## Abstract

This study examines whether it is ever rational for analysts to post biased estimates and how information asymmetry and analyst experience factor into the decision. Using a construct where analysts wish to minimize their forecasting error, we model forecasted earnings when analysts combine private information with consensus estimates to determine the optimal forecast bias, i.e., the deviation from the consensus. We show that the analyst’s rational bias increases with information asymmetry, but is concavely related with experience. Novice analysts post estimates similar to the consensus but as they become more experienced and develop private information channels, their estimates become biased and deviated from the consensus. Highly seasoned analysts, who have superior analytical skills and valuable relationships, need not post biased forecasts.

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## Notes

Beyer (2008) argues that, even without incentives to appease management, analysts may still post forecasts that exceed median earnings because managers can manipulate earnings upward to prevent falling short of earnings forecasts. Moreover, Conrad et al. (2006) find support for the idea that analysts’ “… recommendation changes are “sticky” in one direction, with analysts reluctant to downgrade.” Evidence also indicates that analysts rarely post sell recommendations for a stock, suggesting that losing a firm’s favor can be viewed as a costly proposition. At the extreme, firms even pursue legal damages for an analyst’s unfavorable recommendations. In a 2001 congressional hearing, president and chief executive officer of the Association for Investment Management and Research told the U.S. House of Representatives Committee on Financial Services, Capital Markets Subcommittee, that “…In addition to pressures within their firms, analysts can also be, and have been, pressured by the executives of corporate issuers to issue favorable reports and recommendations. Regulation Fair Disclosure notwithstanding, recent history…has shown that companies retaliate against analysts who issue 'negative' recommendations by denying them direct access to company executives and to company-sponsored events that are important research tools. Companies have also sued analysts personally, and their firms, for negative coverage…” (Association for Investment Management and Research 2001).

Clement and Tse (2005) are the closest to our analysis, however while they admit that the observed link between inexperience and herding can be a complex issue that might have other roots than just career concerns, they do not provide detailed insight as to what and how this complexity develops.

Here, we focus only on the case of one-period sequential forecasting. However, we believe that the main implications of our model hold true for a multi-period sequential forecasting setting. Since we assume that the probabilistic characteristics of different components are known and analysts can gauge each others’ experience and the amount of information asymmetry perfectly, there would be no incentive to deviate from posting commensurate optimal, rational forecasts. If expert analysts intentionally deviate from their optimal forcasts, no other analyst can compete for their experience or information asymmetry (for more discussion see Trueman 1990).

Horizon value and the number of revisions are highly correlated at 65%. We therefore orthogonalize horizon value in the equation to ensure that multicollinearity is not a problem between these two variables.

See Lin and Yang 2010 for a study of how Reg. FD affects analyst forecasts of restructuring firms.

Brokerage reputation and brokerage size are highly correlated at 67%. We therefore orthogonalize brokerage reputation in the equation to ensure that multicollinearity is not a problem between these two variables.

Following Stangeland and Zheng (2007), we measure accruals as income before extraordinary items (Data #237) minus cash flow from operations, where cash flow from operations is defined as net cash flow from operating activities (Data #308) minus extraordinary items and discontinued operations (Data #124).

Following Hirschey and Richardson (2004), we calculate intangibles as intangible assets to total assets (Data 33/Data #6).

As an alternate proxy for industry fixed effects, Fama–French 12 industry classifications (Fama and French 1997) are used. Results using these proxies are available upon request.

As a robustness test, we use I/B/E/S data. Results may be found in “Appendix B”.

Inasmuch as the experience variable is transformed using the natural logarithm; one unit of experience is approximately equal to two quarters of experience. For tractability, we refer to this as a unit in the empirical results.

We are grateful to an anonymous referee for this point.

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## Appendices

### Appendix A: Proofs

### 1.1 A. The objective function:

Given that the analyst’s forecast is a weighted average of the analyst’s unconditional estimate and the consensus, *F* = *w*
*E* + (1 − *w*) *E*
_{
c
}, the objective function can be expressed as:

The first order condition then is:

by collecting terms, we then have:

this means that the optimal weight is:

### 1.2 B. Proof of proposition 1:

By taking the derivative of Eq. 7 with respect to *τ*
_{0}, we have:

Clearly, since the denominator of ∂*w/*∂*τ*
_{0} is positive, then the sign is only a function of the numerator. This implies that the sign changes when the numerator, \( 2\tau_{c}^{{}} \left( {\tau_{0} + \tau (b)} \right) - 2\rho \left( {\tau_{0} + \tau (b)} \right)^{2} - \rho \tau_{c}^{2} , \) is at maximum. To find the maximum, we solve for *τ*
_{0} that satisfies the first order conditions of the numerator. The first order condition yields\( \tau_{c} - 2\rho \left( {\tau_{0} + \tau (b)} \right) \equiv 0 \). Thus, at optimal weight \( \tau_{0} + \tau (b) = 0.5\rho^{ - 1} \tau_{c} . \)

### 1.3 C. Proof of proposition 2:

By taking the derivative of Eq. 7 with respect to bias, we have:

Clearly, since the denominator of ∂*w/*∂*b* is positive, then the sign is only a function of the numerator. This implies (1) that since ∂*τ/*∂*b* is positive, then the optimal weight would be monotonically increasing with ∂*τ/*∂*b* or information asymmetry, and (2) that the optimal weight is nonlinearly, concavely related to private information precision. Since the first term in the numerator is a quadratic function of analyst’s own precision, the maximum in the function is the point at which the numerator changes sign. This point, however, is exactly the same point at which ∂*w/*∂*τ*
_{0} maximizes. For biases at which \( \tau_{0} + \tau (b) \) falls below \( 0.5\rho^{ - 1} \tau_{c} . \), then so long as bias increases so does the optimal weight.

### Appendix B

See Table 6.

### Appendix C

See Table 7.

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Knill, A., Minnick, K. & Nejadmalayeri, A. Experience, information asymmetry, and rational forecast bias.
*Rev Quant Finan Acc* **39**, 241–272 (2012). https://doi.org/10.1007/s11156-011-0252-1

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DOI: https://doi.org/10.1007/s11156-011-0252-1