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Keywords:

  • Analyst forecasts;
  • Bias;
  • Optimism

Abstract

  1. Top of page
  2. Abstract
  3. RELATED RESEARCH
  4. RESEARCH DESIGN
  5. RESULTS:
  6. ADDITIONAL ANALYSES
  7. CONCLUSION
  8. references
  9. Appendix

This paper examines whether the documented bias in analyst earnings forecasts is intentional by examining whether it is related to the market's ability to adjust for this bias. For intentional bias to exist it is not enough for analysts to face incentives but rather, analysts should also be willing to respond to these incentives. As the market's ability to adjust for the bias increases, its market effects decrease while analyst reputation costs increase reducing analyst willingness to bias their forecasts. The paper utilizes a firm-specific design that allows for both the bias component of the forecast error and the market's ability to adjust for the bias to be computed at the firm level. Results suggest that even though forecast error is positive in the latter part of the period under review reflecting overall analyst pessimism, the bias embedded in the forecasts is optimistic throughout the period. More importantly, I find that analyst forecast bias is decreasing in the market's ability to adjust for it. This result provides further evidence that analysts knowingly bias their forecasts and provides support for the existence of reporting bias, in particular. Thus, the evidence provides justification for recent regulatory efforts to increase the objectivity of analyst research reports.

This paper examines whether the bias in analyst earnings forecasts is related to the market's ability to adjust for the bias. The U.S. is used as the testing stage to examine the proposed relation in order to build on and extend the literature on analyst forecast bias that already exists for the U.S. Specifically, the paper adds to relevant research in the area by enhancing our knowledge with respect to the determinants of bias, thus shedding more light on the decision processes and behaviour of financial analysts, who comprise not only the primary users of accounting information but perhaps the most sophisticated ones. Analyst behaviour has come to the forefront of public attention after the recent financial reporting scandals for which analysts have been criticized for not forewarning the market (Nussbaum, 2002). In response to these criticisms, in May 2002 the U.S. Securities and Exchange Commission (SEC) approved new rules to reduce financial analysts' conflicts of interest that compromise the objectivity of analyst research reports. Similarly, in April 2003 the New York District Attorney announced the Global Analyst Research Settlement in an attempt to segment the research and investment banking departments of brokerage firms. Title V, s 501 of the Sarbanes-Oxley Act of 2002 also addresses analyst conflicts of interest by disallowing, among others, the evaluation of research analysts and the clearance of analyst research reports, by members of the investment banking departments. In the midst of the controversy regarding analyst objectivity, this paper examines whether financial analysts intentionally bias their earnings forecasts by offering another potential determinant of analyst forecast bias, namely the market's ability to adjust for bias. This is an important question, since the mere presence of incentives does not necessarily lead to analyst bias, even though it is a necessary condition for intentional bias to exist. Instead, I argue that the extent to which analysts respond to the incentives they face to bias their forecasts is related to the perceived benefits associated with bias, which are negatively related to the market's ability to debias the forecasts.

Analyst research has mostly focused on the incentives analysts face to bias their forecasts optimistically. In particular, previous research has identified three major incentives: First, analysts optimistically bias their forecasts or recommendations to satisfy the investment banking department's current customers or to attract new investment banking business (Dugar and Nathan, 1995; Lin and McNichols, 1998; Michaely and Womack, 1999; Dechow et al., 2000; O'Brien et al., 2005). Second, analysts bias their forecasts to ensure access to firms' private information sets (Francis and Philbrick, 1993; Das et al., 1998; Lim, 2001; Mest and Plummer, 2003; Barber et al., 2006). Finally, analysts bias their forecasts to increase their firm's trading commissions, as positive analyst reports have the potential of generating more trading volume than negative reports where trading is restricted to investors who either already own the stock or who are willing to short sell (Jackson, 2005; Cowen et al., 2006).

Even though analyst optimism is associated with analyst incentives, it is not clear, a priori, whether analysts respond to these incentives by intentionally biasing their forecasts or whether the bias documented by extant research is due to cognitive biases. The investment banking result, for example, can be explained by cognitive biases that are related to analysts ‘falling in love’ with the stocks they help underwrite (Clayman and Schwartz, 1994). This reasoning is well-founded in the psychological literature and is consistent with the ‘inside view’ proposed by Kahneman and Lovallo (1993). In addition, the findings on the access to management incentives are not robust to specific model modifications. Eames et al. (2002) find that once actual earnings are included in the model, ‘buy’ recommendations are associated with optimistic forecasts while ‘sell’ recommendations are associated with pessimistic errors, a result that is contrary to the prediction of the access to management incentive. Thus, even though there seems to be an association between bias and certain analyst incentives, whether the observed bias is a response to these objectives remains unclear.

To examine directly whether the observed bias is intentional and not a product of cognitive biases, I test whether analysts respond to incentives to bias their forecasts by examining whether the magnitude of bias is related to the market's ability to debias the forecast. There are two possible reasons why the market's ability to adjust for the bias may affect analysts' willingness to respond to the incentives they face. First, the market's ability to debias a forecast could serve as a proxy for analyst reputation costs. Analysts value their inclusion in rankings such as the Institutional Investor magazine's All-America Research team or the Wall Street Journal's All-Star Analysts and are concerned about their reputation, especially as this relates to the credibility of their reports (Laderman, 1990; Siconolfi, 1995; Jackson, 2005). Reputation loss can also result in real costs to brokerage firms arising either from loss of investor clients or from legal costs associated with lawsuits related to analyst bias (see, e.g., Siconolfi, 1995).1 If reputation matters to analysts then the market's detection of, and adjustment for bias should compromise their reputation by exposing the intention to mislead. Second, the greater the ability of the market to undo bias, the less its effects and the potential benefits that can accrue to firm management. Unless management is myopic, this would imply less pressure on brokerage firms and analysts for favourable reports, hence the lower the bias. In both of these cases the market's ability to adjust for the bias should be negatively related to the level of bias.

The paper makes several important methodological contributions to the literature as well. First, it implements a time-series design that allows the market's ability to adjust for bias to be computed at the firm level. This design assumes that bias and the corresponding ability of the market to adjust for the bias are, at least to some extent, firm-specific (i.e., analysts set the bias in their forecasts and the market adjusts for this bias according to specific firm characteristics). Even though a number of other papers have attempted to measure the degree to which the market adjusts for forecast bias their analysis was based on a cross-sectional design, which imposes constraints on the estimation of the market's ability to adjust for the bias (Brown and Lo, 1998; Han et al., 2001),2 Second, in order to identify the level of bias embedded in analyst forecasts, this paper decomposes analyst forecast error into a reporting bias and an underreaction component. Examining reporting bias is particularly important as it is the most controversial type of bias, while at the same time being easily discernable, as it is plainly added to the analyst's true forecast of earnings.3 The market's adjustment to each component is then estimated in order to examine whether analysts set their reporting bias based on the market's ability to adjust for it. To derive the market's adjustment to the bias and underreaction components of the forecast error I employ the ERC (earnings response coefficient) theoretical framework which links firm returns to firm earnings, with a greater coefficient on the earnings variable indicating a stronger association. In the paper's formulation explained in detail in the appendix, the market's ability to adjust for the bias is derived from a non-linear estimation model where returns around the earnings announcement are regressed on the negative value of expected (i.e., predicted) bias and underreaction in addition to the observable forecast error variable. In the linear specification of this model the coefficient on the bias variable should then equal the coefficient on overall forecast error if the market completely adjusts for the bias, should be smaller than the earnings coefficient if the market partially adjusts for the bias, and be equal to zero if the market is unable to adjust for the bias. The model is, however, estimated non-linearly so that the coefficient on expected bias reflects the degree of market adjustment as it is computed as the ratio of the coefficient on bias that would have been obtained from the linear estimation to the coefficient on total forecast error; in this nonlinear formulation, the closer the ratio is to −1 the greater the ability of the market to undo the bias in analyst forecasts.

Results, at first glance, suggest that analysts do not incorporate the market's ability to adjust for the total expected (i.e., predicted) forecast error when forming their forecasts. However, when the reporting bias component of the forecast error is examined separately, analysts are found to account for the market's ability to adjust for bias in their forecasts, consistent with expectations. Specifically, analysts tend to reduce the magnitude of reporting bias in their forecasts as the market's ability to adjust for the bias increases. This result provides evidence that bias is intentional since the amount by which analysts inflate their forecasts is inversely related to the market's ability to account for it. Even though prior research results were consistent with bias being intentional, the evidence in this paper now provides greater support for this conjecture, justifying recent regulatory efforts to increase the objectivity of analyst research reports. On the other hand, the evidence also suggests that the magnitude of bias is mitigated by analysts' unwillingness to bias their forecasts, which is increasing in the market's ability to adjust for the bias. This result supports the existence of a market correcting mechanism which, if appropriately reinforced, either through mechanisms that enhance the importance of analyst accuracy and reputation or by increasing the market's awareness of the existence of bias, can also be effective in reducing analyst forecast bias. The paper therefore has important policy implications for regulators who are still concerned over the quality of analyst research output.

The recent financial crisis has hit the investment banking industry in unprecedented ways. The investment bank failures and consolidation of the industry resulted in a shift from standalone investment banks to mega-banking institutions combining both investment and commercial banking activities. The unparalleled number of people forced to leave the financial industry severely limited employment opportunities, in turn leading to a number of senior investment bankers starting their own boutique investment banks. The effect of both of these changes on the U.S. investment banking model, as we know it, can be dramatic. These changes can also affect analyst incentives to bias their forecasts, something that could also impair the market's ability to undo the bias. It is, however, too early to be able to measure the effects of the crisis on analyst forecast bias, the ability of the market to adjust for the bias and the relation between the two. Future research should address these questions as the crisis settles and data become available.

RELATED RESEARCH

  1. Top of page
  2. Abstract
  3. RELATED RESEARCH
  4. RESEARCH DESIGN
  5. RESULTS:
  6. ADDITIONAL ANALYSES
  7. CONCLUSION
  8. references
  9. Appendix

The bias in analyst earnings forecasts has been documented numerous times in the literature (Fried and Givoly, 1982; Brown et al., 1985) with important economic effects. Easton and Sommers (2007), for example, find that the bias in analyst forecasts significantly increases the implied expected rate of return which is computed based on analyst forecast estimates. In addition, a big stream of literature is devoted to explaining the reasons behind the existence of analyst forecast bias. Beyer (2008) proposes that analysts concerned with the accuracy of their forecasts are more likely to bias their forecasts upward than downward because firms are more (less) likely to manipulate earnings towards the forecast when this is optimistic (pessimistic), resulting in greater (lower) accuracy. Kang et al. (1994), find that the analyst forecasting process is not strictly rational. Their evidence is consistent with the existence of incentives for more favourable reports or with the existence of analyst judgmental biases.

Consistent with the former explanation, a number of papers have unravelled incentives analysts face to bias their forecasts. For example, Lim (2001) finds that analysts rationally bias their forecasts to gain access to firm management that, in turn, would help improve the accuracy of their forecasts (see also Francis and Philbrick, 1993; Das et al., 1998). Along the same lines, Chen and Matsumoto (2006) find that analysts receive more management-provided information, proxied by forecast accuracy, following the issuance of more favourable recommendations. Ke and Yu (2006) also find evidence that supports the access to management incentive by showing that analysts whose initial forecasts are more optimistic exhibit greater subsequent accuracy and are less likely to be fired by their employers.

Another well documented incentive for bias is the investment banking incentive according to which analysts bias their forecasts to resolve conflicts between the investment banking and research departments of the brokerage firms they work for. Dugar and Nathan (1995) find that affiliated analyst earnings forecasts are more optimistic than those of non-affiliated analysts while Dechow et al., (2000) find that affiliated analysts also issue more optimistic long-term growth forecasts. Michaely and Womack (1999) examine affiliated and non-affiliated analyst recommendation patterns. They find that, after an IPO, affiliated analysts are more likely to issue a buy recommendation and that, on average, the long-run performance of firms that are recommended by their underwriters is significantly worse than the performance of firms recommended by other brokerage houses. More recently, Barber et al. (2006) find that buy recommendations issued by investment banks underperform buy recommendations issued by independent research firms. Along the same lines, Gu and Xue (2008) find that even though earnings forecasts of independent analysts are less accurate than those of non-independent analysts, they are more strongly associated with stock returns suggesting that the former better represent market expectations.

The access to management incentive and the investment banking incentive are closely related since they are the result of the firm's preference for positive reports. In the first case, the firm itself provides a direct incentive for favourable reporting by controlling access to its private information; in the second case, the incentive is indirect as it is directed at the investment banking department of the brokerage firm which, in turn, is redirected to research analysts. The trading incentive which has been documented recently in the literature is not initiated by the firm being followed, but rather by the investment bank. Jackson (2005) finds that optimism generates more trades while Cowen et al. (2006) find that the optimistic bias of brokerage firms that do not perform any underwriting activities is greater than the optimistic bias of full-service investment banks. Taken together, these results support the existence of a strong commissions incentive. These incentives, that are partly driven by the investment banks themselves, are operationalized mostly by compensation structures which are related to the analyst business generation. Even though the Sarbanes-Oxley Act of 2002 makes an attempt to mitigate the incentives analysts face by limiting the reliance of analyst compensation on investment banking business, it is doubtful whether the regulation will succeed in eliminating bias as employers may still be able to instil incentives through other means. For example, Hong and Kubik (2003) propose that this can be achieved indirectly, through the career prospects of analysts. In particular, Hong and Kubik find that optimistic analysts are more likely to experience favourable job changes.

Another related stream of research, drawing on related psychology literature, proposes that analyst bias is due to cognitive limitations. For example, Abarbanell and Bernard (1992) and Ali et al. (1992) provide evidence that analysts underreact to information impounded in prior earnings. Similarly, Easterwood and Nutt (1999) find that analysts underreact to negative information but overreact to positive information. Their evidence is consistent with systematic optimism in analyst earnings forecasts. More recently, Markov and Tamayo (2006) argue that the correlation in analyst earnings forecast errors is related to analyst learning processes rather than irrational fixation. Finally, analyst bias may be due to analysts falling in love with the stocks they help underwrite (Clayman and Schwartz, 1994), a finding that is consistent with the theory on inside view proposed by Kahneman and Lovallo (1993).

Francis (1997) proposes the existence of three different types of bias that could lead to the observed analyst optimism. The first two, reporting and selection bias, are consistent with a response to the above-mentioned incentives while the third, cognitive bias, assumes that analyst optimism is not intentional but, rather, that it is due to the analyst's inadequate processing of available information. From the first two, only reporting bias reflects the analyst's explicit intention to mislead. Selection bias is observed when analysts, in an effort to avoid issuing a negative report on a company, choose not to issue a report instead. Thus, the observed mean bias in analyst forecasts is not a result of analysts purposefully misleading the market. The same also applies in the case of cognitive bias, where analysts presumably issue favourable reports due to cognitive limitations. McNichols and O'Brien (1997) find evidence supporting the existence of selection bias while Clayman and Schwartz (1994) argue that observed analyst optimism may be due to analysts falling in love with the stocks they follow leading, in turn, to favourable reporting.

This paper examines another factor that can potentially affect the level of analyst forecast optimism, namely, the market's ability to adjust for the bias, and adds to the literature in a number of important ways. First, the market's ability to adjust for the bias captures the analysts' willingness to bias their forecasts, a factor not yet examined in extant research. In order for bias to exist, analysts should face incentives to inflate their forecasts but this condition, even though necessary, it is not sufficient. Rather, in order for analyst bias to be intentional analysts should be willing to respond to the incentives they face. Hence, even in the presence of strong incentives the bias in analyst forecasts may be mitigated by the extent to which analysts are willing to bias their forecasts. Documenting a relation between subsequent forecast error and the market's ability to adjust for the bias will provide more direct evidence that bias is intentional as it will suggest that analysts knowingly adjust the bias in their forecasts based on the expected benefits of this bias. The extent of bias in analyst reports is decreasing in the reputation losses that the analyst will incur if the bias is uncovered (Jackson, 2005) and increasing in the expected effects or benefits to the firm or the investment bank. The market's ability to adjust for bias captures both of these effects. As the market ability's to adjust for the bias increases, potential reputation effects increase while the benefits to the firm itself or the investment bank decrease. In the limit, if the market does not rely at all on the bias in the forecast, that is, the market is able to completely adjust for it, there is no need on behalf of the analyst to bias the forecast since this will not result in any benefit to either the firm being followed or the investment bank, while at the same time could result in significant reputation losses to the analyst.

Finally, the paper extends existing methodology by implementing a time-series design which allows the firm-specific estimation of both bias and the market's ability to adjust for bias. Thus, even though this method requires a considerable number of observations, it relaxes the assumption of prior research that the relation between forecast error and its determinants is constant across firms.

RESEARCH DESIGN

  1. Top of page
  2. Abstract
  3. RELATED RESEARCH
  4. RESEARCH DESIGN
  5. RESULTS:
  6. ADDITIONAL ANALYSES
  7. CONCLUSION
  8. references
  9. Appendix

To test whether the market's ability to adjust for bias is related to subsequent bias the following model is run4:

  • image(1)

Equation (1) is estimated on a cross-sectional basis for each of the fifteen quarters in the period starting from the fourth quarter of 1996 and ending with the second quarter of 2000, while the overall statistical significance of the model variables across the period is assessed using the t-statistic proposed by Fama and MacBeth (1973). FE is analyst forecast error and is computed as the difference between actual earnings of firm i for quarter q and the median analyst forecast measured during the 120-day period ending five days before the earnings announcement date for the quarter. Only the most recent forecast of each analyst for each firm is included in the computation.

In order to derive the variable of interest, γ2, which measures the ability of the market to debias the median analyst forecast, the paper's methodology draws on the ERC (earnings response coefficient) and value relevance literatures. In the ERC framework firm returns are regressed on earnings, with greater coefficients on the earnings variables signifying stronger relations between unexpected earnings and returns, in turn indicating a greater market reliance on, and relevance of earnings. In this context prior literature estimates the differential pricing of different components of earnings by regressing short- or long-run returns on these components (see e.g., Guay et al., 1996; Subramanyam, 1996; Givoly et al., 2009). Typically, in these models net income is decomposed in its two components, accruals and cash flows from operations (which sometimes are further decomposed), and in this context the coefficients on each variable capture the incremental information content of each component. In this paper, and similar to related research, the expected (i.e., predicted) forecast error is included in a return model in addition to the overall forecast error.

Specifically, γ2 is obtained from regressing three-day risk adjusted returns around the earnings announcement on total forecast error (i.e., observable unexpected earnings) and then separately re-entering in the regression the negative value of the expected forecast error, decomposed into its two principal components: expected bias and underreaction. Given that in this setting, however, expected bias and forecast error are included in addition to actual forecast error the coefficient on expected bias in the linear formulation does not reflect its incremental information content. Rather, it reflects the incremental valuation of the expected bias component from the valuation of the unexpected earnings variable so that when the market completely adjusts (does not adjust at all) for the bias the coefficient on the separate bias variable is equal to the coefficient on unexpected earnings (equal to 0). The model, however, is estimated in a non-linear specification so that the coefficient on the bias variable, γ2, reflects the degree of market adjustment, computed as the ratio of the coefficient on bias that would have been obtained from the linear estimation to the coefficient on unexpected earnings; in this nonlinear formulation, the closer the ratio is to −1, the greater is the ability of the market to undo the bias in analyst forecasts. If the market does not separate out expected bias from total forecast error then the pricing of bias in the linear model will be 0 in both the linear and non-linear specifications, consistent with the market placing the same reliance on bias as the reliance on the unexpected earnings.

For each firm-quarter observation, γ2 is estimated using the last 30 quarters of forecast errors ending with the forecast error of q−1. For example, for the first iteration of equation (1), that is, when q represents the fourth quarter of 1996, γ2 is estimated over the 30 quarters from the second quarter of 1989 to the third quarter of 1996. For the second iteration of equation (1), that is, when q represents the first quarter of 1997, γ2 is estimated using the 30 quarterly observations from the third quarter of 1989 to the fourth quarter of 1996. The procedure used to estimate γ2 is outlined in detail in the Appendix.

The relation between the market's ability to adjust for the bias, γ2, and bias in equation (1) is expected to be negative.5 This is based on the assumption that analysts are either concerned with their reputation and perceive that the market's ability to adjust for the bias is related to reputation loss or are under less pressure to bias their forecasts when the market is more able to adjust for it.6

Except for γ2 all other variables are included in the equation as control variables. The willingness of analysts to bias their forecasts is also expected to be related to a number of other firm characteristics related to the complexity of the firm's earnings process which in turn can either make forecasting inherently more difficult, possibly inducing more cognitive bias, or make the detecting of bias more difficult, leading to more intentional bias. These are variables that prior research found to be important in explaining cross-sectional differences in the level of bias. The unpredictability of the firm's earnings process, UNPRED, is proxied by the standard deviation of the forecast error during the estimation period of γ2 and is deflated by beginning price. Das et al. (1998) find that unpredictability is positively related to bias. SIZE, analyst following, FOLL, and dispersion, DISP, proxy for the firm's information environment (see, e.g., Lang and Lundholm, 1993, 1996). Better information environment should be negatively related to bias as it can significantly reduce the benefits of bias. Consistent with this argument, SIZE and FOLL have been found to be negatively related to bias (Brown, 1997; Das et al., 1998; Lim, 2001). SIZE is measured as the natural logarithm of the firm's market value of equity while FOLL is the number of analysts that have issued at least one earnings forecast for quarter q during the 120-day period ending five days before the quarterly earnings announcement. Similarly, DISP is the standard deviation of all forecasts made in the 120-day period ending five days before the earnings announcement date of quarter q. In case of multiple forecasts in the period by the same analyst, only the most recent forecast is kept. Ali et al. (1992) find that earnings persistence, PERS, is negatively related to bias. Following their methodology, I first rank firms based on their earnings–price ratio (EP) measured at q−1, with the first rank including firms with negative EP ratios. Persistence takes the value of 1 if EP falls in ranks 3 to 6, and 0 otherwise. The number of days, DAYS, from the median date of all forecasts in the period to the earnings announcement date controls for the timing effects of bias. The prior quarter's forecast error, FEq−1, is included to control for the documented underreaction to prior earnings changes.

RESULTS:

  1. Top of page
  2. Abstract
  3. RELATED RESEARCH
  4. RESEARCH DESIGN
  5. RESULTS:
  6. ADDITIONAL ANALYSES
  7. CONCLUSION
  8. references
  9. Appendix

Sample and Sampling Procedures

Earnings announcements are obtained from Compustat and supplemented by I/B/E/S. Firm and market returns and daily prices needed for the estimation of γ2 are obtained from CRSP. Analyst earnings forecasts and actual earnings needed to compute forecast errors, analyst following and dispersion and the EP ratio are obtained from I/B/E/S. Quarterly prices are obtained from Compustat while shares outstanding needed for the computation of the market value of equity are also obtained from CRSP.

Table 1 shows the sample elimination procedure. The initial sample ranges from 242 firms for iteration 1 to 483 for the last iteration and includes firms with December year-ends and a total of 47 consecutive quarters required for the estimation of γ2. Firms with non-December year-ends are excluded from the sample since analyst activity differs with time relative to year-end (see, e.g., O'Brien and Bhushan, 1990). The sample per iteration is further reduced due to the lack of actual earnings and the requirement for at least two forecasts of earnings to be available per quarter in order to compute dispersion. More observations are lost due to the lack of return data from CRSP, prices from Compustat and earnings announcement dates either from Compustat or I/B/E/S. Due to these extensive data requirements, the sample ranges from 73 observations for iteration 1 to 188 observations for the last iteration. Finally, I eliminate observations with earnings response coefficients less than 0.1. This is necessary for two reasons. First, to get a meaningful estimation of the market's adjustment for the bias, the estimation of the ERC should also be meaningful. Second, when the estimated ERC is unreasonably small compared to the absolute value of the ability to adjust for the bias, γ1 explodes to unreasonably high numbers. This final restriction results in a final sample that ranges from 69 firms in iteration 1 to 178 firms for the last iteration. Equation (1) is run for the quarter that follows the end of the estimation period for each iteration, that is, the fourth quarter of 1996 for the first iteration, the first quarter of 1997 for the second, while the last iteration is run for the second quarter of 2000.

Table 1.  SAMPLE ELIMINATION PER QUARTER The table indicates the number of firms included in the estimation of equation (1) for each of the fifteen quarterly iterations.
 961297039706970997129803980698099812990399069909991200030006
Total firms in I/B/E/S with 47 consecutive one-quarter ahead forecasts, no change in fiscal year-end, and December fiscal year-ends242241298307307353359365467465477475476479483
With earnings announcement dates and actual EPS208208256263269307312310392397410409416431433
With at least two forecasts per quarter in the period131136160161166207216212272270281272286297297
With return data107105130133135173172176219216228227229244243
With Compustat data7376929296123123123154153162171176185188
With earnings response coefficients greater than 0.16971858894118120119149141153162165174178

The first column of Table 2 shows the average forecast error across all firms in the sample of each iteration, the second column shows mean estimated bias for the full sample of each iteration, and the third column shows mean estimated bias for firms with negative forecasts. Consistent with prior research, I find that mean forecast error becomes increasingly less negative and turns positive from 1998 onwards. This finding is consistent with evidence in related research (Brown, 1997). Interestingly, the amount of bias, that is, the amount by which analysts inflate their forecasts, remains positive and significant throughout the period. Thus, even though analysts become increasingly pessimistic over the latter part of the period covered, their bias remains to be positive. Thus, optimistic bias renders overall optimistic forecasts more optimistic and their related forecast error more negative, and overall pessimistic forecasts less pessimistic and their related forecast error less positive. Thus optimistic bias reduces forecast error. The level of bias, in absolute terms, is greater when the forecast is negative as shown by column three at least for the majority of quarters. The mean underreaction coefficient across all iterations (not tabulated) is 0.07.

Table 2.  FORECAST ERROR AND ESTIMATED BIAS The following models are estimated per firm for each of the quarters from the second quarter of 1989 to the first quarter of 2000 based on the previous fifteen quarterly observations on a rolling basis: FEq=BE(b2−1) +b2FEq-1+vq, if only positive forecasts in the period. FEq=BE+(b2−1) +b2FEq−1 + BE-(b2−1)NGF + vt, if at least one negative forecast in the period. For each quarter q shown in the first column, average bias and forecast error is the average firm bias and forecast error per quarter, over the 30 quarters ending at q−1. Optimistic bias in this design is present when BE is positive.
Iteration forAverage forecast errorAverage biasAverage bias if negative forecasts
  • *, ** and *** 

    significant at the 0.1, 0.05 and 0.01 level, respectively.

9612−0.000520.00109***0.00746***
9703−0.000320.00103***0.00746***
9706−0.000350.00097***0.00683***
9709−0.000280.00114***0.00685***
9712−0.000290.00101***0.00705***
9803−0.000170.00079***0.00425**
98060.0000250.00080***0.00413**
98090.0000730.00078***0.00369**
98120.000220.00057***0.00222**
99030.00021*0.00064***0.00189**
99060.00023*0.00059***0.00145*
99090.00059**0.00053***0.00144*
99120.00032**0.00051***0.00235*
00030.00050**0.00047***0.00030
00060.00053***0.00047***0.00100

Table 3 presents descriptive statistics for the variables used in the regression analysis. Specifically, the average value across the quarterly iterations of the mean, median and standard deviation of the variables is shown in the first, second and third column of the table, respectively. Most of the sample firms exhibit high earnings persistence as evidenced by a mean value of 0.58 (median value of 1.00), are followed on average by 11.20 analysts per quarter while the median date of the forecast is on average 57.87 days before the quarterly earnings announcement. In addition, and in accordance to expectations, the mean values of both γ1 and γ3 are positive. γ1 and γ3 measure the market's ability to adjust for overall expected forecast error and analyst underreaction, respectively. The last row of Table 3 indicates the mean value of γ1q4. The coefficient is obtained by a modification of equation (3c) in the Appendix, where instead of estimating the market's adjustment to expected forecast error based on a firm-specific prediction model, the proxy for the expected overall forecast error is actual forecast error of quarter q−4. Simply put, the coefficient, γ1q4, is obtained by relying on a naïve seasonally adjusted random walk model.

Table 3.  DESCRIPTIVE STATISTICS FOR MODEL VARIABLES The table presents the average values of the mean, median and standard deviation statistics across all fifteen quarterly iterations.
 MeanMedianStandard deviation
  1. UNPRED: Unpredictability is the standard deviation of the forecast error deflated by beginning price during the estimation period of γ2; SIZE: Natural log of MVE at q−1; DISP: Dispersion is the standard deviation of forecasts for quarter q deflated by beginning of period price; FOLL: Number of analysts following the firm in quarter q; PERS: Persistence is based on EP ratio of q−1; NGE: equals 1 if earnings for quarter q are negative, 0 otherwise; NGF: equals 1 if median forecast for quarter q is negative, 0 otherwise; DAYS: Days from median date to the earnings announcement date of quarter q; γ2 is the market's ability to adjust for the bias with more negative values indicating greater ability to adjust; γ3 is the market's ability to adjust for analyst underreaction with greater values indicating greater ability to adjust; γ1 is the market's ability to adjust for the expected forecast error based on equations (2c) and (2d). γ1q4 is the market's ability to adjust for the expected forecast error which is set equal to actual forecast error of quarter q−4.

UNPRED0.00340.00230.037
PERS0.58091.000.4951
SIZE9.24589.08881.2865
FOLL11.207210.33335.4183
DISP0.00360.00150.0049
DAYS57.876558.666623.9555
γ2−0.344−0.0653.5309
γ30.72650.40804.1696
γ10.11250.12242.4524
γ1q40.01120.02942.8805

Finally, the value of γ2 is negative as expected. Recall that γ2 reflects the extent of the market's ability to adjust for the bias. To test whether the value of γ2 implies a complete, partial or no adjustment for the bias, I test for each quarter separately, whether γ2 is significantly negative. Finding such relation would be consistent with either partial or complete market adjustment. If the market completely adjusts for the bias then γ2 should be equal to −1. The test (not tabulated) rejects the null of no market adjustment for nine out of the fifteen quarters examined in the study, implying that the market at least partially adjusts for the bias. In addition, for ten out of the fifteen quarters the test also rejects the null of complete market adjustment. Thus, the evidence is consistent with at least a partial adjustment for bias. Interestingly, only in five out of the fifteen quarters does the test reject the null of no adjustment for γ1, while the null of complete market adjustment is rejected in fourteen out of the fifteen quarters. Qualitatively similar results hold for the case of γ1q4. These results are consistent with the evidence in Han et al. (2001), who also find that the market seems to only partially adjust for the bias in analyst forecasts. Their results, however, are based on a pooled cross-sectional rather than a firm-specific estimation of the coefficient on predictable bias, something that precludes them from testing the relation between the market's ability to adjust for the bias and subsequent analyst forecast bias.

Table 4 presents Pearson correlation coefficients. These are obtained by first estimating the correlation coefficients for each quarter and then testing whether the mean correlation for each pair of variables is statistically different from zero by constructing a standard t-statistic. At first glance, some of the results in the correlation table seem counterintuitive. For example, unpredictability is positively related to forecast error, seemingly in contrast to the results of Das et al. (1998) who find that as unpredictability increases the bias in analyst forecasts also increases, rendering the forecast error more negative. However, it is evident from Table 2 that forecast error in the latter part of the period is positive, reflecting overall pessimistic forecasts, which are nevertheless optimistically biased, as evidenced from the average bias column of the same table. Hence, unpredictability should be positively related to forecast error when the forecast error is positive, that is, forecast error increases as the predictability of earnings forecasts also increases. Similarly, company size is negatively related to forecast error. In a period where forecast error is on average positive, this indicates that greater company size is associated with less error, consistent with the results of prior research. The test variable, γ2, is negatively and significantly related to the forecast error, γ1, and γ3, as expected.

Table 4.  PEARSON CORRELATIONS The table presents the average correlation coefficients and p-values across the fifteen quarters in the period under review.
 FEDPUNPREDSIZEFOLLDISPPERSDAYSFEDP_1γ1γ2γ1q4γ3
  1. UNPRED: Unpredictability is the standard deviation of the forecast error deflated by beginning price; SIZE: Natural log of market value of equity; DISP: Dispersion is the standard deviation of earnings forecasts for quarter q deflated by beginning of period price; FOLL: Number of analysts following the firm in quarter q; PERS: Persistence is based on ranks of the EP ratio; NGE: equals 1 if earnings for quarter q are negative, 0 otherwise; NGF: equals 1 if median forecast for quarter q is negative, 0 otherwise; DAYS: Days from median date to the earnings announcement date of quarter q. FEDP_1 is the Forecast Error of q−1 deflated by beginning price; γ2 is the market's ability to adjust for the bias with more negative values indicating greater ability to adjust; γ3 is the market's ability to adjust for analyst underreaction with greater values indicating greater ability to adjust; γ1 is the market's ability to adjust for the expected forecast error based on equations (2c) and (2d). γ1q4 is the market's ability to adjust for the expected forecast error which is set equal to actual forecast error of quarter q−4.

FEDP1.000.19−0.12220.00140.1758−0.05230.011820.2555−0.01267−0.0645−0.008270.0276
0.00<0.01<0.010.95<0.010.030.65<0.010.53<0.010.640.40
UNPRED 1.00−0.18480.01750.32−0.0711−0.06220.151−0.0023−0.0417−0.04080.0332
0.00<0.010.31<0.010.010.03<0.010.920.02<0.010.29
SIZE  1.000.0746−0.27330.03050.0242−0.0850.04830.064−0.05170.01426
0.00<0.01<0.010.060.440.02<0.01<0.01<0.010.54
FOLL   1.000.1082−0.07566−0.10150.02480.05530.0018−0.00550.0605
0.000.84<0.01<0.010.470.010.940.80<0.01
DISP    1.000.08140.113580.25220.0149−0.01640.02630.0345
0.00<0.01<0.010.200.600.410.540.37
PERS     1.000.0635−0.0547−0.012870.0356−0.03553−0.01
0.000.020.020.630.270.170.68
DAYS      1.000.0338−0.0342−0.02010.01678−0.0341
0.000.200.160.370.500.18
FEDP_1       1.000.03370.04210.02190.0743
0.000.090.180.250.08
γ1        1.00−0.07330.35020.606
0.000.02<0.01<0.01
γ2         1.000.0257−0.3112
0.000.23<0.01
γ1q4          1.000.022
0.000.65

Results on the Relation Between Bias and the Market's Ability to Adjust for the Bias

Equation (1) results are shown in Table 5. The elimination of influential observations (studentized residual > |2.5|) affects the number of observations included in each reported model.7 The table presents the mean coefficients of fifteen quarterly regressions along with the respective p-values computed by Fama and MacBeth (1973) t-statistics. The first column of Table 5 presents the results of equation (1). The second column extends the model by including γ3, the proxy for the market's ability to adjust for analyst underreaction.8 The third column presents the results with γ1 instead, that is, the proxy for the market's ability to adjust for total expected forecast error. Likewise, the model in column four includes the proxy for the market's adjustment for total expected forecast error when expectations are based on seasonally adjusted random walk. The final column of Table 5 presents the results when the dependent variable is estimated bias for the quarter in question rather than signed forecast error.

Table 5.  REGRESSION RESULTS (p-values in second line)a The table presents average coefficients obtained from quarterly regressions together with p-values of Fama and MacBeth (1993) t-statistics. Number of observations, N, presents the quarterly average. inline image
Dependent variableFEFEFEFEBE
  • *, ** and *** 

    significant at the 0.10, 0.05 and 0.01 level respectively.

  • a 

    p-values are based on two-tail tests.

  • FE: Actual less forecasted earnings for firm i and quarter q; P: end of year price; UNPRED: Unpredictability is the standard deviation of the forecast error deflated by beginning price; SIZE: Natural log of the market value of equity; DISP: Dispersion is the standard deviation of earnings forecasts deflated by beginning of period price; FOLL: Number of analysts following the firm; PERS: Persistence of earnings based on ranks of the EP ratio; NGE: equals 1 if earnings for quarter q are negative, 0 otherwise; NGF: equals 1 if median forecast for quarter q is negative, 0 otherwise; DAYS: Days from median date to the earnings announcement date of quarter q; γ2 is the market's ability to adjust for the bias with more negative values indicating greater ability to adjust; γ3 is the market's ability to adjust for analyst underreaction with greater values indicating greater ability to adjust; γ1 is the market's ability to adjust for the expected forecast error based on equations (2c) and (2d). γ1q4 is the market's ability to adjust for the expected forecast error which is set equal to actual forecast error of quarter q−4.

Intercept0.00020680.000193380.000489**0.0010613**−0.000193
0.680.700.050.020.34
UNPRED0.06432***0.06756***0.049577***0.0735368***−0.030687***
<0.01<0.01<0.01<0.01<0.01
PERS0.00004570.00003850.00003238−0.00000450.000055
0.640.690.570.970.12
SIZE−0.0000489−0.00005031−0.0000755−0.0001804−0.0000246
0.360.360.040.020.21
FOLL−0.0000014−0.000000470.0000130.00003150.0000119***
0.910.970.250.130.01
DISP0.183404*0.181269*0.110130.357323**−0.000855
0.090.100.250.040.98
FEq-1/Pt-20.17919***0.1803568***0.180127***−0.005953−0.083796***
<0.01<0.01<0.010.83<0.01
DAYS0.000004330.00000450.000002940.0000062**0.0000006
0.110.110.060.020.46
γ1  0.00000374  
0.72 
γ1q-4   0.000012 
0.44
γ2−0.000021**−0.000024**  0.0000935***
0.020.02  <0.01
γ3 −0.0000032   
0.64
Adj. R20.110.110.240.100.15
N126126123132127

In the first two models presented in Table 5 which include the market's ability to adjust for the bias component of the forecast error, the coefficient on γ2 is negative and significant.9 Paradoxically, these results do not hold when proxies for the market's ability to adjust for total forecast error are included in the model, suggesting that analysts only account for the market's ability to adjust for the bias component of the forecast error. This result suggests that on the one hand, bias is intentional since analysts reduce their level of bias when forming their forecasts as the market is more able to undo it, and on the other, provides evidence on the existence of reporting bias in particular. At the very least, the paper documents that the market's reaction to analyst bias is an important determinant of subsequent analyst forecast error.

The inability of the test to document a relation between the market's ability to adjust for total expected forecast error, γ1 and γ1q4, and subsequent forecast error, coupled with the results on γ3, that is, the effect of the market's ability to adjust for analyst underreaction, suggests that only the bias portion of the forecast error is intentional. To provide further support for this result the estimated expected bias for each quarter in the test period is regressed on the market's adjustment of prior quarter bias. The results are shown in the last column of Table 5 and corroborate the results of the first two columns of the same table. Noting that in this design the estimated bias is a positive number reflecting the amount by which analysts inflate their forecasts, the coefficient on γ2 is positive and significant as expected.

Overall, the evidence in this paper corroborates the results of prior research, which suggest that bias increases with the strength of incentives analysts face (Dugar and Nathan, 1995; Das et al., 1998; Cowen et al., 2006). These results provide indirect evidence that bias is intentional. In contrast, the results of this paper suggest that bias is intentional with analysts responding to incentives by knowingly inflating their forecasts and that the magnitude of bias is mitigated by the market's ability to undo it. This latter result suggests that analysts may be concerned with their reputation by not inflating their forecasts when this will not result in the desired result or when their bias will be uncovered. This result is in line with the results in Jackson (2005), who suggests that analyst optimism is related to the expected loss in reputation analysts would suffer when lying about their private information signals.

Turning to the control variables, the standard deviation of prior forecast error, the proxy for earnings unpredictability, is positively related to forecast error. The access to management incentive would predict an opposite sign. Das et al. (1998) find for example that in the face of greater uncertainty, analysts increase the bias in their forecasts in order to gain access to firms' private information. However, the average forecast error in my sample is positive and the positive relation between forecast error and UNPRED thus indicates that high unpredictability increases the forecast error, or equivalently, makes earnings forecasting more difficult. Prior quarter forecast error is positively and significantly related to current quarter's forecast error in line with the results of prior research (Abarbanell and Bernard, 1992; Ali et al., 1992).

Finally, in the last column of Table 5, unpredictability is negatively related to bias while analyst following is positively related to estimated forecast bias. The results on analyst following are consistent with larger following indicating greater analyst competition, which in turn increases the importance of access to management and leading to increased bias (O'Brien and Bhushan, 1990).

ADDITIONAL ANALYSES

  1. Top of page
  2. Abstract
  3. RELATED RESEARCH
  4. RESEARCH DESIGN
  5. RESULTS:
  6. ADDITIONAL ANALYSES
  7. CONCLUSION
  8. references
  9. Appendix

An obvious question that arises from the aforementioned analysis relates to the determinants of the market's ability to adjust for the bias. According to Table 4, the correlation coefficient between the ability to adjust for the bias and firm size (unpredictability of earnings) is positive (negative), indicating that size (unpredictability) impairs (enhances) the ability of the market to undo the bias in analyst forecasts. These correlations are counterintuitive, but remain only a univariate test that renders the documented relation indicative at best. More importantly, the correlation between γ2 and the rest of the explanatory variables can not really be used to deduce the determinants of γ2, given that γ2 is estimated over a 30-quarter period while most of these variables are measured at the last quarter of the period.

In order to shed some light on the determinants of the market's ability to adjust for the bias, I have run a simple model where γ2 is regressed on the average value of firm size, analyst following and dispersion, number of days and estimated bias. Ideally, the values of the explanatory variable ought to be measured during the same estimation period used to measure γ2. In the present sample, however, the values of dispersion, following, days and size are only available for the period from the fourth quarter of 1996 to the second quarter of 2006. The number of observations used to average out the independent variables range from five observations for the first iteration of the model run for the fourth quarter of 1997 to fifteen observations for the last iteration run for the second quarter of 2000. The only variable for which there are 30 observations available and is therefore averaged out over the entire estimation period of γ2 is the estimated bias as obtained from Step 1 of the appendix. Untabulated results indicate that according to expectations the market's ability to adjust for the bias is increasing both in analyst following, a proxy for the firm's information environment (p-value = 0.05) and in the magnitude of bias (p-value = 0.05), a result that suggests that the market can undo the bias as it becomes more detectable. Finally, and counterintuitively, the ability of the market to adjust for the bias is hampered by company size. The same results hold when the level of bias is not included in the model.

A major drawback of this design is, of course, the fact that the variables cannot be measured contemporaneously with the dependent variable. Therefore the above results should be interpreted with caution. However, these preliminary findings provide opportunity for further research in the area. Such research could utilize a more appropriate methodology to examine the determinants of the market's ability to adjust for the bias. For example, the market's ability to adjust for the bias can be estimated at the analyst-firm level, a design that allows for analyst characteristics to be factored in the model as well.

Finally, even though the paper's period covers quarters from the second quarter of 1985 to the second quarter of 2000, the main proposition of the paper is only tested for the quarters starting from the fourth quarter of 1996 to the second quarter of 2000. Therefore, the relation between bias and the market's ability to adjust for the bias is examined in a predominantly bull market casting doubts on the generalizability of results in other periods. However, in March of 2000 the Nasdaq fell nearly 9% from 10 March (when the Nasdaq composite index reached an all time high of 5,048.62) to 15 March signifying the start of a bear market period. In order to test the effects of these events, I have excluded the two quarters of the year 2000 and re-run the analysis. Results pertaining to the main research question are qualitatively similar for all the models presented in Table 5.

In addition, I have examined the two quarters of 2000 separately. In both quarters of 2000, γ2 is negative but not significant in either quarter; γ2, however, is significantly negative if both quarters are combined. In addition, when both γ2 and γ3 are included in the model (second column of Table 5) both periods return a negative and statistically significant coefficient on γ2. Therefore these results do not suggest that the documented negative relation between the market's ability to adjust for the bias and analyst forecast bias is different during periods when the market is down; however, the time series for this test is not long and results should be interpreted with caution, especially as they apply to the current financial crisis. Even though this paper's results might hold during the current financial crisis as the evidence in this section suggests, the effect of the current crisis on the investment banking industry has been so pronounced that it is important for future research to reassess analyst forecast properties in the post-crisis period.

CONCLUSION

  1. Top of page
  2. Abstract
  3. RELATED RESEARCH
  4. RESEARCH DESIGN
  5. RESULTS:
  6. ADDITIONAL ANALYSES
  7. CONCLUSION
  8. references
  9. Appendix

This paper examines whether the bias in analyst forecasts is related to the market's ability to adjust for this bias. The question addresses a timely issue, that is, whether analysts knowingly inflate their forecasts. Analyst behaviour has come under scrutiny after the recent financial scandals that brought into question the objectivity of analyst reports. The paper contributes to the literature in three ways. First, by utilizing a firm-specific design that allows the market's ability to adjust for bias to be computed at the firm level and, second, by separating the effects of bias from other components of the forecast error. Third and more importantly, by examining the effect of the market's ability to adjust for the bias on subsequent forecast error, the paper provides a more direct test of whether bias is intentional, and identifies another potential factor that relates the magnitude of bias to the analysts' willingness to bias their forecasts.

The paper finds that even though forecast errors are positive in the latter part of the period examined, that is, reflecting overall pessimistic forecasts, the amount of bias is positive and optimistic. More importantly, the paper provides evidence that the bias in analyst forecasts is a function of the market's ability to adjust for the bias. In particular, analysts tend to reduce the bias in their forecasts as the market's ability to undo the bias increases. This evidence is consistent with bias being intentional, and documents the existence of reporting bias, in particular. Thus, financial analysts, at least in the period under review, positively inflated their forecasts while the amount of bias was mitigated by the market's ability to adjust for the bias. This evidence therefore justifies recent regulatory actions to increase analyst objectivity.

On the other hand, the evidence presented in this paper also suggests that the magnitude of bias is mitigated by analysts' willingness to bias their forecasts, which is increasing in the market's ability to adjust for the bias. This result supports the existence of a self-correcting market mechanism which, if appropriately reinforced, can also be effective in bias reduction. The market's ability to undo the bias may be mitigating analyst bias through two different, yet related, mechanisms. First, analysts may decrease the bias in their forecasts when the market can adjust for it as a means of protecting their reputation. Second, they might do so as the market's increasing ability to undo the bias also diminishes the benefits derived from this bias. Therefore, analyst objectivity can be enhanced either by building mechanisms that make analysts more concerned about their reputation or by increasing the market's awareness of analyst bias as a way of also increasing the market's ability to adjust for it. The results of this paper should thus be useful to regulators who are concerned with the lack of objectivity in analyst research reports, as they suggest other possible venues for increasing research quality, in addition to actions targeted at mitigating the incentives for bias.

The evidence in this paper can be extended by future research in a number of ways. First, future research can address whether the documented negative relation between the market's ability to adjust for bias and subsequent bias is the result of analysts being concerned about their reputation when bias can be detected by the market or the result of less pressure exerted on analysts by firm management on realization that the benefits of bias are reduced. In addition, as more data become available, future research can examine whether the market's ability to adjust for the bias and in turn its relation to analyst bias vary over time, especially during periods of financial crisis. Finally, it is also important to more thoroughly examine the factors that affect both the market's ability to adjust for the bias and its relation to analyst bias (including the effects of macroeconomic factors).

references

  1. Top of page
  2. Abstract
  3. RELATED RESEARCH
  4. RESEARCH DESIGN
  5. RESULTS:
  6. ADDITIONAL ANALYSES
  7. CONCLUSION
  8. references
  9. Appendix
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Footnotes
  • 1

    These lawsuits are more often settled out of court.

  • 2

    The period examined by Han et al. (2001) covers analyst earnings forecasts up to 1990.

  • 3

    Francis (1997) identifies three different types of bias: reporting, selection and cognitive bias. Selection bias arises from analyst tendency not to issue forecasts if these are favourable, resulting in a distribution of forecasts that is truncated from below, and in turn causing the observed mean to be higher than the true mean of all forecasts. Cognitive bias (or processing bias), is due to analysts issuing optimistic forecasts that happen to reflect their true beliefs, that is, analysts are unable to process their information in an unbiased manner. Arguably, reporting bias, which arises when analysts inflate their true earnings expectations, is the most controversial type as it represents an intentional act on behalf of the analyst to misinform the market.

  • 4

    Firm subscripts are dropped for ease of exposition.

  • 5

    Since γ2 is expected to be negative smaller values of this variable are consistent with a greater ability to adjust for the bias.

  • 6

    A positive relation between bias and the market's ability to adjust for it could be observed in the case where analysts increase the bias in their forecasts when their clients are able to undo it. This, however, presupposes that firm or brokerage management is myopic.

  • 7

    Using a cut-off of |2.0| or |3.0| to eliminate influential observations based on the studentized residual does not change the results. Results without outlier elimination are qualitatively the same with respect to the test variable γ2.

  • 8

    The heteroskedasticity test (White, 1980) does not reject in either model.

  • 9

    The proxy for the market's ability to adjust for the bias, γ2, was also computed by two modifications of equation (3e). First, the equation was expanded to allow the relation between returns and contemporaneous forecast error to vary depending on the sign of the earnings surprise (Hayn, 1995). Second, the model also allowed the relation between expected bias and returns to vary based on the sign of the median forecast, that is, allowing the market's ability to adjust for the bias to differ for firms with negative earnings forecasts in the estimation period. Results with respect to the variable of interest, γ2, were qualitatively similar.

  • 10

    Firm subscripts are dropped for ease of exposition.

  • 11

    In-sample tests show that breaking analyst forecast error into its two components, bias and underreaction, predicts one quarter ahead forecast error with significant less error than using past forecast error (either q−1 or q−4) as the basis of expectation.

Appendix

  1. Top of page
  2. Abstract
  3. RELATED RESEARCH
  4. RESEARCH DESIGN
  5. RESULTS:
  6. ADDITIONAL ANALYSES
  7. CONCLUSION
  8. references
  9. Appendix
Step 1: Estimating Expected Bias and Analyst Underreaction

In this section of the Appendix I explain how the firm-specific bias in analyst forecasts is estimated. First, note that Ali et al. (1992) and Raedy and Shane (1999) use the following equation to estimate the bias in analyst earnings forecasts10:

  • image(2a)

Under the assumption that the bias in analyst forecasts is manifested by adding a constant value to the analyst's true forecast of earnings, the forecast error, FE, at time q and q-1 can be decomposed into its true forecast error and bias components. Solving this expanded form of equation (2a) for bias yields equation (2b):

  • image(2b)

where BE is the bias in the earnings forecast for firm i while b2, the coefficient on the lagged forecast error variable, represents analyst underreaction to information in last quarter's earnings. In this formulation, BE is positive when bias is optimistic and it represents the amount by which analysts inflate their forecasts. In order to be able to estimate BE, I substitute (2b) into (2a):

  • image(2c)

This equation assumes that the bias in analyst forecasts is not a function of the sign of the forecast. A number of papers, however, suggest that the bias in analyst forecasts is greater when the firm reports negative earnings or when recent earnings are negative (see, e.g., Ali et al., 1992; Hwang et al., 1996). In a related vein, Brown and Lo (1998) find that bias is substantially higher in negative earnings forecasts while Francis and Philbrick (1993) find that the bias in analyst earnings forecasts is greater when analysts issue unfavourable recommendations consistent with the access to management incentive. In general, this evidence suggests that analysts are more optimistic either when they are conveying bad news to the market through negative earnings forecasts or when the firm reports negative earnings. To allow for differences in bias depending on the sign of the forecast I expand (2c) as follows:

  • image(2d)

where NGF takes the value of 1 when at least one forecast is negative and 0 otherwise. BE+ is estimated bias for quarters with good news and BE- estimated bias for quarters with bad news.11

To estimate bias for each firm in the sample I run equation (2c) if during the estimation period analyst forecasts were positive, or (2d) if there was at least one negative forecast. The equations are estimated using non-linear least squares as this method allows for the direct estimation of bias. Equations (2c) and (2d) are estimated on a rolling basis based on fifteen observations per firm per iteration to yield expected bias and underreaction results for the quarters starting from the second quarter of 1989 to the first quarter of 2000 for each firm in the sample. For example, to obtain expected bias and underreaction for company i for the second quarter of 1989, equations (2c) and (2d) are estimated using the fifteen quarterly observations spanning the quarters from the third quarter of 1985 to the first quarter of 1989. Similarly, to obtain the expected bias and underreaction for the third quarter of 1989 the equations are estimated on a firm basis using observations from the fourth quarter of 1985 to the second quarter of 1989. The procedure is repeated for all quarters up to the first quarter of 2000. The estimated bias and underreaction observations are used in Step 2.

Step 2: Estimating the Market's Ability to Adjust for Expected Bias and Underreaction

Step 1 above outlines the method followed to estimate expected bias for each firm in the sample from the second quarter of 1989 to the first quarter of 2000. Finding evidence that estimated bias is positive and significant is consistent with both reporting and cognitive bias explanations. Thus, it is still an empirical question whether analysts knowingly inflate their forecasts or do so as a result of cognitive limitations. In this section, I describe the method used to derive the market's adjustment to the expected bias in order to then test its relation to subsequent forecast error that will provide evidence on whether bias is intentional. Examining the extent to which the market adjusts for the bias is of course an interesting question in and of itself.

To estimate the market's ability to adjust for the bias for each firm in the sample, consider the typical earnings response coefficient (ERC) model estimated on a firm-specific basis:

  • image(3a)

where Pt−1 is the price at the beginning of the 120-day period ending five days before the earnings announcement for quarter q; and Rq is the three-day cumulative abnormal return around the earnings announcement of quarter q.

To account for the possibility that the market adjusts for the expected forecast error I expand (3a) as follows:

  • image(3b)

where inline imageis the predicted value from estimating (2c) or (2d) in Step 1.

In this formulation if the market adjusts for the expected forecast error, δ should be positive and if the market adjusts completely δ should be equal to β1. Since I am interested in examining the effects of the market's ability to adjust for the bias, a proxy for the relative (i.e., proportional) adjustment for the bias is more appropriate than the absolute adjustment proxied by δ. I thus estimate (3c) which is mathematically equivalent to (3b):

  • image(3c)

whereinline image

Equation (3c) can be expanded to examine the market's adjustment to the individual components of the expected forecast error by decomposing the expected forecast error into its bias and underreaction components, as estimated in Step 1, as follows:

  • image(3d)

which can be rewritten as,

  • image(3e)

where γ2 is the market's adjustment for the expected bias in the earnings forecast and γ3 is the market's adjustment for analyst underreaction.

Equation (3e) allows for the possibility that the market adjusts differently for the different components of the expected forecast error. Note that γ2 equals γ1* (b2–1) and γ3 equals γ1*b2. Since analyst underreaction predicts b2 to have a value between 0 and 1, then if the market adjusts for the expected bias and underreaction in analyst forecasts, γ2 should be significantly negative and γ3 should be significantly positive. If the market adjusts completely for bias and/or underreaction then γ2 and γ3 should equal −1 and 1, respectively.

Thus to estimate the coefficients γ2 and γ3 I first compute the three-day risk-adjusted cumulative returns around the earnings announcement day for quarter q, Rq. The market-model parameters are estimated over the 120-market-day period ending five days before the earnings announcement date for quarter q. The three days around the earnings announcement of quarter q−1 are excluded from the computation.

Recall that equation (1) is estimated for fifteen quarters, from the fourth quarter of 1996 to the second quarter of 2000. In order to obtain γ2 for the first iteration of equation (1), that is, for the fourth quarter of 1996, equation (3e) is estimated using the first 30 observations of estimated bias and underreaction from Step 1, that is, the estimated values for the second quarter of 1989 to the third quarter of 1996. In order to obtain γ2 for the second iteration of equation (1), that is, for the first quarter of 1997, equation (3e) is estimated using the 30 observations of estimated bias and underreaction spanning the quarters from the third quarter of 1989 to the fourth quarter of 1996. The procedure is repeated until the last estimation of γ2 is obtained, based on quarters from the fourth of 1992 to the first quarter of 2000, to be used in the last iteration of equation (1), that is, when q represents the second quarter of 2000.