). To relax the ‘‘equal weight’’ assumption,
which is refuted by our evidence, future studies should at
least include Width in the analyst revision model to allow
analysts to place unequal weights on the endpoints of
management range forecasts.
We also emphasize and caution readers to distinguish
the ‘‘weight’’ from the ‘‘distance.’’ Analysts’ overweight on
the lower bound does not con?ict with our previous result
in Table 2 that analysts’ revised forecasts are actually ‘‘clo-
ser’’ to the upper bound (also see Ciconte et al., 2014).
Recall that the ‘‘weight’’ is the empirical sensitivity of ana-
lyst forecast revision to the forecast news conveyed from
management forecast endpoints. Therefore, even though
analyst forecast revision is more sensitive to the lower
bound of management range forecasts, analysts respond
positively to managers’ action of providing forecasts (evi-
denced by a positive intercept in Column (2)), resulting in
the revised forecasts actually above the midpoint.
Overall, the results in Table 4 provide strong evidence
that analysts place unequal weight on the upper and lower
15
The positive effect of the mere act of providing voluntary disclosure is
twofold. First, investors will only dismiss the belief that the ?rm is hiding
the worst news when they receive a disclosure, regardless of the content
(Grossman & Hart, 1980). Second, the disclosure itself reduces uncertainty
about the future (Clement et al., 2003).
16
Despite concerns of multi-collinearity, in an untabulated test, we
regress Revision on news measured from both the Upper Bound and Lower
Bound, and we continue to ?nd a positive intercept (t = 7.02) and h À 0.5
signi?cantly negative (t = À7.44).
17
For the same reason, we include industry and year ?xed effects in all
our remaining analyses.
56 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
bounds of management range forecasts, with signi?cantly
more weight placed on the lower bound than on the upper
bound, consistent with the prediction of H1.
Addressing concerns of management forecasts bundled with
earnings announcements
Because our dependent variable – analysts forecast
revision – can be affected also by any concurrent release
of information with management forecasts, we conduct a
battery of analyses to mitigate the impact of the most com-
mon concurrent information – bundled earnings news
(e.g., Rogers & Van Buskirk, 2013). The results are present-
ed in Table 5.
In Column (1), we directly control for the bundled earn-
ings news. The implied h is 0.197 and remains signi?cantly
less than 0.5 (t = À9.72). In Column(2), we exclude all ‘‘bun-
dled’’ management forecasts and retain only ‘‘stand-alone’’
forecasts, reducing the sample size to 1927. The implied h is
0.060 and remains signi?cantly less than 0.5 (t = À4.91). In
Column (3), we restrict the sample to only bundled fore-
casts, and the implied h is 0.217 and remains signi?cantly
less than 0.5 (t = À8.90). Next we separate forecasts bun-
dled with positive earnings news (Bundle_Eanews P0 in
Column (4)) from forecasts bundled with negative earnings
news (Bundle_Eanews < 0 in Column (5)). In both cases, the
implied h remains signi?cantly less than 0.5 (t = À7.85 and
À5.57). In Column (6), we follow the procedure described
in Rogers and Van Buskirk (2013) to calculate analysts’ pre-
dicted revision in response to bundled earnings news, and
measure management forecast news against this predicted
analysts’ revised forecasts. The implied h is 0.218 and
remains signi?cantly less than 0.5 (t = À3.15). However,
the sample size is substantially reduced due to the require-
ment of additional variables, limiting the testing power.
Therefore, we choose to directly control for bundled earn-
ings news in our remaining analyses.
Overall, our ?nding that analysts overweight the lower
bound of management forecasts is robust to a battery of
tests that mitigate the confounding effect of ‘‘bundled’’
earnings news.
Cross-sectional variations in analysts’ weights on
management forecast bounds (H2)
Results in Tables 3 and 4 suggest that, on average, ana-
lysts place more weight on the lower bound than on the
upper bound of management range forecasts. However,
we expect the degree of such unequal weight to differ
across subsamples. Speci?cally, if analysts’ overweight on
the lower bound is a result of following the ‘‘max–min’’
axiom of decision making behavior, then we expect their
overweight on the lower bound to be more pronounced
when uncertainty is higher, predicted in our H2. To exam-
ine this prediction, we re-estimate Model (1M), interacting
Width with different measures of uncertainty, in the fol-
lowing form.
18
Revision
i;t
¼ b
0
þ b
1
ðNews Mid
i;t
Þ þ b
2
Width
i;t
þ b
3
ðWidth
i;t
à X
i;t
Þ þ b
4
X
i;t
þ b
5
Bundle Eanews þe ð2Þ
where X is the variable that we expect to change analysts’
relative weights on the upper and the lower bounds of
management forecast ranges.
Table 4
Analysts’ weights on the upper and lower bounds of management range forecasts.
Revision
i;t
¼ a þ bðNews Mid
i;t
Þ þ bðh À 0:5Þ Ã Width
i;t
þ
Base Model Model (1M) Base Model Model (1M)
(1) (2) (3) (4)
Intercept À0.0002
***
0.001
***
À0.001 À0.001
(À3.25) (8.00) (À0.79) (À0.46)
News_Mid 0.788
***
0.775
***
0.785
***
0.771
***
(55.05) (55.06) (54.58) (54.38)
Width À0.177
***
À0.198
***
(À8.56) (À9.09)
h À 0.5 À0.229
***
À0.256
***
(t-stat) (À8.24) (À8.71)
Implied h 0.271
***
0.244
***
(t-stat) (9.75) (8.29)
Industry Fixed Effect No No Yes Yes
Year Fixed Effect No No Yes Yes
No of OBS 10,989 10,989 10,989 10,989
Adjusted R-Squared 61.6% 62.9% 62.5% 63.8%
This table presents results from OLS regressions of analyst forecast revisions on management forecast news and range widths. The sample includes 10,989
management range forecasts of annual earnings of ?scal years between 1996 and 2011. Revision is the mean revision of all analysts that issue forecasts both
before and after a management forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast
minus the prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance between the upper bound and
the lower bound of a management range forecast, de?ated by the stock price at the beginning of the year. t-Stats are based on standard errors clustered on
the ?rm level. h is the hypothetical weight that analysts place on the upper bound of management forecast ranges when revising their own forecasts. t-Stats
about h are calculated using the delta method (Rao, 1965).
?
Signi?cance level lower than 10%.
??
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
18
Although we do not expect the coef?cient on News_Mid to vary with X,
nevertheless, in untabulated tests, we also control for the interaction of X
with News_Mid and obtain qualitatively similar results.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 57
If analysts increase (decrease) their relative overweight
on the lower bound when X takes a higher value, we expect
the coef?cient on the corresponding interaction term to be
signi?cantly negative (positive).
19
For ease of interpreting
the results, we transform continuous variables into indicator
variables that are set to one for observations above sample
medians and zero otherwise. Hence the coef?cient on Width
in Model (2) is (b
2
+ b
3
X), which should be equal to
b ? (h À 0.5) as in Model (1M). Drawing from Model (1M),
the coef?cient ratio of (b
2
+ b
3
X)/b
1
in Model (2) should be
equal to h À 0.5, which allows h to be a function of X. For
observations where X = 0, the implied h
X=0
= b
2
/b
1
+ 0.5,
whereas for observations where X = 1, the implied h
X=1
=
(b
2
+ b
3
)/b
1
+ 0.5; the difference in the implied Dh = h
X=1
À
h
X=0
= b
3
/b
1
.
The results are reported in Table 6. In Column (1), we
test our H2a and examine whether analysts increase their
weight on the lower bound of forecasts issued in earlier
quarters, indicated by three dummy variables for the ?rst,
second, and third quarter (Fq1, Fq2, and Fq3), using the
fourth quarter as the benchmark. The coef?cient on the
interaction term Width ? Fq1 is negative and signi?cant at
À0.144 (t = À3.03), suggesting that analysts overweight
the lower bound to a larger extent in the ?rst quarter than
in the fourth quarter. Using the coef?cients to infer ana-
lysts’ weight on the lower bound (h), analysts add another
0.204 weight on the lower bound in the ?rst quarter than
in the fourth quarter. Because earlier management fore-
casts tend to contain higher uncertainty, this ?nding is
consistent with analysts shifting more weight to the worse
scenario as they face more uncertainty, which is consistent
with the ‘‘max–min’’ axiom (Gilboa & Schmeidler, 1989).
The interaction terms Width ? Fq2 and Width ? Fq3 are
negative but not signi?cant (t = À1.26 and À0.36), but
the standalone term Width is signi?cantly negative
(t = À4.19), suggesting that analysts still overweight the
lower bound even when management forecast is issued
in the fourth quarter, when uncertainty about the annual
earnings is the lowest.
20
In Column (2), we test our H2b and examine whether
analysts increase their weight on the lower bound of fore-
casts with wider ranges (D_WideRange is set to one if Width
is larger than the median). Consistent with this prediction,
the coef?cient on the interaction term Width ? X is nega-
tive and signi?cant at À0.110 (t = À2.02). The coef?cients
imply that analysts shift additional weight of 0.155 from
the upper bound to the lower bound when management
range forecasts are wider, even though the weight is
already signi?cantly less than 0.5 on the upper bound
(t = À2.31) for narrow ranges. This ?nding is consistent
with analysts viewing wider range forecasts as more
uncertain and shift even more weight on the lower bound,
consistent with the ‘‘max–min’’ axiom (Gilboa &
Schmeidler, 1989).
Both Columns (1) and (2) of Table 6 examine the uncer-
tainty conveyed by the properties of management fore-
casts, that is, the timing and the range width. Next we
examine whether uncertainty re?ected in the ?rm’s infor-
mation environment also affects analysts’ weight on the
endpoints of management range forecasts. We use analyst
forecast dispersion and return volatility as measures of
information uncertainty following prior literature (e.g.,
Feng & Koch, 2010; Chen et al., 2011) and report the results
in Columns (3) and (4). Consistent with our H2c and H2d,
we ?nd that analysts further reduce weights on the upper
bound when facing higher uncertainty as the interaction
terms are signi?cantly negative (t = À3.99 and À4.53).
Moreover, the coef?cient on Width remains signi?cantly
negative (t = À3.41 and À1.85), suggesting that even when
the information environment contains relatively little
uncertainty, analysts still view range forecasts from man-
agers as ambiguous signals and overweight the lower
bound, consistent with the ‘‘max–min’’ axiom.
While analysts shift more ‘‘weight’’ to the lower bound
as uncertainty increases, their revised forecasts do not nec-
essarily get ‘‘closer’’ to the lower bound, echoing our earlier
caveat on the distinction between the ‘‘weight’’ and the
‘‘distance’’.
21
The max–min axiom applies when a decision-
maker faces a set of possibility distributions and makes
choices by weighing different possible scenarios (e.g., weigh-
ing the upper and lower bounds of management range fore-
casts) (Epstein & Schneider, 2008), but the resulting decision
might not necessarily be pessimistic. Consistent with this, in
Table 6, while we ?nd that analysts overweight the lower
bound more when uncertainty is higher, most of the
stand-alone indicators of high uncertainty (Fq1, Fq2, and
Fq3 in Column (1), and X in Columns (2) to (4)) are sig-
ni?cantly positive (e.g., t = 2.90 for Fq1 in Column (1)), which
echoes our ?nding of a positive intercept in Model (1M) and
suggests that analysts actually value managers’ provision of
forecasts even more in face of more uncertainty. Therefore,
our results suggest that the max–min axiom applies only to
the ‘‘weight’’ that analysts choose but not to the ‘‘distance’’
of their revised forecasts from managers’ range forecasts.
In summary, the results in Table 6 are consistent with
our H2 cross-sectional predictions of the ‘‘max–min’’
axiom. We ?nd that analysts shift more ‘‘weight’’ to the
lower bound when uncertainty is higher.
Are analysts ‘‘Bayesian’’ and learn from the past?
We next investigate whether analysts are ‘‘Bayesian’’ in
the sense that they adjust their weights on management
forecast bounds based on past experience. Two reasons
19
Note that we are comparing the weight analysts put on the lower
bound in the cross-sectional analyses, although on average analysts still
place less weight on the upper bound than on the lower bound (i.e., h < 0.5)
in most cases.
20
These results are similar in the subsample of bundled forecasts.
However, all three interaction terms (Width ? Fq1, Width ? Fq2, and
Width ? Fq3) are insigni?cant in the subsample of unbundled forecasts
(untabulated t-stats = À0.55, 0.87, and 0.96, respectively). One possible
explanation is the smaller sample size (only 1927 unbundled compared
with 9062 bundled). Another explanation is that the timing of unbundled
forecasts is unpredictable by their nature, regardless of when they are
provided. Hence, analysts’ weights do not vary signi?cantly with their
forecast timing.
21
Indeed, analysts’ revised forecasts, on average, shift ‘‘closer’’ to the
upper bound (see Table 2). The ‘‘distance’’ of analysts’ revised forecasts to
managers’ range forecasts depend on both their ‘‘weight’’ on the end-points
and their reaction to managers’ provision of the range forecasts.
58 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
motivate this analysis. First, many managers provide earn-
ings forecasts regularly (e.g., Rogers, Skinner, & Van
Buskirk, 2009; Tang, 2013), thus providing the opportunity
for analysts to learn from past management forecasts
(Hilary & Shen, 2013). Second, prior literature also provides
evidence consistent with analysts facing parameter uncer-
tainty and learning rationally about the parameters over
time (Markov & Tamayo, 2006). Table 7 presents the
results from this analysis.
First, if actual earnings were closer to the upper bound
than to the lower bound of management forecast in the
previous year (D_LastActualCloserToUpper = 1), a ‘‘Baye-
sian’’ analyst is likely to shift more weight from the lower
bound to the upper bound. To ensure that the current man-
agement forecast is comparable to that in the previous
year, we require them to be issued in the same quarter,
which reduces the sample size to 7617. In Column (1),
we ?nd a marginally signi?cant and positive coef?cient
on the interaction term (t = 1.73), providing some evidence
that analysts place more weight on the range endpoint that
was previously proven to be more accurate. Importantly,
the coef?cients continue to imply a weight of less than
0.5 on the upper bound (0.170 + 0.113 = 0.283) even when
the actual earnings were closer to the upper bound in the
previous year, consistent with our main hypothesis.
Next, in Column (2), we examine whether analysts
compare the range width with past forecasts and adjust
their weights accordingly. If the current forecast is wider
than that in the same quarter in the previous year
(D_WiderThanLast = 1), we ?nd that analysts shift sig-
ni?cantly more weight from the upper bound to the lower
bound, as the interaction term is signi?cantly negative
(t = À7.95). This result shows that as uncertainty increases,
the weight on the lower bound increases. This is consistent
with the results in Table 6, where uncertainty is measured
in the cross section, whereas in Table 7 uncertainty is mea-
sured with respect to each ?rm’s own time series, both of
which are consistent with the max–min axiom.
Taken together, Columns (1) and (2) in Table 7 provide
evidence that analysts are Bayesian and learn from past
experience. While we ?nd some evidence that analysts
adjust their weights based on whether actual earnings
were closer to the upper or lower bound, we ?nd strong
evidence that their overweight on the lower bound is more
pronounced when the current forecast range is wider than
before, consistent with the ‘‘max–min’’ explanation.
22
Table 5
Accounting for earnings news bundled with management range forecasts.
Revision
i;t
¼ a þ bðNews Mid
i;t
Þ þ bðh À 0:5Þ Ã Width
i;t
þ c Bundle Earnews þe
All
management
forecasts
Stand-alone
management
forecasts
Bundled
management
forecasts
Bundled management
forecasts with positive
earnings news
Bundled management
forecasts with negative
earnings news
Bundled
management
forecasts
a
(1) (2) (3) (4) (5) (6)
Intercept À0.001 0.003
**
À0.001 À0.001 À0.001 0.003
***
(À0.57) (2.11) (À0.73) (À0.61) (À0.52) (7.94)
News_Mid 0.709
***
0.710
***
0.704
***
0.703
***
0.698
***
0.549
***
(45.83) (17.30) (40.04) (32.53) (24.26) (6.95)
Width À0.215
***
À0.312
***
À0.199
***
À0.175
***
À0.242
***
À0.155
***
(À10.35) (À5.53) (À9.42) (À8.02) (À6.08) (À3.03)
Bundle_Eanews 0.422
***
0.422
***
0.399
***
0.321
***
(15.81) (14.67) (10.82) (5.58)
h À 0.5 À0.303
***
À0.440
***
À0.283
***
À0.249
***
À0.346
***
À0.282
***
(t-stat) (À9.72) (À4.91) (À8.90) (À7.85) (À5.57) (À3.15)
Implied h 0.197
***
0.060 0.217
***
0.251
***
0.154
**
0.218
**
(t-stat) (6.30) (0.67) (6.81) (7.88) (2.47) (2.43)
Industry Fixed
Effect
Yes Yes Yes Yes Yes Yes
Year Fixed
Effect
Yes Yes Yes Yes Yes Yes
No of OBS 10,989 1,927 9,062 6,966 2,096 4,874
Adjusted R-
Squared
67.4% 57.7% 69.7% 65.5% 66.9% 55.9%
This table presents results from OLS regressions of analyst forecast revisions on management forecast news and range widths, controlling bundled earnings
announcement news. The sample includes 10,989 management range forecasts of annual earnings of ?scal years between 1996 and 2011, of which 9062
management forecasts are bundled with quarterly earnings announcements. Revision is the mean revision of all analysts that issue forecasts both before and
after a management forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast minus the
prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance between the upper bound and the lower
bound of a management range forecast, de?ated by the stock price at the beginning of the year. Bundle_Eanews is the actual earnings announced along with
a management range forecast minus the median analyst forecast for the actual earnings, de?ated by the stock price at the beginning of the year. t-Stats are
based on standard errors clustered on the ?rm level. h is the hypothetical weight that analysts place on the upper bound of management forecast ranges
when revising their own forecasts. t-Stats about h are calculated using the delta method (Rao, 1965).
?
Signi?cance level lower than 10%.
**
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
a
This column uses conditional expectations to calculate analyst forecast revisions and management forecast news, following the method described in
Rogers and Van Buskirk (2013).
22
In untabulated analysis, we ?nd the ‘‘Bayesian’’ results to be slightly
more signi?cant (slightly less signi?cant) in the subsample of bundled
(unbundled) forecasts, possibly due to a larger (smaller) sample size.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 59
Does ‘‘Lowballing’’ explain analysts’ overweight on the lower
bound?
Prior research suggests that analysts have incentives to
‘‘lowball’’ their forecasts so that managers could meet or
beat their forecasts more easily and possibly return the
favor with more private communication (Hilary & Hsu,
2013; Ke & Yu, 2006). However, analysts also want to avoid
issuing forecasts that are too gloomy because poor
expectations could hurt the ?rm’s stock price and anger
managers to limit the analysts’ access to management
(Brown, Call, Clement, & Sharp, 2013). It is possible that
management range forecasts offer the lower bound as an
apparent target for analysts to ‘‘lowball’’ their forecasts.
To evaluate this explanation, we examine whether ana-
lysts’ overweight on the lower bound becomes more pro-
nounced when ‘‘meeting and beating’’ analysts’ forecasts
is more important to managers, who therefore are more
Table 6
Cross-sectional analysis of analysts’ weights on range forecast bounds.
Revision
i;t
¼ b
0
þ b
1
ðNews Mid
i;t
Þ þ b
2
Width
i;t
þ b
3
ðWidth
i;t
à X
i;t
Þ þ b
4
X
i;t
þ b
5
Bundle Eanews
i;t
þe
X As D_WideRange D_Dispersion D_RetVol
(1) (2) (3) (4)
Intercept À0.001 À0.001 À0.001 À0.001
(À0.78) (À0.74) (À0.77) (À0.90)
News_Mid 0.706
***
0.709
***
0.716
***
0.708
***
(45.43) (45.83) (47.34) (46.11)
Width À0.147
***
À0.115
**
À0.098
***
À0.066
*
(À4.19) (À2.32) (À3.41) (À1.85)
Width ? Fq1 À0.144
***
(À3.03)
Width ? Fq2 À0.062
(À1.26)
Width ? Fq3 À0.018
(À0.36)
Width ? X À0.110
**
À0.139
***
À0.182
***
(À2.02) (À3.99) (À4.53)
Fq1 0.001
***
(2.90)
Fq2 0.0004
**
(2.43)
Fq3 0.0002
(1.07)
X 0.0003
*
0.0003
**
0.0003
**
(1.71) (2.29) (2.23)
Bundle_Eanews 0.420
***
0.421
***
0.412
***
0.420
***
(15.80) (15.77) (14.97) (15.74)
Implied h When X = 0 0.292
***
0.338
***
0.363
***
0.407
***
(t-stat) (5.78) (4.84) (8.98) (8.05)
h À 0.5 When X = 0 À0.208
***
À0.162
**
À0.137
***
À0.093
*
(t-stat) (À4.13) (À2.31) (À3.37) (À1.84)
Difference in Implied h À0.204
*** a
À0.155
**
À0.195
***
À0.258
***
(t-stat) (À3.00) (À2.02) (À3.96) (À4.50)
Industry Fixed Effect Yes Yes Yes Yes
Year Fixed Effect Yes Yes Yes Yes
No of OBS 10,989 10,989 10,599 10,983
Adjusted R-Squared 67.6% 67.4% 68.3% 67.7%
This table reports results from OLS regressions to examine the cross-sectional variations in the weight analysts place on the upper and lower bounds of
management range forecasts. The sample includes 10,989 management range forecasts of annual earnings of ?scal years between 1996 and 2011. The
actual sample size varies due to the unavailability of independent variables. The dependent variable is Revision. Revision is the mean revision of all analysts
that issue forecasts both before and after a management forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a
management range forecast minus the prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance
between the upper bound and the lower bound of a management range forecast, de?ated by the stock price at the beginning of the year. Fq1(Fq2, Fq3) is an
indicator variable set to one if a management forecast is issued in the ?rst (second, third) ?scal quarter, and zero otherwise. D_WideRange is an indicator
variable set to one if the width of management forecast range is higher than the sample median, and zero otherwise. D_Dispersion is an indicator variable set
to one if Dispersion is higher than the median, and zero otherwise, where Dispersion is the standard deviation of analyst forecasts issued within 90 days
before the management forecast announcement, de?ated by the stock price at the beginning of the year. D_RetVol is an indicator variable set to one if RetVol
is higher than the median, and zero otherwise, where RetVol is the stock return volatility measured as the standard deviation of daily stock returns from day
À120 to day À1 relative to the management forecast date. Bundle_Eanews is the actual earnings announced along with a management range forecast minus
the median analyst forecast for the actual earnings, de?ated by the stock price at the beginning of the year. t-Stats are based on standard errors clustered on
the ?rm level. h is the hypothetical weight that analysts place on the upper bound of management forecast ranges when revising their own forecasts. t-Stats
about h are calculated using the delta method (Rao, 1965).
*
Signi?cance level lower than 10%.
**
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
a
The difference in implied h in this case is between Fq1 and Fq4.
60 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
likely to favor analysts issuing ‘‘low ball’’ forecasts (Hilary
& Hsu, 2013). Prior literature suggests that managers have
stronger incentives to meet and beat analyst forecasts if
they have done so in the recent past (Kross et al., 2011).
Therefore, if the actual earnings met or beat analyst con-
sensus forecasts in the previous year (D_MeetAF = 1), we
would expect analysts to overweight the lower bound to
a greater extent if ‘‘low balling’’ is the primary reason for
them to overweight the lower bound. We report the results
in Column (3) of Table 7 and the interaction term is insig-
ni?cant (t = 0.13).
23
Hence, we do not ?nd evidence that
they overweight the lower bound more when the incentive
to ‘‘low ball’’ forecasts is stronger.
Related to analysts’ incentives to ‘‘lowball’’ their fore-
casts, it has been documented that managers often use
earnings forecasts to ‘‘walk down’’ analyst forecasts (e.g.,
Cotter et al., 2006; Matsumoto, 2002). To examine whether
our result of analysts’ overweight on the lower bound is
driven by managers ‘‘walking down’’ analyst expectation,
we de?ne a dummy variable for ‘‘guide-down’’ guidance
(D_GuideDown), which is set equal to one if the entire
range of management forecasts falls below the prevailing
analyst consensus, and zero otherwise.
24
If our result is dri-
ven by managers’ guiding down analyst forecasts, then we
would expect the overweight on the lower bound to be more
pronounced for ‘‘guide-down’’ forecasts and hence the inter-
action term of D_Guidedown ? Width should be negative. The
result, reported in Column (4) in Table 7, shows that this
interaction term is insigni?cant (t = À0.85). Therefore, we
do not ?nd evidence that analysts’ overweight on the lower
Table 7
Additional cross-sectional analysis of analysts’ weights on forecast bounds.
Revision
i;t
¼ b
0
þ b
1
ðNews Mid
i;t
Þ þ b
2
Width
i;t
þ b
3
ðWidth
i;t
à X
i;t
Þ þ b
4
X
i;t
þ b
5
Bundle Eanews
i;t
þe
X As Are analysts ‘‘Bayesian’’? Is ‘‘Lowballing’’ the explanation?
D_LastActualCloser-toUpper D_WiderThanLast D_MeetAF D_GuideDown
(1) (2) (3) (4)
Intercept À0.001
**
À0.003
***
À0.001 À0.001
(À2.54) (À5.23) (À0.81) (À0.50)
News_Mid 0.724
***
0.726
***
0.709
***
0.682
***
(36.51) (38.13) (43.85) (33.66)
Width À0.239
***
0.062
*
À0.215
***
À0.209
***
(À7.60) (1.79) (À4.88) (À9.16)
Width ? X 0.082
*
À0.323
***
0.006 À0.037
(1.73) (À7.95) (0.13) (À0.85)
X 0.0001 0.001
***
0.0001 À0.0004
***
(0.53) (4.06) (0.71) (À2.68)
Bundle_Eanews 0.387
***
0.387 0.418
***
0.422
***
(12.29) (12.26) (14.55) (15.86)
Implied h When X = 0 0.170
***
0.586
***
0.197
***
0.193
***
(t-stat) (3.75) (12.21) (3.09) (5.57)
h À 0.5 When X = 0 À0.330
***
0.086
*
À0.303
***
À0.307
***
(t-stat) (À7.31) (1.79) (À4.76) (À8.84)
Difference in Implied h 0.113
*
À0.445
***
0.009 À0.054
(t-stat) (1.73) (À7.64) (0.13) (À0.85)
Industry Fixed Effect Yes Yes Yes Yes
Year Fixed Effect Yes Yes Yes Yes
No of OBS 7,617 7,660 9,730 10,989
Adjusted R-Squared 68.0% 68.7% 67.8% 67.5%
This table reports results from OLS regressions to examine: (a) whether analysts are ‘‘Bayesian’’ and learn from their past experience, and (b) whether
analysts’ overweight on the lower bound of management range forecast can be explained by their incentives of ‘‘lowballing.’’ The sample is based on 10,989
management range forecasts of annual earnings between 1996 and 2011. The actual sample size varies due to the unavailability of independent variables.
The dependent variable is Revision. Revision is the mean revision of all analysts that issue forecasts both before and after a management forecast, de?ated by
the stock price at the beginning of the year. News_Mid is the midpoint of a management range forecast minus the prevailing consensus analyst forecast,
de?ated by the stock price at the beginning of the year. Width is the distance between the upper bound and the lower bound of a management range
forecast, de?ated by the stock price at the beginning of the year. D_LastActualClosertoUpper is an indicator variable set to one if the previous year’s actual
earnings are closer to the upper bound of the management forecast issued in the same quarter of the previous year, and zero otherwise. D_WiderThanLast is
an indicator variable set to one if the current range forecast width is wider than the range width of the management forecast issued in the same quarter of
the previous year, and zero otherwise. D_MeetAF is an indicator variable set to one if a company’s actual earnings meet analysts’ consensus in the previous
year, and zero otherwise. D_GuideDown is an indicator variable set to one if the upper bound of a management range forecast is lower than the prevailing
analyst consensus, and zero otherwise. Bundle_Eanews is the actual earnings announced along with a management range forecast minus the median analyst
forecast for the actual earnings, de?ated by the stock price at the beginning of the year. t-Stats are based on standard errors clustered on the ?rm level. h is
the hypothetical weight that analysts place on the upper bound of management forecast ranges when revising forecasts. t-Stats about h are calculated using
the delta method (Rao, 1965).
*
Signi?cance level lower than 10%.
**
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
23
The interaction remains insigni?cant in both the bundled and unbun-
dled subsamples (t-stats = À0.01 and 0.23).
24
Our results remain qualitatively the same if we de?ne D_GuideDown as
one if the midpoint of the range forecast (rather than the entire range) is
below the prevailing analyst consensus forecast, and zero otherwise.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 61
bound is more pronounced when management forecasts
‘‘walk down’’ analyst expectations. Note that the coef?cient
on Width remains signi?cantly negative (t = À9.16), suggest-
ing that even if management forecasts do not ‘‘walk down’’
analyst expectations, analysts still overweight the lower
bound as h is signi?cantly less than 0.5 (t = À8.84).
We conduct several additional analyses (untabulated)
regarding ‘‘guide-down’’ forecasts and we ?nd mixed
results, suggesting that ‘‘low-balling’’ at best only partially
explains analysts’ over-weight on the lower bound of man-
agers’ range forecasts. First, we ?nd that the coef?cient on
Width ? D_GuideDown becomes signi?cantly negative
(marginally positive) in the subsample of bundled (unbun-
dled) forecasts with a t-stat of À2.37 (1.88), suggesting that
‘‘lowballing’’ partially explains analysts’ overweight on the
lower bound for bundled forecasts, but not for unbundled
forecasts. Second, for the subset of updated forecasts, we
de?ne ‘‘D_GuideDown’’ by comparing the current manage-
ment forecast with the previous forecast (using either the
midpoint or the upper or the lower bound for comparison),
and we ?nd the interaction term to be signi?cantly
negative (t-stats = À4.40, À4.95, and À4.54 respectively),
consistent with analysts overweighting the lower bound
for downwardly revised forecasts. Finally, when we de?ne
‘‘D_GuideDown’’ by requiring only the lower bound to be
below analysts’ preexisting consensus, we ?nd the interac-
tion to be signi?cantly positive (t-stat = 3.36), inconsistent
with ‘‘lowballing’’ explanation. Across all these speci?ca-
tions, the Width term remains signi?cantly negative (t-stat
ranging from À2.45 to À7.65), suggesting that analysts’
overweight on the lower bound of managers’ forecasts can-
not be fully explained by analysts’ incentives to ‘‘lowball’’
their forecasts.
To summarize, in Table 7 Columns (3) and (4), we do
not ?nd evidence that analysts’ overweight on the lower
bound of management range forecasts is more pronounced
when they have stronger incentives to ‘‘lowball’’ their fore-
casts, proxied by recent success of managers meeting or
beating analyst forecasts and by managers’ explicit
‘‘guide-down’’ forecasts. These results suggest that our
?nding of analysts’ overweight on the lower bound of man-
agement range forecasts is distinct from the documented
phenomena of analysts ‘‘lowballing’’ their forecasts and
managers’ ‘‘walking down’’ analyst expectations (e.g.,
Cotter et al., 2006; Hilary & Hsu, 2013; Ke & Yu, 2006;
Matsumoto, 2002). While these phenomena focus on the
‘‘distance’’ of analysts’ forecasts to management forecasts
or to actual earnings, our focus is on the ‘‘weight’’ of ana-
lyst forecast revision on the upper and lower bounds of
management range forecasts.
Table 8
Optimal weights on management range forecast bounds.
AFE PRE
i;t
¼ a þ bðNews Mid
i;t
Þ þ bðh À 0:5Þ Ã Width
i;t
þ cBundle Eanews
i;t
þe
All
management
forecasts
All
management
forecasts
Bundled
management
forecasts
Bundled
management
forecasts
Bundled management
forecasts with positive
earnings news
Bundled management
forecasts with negative
earnings news
(1) (2) (3) (4) (5) (6)
Intercept À0.001
**
À0.0004 À0.001
***
À0.002 À0.0002 À0.009
(À2.56) (À0.08) (À2.70) (À0.44) (À0.05) (À0.67)
News_Mid 0.889
***
0.867
***
0.826
***
0.819
***
0.890
***
0.711
***
(15.75) (16.07) (13.64) (14.24) (12.49) (7.37)
Width À0.592
***
À0.722
***
À0.573
***
À0.680
***
À0.502
***
À0.917
***
(À5.89) (À7.29) (À5.58) (À6.56) (À4.17) (À6.07)
Bundle_Eanews 1.391
***
1.250
***
1.426
***
1.293
***
1.065
***
1.337
***
(13.45) (12.48) (13.40) (12.46) (7.13) (6.01)
h À 0.5 À0.666
***
À0.832
***
À0.694
***
À0.830
***
À0.564
***
À1.290
***
(t-stat) (À5.31) (À6.27) (À5.02) (À5.76) (À3.82) (À4.72)
Implied h À0.166 À0.332
**
À0.194 À0.330
**
À0.064 À0.790
***
(t-stat) (À1.32) (À2.50) (À1.40) (À2.29) (À0.43) (À2.89)
Industry Fixed
Effect
No Yes No Yes Yes Yes
Year Fixed
Effect
No Yes No Yes Yes Yes
No of OBS 10,989 10,989 9,062 9,062 6,966 2,096
Adjusted R-
Squared
21.2% 26.3% 21.7% 26.8% 20.3% 27.6%
This table reports results from OLS regressions to examine the optimal weights on the upper and lower bounds of management range forecasts, assuming
that analysts possess perfect foresight of actual earnings. The full sample includes 10,989 management range forecasts of annual earnings of ?scal years
between 1996 and 2011. The actual sample size varies due to the unavailability of independent variables. The dependent variable is AFE_PRE, which re?ects
the optimal revision assuming perfect foresight of actual earnings. AFE_PRE is the difference between the actual earnings and the median analyst earnings
forecast prior to a management range forecast, de?ated by the stock price at the beginning of the year. News_Mid is the midpoint of a management range
forecast minus the prevailing consensus analyst forecast, de?ated by the stock price at the beginning of the year. Width is the distance between the upper
bound and the lower bound of a management range forecast, de?ated by the stock price at the beginning of the year. Bundle_Eanews is the actual earnings
announced along with a management range forecast minus the median analyst forecast for the actual earnings, de?ated by the stock price at the beginning
of the year. t-Stats are based on standard errors clustered on the ?rm level. h is the hypothetical weight that the optimal analyst forecast revisions should
place on the upper bound of management forecast ranges. t-Stats about h are calculated using the delta method (Rao, 1965).
?
Signi?cance level lower than 10%.
**
Signi?cance level lower than 5%.
***
Signi?cance level lower than 1%.
62 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
Optimal weights on management forecast bounds
So far we have documented strong and robust evi-
dence that analysts place signi?cantly more weight on
the lower bound of management range forecasts and that
such overweight on the lower bound is stronger when
uncertainty is higher. However, it is unclear whether
overweighting the lower bound of management range
forecasts leads to more accurate forecast revisions. To
investigate this, we estimate the ‘‘optimal weights’’ on
the upper and lower bounds of management forecast
ranges assuming perfect foresight of the actual reported
earnings is available to analysts. Therefore, we replace
the dependent variable in the previous models with
AFE_PRE, measured as the actual earnings minus the con-
sensus analyst forecast prior to the management forecast,
de?ated by the beginning stock price. If analysts could
forecast earnings accurately with perfect foresight, then
the optimal weight they place on the lower bound should
be consistent with the h implied from the AFE_PRE regres-
sion reported in Table 8. We admit that analysts have
imperfect information about actual reported earnings;
hence we do not expect analysts’ weights in Table 4 to
be perfectly aligned with the ‘‘optimal weights’’ in Table 8.
The purpose of this analysis is rather to answer the fol-
lowing question: compared with placing equal weights
on the upper and lower bounds of management range
forecasts, as implied in the extant research, is analysts’
overweight on the lower bound qualitatively consistent
with the optimal weight implied from actual reported
earnings? If so, we expect the implied h in the AFE_PRE
regression to be signi?cantly less than 0.5.
Table 8 reports the results on ‘‘optimal weights’’ in the
same format as in Table 5, which accounts for bundled
earnings news. Across all speci?cations, the ‘‘optimal
weight’’ on the upper bound implied from actual earnings
is signi?cantly less than 0.5 with t-stats ranging from
À3.82 to À6.27, thus rejecting the null hypothesis that
equal weights on the upper and lower bounds of manage-
ment range forecasts should be the optimal weights, as
implicitly assumed in the existing research design in
empirical accounting literature.
One caveat exists about the ‘‘optimal weight’’. Although
we ?nd it to be ‘‘optimal’’ to overweigh the lower bound,
which is consistent with analysts’ weighting, analysts’
behavior is more consistent with the ‘‘max–min’’ axiom
than with them anticipating the ‘‘optimal weight’’ for
two reasons. First, while analysts shift more weight to
the lower bound for range forecasts that are issued earlier
or that have wider ranges, we ?nd that the ‘‘optimal
weight’’ does not behave in such an ‘‘ambiguity-averse’’
manner (p-value >0.10, untabulated). Second, if analysts
base their weight on their rational anticipation of the opti-
mal weight, there is no clear prediction as to how analysts’
‘‘weight’’ would vary with uncertainty, which we ?nd a
systematic correlation in Table 6. Third, while analysts
overweight the lower bound, the magnitude of their over-
weighting, still appears too small (implied h appears too
large) compared with the ‘‘optimal weight’’. If they antici-
pate the ‘‘optimal weight’’, they should overweight the
lower bound much more heavily.
In summary, using the actual reported earnings to com-
pute ‘‘optimal revisions’’, we ?nd evidence that the ‘‘opti-
mal weight’’ is also signi?cantly higher on the lower
bound. Therefore, even though as a result of their ambi-
guity-averse behavior, analysts’ overweighting on the low-
er bound of management range forecasts indeed leads to
more accurate revisions than if they place equal weights
on management forecast bounds.
Additional tests and robustness checks
Throughout the paper, we use the revision in analysts’
consensus forecasts, because we are interested in whether
the average analyst places equal weights on the upper and
lower bounds of management range forecasts. In unt-
abulated tests, we use individual analyst forecast revisions
so that the benchmark for each analyst’s revision is his or
her own forecast prior to management forecasts. The ana-
lyst-level design results in a sample of 22,407 unique ana-
lyst revisions. Using this sample, we continue to ?nd that
individual analysts’ weight on the lower bound signi?cant-
ly exceeds 0.5 (untabulated t-stat = 7.03), with no sig-
ni?cant difference in the weighting between analysts
whose preexisting forecasts are above the midpoint of
management range forecasts and those below the mid-
point (untabulated t-stat = 1.28).
25
Moreover, when we
alternatively measure revision as the highest or the lowest
analyst forecast minus the preexisting consensus, we again
obtain similar result that analysts’ weight on the lower
bound is signi?cantly more than 0.5 (t-stats = 3.94 and
12.60 respectively).
26
Another possible explanation for analysts to overweight
one endpoint over another is that they might place more
weight simply on the bound that is closer to their preexist-
ing consensus, because psychology research suggests that
people tend to interpret information in a biased way that
con?rms their existing expectations, so-called ‘‘con?rma-
tion bias’’ (e.g., Lord, Ross, & Lepper, 1979). We investigate
this explanation by estimating analysts’ weight on the low-
er bound separately for forecasts that are above the preex-
isting consensus (where the lower bound is closer to
current expectation) and for forecasts that are below the
preexisting consensus (where the upper bound is closer
to current expectation). In both cases, we continue to ?nd
that analysts’ weight on the lower bound is signi?cantly
higher than 0.5 (untabulated t-stats = 8.13 and 6.39
respectively). We extend this analysis by partitioning the
sample into four mutually exclusive cases, depending on
whether the preexisting consensus is: (a) less than or equal
to the lower bound of managers’ range forecast, (b) greater
25
To investigate whether analysts with later preexisting forecasts have
less stale benchmarks and are more likely to herd with other analysts, we
partition the sample by the median number of lead days from analysts’
preexisting forecasts to the release of management forecasts (14 days). In
both samples we ?nd similar evidence that analysts overweight the lower
bound (untabulated t-stats = 8.20 and 7.45 for earlier and later analysts,
respectively).
26
As an additional robustness check, we follow Gu and Wu (2003) and
include the skewness of earnings to account for the possibility that analysts
may aim to forecast the median rather than the mean of earnings. Our
result from this analysis is qualitatively the same as our main result.
M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66 63
than the lower bound but less than or equal to the mid-
point of managers’ range forecast, (c) greater than the mid-
point but less than or equal to the upper bound of
managers’ range forecast, or (d) greater than the upper
bound of managers’ range forecast. Across all cases, we
continue to ?nd that analysts signi?cantly overweight
the lower bound (untabulated t-stats = 3.60, 2.90, 2.75,
and 2.19, respectively).
Next, we examine whether the weighting of analyst
revision is different when responding to ?rms issuing only
a single annual forecast versus to those issuing multiple
forecasts. Tang et al. (2014) document an increasingly large
number of ?rms that issue multiple annual forecasts with-
in the year. To the extent that an updated forecast might
offer more information on how to weight the upper and
lower bounds to analysts, we partition the sample into
three groups: (a) ?rm-years with only a single annual fore-
cast, (b) initial forecasts of those with multiple forecasts,
and (c) forecast updates. Across all three cases, we contin-
ue to ?nd that analysts put signi?cantly more weight on
the lower bound (untabulated t-stats = 3.19, 5.25, and
7.46, respectively).
Finally, we assess whether macro-economic conditions
play a role in analysts’ weights on management forecast
bounds. Following NBER’s de?nition of recessions, we ?nd
that analysts’ weight on the upper bound is lower during
recessions (h = 0.098) than during expansions (h = 0.308),
although both are signi?cantly less than 0.5 (t-
stats = À7.59 and À5.05 respectively). To the extent that
uncertainty tends to be higher during recessions, this ?nd-
ing is consistent with our H2 that heightened uncertainty
exacerbates analysts’ overweight on the lower bound.
Conclusion
Range forecasts have evolved to be the most common
form of management forecasts. Most prior studies use
the midpoint to evaluate analyst reaction to range fore-
casts, implicitly assuming that analysts place equal
weights on the upper and lower bounds of management
range forecasts. In this study, we relax this restrictive
assumption and ?nd strong empirical evidence of unequal
weights: analysts place signi?cantly more weight on the
lower bound than on the upper bound of management
range forecasts. Moreover, analysts’ overweight on the
lower bound is more pronounced when ambiguity is high-
er, consistent with the ‘‘max–min’’ axiom that decision-
makers facing ambiguity tend to assign higher probability
to the worst-case scenario.
Our results are robust to a host of tests controlling for
‘‘bundled’’ earnings news (Rogers & Van Buskirk, 2013)
and are distinct from the documented phenomena of ana-
lysts ‘‘lowballing’’ their forecasts or managers ‘‘walking
down’’ analyst expectations (Cotter et al., 2006). Analysts
also appear to be ‘‘Bayesian’’ and overweight the lower
bound to a greater extent when facing range forecasts that
are wider than previously observed. Additional analyses
show that ‘‘optimal revisions’’ with perfect foresight of
actual earnings also overweight the lower bound, suggest-
ing that analysts’ overweight on the lower bound of
management range forecasts facilitates accurate forecast-
ing compared with equal weighting on both endpoints of
management range forecasts.
Our study is of interest to managers that issue range
forecasts, to investors and analysts who use range fore-
casts, and to the growing literature on expectation man-
agement that examines analyst reactions to management
forecasts. Building upon analysts’ unequal weights placed
on the upper and lower bounds of management range fore-
casts, future studies can further explore whether the accu-
racy and credibility of management range forecasts can
affect analysts’ unequal weights on the forecast bounds.
Another promising avenue for future research is to exam-
ine the range of analyst forecasts and to explore its interac-
tion with the range of management forecasts.
Appendix A. Adapting Model (1M) to consider three
points of the range forecasts
In this appendix, we illustrate an alternative model, in
which analysts choose to allocate their weights on three
points of the management range forecasts – the upper
bound, the lower bound, and the midpoint. Assume that
h
1
and h
2
are analysts’ weights on the upper and lower
bounds respectively, then the weight on the midpoint is
(1 À h
1
À h
2
).
Following the derivation in the paper, Model (1) can be
revised as follows, in which we now allow the weight on
the mid-point to be non-zero while still allowing the
weights on the upper and lower bounds to differ:
Revision ¼ a þ b½h
1
à Upper Bound þ h
2
à Lower Bound þ ð1 À h
1
À h
2
Þ
à Mid-Point À AF? þe ðA1Þ
Subscripts are suppressed for brevity and all variables
are de?ned as the same in original Model (1), with the
additional Mid-Point equals the midpoint of management
range forecasts.
Now consider the following:
Upper Bound ¼ Mid-Point þ1=2 Width ðA2Þ
Lower Bound ¼ Mid-Point À1=2 Width ðA3Þ
Substitute (A2) and (A3) into (A1) and we arrive at the
following model:
Revision
¼ a þ b½h
1
à ðMid-Point þ1=2 WidthÞ
þ h
2
à ðMid-Point À1=2 WidthÞ
þ ð1 À h
1
À h
2
Þ Ã Mid-Point À AF?
¼ a þ b½Mid-Point À AF þ1=2ðh
1
À h
2
Þ Ã Width?
¼ a þ b News Mid þ1=2bðh
1
À h
2
Þ Ã Width ðA4Þ
Compare (A4) with equation (1M) in the paper, the
only difference is the coef?cient on Width, which is now
½b(h
1
À h
2
) instead of b(h À 0.5). Recall that our prediction
following the max–min axiom is that analysts’ weight on
the upper bound (h
1
) should be less than their weight on
64 M. Tang et al. / Accounting, Organizations and Society 42 (2015) 48–66
the lower bound (h
2
), and hence (h
1
À h
2
) < 0, which is
equivalent to our original prediction of (h À 0.5) < 0 in
Model (1M).
As shown above, our method can be readily adapted to
a framework where analysts allocate weights over three
points of management range forecasts – the upper bound,
the lower bound, and the midpoint, without forcing the
weight on the midpoint to be zero. All inferences in our
paper remain qualitatively unchanged under this alterna-
tive framework.
Appendix B. Variable name and de?nition
Dependent variables
Revision = the mean revision of all analysts that issue
forecasts both before and after a management forecast,
de?ated by the stock price at the beginning of the year.
AFE_PRE = the difference between the actual earnings
and the median analyst earnings forecast prior to a
management range forecast, de?ated by the stock price
at the beginning of the year.
Independent variables
News_Mid = the midpoint of a management range fore-
cast minus the prevailing consensus analyst forecast,
de?ated by the stock price at the beginning of the year.
Width = the distance between the upper bound and the
lower bound of a management range forecast, de?ated
by the stock price at the beginning of the year.
Bundle_Eanews = the actual earnings announced along
with a management range forecast minus the median
analyst forecast for the actual earnings, de?ated by
the stock price at the beginning of the year.
Fq1 = an indicator variable set to one if a management
forecast is issued in the ?rst ?scal quarter, and zero
otherwise.
Fq2 = an indicator variable set to one if a management
forecast is issued in the second ?scal quarter, and zero
otherwise.
Fq3 = an indicator variable set to one if a management
forecast is issued in the third ?scal quarter, and zero
otherwise.
D_WideRange = an indicator variable set to one if the
width of management forecast range is higher than
the sample median, and zero otherwise.
D_Dispersion = an indicator variable set to one if Disper-
sion is higher than the median, and zero otherwise, Dis-
persion is the standard deviation of analyst forecasts
issued within 90 days before the management forecast
announcement, de?ated by the stock price at the begin-
ning of the year.
D_RetVol = an indicator variable set to one if RetVol is
higher than the median, and zero otherwise, where
RetVol is the stock return volatility measured as the
standard deviation of daily stock returns from day
À120 to day À1 relative to the management forecast
date.
D_LastActualClosertoUpper = an indicator variable set to
one if the previous year’s actual earnings are closer to
the upper bound of the management forecast issued
in the same quarter of the previous year, and zero
otherwise.
D_WiderThanLast = an indicator variable set to one if the
current range forecast width is wider than the range
width of the management forecast issued in the same
quarter of the previous year, and zero otherwise.
D_MeetAF = an indicator variable set to one if a compa-
ny’s actual earnings meet analysts’ consensus in the
previous year, and zero otherwise.
D_GuideDown = an indicator variable set to one if the
upper bound of a management range forecast is lower
than the prevailing analyst consensus, and zero
otherwise.
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