The Rational Modeling Hypothesis for Analyst Underreaction to Earnings News*

Transcription

1 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 and Zachary R. Kaplan Booth School of Business, University of Chicago, 5807 S. Woodlawn Ave., Chicago, IL 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.

2 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 crosssectional 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.

3 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 1

4 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 2

5 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 3

6 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 4

7 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. 5

8 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 nonearnings 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 6

9 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 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 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. 7

10 (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-allstars. 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 8

11 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 represent 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. 9

12 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 β 1 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. 10

13 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 11

14 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 12

15 estimate of β 1 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. 13

16 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): 14 4

17 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 β 2 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 allstar status (an indicator variable, II, set equal to one for Institutional Investor all-stars and to zero otherwise). 1 We find that the coefficient β 2 is negative and statistically insignificant ( 0.008, 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 In future versions of the paper, we will re-run this analysis matching all Institutional Investor all-star observations for the period

18 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 allstar 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, 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 16

19 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. 17

20 =0.37), but slightly overestimate the persistence of the forecasted component ( = ). 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 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 matchedpair 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. 18

21 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 β 3 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 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 19

22 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 timeseries 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 timeseries 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 20

23 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. 21

24 % % % % 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). 22

25 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 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 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 23

26 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: 24