The Rational Modeling Hypothesis for Analyst Underreaction to Earnings News*

Philip G. Berger Booth School of Business, University of Chicago, 5807 S. Woodlawn Ave., Chicago, IL 60637

and

Zachary R. Kaplan

Booth School of Business, University of Chicago, 5807 S. Woodlawn Ave., Chicago, IL 60637

February 26, 2013

Please do not circulate or cite without permission. Comments welcome.

* We appreciate a helpful discussion with Jonathan Rogers and helpful comments from participants of workshops at ChicagoBooth and Cass Business School. We thank Gus DeFranco and Yibin Zhou for sharing their Institutional Investor all-star analyst data with us. We both gratefully acknowledge financial support from the University of Chicago Booth School of Business.

Abstract We hypothesize that serially correlated forecast errors may arise out of a forecasting methodology

where analysts model earnings as a function of a limited number of inputs which drive earnings. If the model forecasts earnings with error, this suggests that the analyst modeled the relationships between inputs and earnings with error. While rational analysts will re-think the relations between forecast inputs in response to the earnings realization, we hypothesize that because this re-evaluation requires thought, it will occur gradually. In contrast, these models facilitate the rapid incorporation of input changes into earnings forecasts. Consistent with analysts reacting differently to earnings and non-earnings news, we find that analyst forecasts exhibit greater underreaction around earnings announcements than at other times, and underreact more to earnings news than macro-economic news. While analysts may fully incorporate the implications of an earnings surprise into their forecast without fully understanding its implications for their model of a company’s operations, we hypothesize institutional investors will not demand such naïve revisions from analysts. Consistent with this hypothesis, we find that institutional investors vote analysts all-stars who better incorporate non-earnings news into their forecasts, but do not reveal a preference for analysts who better incorporate last quarter’s earnings surprise into this quarter’s forecast. We also demonstrate that while analysts underreact to earnings surprises, they identify cross-sectional and inter-temporal variation in the persistence of earnings surprises, consistent with analysts rationally modeling the surprises rather than naively reacting to them. Overall, we hypothesize that serially correlated forecast errors may arise out of a rational system where analysts choose a number of inputs to include in a model to forecast earnings. They adjust this model rapidly in response to changes in inputs and adjust the model gradually in response to changes in the relation between the inputs.

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1. Introduction

We develop the rational modeling hypothesis to explain analysts' underreaction to

earnings announcements and compare our hypothesis to the explanations offered in the prior

literature. Prior literature has produced evidence that analyst forecasts have serially correlated

forecast errors, suggesting analysts do not use all available information to forecast earnings

(Abarbanell and Bernard 1992). We propose the serial correlation in forecast errors may arise out

of a forecasting system where the analyst selects a limited number of inputs to model the

operations of a firm and predict earnings. Ex-post, if the earnings realization differs from

reported earnings, the analyst modeled the relation between the inputs and earnings with error or

omitted one or more inputs from his forecasting model. We propose that, in response to the

earnings realization, the rational analyst will re-think the relations between forecast inputs and

consider adding new inputs to his model. However, we argue for two reasons this re-evaluation

will likely take longer than it would take the analyst to simply adjust one of the inputs. First,

adding omitted factors to a model or changing relations among inputs takes considerable thought.

Second, analysts often distribute their models to clients and publish tables based on their models

in their reports. Model dissemination disciplines the analyst to create an internally consistent

representation of how the company generates earnings, and limits the analyst’s ability to “fudge”

his prediction by inserting an earnings forecast component without an economic rationale. A

consequence of analysts’ slow-response to earnings news is that models will produce forecasts

biased in the direction of last period’s forecast error.

An illustrative example is that analyst forecasting models of airlines frequently include

fuel costs but forecasting models for retailers rarely do. Although fuel costs likely have an effect

on the profitability of retailers, fuel costs have a major effect on airline profitability. Given the

limited impact of fuel costs on retailers’ earnings, retail analysts may rationally ignore this input

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to focus on more relevant inputs (or wait for the increase in fuel costs to be reflected in other

inputs) while airline analysts include fuel costs in their model. A result of this choice is that,

when fuel costs increase, retail analysts’ forecasts of earnings will be biased in the opposite

direction of the earnings surprise related to the fuel cost shock. Given that fuel prices are serially

correlated, the analyst forecast errors will be as well.

Prior papers investigating the serial correlation in analyst forecast error primarily

investigate only that component of forecast error implied by last period’s forecast error. Viewed

in isolation the omission of last period’s forecast error from this period’s forecast appears

irrational. We argue, however, this omission can be rational when viewed in the context of a

forecasting method that delivers insights about future earnings.

To assess how much analysts learn about earnings changes during the period, we examine

how much the forecast error of the average forecast declines during the period. We find that

analysts reduce their beginning of quarter forecast error by approximately 46 percent by the end

of the quarter. In contrast, a forecast strategy which fully incorporated last quarter’s forecast

error but ignored other information would only reduce forecast error by an average of 15 percent.

When we divide the beginning of quarter forecast error into two components, a component

implied by last period’s earnings surprise (“residual forecast error”) and a component orthogonal

to it (“novel forecast error”), we find that analysts on average incorporate significantly less of the

residual forecast error relative to the novel forecast error. This suggests that analysts do not on

average intensively use last quarter’s forecast error to identify errors in their initial forecast in the

current quarter.

Broadly, these descriptive statistics may be consistent with a forecasting method where

analysts focus on incorporating forecast inputs other than last quarter’s forecast error, because

these inputs have more ability to explain this period’s earnings. To specifically test whether the

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way analysts react to information is consistent with rational modeling we examine whether

analyst revisions underreact more to earnings related information than non-earnings related

information. Examining specific news events, we compare the degree to which the average

analyst incorporates firm-specific earnings news to macro-economic news. We find that analysts

nearly completely incorporate the implications of macro-economic news into their forecasts,

while they incorporate less than half of earnings related news. Second, we assume that the

earnings content of revisions around earnings announcements will be higher than those forecast

revisions which occur later in the quarter. While we find that both revisions underreact to news,

consistent with rational modeling the revisions with higher earnings content underreact more

than twice as much.

Although the average revision may react differently to earnings and non-earnings news,

this does not imply that doing so is the optimal strategy for investors. To test whether investors

prefer forecast methodologies which correct residual forecast error or novel forecast error, we

examine whether analysts selected by institutional investor magazine as all-stars better

incorporate novel forecast error and/or residual forecast error. We find that analysts incorporate

a significantly larger percentage of their novel forecast error. We find that all-star analysts do

not incorporate more of their residual forecast error, although this result is not statistically

significant.

Finally, we examine cross-sectional and inter-temporal variation in the persistence of

residual forecast error, to better understand the forecasting method the analyst uses to respond to

errors in his forecast. A naïve method will simply incorporate a portion of residual forecast error

into next period’s forecast. A sophisticated method will re-think the relations between the

forecast inputs and earnings, and correctly identify when the residual forecast error will be more

or less persistent. Consistent with analysts using a sophisticated forecasting method, we find

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that forecasts covary strongly with variation in the persistence of residual forecast error.

We propose the rational modeling theory to explain analysts' underreaction to public

information because we believe there are significant weaknesses in existing explanations. Prior

papers suggest three causes (1) analysts' misunderstanding of the time-series properties of

earnings (Abarbanell and Bernard 1992), (2) analysts responding to incentives to optimistically

bias their research (Easterwood and Nutt 1999) and (3) analysts’ preference for issuing forecasts

with forecast errors and revisions with similar signs (Smith-Raedy et al. 2006; henceforth SSY).

A concern with the first explanation is that it relies on analysts being naïve. Forecasts have been

positively serially correlated in every quarter for over twenty years. Why haven’t analysts and

brokerages noticed and adapted? A weakness of the second explanation is that it does not

specify why managers' or investors' demand for positive or negative forecast errors would be

correlated with last period’s error (i.e., the second explanation can explain persistent analyst

optimism but cannot explain positive serial correlation in analyst forecast errors).

The third explanation is most similar to what we propose -- a rational theory for analysts

to underreact to the information in earnings. Consistent with the predictions of rational

modeling, SSY demonstrate that forecast errors become less serially correlated as this quarter’s

earnings announcement approaches. In a forecasting system where analysts respond to forecast

error by rethinking the relations between the inputs of their model and earnings, we would expect

analysts to reduce forecast error over time as they learn more about the implications of the

surprise for their model of a company’s operations. In a simple forecasting system, where

analysts respond to forecast errors by adding a multiple of last period’s surprise to their earnings

forecast, we would expect reaction to be immediate.

However, the theory that analysts underreact to earnings because they prefer their

forecast errors to be correlated with their revision cannot fully explain differences between

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beginning of quarter and end of quarter forecast revisions. While analysts underreact to earnings

and non-earnings news, we find that the underreaction to earnings news is more than twice as

large. Overall, we argue that the data better fits a model where analysts react differently to

earnings and non-earnings information.

Finally, we propose rational modeling may also explain why managers’ forecast errors

are serially correlated (Gong et al. 2011), as managers often produce forecasts using models as

well. Anecdotal evidence suggests that accountants and board members occasionally audit the

forecasts managers use, suggesting managers may have difficulty deviating from the forecasts

their models produce.

We conduct additional analyses motivated by two papers that assert analysts react to the

available time-series of forecast errors and use this information to reduce the serial correlation in

their forecast errors (Mikhail et al. 2003; Markov and Tamayo 2006). These papers conclude

that experience improves an analyst’s understanding of the firm’s earnings process and the

analyst underreacts less as he gains experience. If this conclusion is correct, then analysts

demonstrate a preference for learning to react fully to earnings news. In contrast, the theory we

advocate argues that underreacting to earnings news increases the value of earnings forecasts.

Although we believe the tests we summarize above are inconsistent with the

unintentional bias these two papers advocate, we explore the unintentional bias explanation

further by re-examining the evidence from Mikhail et al. and Markov and Tamayo. Both of

these papers use a lengthy time series of data to identify their variables of interest. A potential

problem with a time-based identification strategy is that many things change over time, making it

difficult to isolate the effect of time on the variable of interest. We present empirical results that

suggest both papers’ findings are driven by changes in the characteristics of the firms in their

samples over time rather than by analysts learning.

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In summary, we develop and test the rational modeling hypothesis for analysts’

underreaction to earnings news. The earnings announcement reveals errors and omissions in the

way the analyst modeled earnings. We hypothesize that analysts will react to these errors, but

given limited resources and constraints on the analyst’s ability to “fudge” earnings estimates, the

optimal forecasting method may not fully respond to earnings information.

The paper proceeds as follows. Section two reviews the prior literature and develops our

hypotheses. Section three contains tests relating to the average reaction to earnings and non-

earnings news. Section four tests hypotheses related to the incorporation of specific news events.

Section five assesses the competing theory that analysts find autocorrelation in their forecast

errors to be undesirable and are successful in learning from experience to reduce their forecast

error autocorrelation. Section six concludes. 2. Theory and Hypotheses

An analyst typically forecasts earnings using a model which expresses earnings as a

function of a number of inputs. The analyst will typically publish the model in his report or

make the model available to select institutional clients. For instance, an airline analyst may

forecast earnings as a function of fuel costs, labor costs, price per seat mile and number of seat

miles. These inputs can be publicly available, such as average crude oil prices, or forecasts

themselves such as price per seat mile. The role of the model in this instance is to structure the

analysts’ thoughts about the earnings process of the firm. Buy-side clients can then take this

basic structure and adjust it to represent their views.

Ultimately, the forecasting method an analyst adopts, by which we mean the system the

analyst designs to make adjustments to both his model and earnings forecast, will depend on his

incentives. Groysberg et al. (2011) find that buy-side client votes on analyst research quality are

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used to allocate soft commissions across investment banks and across analysts within a bank.

Thus, a key consideration for an analyst seeking to maximize his compensation is for the

forecasting methodology to create a more favorable opinion of the analyst’s research quality.

Two pieces of evidence suggest public earnings forecast accuracy may not be among the

most important attributes to sell-side analysts or their clients. First, Institutional Investor asks

respondents to the All-America Research Team survey to rank specified attributes in order of

importance in assessing the worth of an equity analyst and his/her firm. Bagnoli et al. (2008)

examine the results from these surveys published in the October issue of Institutional Investor

magazine for the years 1998 - 2003 and report (in their Table 1) the results, which show that

"Earnings Estimates" rank anywhere from 12th of 15 attributes (for 2002 and 2003) to 5th of 10

attributes (for 2000). In contrast, "Industry Knowledge" ranks as the top attribute every year

during 1998 - 2003 and "Written reports" ranks above "Earnings Estimates" in all of these years.

Thus, buy-side users usually place earnings forecast accuracy toward the bottom of the attributes

they value, whereas attributes related to qualitative insights are ranked higher.1 Second,

Groysberg et al. (2011) find that earnings forecast accuracy is not correlated with compensation

after controlling for institutional investor status. Collectively, these facts suggest a sell-side

analysts forecast method should not unconditionally attempt to maximize forecast accuracy.

In light of the evidence about analyst incentives and the preferences of buy-side clients,

we consider the way an analyst will respond to an earnings surprise. If the analyst incorrectly

predicts earnings, and all of the inputs to his model were accurate, this suggests that the model

imperfectly represents the way in which the firm generates accounting earnings. The analyst can

deal with this in several ways 1) re-think the relationships between the inputs of the model

1 We confirmed that the same pattern of ranking of attributes still persists in the Institutional Investor survey by viewing the 2012 ranking at the Institutional Investor website and found that "Earnings Estimates" was ranked ninth among 12 attributes, whereas "Industry Knowledge" was ranked first and "Written Reports" sixth.

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(and/or potentially add or subtract a model input) or 2) insert a “fudge factor,” add or subtract a

number from earnings (or revenue) not attributable to one of the modeled inputs.

The adjustment the analyst makes will depend on the cost in terms of time the adjustment

takes and the value the adjustment delivers to clients, both now and in the future. Re-thinking

the relationship between the inputs to the model, offers two potential benefits, first it has the

potential to identify whether this period’s earnings surprise is persistent or transient and second,

it has the potential to better capture the effect of future input changes on earnings. Adding a

“fudge” factor to earnings should allow the analyst to quickly improve the accuracy of his

forecast in response to earnings news. However, this quick adjustment will miss any changes to

the economics of the firm. We predict that analysts will fully model the changes to the

economics of the firm and that this will result in forecasts more gradually responding to earnings

news than non-earnings news:

H1: Analysts will react more gradually to earnings news than non-earnings news.

If investors demanded quick adjustments, given the low cost at which they can be made,

we anticipate the forecasting methods of many analysts would have evolved to fully incorporate

last quarter’s earnings surprise. To formally study the preferences of investors, we examine how

Institutional Investor all-stars incorporate information into their forecasts of earnings to non-all-

stars. Specifically, we first partition the analysts initial forecast error into two components, a

residual component related to last quarter’s forecast error and a novel component, unrelated to

last quarter’s forecast error. We predict the abilities of all-stars relative to non-all-stars will

differ over the two components:

H2: All-star analysts will better incorporate novel forecast error than those not

selected as all-stars, but will not significantly better incorporate residual forecast error.

Next, we examine how analysts respond to last quarter’s forecast error. If analysts are

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sophisticated processors of the information in earnings announcements, and use this information

to adjust the relation between the inputs in their models, analyst revisions around the earnings

announcement should anticipate variation in revision persistence. If analysts are naïve processors

of the information in earnings announcements, they would not identify variation in the

persistence of the earnings surprise.

H3a: Variation in the magnitude of the analyst's revision following earnings

announcements will predict variation in the persistence of the earnings surprise.

Next, we demonstrate there is substantial inter-temporal variation in the persistence of

earnings surprises. If analyst forecasts reflect this inter-temporal variation in earnings

persistence it becomes less plausible that analysts' consistent underestimation of earnings

persistence is the result of naïve information processing.

H3b: Inter-temporal variation in analyst estimates of the persistence of last

quarter's earnings surprise will covary with inter-temporal variation in the actual

persistence of last quarter's earnings surprise.

3. Forecasting method

3.1 Forecasting method summary

We begin investigating the way analysts react to information by reviewing the prior

literature and describing how the empirical evidence found in this literature is consistent with

rational modeling. For certain empirical facts, we will simply reference the prior literature, but

for others, where we want to address a consideration raised by a subsequent literature, we will re-

present new analysis based on prior work. Finally, we will test H1 and H2.

We claim that overall these findings are consistent with (i) analysts reacting more

deliberately to earnings news than non-earnings news and (ii) analysts rationally choosing to

focus more attention on forecasting novel forecast error rather than residual forecast error.

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3.2 Serial correlation in forecast error

To investigate the serial correlation in forecast error we estimate model (1):

∝                        1

We present estimates of model (1) in Table I. We define forecast error as actual earnings

minus forecasted earnings. For all estimates, we treat each analyst-firm-quarter as an

observation and cluster standard errors at the firm level. We treat each analyst as an individual

observation because we expect the strategy an analyst follows will be related to his own forecast

error. In addition, recent evidence on the herding behavior of analysts suggests the average

analyst anti-herds, consistent with analysts not intensively using information from the forecasts

of competing analysts (Chen and Jiang 2006; Bernhardt et al. 2006).2

In Panel A column (1), we present analysis using OLS (Abarbanell and Bernard 1992).

This column demonstrates that, if analysts attempt to minimize their mean-squared forecast

errors, they do not sufficiently adjust their forecasts in response to last quarter’s earnings. In

column (2) we present results using median regression, which assumes the analyst attempts to

minimize the absolute deviation in his forecast (Gu and Wu 2003). The coefficient of interest β1

is still highly significant, inconsistent with the significant coefficient in (1) being attributable to

the particular analyst loss function implicit in the OLS estimation. Finally, column (3) presents

results from regressing the sign of this quarter’s earnings surprise on the sign of last quarter’s

earnings surprise. The column (3) results demonstrate that beating the analyst’s forecast last

quarter shifts the probability upward of beating the forecast again this quarter. Collectively,

these three columns of results suggest that last quarter’s forecast error shifts the distribution of

2 We note that the evidence that analysts do not herd in their earnings estimates is consistent with the incentives that underlie our rational modeling hypothesis for analyst underreaction to earnings news. Although the analyst can improve forecast accuracy in a number of ways (including by incorporating information into his forecast from the consensus), investors do not demand this type of forecast revision from analysts because it does not present original insights.

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this quarter’s error and that this finding is robust to varying the implicit loss function of analysts

via variation in the regression approach used to estimate the relation.

Column (4) presents results including only firms with a positive earnings surprise last

quarter and column (5) presents results including only firms with a negative earnings surprise.

The positive coefficient in each regression suggests that the serial correlation does not relate to

analysts intensively incorporating positive or negative news (Easterwood and Nutt), and is more

consistent with a general underreaction to all news. Although columns (4 – 5) present results

using OLS, in untabulated analysis we estimate model (1) using median regression and confirm

that the results are not driven by the choice of (implicit) loss function. We conclude that serial

correlation is distinct from the optimistic-pessimistic bias documented in the prior literature (Ke

and Yu 2006; Libby et al. 2008; Richardson et al. 2004), as it seems to affect forecasts with both

negative and positive earnings surprises last quarter.

In panel B columns (1-3) we examine how the serial correlation in analyst forecasts

decays over time by presenting this quarter’s forecast error regressed on forecast error from two,

three and eight quarters ago. In column (1), we find that the estimated serial correlation declines

by 19% at lags of two quarters, compared to one-quarter, suggesting that serial correlation is

distinct from the forecast consistency Giles and Hillery (2012) report. In column (2), we

demonstrate that the serial correlation declines another 8% at three lags, but we note that the

decay in the serial correlation is far less than we would expect if forecast error followed an

AR(1). Finally, column (3) demonstrates that over long lags forecast errors are essentially

uncorrelated.

Another aspect of serial correlation which has been noted in the prior literature is that

analysts incorporate more of last period’s forecast error into this period’s forecast as the next

quarter approaches (SSY). In columns (4) and (5) of panel B, we present the results of

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estimating model (1) using only the first revision of the quarter and again using only the final

revision. The serial correlation declines by 36% during the quarter. This suggests non-earnings

announcement information revealed during the quarter plays a role in correcting analysts' initial

underreaction to last quarter's earnings surprise.

We conclude from the results in this section that any rational theory of the serial

correlation in analysts' forecast errors must demonstrate why it is optimal for analysts to

gradually react to last quarter's earnings information over the course of the current quarter.

3.3 Analyst response to news

Prior literature has demonstrated that analysts underreact to a variety of information (Lys

and Sohn 1990; Abarbanell 1991). SSY assert that the general tendency of analysts to underreact

to news may be attributable to an incentive for analysts to issue revisions positively correlated

with the forecast news they disclose in the revision to the market. Although it is not completely

clear why investors would demand analyst underreaction, a theory of analyst underreaction based

on investor demand for such behavior has the potential to unify the literature on the way analysts

respond to information.

To investigate analysts’ reaction to news further, we estimate model (2):

∝                        2

The dependant variable measures the forecast error before the analyst issues the revision.

The revision is the variable of interest. If analysts fully incorporate their information into the

forecast of earnings the coefficient on the revision will be one. If analysts underreact (overreact)

to information, the revision will be larger (smaller) than one, with the deviation from one

increasing in the degree of underreaction (overreaction).

In Table II, column (1), we estimate model (2) using the final forecast revision of the

quarter. Consistent with analysts under-reacting to information on average, we find that the

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estimate of β1 is 1.26, suggesting analysts would minimize forecast error if they increased the

magnitude of their revisions by had 26%. To compare the reaction to earnings news to the

reaction to non-earnings news, in column (2) we estimate model (2) using only observations

where the analyst revises his forecast of earnings within three days of the earnings

announcement. For these observations, the coefficient of interest is 1.5, significantly larger than

the coefficient in column (1). Finally, in column (3) we estimate model (2) using the final

revision of the quarter for all revisions where the analyst had already issued a revision after the

prior quarter’s earnings announcement. We assert that these revisions will more likely relate to

non-earnings news rather than earnings news. Comparing the coefficients in columns (2) and

(3), we find the deviation from one is nearly 2.5 times larger in column (2) than in column (3).

We conclude that analysts underreact substantially more to information when the information

relates more to earnings news than non-earnings news.

3.4 Decomposing forecast error

To analyze the relative importance of responding to last quarter’s earnings surprise, we

decompose the analyst’s beginning of quarter forecast error into a component related to last

quarter’s earnings surprise (“residual forecast error”) and a component orthogonal to it (“novel

forecast error”).

We estimate the residual forecast error by regressing last quarter’s forecast error on the

analysts forecast error for this quarter, calculated at the time the firm announces earnings.3 We

find, in untabulated tests, that the R-squared of the regression is 15 percent. Thus, fully

incorporating last quarter’s forecast error using a naïve strategy where the analyst assumes all

earnings surprises have average persistence would reduce forecast error by roughly 15 percent.

3 This is model (1) with initial forecast error for the quarter (instead of the final forecast error for the quarter) as the dependent variable.

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This implies that the magnitude of novel forecast error is roughly 85 percent of earnings. When

estimating this regression, we obtain a coefficient estimate of 0.76, suggesting that 76% of last

quarter’s forecast error affects this quarter’s beginning of period forecast error.

To identify the amount of residual forecast error the analyst identifies during the quarter,

we compare the coefficient from regressing last quarter’s forecast error on the beginning of

quarter forecast error (above) to the coefficient when this quarter’s final forecast error is the

dependent variable (model 1). We find a coefficient estimate of 0.4 for the model (1) regression.

The ratio of the coefficient estimates ([1 - 0.4] / 0.76) suggests analysts incorporate 47% of

residual forecast error into this period’s forecast.

To identify the amount of novel forecast error the analyst identifies during the period, we

first orthogonalize both initial forecast error and final forecast error with respect to last quarter’s

earnings surprise. This creates initial and final novel forecast error. To identify the percentage

of initial forecast error which remains after the average analyst makes his revisions for the

quarter, we take the absolute value of both initial and final novel forecast error and regress them

on each other (Model 3).

    ∝                            3

We present the results of estimating model (3) for the universe of firms in Table III

column (1). We find a statistically significant coefficient estimate of approximately 0.54,

indicating that on average analysts identify roughly 46 percent of the novel forecast error (1 –

0.54). The preceding results suggest analysts more intensively identify novel forecast error than

residual forecast error, although the difference is extremely small.

To test whether variation in last quarter’s forecast error increases or reduces this quarter’s

forecast error, we estimate model (4):

  ∝                          4

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The dependant variable is the absolute value of the final forecast error and the control

variable is the absolute value of the initial forecast error. If analysts more intensively identify

residual forecast error, than holding initial forecast error constant, when last period’s forecast

error is larger, the final forecast error should be smaller. We present estimates of model (4) in

Table III column (2). Consistent with analysts less intensively identifying residual forecast error,

the coefficient on β2 is significantly positive. We conclude that the forecast strategy of the

average analyst is not focused on correcting residual forecast error and that this is plausibly

rational given the relative magnitudes of novel and residual forecast error.

3.5 Revealed preference tests

To test institutional investors’ demands for forecast methodologies we interact the

independent variables in models (1) and (3) above with Institutional Investor all-star status. If

investors elect analysts who issue forecasts with certain properties more frequently to be

Institutional Investor all-stars, then investors reveal a preference for those forecast methods.

This creates an incentive for analysts to adopt those forecast methods.4

To test investors’ preference for forecasts which reduce residual forecast error, we

estimate model (1A), which is model (1) with the independent variables fully interacted with all-

star status (an indicator variable, II, set equal to one for Institutional Investor all-stars and to zero

otherwise).

∝ ∗                        1

We find that the coefficient β2 is negative and statistically insignificant (

0.008, 0.21 . The small economic magnitude of the reduction in residual forecast error for

all-stars, along with the insignificant t-statistic, suggest reducing residual forecast error does not

4 We obtain Institutional Investor all-star status for all analysts whose reports appear on Investext from 2002 – 2010. In future versions of the paper, we will re-run this analysis matching all Institutional Investor all-star observations for the period 2002 – 2010.

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have a large impact on Institutional Investor all-star votes.

To test investors’ preference for forecasts which reduce residual forecast error, we

estimate model (3A), which is model (3) with the independent variables fully interacted with all-

star status.

_ ∝ _ _ ∗           3

We report the result of estimating model (3A) in Table III, column (3). Consistent with

investors demanding forecast methods that reduce novel forecast error, we find that the

coefficient estimate on is statistically significant. The coefficient estimate suggests

Institutional Investor all-stars on average identify five percent more of the initial forecast error

than non-all-stars.

Finally, in column (4), we fully interact model (4) with Institutional Investor all-star

status. We find that on average all-stars incorporate more of their beginning of period forecast

error ( 0.066, 3.77 into their forecasts, but that on average this does not apply to the

component related to last quarter’s forecast error ( 0.088, 2.76 .

We conclude that Institutional Investor all-star votes suggest institutional investors prefer

forecast methods that identify residual forecast error, but that variation in ability to incorporate

residual forecast error does not seem to have a great impact on voting. Perhaps this explains why

analysts on average incorporate only about half of residual forecast error even when

incorporating the other half appears so simple.

4. Responding to news

4.1 Methodology

In this section, we examine how forecasts of earnings and actual earnings respond to

specific news events. Testing the properties of reported and forecasted earnings requires a model

of the way in which past earnings and forecasts map into future earnings and forecasts. Previous

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research (Ball and Bartov, 1996; Markov and Tamayo 2006) assumes quarterly earnings and

expectations of quarterly earnings follow an auto-regressive process in fourth differences with a

drift.

                       5

                       5

Where and are the true drift and auto-regressive parameters. A potential problem with this

model is that analysts forecast a portion of the change in earnings . If analysts’

expectations differ systematically over the previously forecasted component of earnings and the

surprise component of earnings, failing to decompose the change in earnings into a forecasted

and surprise component may affect inferences. Therefore, we decompose into a

component related to previously forecasted earnings change and earnings

surprise .

                 6

       6

We use the same variables to estimate analysts’ expectations of earnings and the actual

earnings process, with any differences between the actual model and the expectations model

resulting in error. Table IV contains estimates of model (6), for both actual earnings and

expectations of earnings.5

The differences in the coefficient estimates from model (6A) and model (6B) suggest that

analysts considerably underestimate the persistence of the surprise component (

5 All variables are winsorized at the first and ninety-ninth percentiles. The inferences are unchanged using data scaled by price, but in many instances the coefficient estimates are different using the two techniques. We elect to present all results using unscaled data because scaling by price results in a few very small firms receiving large weights (having high expected values of variance). To the extent that not all firms receive the same weight in a regression equation, we prefer to assign larger weights to the largest firms in the economy, which make up a greater fraction of the economic activity. In untabulated analysis we find the coefficient estimates are similar using a GLS procedure to weight each observation by an expectation of the variance.

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=0.37), but slightly overestimate the persistence of the forecasted component ( = -

0.03). These results strongly suggest that the forecasted and surprise components of earnings

change do not have an equal effect on next period’s forecast of earnings. As a result, all

subsequent analysis will deviate from the prior literature and estimate model (6) in testing how

expectations of earnings differ from actual earnings.6

4.2 Cross-sectional variation in earnings persistence

To test the degree to which analyst estimates change with variation in the persistence of

earnings, we match firms by lagged forecast error, analyst (or industry), and fiscal period end

date and examine how variation in the magnitude of the revision on average predicts actual

change in earnings. We require that each analyst respond to the earnings report within three days

of the earnings announcement and that analysts’ revisions of their EPS forecasts across the

matched firms have the same sign and are different from each other by more than one cent. We

predict that variation in the revision surrounding the earnings announcement will predict

variation in the persistence of earnings. To test our prediction, we estimate the following model:

∝

                       7

The coefficient of interest is , the difference in the revisions between matched pairs.

We set this variable equal to the signed difference of the revisions for the firm in the matched-

pair with the revision largest in absolute value and to zero for the firm in the matched-pair with

the revision smallest in absolute value. If analysts possess a sophisticated understanding of the

6 From column (1) of Table IV it appears there may be a small systematic difference between the persistence of the forecasted component and the surprise component of earnings. This suggests either that there is a systematic difference between the earnings innovations analysts do and do not impound into earnings or that firms systematically manage earnings to exceed earnings expectations, and the managed earnings do not recur in the subsequent period. The difference in persistence between the surprise and forecasted components of earnings is not pursued further in this paper.

19

implications of earnings announcements for future earnings, controlling for forecast error,

variation in the revision should predict variation in actual earnings. In column (1), we match

firms on analyst, fiscal period end date and forecast error. Matching on analyst eliminates

variation in cognitive abilities between matched pairs, but leaves us with a relatively small

sample. In column (2), we relax the restriction that the same analyst issues the revisions and

instead match firms by four-digit SIC code.

The estimates of β3 are large and are statistically significant in both columns, consistent

with analysts possessing a sophisticated understanding of variation across firms in the

persistence of earnings.

4.3 Inter-temporal variation in earnings persistence

To obtain additional evidence on analysts’ ability to identify variation in the persistence

of earnings, we examine whether analysts’ forecasts incorporate more of last period’s earnings

change when earnings have more persistence. Figure one (two) plots estimates for each quarter

from 1991 - 2009 of the estimated persistence of actual and forecasted earnings surprise (forecast

change),   from model (6A) and   from model (6B). As the figures show, the

forecasted persistence moves with the actual persistence, for both earnings surprise and forecast

change.

To test how closely the estimates of actual and forecasted persistence covary, we regress

estimates of   from equation 6B on estimates of  . The results of this regression are

reported in Table VI. The coefficient estimate on the actual persistence is 0.52, meaning that

forecasts of earnings incorporate almost half of the inter-temporal variation in the persistence of

earnings. The intercept is near-zero, suggesting that all of the variation in the persistence of

earnings causes variation in the persistence of forecasted earnings. If analysts followed a naive

process in which they consistently adjusted next quarter's forecast by a constant fraction of last

20

quarter's earnings news, forecasted earnings would capture none of the inter-temporal variation

in earnings persistence.

The column (1) results suggest analysts integrate substantial information about the time-

series variation in earnings persistence into their earnings forecasts. One possible objection to

this representing sophistication on the part of analysts would be if analysts simply adjusted their

forecasts in response to observable properties of earnings. For instance, some periods contain a

greater number of observations with negative earnings and negative earnings have less

persistence. If analysts are aware of this, they may correctly forecast variation in the aggregate

persistence of earnings without integrating information from sources other than the earnings

number. We therefore address the possibility that variation in the persistence of earnings can be

predicted by observable time-series variation in the distribution of earnings surprises. In

untabulated analysis, we pool observations across time periods and orthogonalize forecasted

earnings and actual earnings with respect to a number of earnings variables to control for time-

series variation in the properties of actual earnings (percentage change in revenue, a flag

indicating revenue increased, and separate dummies indicating Q1 and/or Q5 was a loss year, as

well as these four variables interacted with the two components of earnings). We then regress the

residual forecasted change in earnings and the residual actual change in earnings on earnings

surprise and forecast change in each quarter. After eliminating the effect of observable

differences from the time-series variation in actual and forecasted earnings persistence, we find

almost no change in the coefficient estimate on the variable of interest. We conclude that

analysts process non-earnings information in a sophisticated way to produce earnings forecasts.

4.4 Incorporation of macro-economic information

To better learn about the heuristic analysts use to forecast earnings, we suggest that firm

earnings are a function of both firm-specific factors (such as the quality of a firm's production

21

technology) and non-firm specific factors (such as macroeconomic shocks). We predict that

analysts have strategic incentives that affect their forecast changes related to firm-specific

factors, but that these strategic incentives are largely absent for non-firm specific factors. We

thus predict that analysts more fully incorporate shocks to firm earnings implied by shifts to the

macro-economy than shocks to firm earnings resulting from firm-specific factors.

To test our view, we first examine how changes in expectations of GDP growth affect

earnings realizations. We estimate the following model:

∝ %∆ %∆ %∆

%∆                        8

The subscript on the expectations denotes the time at which the expectations are

measured. The subscript on ∆ denotes the final time period used to compute the change in

GDP, so that %∆ . We assume and find that changes in

expectations of GDP growth are generally correlated with changes in firms’ earnings. We obtain

data on expectations of real GDP from the Philadelphia Federal Reserve Website (“Philly Fed”).

The Philly Fed surveys economists in the middle of the quarter on their expectations of the level

and change in GDP for the past quarter, the current quarter, and four future quarters. Although

the past quarter ended six weeks previously, the actual GDP number for the past quarter will not

be released until twelve weeks after the end of the past quarter, so expectations of last quarter’s

GDP change may still deviate from the published number. For this reason may not

equal , but will generally be fairly close.

We test how well analysts incorporate information about changes in the expected value of

future GDP into their earnings forecasts by estimating a similar model to (8A) above, but with

forecasted earnings substituted for actual earnings.

22

∝ %∆ %∆ %∆

%∆                        8

Although the final GDP estimate of the Philly Fed used as the independent variable in the

regression will often be released after the final analyst forecast revision of the quarter, the

individual economists’ GDP estimates available at the time of the firm’s earnings announcement

will often provide similar information to analysts. First, we estimate both models (8A) and (8B)

for all firms in the sample, as reported in columns (1) and (2) of Table VII. We take the ratios of

and from columns (1) and (2) as measures of the amount of the earnings-relevant

information about changes in expectations of GDP that analysts include in their earnings

forecasts. We find the ratio .

.91.3% and

.

.88.2%, suggesting that

analysts incorporate into their forecasts most of the change in earnings caused by changes in

expectations of GDP growth.

Second, we estimate both models (8A) and (8B) for all four-digit SIC codes in our

sample having at least 250 observations (dropping coefficients and ). Estimating the

regression at the four-digit SIC code level tests whether, on average, analysts modify their

earnings forecasts to incorporate inter-industry variation in the effect of changes in GDP

expectations on earnings. There are 105 such four-digit SIC codes in the economy. We then

extract the 105 estimated and coefficients and regress them on each other. We require a

large number of observations in each SIC code because in small samples random variation in the

dependant variable will covary with the independent variables, creating an errors-in-variables

concern in our independent variable in the second stage regression (which would bias the

coefficient estimate in that regression downward).

23

The variable measures how much the estimated coefficients covary. As shown in

column (3) of Table VII, we obtain a highly statistically significant estimate for of 0.86.

Finally, we repeat the preceding procedure using two-digit instead of four-digit SIC

codes. Thus, we estimate both models (1) and (2) for all two-digit SIC codes in our sample

having at least 500 observations. We then extract the 39 estimated and coefficients and

regress them on each other. As reported in column (4) of Table VII, we obtain a highly

significant estimate for of 0.94. Overall, we conclude that analysts incorporate a greater

fraction of the change in earnings implied by changes in the macroeconomy into their forecasts

of earnings than they do for changes in earnings which are not correlated with shifts in the

macroeconomy.

5. Do analysts learn over time?

There are two findings in the literature (Mikhail, Walther and Willis 2003; Markov and

Tamayo 2006) that suggest analysts respond to increased knowledge of the time-series of

earnings by incorporating more of last quarter's earnings surprise into this quarter’s forecast of

earnings. These results suggest that the serially correlated errors in analyst forecasts are

undesirable, because analysts respond to the increased accessibility of information by decreasing

the serial correlation in their forecast errors. The notion that analysts find serially correlated

errors undesirable contradicts the theory advanced in our paper, that analysts strategically bias

their forecasts to allow them to vary with key qualitative insights in analysts’ reports.

To examine the implications of each study for the theory tested in our paper, we examine

the identification strategy employed in each study. Both rely on the passage of time to identify

the effect of experience on forecast errors. In particular, each paper compares forecast errors in

an earlier period to forecast errors in a later period and attributes any difference between time

periods to experience. A threat to the internal validity of this identification strategy is that many

24

firm characteristics change systematically over time and these characteristics may themselves

cause analyst forecasts to be more or less autocorrelated. To address this potential threat to the

internal validity of each study, we investigate the same question with an identification strategy

that we argue better isolates the effect of experience on forecast errors.

First, Mikhail, Walther and Willis (2003, henceforth MWW) hypothesize that more

experienced analysts better learn a firm’s earnings process and, as a result, issue forecasts with

less serially correlated forecast errors. To test this hypothesis, the authors define experience as

the number of prior forecasts issued by a unique analyst-firm combination and estimate model

(9) below:

∝ ∗                        9

The authors find a significantly negative estimate for and conclude from this that

experience reduces the serial correlation in forecast error. While the finding is consistent with

experience reducing forecast error, firms that have been followed by analysts for a long period of

time are necessarily surviving firms. These firms’ information environments may have evolved

over time in a way that would affect the serial correlation in forecast error for the average

analyst. In particular, surviving firms are larger and more profitable than the average firm. In

untabulated analysis, we find that both of these characteristics are significantly negatively

associated with the serial correlation in forecast error. As a result, it is unclear if experience

causes the decrease in the serial correlation of forecast error, or if the changing firm

characteristics affect the information environment in a way that causes all analysts (regardless of

experience level) to issue forecasts with less serially correlated errors. To control for any

possible change in firm characteristics, we match experienced analysts to less experienced

analysts following the same firm, and compute the difference in their experience levels. Then we

estimate the following regression:

25

∝ _ _ ∗                        10

The coefficient of interest is , which measures the effect of experience on the serial

correlation of the forecast error. (We set Diff_Exp to zero for the less experienced analyst).

MWW obtain their data from a different database and for an earlier time period. When

we replicate their study using IBES data from 1992 - 2010, we find a significantly negative

coefficient estimate, consistent with their findings.

When we implement the matching procedure that aims to control for changing firm

characteristics, we obtain a small and insignificantly positive coefficient estimate

( =0.0007,t=0.25). This regression has considerable power because there are over 58,000

unique firm-quarters for which analysts with different levels of experience issue a forecast.

Matching by firm eliminates the effect of changing firm characteristics on the coefficient of

interest and isolates the effect of experience on the serial correlation in forecast error. We find

that the difference between the coefficient estimates obtained estimating equations (9) and (10) is

statistically significant at the 1% level, suggesting that the two designs are unlikely to be

measuring the same effect. We argue the matched estimate provides a better measure of the

effect of experience on the serial correlation of analyst forecast errors, because it controls for all

unobserved firm characteristics. Our finding suggests the results MWW report differ from the

matched sample results because, as the analysts gain experience, the firms they continue to

follow change and the change in firm characteristics drives the statistically significant coefficient

estimate on experience that they document.

Markov and Tamayo (2006, henceforth MT) show that companies with a longer time-

series of available forecasts incorporate more of last quarter’s earnings change into this quarter’s

forecast. MT argue that this result is inconsistent with irrationality, which they define as

“fixation on a random walk or some other dogmatic belief.” We agree with this contention. MT

26

argue the failure of fixation to describe the data suggests “analysts learn rationally over time

about the parameters of the quarterly earnings process.” We agree that this interpretation is

consistent with the data, but contend that an alternative explanation is also plausible.

Specifically, the pattern of data documented in our paper's Table VI and Figures I and II suggests

that analysts respond to changes in the persistence of earnings this period by changing their

forecasts for this period. Such patterns of contemporaneous learning are not the same as

parameter learning, which asserts that analysts learn about the future persistence of earnings

from past realizations of earnings.

To distinguish between the alternative explanations, we replicate the table from MT's

study that examines persistence of earnings and then conduct additional analysis to understand

the source of the variation in the persistence of forecasted earnings that MT document in their

later analyses. MT conduct their study using equation (5a), so (unlike the results reported

previously in this paper) they do not decompose earnings changes into surprise and forecasted

components.

                       5

MT select all firms with consensus earnings estimates on IBES for at least 64 consecutive

quarters during the period 1983 - 2003. They partition their sample into three groups based on

the number of quarters elapsed since the firm’s consensus earnings forecast began appearing on

IBES (1- 20, 21 - 40 and 41 - 64). MT estimate the above equation for each of the three groups

separately. These estimates are shown in row one of Panel A in Table VIII, and are very similar

to those reported by MT in their Table I, Panel B. The results in row one of Panel A indicate that

the persistence of actual earnings increases with the number of quarters the firm has been in the

sample, moving from a coefficient estimate of 0.44 for periods of 1 to 20 quarters, to 0.64 for

periods of 21 - 40 quarters, and finally to 0.70 for periods of 41 - 64 quarters. The differences in

27

the estimates between the three partitions are significant at conventional levels, suggesting that

the upward trend in the persistence of actual earnings is not random during 1983 - 2003.

We next estimate the above equation substituting forecasted earnings for actual earnings.

These estimates can be found in row two of Panel A in Table VIII. The persistence of forecasted

earnings increases over time, with the coefficient estimate going from 0.39 for periods of 1 to 20

quarters to 0.56 for periods of 21 - 40 quarters and, finally, to 0.63 for periods of 41 - 64

quarters. These results are consistent with parameter learning, but are also consistent with

analysts having information about the contemporaneous actual persistence of earnings and

incorporating that contemporaneous information into their forecasts. The plausibility of the latter

explanation is illustrated by the results in row three of Panel A in Table VIII. This row presents

the differences in the coefficient estimates for the persistence of actual earnings from row one

and the persistence of forecasted earnings from row two. Two aspects of the differences reported

in row three are noteworthy. First, the differences are quite small relative to the actual

persistence of earnings (generally being about 10% of the actual persistence), which indicates

that analysts’ forecasts capture the vast majority of the persistence of actual earnings regardless

of whether the number of consecutive quarters that have been forecast for the firm in question is

small or large. Second, there is no indication that the portion of the persistence of actual earnings

captured by the persistence of forecasted earnings increases as the number of consecutive

quarters that has been forecasted grows larger (i.e., the figures in the Difference row do not

become a smaller percentage of the persistence of actual earnings as the periods increase from 1-

20 quarters to 21-40 quarters and 41-64 quarters).

Our paper has argued that analysts learn about the persistence of earnings from

information released during the period. Information about the persistence of earnings thus does

not have to come from prior quarter’s earnings realizations. Analysts conducting fundamental

28

analysis of an individual firm can incorporate information about the persistence of shocks to

earnings that is not observable for purposes of regression estimation. The fact that analysts on

average fail to correctly assess the persistence of last quarter’s earnings surprise does not

necessarily imply analysts ignore all dimensions of information related to the persistence of

earnings. As there are two plausible theories for the persistence of analysts’ forecasted earnings

increasing over time, the cause of the increase is unidentified from the results in Panel A alone.

Therefore, as an additional test, we replicate in Panel B of Table VIII MT’s study using a

different time period (the latest time period available on I/B/E/S). If parameter learning drives

the increase in the forecasted persistence of earnings MT report, we should find similar results

using a different sample. Using the same sample selection rules as MT for analyst earnings

forecasts issued between 1990 - 2010, we obtain a sample of 538 firms with an uninterrupted 64

months of IBES consensus earnings forecasts. We again partition the firm-quarters by the length

of time they have been included in the IBES consensus estimate and estimate equations (5a) and

(5b) for each of the partitions (Obs 1- 20, 21 - 40 and 41 - 64). For this sample of firms, the

persistence of actual earnings remains approximately the same across partitions. Parameter

learning suggests that analysts initially underestimate the persistence of earnings but increase

their estimate of the persistence of earnings as more earnings realizations become available upon

which to condition their estimate. This suggests that the forecasted persistence of earnings should

be strictly increasing. However, the forecasted persistence of earnings actually decreases

between quarters 21 - 40 and quarters 41 - 64 and the difference is statistically significant. This is

inconsistent with parameter learning. Inconsistent with parameter learning, but consistent with

rational modeling, the difference between the auto-regressive parameter for actual earnings and

the auto-regressive parameter for forecasted earnings remains constant at 0.08 (row 3).

As a final test, we combine the test periods used in the first two panels of Table VIII and

29

also extend the number of required consecutive periods with consensus IBES forecasts to be 84

rather than the 64 periods required in the top two panels. If analysts engage in parameter

learning, we would expect the estimates of the forecasted persistence of earnings to continue to

increase as analysts obtain more information about the true persistence of earnings. The results

are presented in Panel C of Table VIII. The first row of results shows that the persistence of

actual earnings does not continue to increase as the number of consecutive quarters on IBES

increases beyond 64. Instead, the estimate for the persistence coefficient declines to 0.64 for the

partition containing observations with 65 - 84 consecutive quarters on IBES. For the other three

partitions (1 - 20 consecutive quarters, 21 - 40 consecutive quarters, and 41 - 64 consecutive

quarters) the pattern from Panel A, an increase in the persistence of actual earnings and

forecasted earnings, is repeated. The fact that the persistence of actual earnings decreases when

the length of the period with consecutive IBES consensus forecasts increases beyond 64 quarters

is helpful in distinguishing between the parameter learning explanation of MT and our

alternative strategic bias theory. If parameter learning explains analysts' forecasting, the

persistence of forecasted earnings should increase for the partition with 65 - 84 consecutive IBES

quarters. Conversely, if analysts learn contemporaneously about changes in the persistence of

actual earnings and modify their forecasts of earnings in response, the persistence of forecasted

earnings should decrease for the partition with 65 - 84 IBES quarters because of the decline in

the persistence of actual earnings for this partition.

As the second row of Panel C shows, the results are consistent with the contemporaneous

learning explanation, as the coefficient estimate on the persistence of forecasted earnings

decreases from 0.63 for the partition with 41 - 64 consecutive quarters on IBES to 0.56 for the

partition with 65 - 84 consecutive quarters. As in the earlier panels, the third row of results for

Panel C indicates the difference between the estimate on the persistence of actual earnings (row

30

1) and that on the persistence of forecasted earnings (row 2) does not decrease as one moves

from left to right across partitions (toward partitions with more consecutive quarters of

forecasts). The fact that this difference does not decrease as the partition examined includes more

consecutive quarters of forecasts is also inconsistent with parameter learning.

Overall, the results suggest analysts likely respond to contemporaneous information

released during the period, and incorporate this information into their estimates of earnings,

inconsistent with the parameter learning theory advocated by MT.

6. Conclusion

Financial analysts use models to help predict earnings. Financial models generate

earnings predictions by assuming a relation between a series of known inputs and next period’s

earnings. The economic relation between these inputs and earnings is uncertain and likely

modeled with error. Thus, a rational Bayesian seeking to minimize forecast error would adjust

his posterior expectation of the relation between the inputs and the outputs each time he observes

an earnings realization which differs from the forecast.

We assert that analysts instead adjust their models gradually as their thinking about the

economics of the company evolves. We assert gradual adjustment may be incentive compatible

for the analyst, as institutional investors do not seem to reward analysts who more fully respond

to last quarter’s surprise with Institutional Investor all-star status. We also demonstrate that

analyst revisions capture variation in the persistence of last quarter’s earnings surprise, consistent

with analysts rationally modeling rather than naively responding to the earnings surprise.

Overall, we hypothesize that serially correlated forecast errors may arise out of a rational

system where analysts choose a number of inputs to include in a model to forecast earnings.

They adjust this model rapidly in response to changes in inputs and adjust the model gradually in

response to changes in the relation between the inputs.

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31

32

Appendix A: Variable Definitions This appendix describes each variable used in our study. All data are from I/B/E/S for the years 1983 – 2010. (i = firm; t = time of the fiscal period end, t’ = time of forecast (if different than end of fiscal period); j = analyst)

Variable Description Formula Forecast Error (also called final forecast error)

Actual earnings minus the last forecast of earnings issued by the analyst. Forecast of earnings must be issued after last quarter’s earnings announcement.

,i t itjActual Forecast

Initial forecast Error (also called final forecast error)

Actual earnings minus the last forecast of earnings issued by the analyst. Forecast of earnings must be issued before last quarter’s earnings announcement.

, , , ' 1,i t i t t jActual Forecast

Forecast Change The difference between earnings five quarters ago and the analyst’s forecast of last quarter’s earnings

, 1 , 5,i t i tForecast j Actual

Actual Change The difference between earnings four quarters ago and this quarters actual earnings , , 4i t i tActual Actual

Residual Forecast Error

The portion of this quarter’s forecast error implied by last quarter’s forecast error. This is equal to the last quarter’s forecast error multiplied by the coefficient estimate obtained from regressing initial forecast error on last quarter’s forecast error.

Novel Forecast Error The initial forecast error minus the portion which can be explained by last quarter’s forecast error.

Initial FE - Residual FE

Revision Forecast of earnings minus the same analysts previous forecast of earnings

Last quarter’s forecast error (earnings surprise)

Actual earnings for last quarter minus the last forecast of earnings issued by the analyst. Forecast of earnings must be issued after the earnings announcement from two quarters ago.

, 1 , 1,i t i t jActual Forecast

Institutional Investor All-star

A flag set equal to one if the analyst was voted as an institutional all-star in either the year the fiscal period ended or the year after the fiscal period ended. We have this variable populated for all investext analysts between 2002 – 2010.

Difference in revisions The signed difference in the revisions for the firm with the revision largest absolute value and zero for the firm with the revision smallest in absolute value.

, ,Re i t i tv rev rev

33

(1) (2) (3) (4) (5)

Forecast Errort=0 Forecast Errort=0 Forecast Errort=0 Forecast Errort=0 Forecast Errort=0

Intercept 0.001 0.008 0.227 0.009 0.003(0.10) (360.63) (49.73) (4.54) (0.79)

Lagged forecast error 0.351 0.250 0.210 0.250 0.383(16.61) (87.85) (55.48) (6.86) (12.55)

Restriction on independent variable NONE NONE NONE Positive Negative

Type of regression OLS Median Signed OLS OLS OLS

N 427,672 427,672 427,672 252,266 129,355R-squared 0.093 -- 0.044 0.026 0.114

(1) (2) (3) (4) (5)Forecast Errort=0 Forecast Errort=0 Forecast Errort=0 Forecast Errort=0 Forecast Errort=0

Intercept 0.000 0.000 0.002 -0.054 0.000(0.16) (0.30) (1.23) (-17.46) (-0.08)

Lagged forecast error 0.286 0.257 0.067 0.540 0.347(12.48) (11.61) (6.49) (12.14) (12.74)

Observation Final Final Final First Final

Number of lags 2 3 8 1 1

N 427,672 427,672 346,439 242,239 242,239R-squared 0.054 0.041 0.013 0.083 0.075

Panel B: variation in time of forecast

See Appendix A for variable definitions. Reported below the coefficients are t-statistics. All t-statistics, except the t-statistics reported in panel A, column (2) are clustered by firm. All variables are Winsorized at the first and ninety-ninth percentiles.

Panel A: variation in loss function and sign

Table I: Effect of prior period's forecast error on this period's forecast error -- This table presents the results of regressing one quarter's forecast error on a previous quarter's forecast error. For all columns in Panel and (1) - (2) in panel B, we include all observations where the analyst issue a forecast of this quarter's earnings announcement after last quarter's earnings announcement for the same firm for three consecutive quarters. For column (3) in panel B, we require the analyst issue a forecast of this quarter's earnings announcement after last quarter's earnings announcement, and do similarly for the earnings announcement eight quarters prior. For columns (4) and (5) of panel B, we require the firm issue two forecasts after last quarter's earnings announcement and a forecast of last quarter's earnings. Panel A: All columns present the results of regressing this quarter's final forecast error on last quarter's forecast error. Column (1) presents OLS, Column (2) presents median regression and column (3) takes the sign of both the independant and dependent variable before performing OLS. Columns (4) and (5) include only observations with prior quarter forecast errors which are positive and negative respectiviely ("Restriction on independent variable"). Panel B: In panel B, all results use OLS and include all observations, but differ as far as the time the analyst issued the revision. In columns (1), (2) and (3) we present results where the prior quarter's forecast error is taken from the quarter two, three and eight quarters prior, respectively. In column (4) we present results using the forecast error calculated using the first forecast an analyst issues during the quarter. In column (5) we present results using the same sample of firms, but the final forecast of the quarter.

34

(1) (2) (3)Initial FE Initial FE Initial FE

Intercept 0.008 -0.008 0.010(5.23) (-3.78) (5.87)

Lagged forecast error 1.266 1.506 1.203(60.17) (53.40) (47.54)

Sample Selection Final Forecast EAD Window 2nd Revision

N 715,008 429,562 328,274R-squared 0.402 0.286 0.454

See Appendix A for variable definitions. Reported below the coefficients are t-statistics. All t-

statistics are clustered by firm. All variables are Winsorized at the first and ninety-ninth percentiles.

Table II: Correlation between revisions and forecast error -- This table presents the results of regressing the analysts initial forecast error on a revision the analyst issues during the quarter. Column (1) reports results for the final revision the analyst issues during the quarter. Column (2) reports results for all analysts who issue an earnings forecast within three days of the prior quarter's earnings announcement. Column (3) reports results for the final revision of the quarter for all analysts who issued a revision after last quarter's earnings announcement prior to their final revision.

35

(1) (2) (3) (4)Abs(Final FE) Abs(Final FE) Abs(Final FE) Abs(Final FE)

Intercept 0.005 0.001 0.006 0.003(3.27) (1.01) (3.02) (2.14)

Absolute Initial FE 0.543 0.512 0.551 0.515(45.62) (45.18) (33.67) (32.55)

Absolute Last Quarter FE 0.001 0.152(1.01) (8.29)

II Status 0.543 0.512 0.004 -0.001(45.62) (45.18) (1.54) (-0.36)

ABS(Init_FE)*II -0.053 -0.066(-3.01) (-3.77)

ABS(Last_FE)*II 0.088(2.76)

N 593,629 593,629 204,059 204,059R-squared 0.642 0.715 0.637 0.703

Table III: Relationship between initial forecast error and final forecast error -- This table presents results of

regressing the final forecast error of the quarter on the initial forecast error, to estimate the percentage of forecast error

analysts identify during the quarter. We include all observations where (1) the analyst issues a forecast of this quarter's

earnings both before and after last quarter's earnings announcement and (2) the analyst issues a forecast of last quarter's

earnings after the announcement of earnings two quarters ago. In columns (1) and (3), both the dependent variable and

initial forecast error are first regressed on last quarter's forecast error before we take their absolute value and regress

them on each other (model 3). In columns (2) and (4) we use raw values. In columns (3) and (4) all independant

variables are interacted with all-star status and we only include observations for which we have all-star status available.

See Appendix A for variable definitions. Reported below the coefficients are t-statistics. All t-statistics are clustered by firm. All variables are Winsorized at the first and ninety-ninth percentiles.

36

(1) (2) (3)Actual Change Forecast Change Forecast Error

Intercept -0.008 0.002 -0.008(-9.95) (2.86) (-10.85)

Earnings Surprise 0.523 0.146 0.370(31.72) (9.23) (20.61)

Forecast Change 0.578 0.607 0.000(48.78) (56.43) (-0.02)

N 171,338 171,338 171,338R-squared 0.256 0.324 0.102

Table IV: Effect of earnings surprise and forecast change components of current quarter earnings -- This table contains OLS regressions of actual change in earnings (column 1), forecasted change in earnings (column 2) and forecast error (column 3) on last quarter's forecasted change in earnings and forecast error. All observations are taken from the split-adjusted I/B/E/S

detail file between 1993 and 2009.

We compute the forecast of earnings in both this quarter (dependent variable) and the prior quarter

(independent variable) as the average forecast from all analysts who issue a forecast in each

quarter. We only include forecasts issued after the prior quarter's earnings announcement.

Forecast Change is the average forecast of earnings minus actual earnings four quarters ago.

Actual change is this quarter's earnings minus actual earnings four quarters ago.

See Appendix A for variable definitions. Reported below the coefficients are t-statistics. All t-

statistics are clustered by firm. All variables are Winsorized at the first and ninety-ninth percentiles.

37

(1) (2)Actual Change Actual Change

Intercept -0.004 0.002(-0.90) (0.81)

Earnings Surprise 1.953 1.058(10.56) (13.70)

Forecast Change 0.719 0.671(22.96) (29.47)

Difference in revisions 0.761 0.954(5.48) (9.96)

N 6,088 37,265R-squared 0.458 0.314

Table V:The average effect of variation in the size of the revision at earnings announcement on actual earnings -- This table contains OLS regressions of the actual earnings change on the difference in the revisions analysts issue using pairs of firms matched on last quarter's earnings surprise. We define the difference in revisions as the signed difference between revisions for the firm with the larger revision, and zero for the firm with the smaller revision. All observations are taken from the split-adjusted I/B/E/S detail file between 1993 and 2009. Columns (1) contain all observations where the same analyst issues a revision for different firms in the same quarter, where the analyst’s prior forecast had the same forecast error for both firms. We also require that the analyst issue a revision within three days of the earnings announcement for both firms and that the revision has the same sign as the prior quarter’s earnings surprise. Column (2) contains all observations where two firms in the same four digit SIC-code have the same forecast error for at least one analyst in the same quarter (not the same analyst). We also require that each analyst issue a revision within three days of the earnings announcement date and that the revision has the same sign as the prior quarter’s earnings surprise.

See Appendix A for variable definitions. Reported below the coefficients are t-statistics. All t-statistics are clustered by firm. All variables are Winsorized at the first and ninety-ninth percentiles.

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(1)Estimated Actual Persistence

Intercept -0.110(-2.64)

Estimated Actual Persistence 0.524(7.28)

Reported Results 2nd Stage

N 67R-squared 0.449

Table VI. Effect of Actual Persistence of Earnings on the Forecasted Persistence of Earnings -- This table contains OLS regressions of the estimated actual persistence of earnings on the estimated forecasted persistence of earnings for each quarter from 1993 - 2009. The dependant

variable, the estimated actual persistence of earnings is β1 in the following regression, estimated

separately for each quarter: Actual Earnings Change =

α+β1*Earnings_Surprise+β2*Forecast_Change + ε. The independent variable, the estimated

forecast persistence of earnings is β1 in the following regression, estimated separately for each

quarter: Forecasted Earnings Change = α+β1*Earnings_Surprise+β2*Forecast_Change + ε.

We define forecasted change as the forecast of last quarter’s earnings minus actual earnings

reported the same quarter the prior year (Foret-1- Actualt-5). We compute the forecast of last

quarter’s earnings as the average of the final forecast on the I/B/E/S detail file. We exclude all forecasts issued before the previous quarter’s earnings announcement from the consensus. We also exclude firms without earnings information on COMPUSTAT. We define earnings surprise as

the difference between last quarter’s actual earnings and last quarter’s forecast (Actualt-1- Foret-1).

We define the actual change in earnings as the actual earnings reported this quarter minus the

actual earnings reported the same quarter the prior year (Actualt- Actualt-4). We define the

forecasted earnings change as the consensus forecast of earnings this quarter minus the actual

earnings reported the same quarter the prior year (Foret- Actualt-4).

See Appendix A for variable definitions. Reported below the coefficients are t-statistics. In the first stage variables are Winsorized at the first and ninety-ninth percentiles.

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Table VII. Average Effect of a Change in the Expected Value of GDP on Actual Earnings and Forecasts of Earnings This table contains OLS regressions of the change in actual earnings and forecasts of earnings on changes in the expected value of GDP for both the forecasted quarter and the prior quarter. All forecasts of earnings and actual earnings are taken from the I/B/E/S detail file between 1993 and 2010. All estimates of GDP are taken from the Philadelphia Federal Reserve website (http://www.philadelphiafed.org/research-and-data/regional-economy/business-outlook-survey/). We measure the change in expectations of GDP as the difference between forecasted GDP reported in the survey released in the middle of the current fiscal quarter and the survey released in the middle of the prior fiscal quarter. Although the period during which GDPt-1 is measured has been completed as of the time of the survey, the official GDP number will not be released by the Bureau of Labor Statistics for another six weeks, and as a result, the surveyed figure is still an expected value. Although many analysts will have issued their forecasts for the current quarter’s earnings at the time of the release of the survey, we assume that analysts will have access to reports about the macro-economy and as a result incorporate much of the information released in the survey in their estimates. We define the actual change in earnings as the actual earnings reported this quarter minus the actual earnings reported the same quarter the prior year (Actualt- Actualt-4). We define the forecasted change in earnings as the consensus forecast of earnings this quarter, where we compute the consensus as the average forecast issued by an analyst this quarter, minus the actual earnings reported the same quarter the prior year (Foret- Actualt-4). We require all firms to have a fiscal quarter end which coincides with the end of the calendar year. Column (1) reports the actual change in earnings regressed on changes in the expectation of GDP for the current quarter and the prior quarter. Column (2) reports the forecasted change in earnings regressed on changes in the expectation of GDP for the current quarter and the prior quarter. Column (3) reports estimates for the second step of a two-step procedure. First, for all SIC codes we regress the actual change in earnings and the forecasted change in earnings on changes in the expectations of GDP for the current quarter. For an SIC codes to be included in the sample it must have at least 250firm-quarters. We extract the coefficient estimates on expected change in GDP from each regression. We then regress the coefficient obtained from the actual regression on the coefficient obtained from the forecast regression and report this quantity in column three. Column four reports estimates obtained from an analogous procedure where we estimate our first-stage regressions on all two-digit SIC codes having at least 500 firm-quarters. Estimates in columns one and two (three and four) are clustered at the firm level (not clustered). Variables related to changes in the expectation of GDP (firm earnings) are not (are) Winsorized at 99%.

40

DEP_VARt = α+β1*Et-1[GDPt]-Et-2[GDPt]+β2*Et-1[GDPt]-Et-2[GDPt]+β3*Actualt-2-Actualt-6+εit

1 2 2 3

Dependant VariableActual

ChangeForecast Change

Estimated Actual

Change

Estimated Actual

Change

(1) (2) (3) (4)

Intercept 0.001 0.016 0.002 -0.001(0.76) (10.26) (1.40) (-0.61)

Et-1[GDPt]-Et-2[GDPt] 0.009 0.008(3.49) (4.14)

Et-1[GDPt-1]-Et-2[GDPt-1] 0.042 0.037(9.64) (10.51)

Estimated Forecast Change 0.86 0.94(34.67) (28.18)

R-squared 0.093 0.086 0.921 0.955

Number of Observations 114,649 105 39

41

Table VIII. Re-examination of Markov and Temayo (2006) Results This table contains OLS regressions of the actual change in earnings and the forecasted change in earnings on the actual change in earnings in the prior quarter. All observations are taken from the split-adjusted I/B/E/S consensus file between 1983 and 2010. For all regressions the dependent variable appears in the first column. We define the actual earnings change as earnings reported this quarter minus actual earnings reported the same quarter the prior year (Actualt- Actualt-4). We define forecasted change as the consensus forecast of this quarter’s earnings minus actual earnings reported the same quarter the prior year (Foret

- Actualt-4). We use the consensus as reported in the I/B/E/S consensus file, consistent with Markov and Temayo. We define the difference as (Actualt - Foret). The independent variable is the same in all regressions, the actual change in earnings from the prior quarter (Actualt-1- Actualt-5). In Panel A, we report results for all firms with a minimum of 64 consecutive quarters with available data to compute all variables during the period 1983 - 2003. We run firm level regressions for quarters 1-20, quarters 21 – 40 and quarters 41 – 64. We report the mean value of the firm-level regressions for each quarter. This is the same sample-selection criteria as Markov and Temayo and similar to their results, the forecasted earnings change increases over time. This is consistent with their hypothesis that analysts engage in parameter learning. In Panel B, we report results for all firms with a minimum of 64 consecutive quarters with available data to compute all variables during the period 1990 - 2010. We run firm level regressions for quarters 1-20, quarters 21 – 40 and quarters 41 – 64. We report the mean value of the firm-level regressions for each quarter. This is the latest twenty-year period on the I/B/E/S detail file. For this sample of firms forecasted earnings change decreases, inconsistent with parameter learning. In Panel C, we report results for all firms with a minimum of 84 consecutive quarters with available data to compute all variables during the period 1983 - 2010. We run firm level regressions for quarters 1-20, quarters 21 – 40, quarters 41 – 64 and quarters 65 - 84. We report the mean value of the firm-level regressions for each quarter. This essentially extends the Markov and Temayo sample forward. In the subsequent five year period, forecasted earnings change declines, inconsistent with parameter learning. All standard errors are clustered at the firm level. All variables are Winsorized at the 99% level.

Observations

1983‐2003 (344 Companies) 1‐20 21 ‐ 40 41 ‐ 64Qt‐Qt‐4 = α+β*(Qt‐1‐Qt‐5)+ε

Actual Earnings Change 0.44 0.64 0.70

Forecasted Earnings Change 0.39 0.56 0.63

Difference 0.04 0.08 0.07

1990‐2010 (538 Companies) 1‐20 21 ‐ 40 41 ‐ 64Qt‐Qt‐4 = α+β*(Qt‐1‐Qt‐5)+ε

Actual Earnings Change 0.62 0.70 0.66

Forecasted Earnings Change 0.54 0.63 0.58

Difference 0.08 0.08 0.08

1983‐2010 (331 Companies) 1‐20 21 ‐ 40 41 ‐ 64 65 ‐ 84

Qt‐Qt‐4 = α+β*(Qt‐1‐Qt‐5)+ε

Actual Earnings Change 0.46 0.66 0.70 0.64

Forecasted Earnings Change 0.42 0.57 0.63 0.56

Difference 0.05 0.09 0.07 0.08

42

Figure 1. Time-Series Variation in the Persistance of Actual and Forecasted Earnings Surprise The blue series, the estimated actual persistence of earnings is β1 in the following regression, estimated separately for each quarter: Earnings Change = α+β1*Earnings_Surprise+β2*Forecast_Change + ε. The red series, the estimated forecast persistence of earnings is β1 in the following regression, estimated separately for each quarter: Forecast Change = α+β1*Earnings_Surprise+β2*Forecast_Change + ε. All regressions were estimated using the last IBES consensus forecast prior to the earnings announcement date. Estimating the regression requires actual earnings data for Qt, Qt-1 and Qt-4 and forecasted earnings data for Qt and Qt-1.

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Figure 2. Time-Series Variation in the Persistance of Actual and Forecasted Forecast Change The blue series, the estimated actual persistence of earnings is β2 in the following regression, estimated separately for each quarter: Earnings Change = α+β1*Earnings_Surprise+β2*Forecast_Change + ε. The red series, the estimated forecast persistence of earnings is β2 in the following regression, estimated separately for each quarter: Forecast Change = α+β1*Earnings_Surprise+β2*Forecast_Change + ε. All regressions were estimated using the last IBES consensus forecast prior to the earnings announcement date. Estimating the regression requires actual earnings data for Qt, Qt-1 and Qt-4 and forecasted earnings data for Qt and Qt-1.

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