Opinion-producing agents career concerns and exaggeration

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Unformatted text preview: Opinion-producing agents: career concerns and exaggeration Eric Zitzewitz1 Stanford Graduate School of Business June 2001 1 Address: Stanford Graduate School of Business, Stanford, CA 94305. Email: zitze- [email protected] The author would like to thank Glenn Ellison, Bengt Holmstrom, Dean Karlan, Leigh Linden, Sendhil Mullainathan, Nancy Rose, Jean Tirole, Ezra Zuckerman and seminar participants at Berkeley, Harvard, London Business School, Michigan, MIT, Northwestern, Stanford, Washington University-St. Louis, and Yale for helpful comments and suggestions. Particular thanks are due to my primary advisor, Robert Gibbons. All errors are my own. The …nancial support of an NSF Graduate Research Fellowship is gratefully acknowledged. I also thank I/B/E/S for providing me with access to their analyst data. Abstract This paper models the incentives created by career concerns for opinion-producing agents. We …nd that career concerns can create an incentive for exaggeration or anti-herding, since high-ability agents will have opinions that are more di¤erent from the consensus on average and potential clients will learn more quickly about how di¤erent an agent’s opinions are from the consensus on average that about whether or not they are exaggerating. The model predicts that agents should exaggerate more when they are under-rated by their clients, when the realizations of the variables they are forecasting are expected to be especially noisy, and when they expect to make fewer future forecasts. We …nd that these predictions are consistent with the empirical data on equity analyst’s earnings forecasts. 1 Introduction Much of the information in the so-called information economy is not verifyable information as economists normally de…ne it, but is rather opinion. Opinion goods such as forecasts, consulting advice, and product reviews are sold in markets, and the production of these and other types of opinions is also the primary job of many professionals within organizations. Unlike most traditional goods, the quality of information or opinion goods cannot be readily observed prior to purchase. In addition, opinions that are not veri…able can be manipulated by their producer. Reputational or career concerns are thus likely to be especially important to opinion producers. This paper examines the relationship between the reputational or career concerns of opinion producers and their incentives to engage in a particular type of opinion manipulation, namely exaggerating their di¤erences with the existing consensus. It essentially asks the question: do people exaggerate in order to appear smart? Most opinions can be thought of as forecasts of a random variable that will be realized in the future. We develop a model in which potential clients attempt to learn the ability of forecasters from their track record. In the model, an incentive to exaggerate arises because high-ability agents have access to more private information and thus have unbiased beliefs that are more di¤erent from the prior consensus on average. Clients learn more quickly about how di¤erent an agent’s forecasts are from the consensus on average than about whether or not they are exaggerating, and thus agents can temporarily raise estimates of their ability by exaggerating. The model also yields cross-sectional predictions about when we should expect agents to exaggerate more. This is potentially useful to consumers of opinions, since they will want to back out expected exaggeration to form unbiased beliefs. One source of variation arises from the fact that the di¤erence in learning speed discussed above is more pronounced when forecast variable realizations are noisier, so agents should 1 exaggerate more under these circumstances. Likewise, agents expecting a shorter future career length should exaggerate more. Agents should also exaggerate more when they have had bad luck in the past (and are consequently under-rated by the market) in order to increase the weighting on future observations of their ability. We …nd that both the general …nding of exaggeration and these cross-sectional predictions are consistent with the empirical evidence when we examine the exaggeration of equity analysts forecasting earnings using the methodology developed in Zitzewitz (2001). The model of career concerns and exaggeration in this paper draws on the literature on career concerns, reputational concerns for producers of goods of unobservable quality, and herding theory.1 It is particularly related to three recent papers. Scharfstein and Stein (1990) provide a model of sequential investment decisions in which a herding equilibrium exists. A key assumption they make is that agents do not know their ability and thus low-ability agents (who receive noisier signals) do not know that their signals are noisier and do not know to reduce their reliance on their private information and therefore make reports that deviate more from the consensus. Repeating the consensus is therefore a signal of ability, and a herding equilibrium can result. Avery and Chevalier (1999) extend this equilibrium to allow agents to learn their own ability and …nd that anti-herding will be an equilibrium rather than herding once agents are expected to have a su¢ciently precise knowledge of their own 1 For general career concerns theory see Fama (1980), Holmstrom (1982), and Gibbons and Mur- phy (1992). The industrial organizations literature on reputational concerns includes Nelson (1974), Schmalensee (1978), Klein and Le-er (1981), and Shapiro (1983). Herding models include information cascade models (Banerjee, 1992; Bikhchandani, Hirshleifer, and Welch, 1992; Welch, 1999), incentive-concavity models (Holmstrom and Ricart i Costa, 1986; Zweibel, 1995; Chevalier and Ellison, 1997 and 1999; Laster, Bennett and Geoum, 1999), and career-concerns models (Scharfstein and Stein, 1990; Brandenburger and Polak, 1996; Trueman, 1994; Ehrbeck and Waldmann, 1996; Prendergast and Stole, 1996; Avery and Chevalier, 1999; Ottaviani and Sorensen, 2000; E¢nger and Polborn, 2000). 2 ability. In Prendergast and Stole (1996), agents know their own ability perfectly and they anti-herd or exaggerate in order to signal ability. Prendergast and Stole (1996) also allow the set of possible investments to be continuous rather than restricting it to having only two possible values. This paper is closest in setup to Prendergast and Stole (1996); its main departure is to examine an environment in which there is learning from investment outcomes (or, in the language of this paper, from the realizations of the variables being forecast). This seemingly trival extension yields the cross-sectional predictions about the degree of exaggeration mentioned above that we can test empirically. The extension comes at a cost, however, since modelling the learning from realizations is too complicated to handle in a fully Bayesian way. Rather than assuming that potential clients conduct a Bayesian estimate of an opinion seller’s ability, we instead assume that they use an econometric methodology that approximates a maximum-likelihood estimate of ability. The results from this model can therefore be viewed either as an approximation of the results from a Bayesian model or as the results from a behavioral model in which we make the arguably realistic assumption that clients use econometric approximations when faced with a Bayesian problem that is too di¢cult to them to solve. The remainder of the paper is organized into two sections. The …rst develops the model and the cross-sectional predictions. The second section presents evidence that equity analyst’s earnings forecasts are consistent with these predictions. A conclusion follows. 2 Career-concerns model In this section, we model the incentives created by the career concerns of an agent who forecasts a series of random variables. We …rst present a two-period model in 3 which agents issue forecasts in the …rst period and receive revenue in the second period proportional to clients’ valuation of their forecasts based on their …rst period performance. We then extend the model to three periods in order to examine how past forecasting performance a¤ects an agent’s incentives to exaggerate. From the two-period model we conclude that agents have an incentive to exaggerate and this incentive to exaggerate will be greater when earnings realizations are expected to be noisy or when agents expect to make a limited number of forecasts in the future. From the three-period model, we conclude that agents will also exaggerate more when they have had bad luck in the past and thus are underrated by their clients. 2.1 Two-period model The model has two periods. In the …rst period, the agent issues forecasts of J random variables after observing a private signal and a common prior. In the second period, the agent sells early access to their forecasts to clients, receiving revenue proportional to clients’ valuation of their forecasts based on their …rst-period performance. Agents also face an exogenous incentive for forecast accuracy, and thus receive revenue proportional to b ¡ ¸ ¢ M SE , where b is the estimate of the value of new information in v v the agents forecasts and ¸ is the size of the incentive for accuracy. The role of the incentive for accuracy is to make the language analysts use relevant; we can think of this incentive as the result of clients’ costs of translating exaggerated forecasts into unbiased expectations or of industry institutions that measure analysts based on mean squared error. The timing of the model is as follows: 1. Nature chooses an ability, a, and an accuracy incentive, ¸, for the agent from a prior distribution g (a; ¸). Both parameters are observed by the agent but are unknown to their potential customers. 4 2. The agent forecasts a series of J random variables Aj . For each Aj , the agent observes a public consensus prior that Aj is distributed N (Cj ; §¡1), where § is the precision of the prior. Since Cj is public, we can think of the agent as forecasting yj = Aj ¡ Cj , i.e. the di¤erence between the actual realization and its consensus prior expectation. 3. In addition, the agent observes an independent private signal s j » N (Aj ; p¡1 ), where p = a§2 (1¡a§) > 0 is the precision of the signal. p is an increasing function of a; higher ability agents receive higher precision private signals. 4. Based on the consensus priors and her private signals, the agent issues forecasts using a forecasting rule x = x(s; C; p; ¸), where xj = Fj ¡ Cj is a forecast of yj . All forecasts are made before any of the earnings variables are realized. 5. Clients with early access to forecasts can make investments in securities with returns that are proportional to yj . 6. Current and potential clients observe the forecasts x and realizations y and estimate the value of the information content of the agent’s forecasts using a valuation rule v = v(x; y ). b 7. Agents sell early access to their second-period forecasts and receive revenue 2.1.1 proportional to b ¡ ¸ ¢ M SE. Agents consume and experience linear utility. v Forecast information content and clients valuation of forecasts After the agent observes the consensus prior and the private signal, her posterior expectation of yj is E( yj jC j; s j ) = (sj ¡ C j) 5 p , p +§ (1) where a higher-precision private signal receives a higher weight. Notice that the variance of the di¤erence between an agent’s unbiased beliefs and the prior consensus is increasing in p: V ar[ E(yj js j; C j)] = p = a. (p + §)§ (2) That is, higher-ability agents have opinions that are more di¤erent from the consensus, on average. We will also refer to this variance as the information content of an agent’s forecasts, since it is equal to the reduction in mean-squared error in the expection of yj or Aj due to the agent’s private information: 2 V ar[ E(yj jsj ; Cj )] = V ar (yjj Cj ) ¡ V ar [yj ¡ E(yj js j ; Cj )]. (3) A mean-variance client with early access to a forecast investing in a security with returns that are linear in yj will invest to maximize 2 max Ij ¢ E(yj jxj ) ¡ Ij ¢ Ij r ¢ V ar(yj jxj ), 2 (4) where Ij is the client’s exposure to yj and r is the coe¢cient of absolute risk aversion. The optimal investment is: ¤ Ij = E (yj j xj) r ¢ V ar(yj jxj ) (5) and such an investment has an ex-ante certainty-equivalent value of CE = [E (yj j xj )] 2 . 2r ¢ V ar(yj jxj ) (6) The value of early access to an agent’s forecasts will be proportional to the variance of E(yj jxj ). If an agent’s forecasts are fully revealing of her signal, this will be the same as V ar [E (yj js j ; Cj )] = a, otherwise it will be a less a discount for uncertainty regarding an agent’s forecasting strategy. For simplicity, we will assume that the 2 This is true since by the law of iterated expectations, y j ¡ E (y j jsj ; Cj ) must be uncorrelated with E (y j jsj ; Cj ) ¡ E (yj jCj ). 6 i nformation lost in communicating the signal is small in the long run and thus that clients are interested in estimating a as the long-run value of a client’s forecasts, so va b = b.3 2.1.2 Solution We will look for a consistent-exaggeration forecasting equilibrium in which agents use the forecasting rule: xj = b(a; ¸) ¢ E (yj j sj ; Cj ) with some constant exaggeration factor b that can depend on a or ¸. This forecasting rule implies that agents exaggerate their di¤erences with the consensus when b > 1, herd when b < 1, and report their expectation when b = 1. The standard solution approach would be to solve for a Bayesian equilibrium in which the analyst chooses her forecasts to maximize expected utility, given the clients’ valuation rule, and the valuation rule produces an unbiased and e¢cient estimate, given the analyst’s forecasting rule. Unfortunately, the standard Bayesian estimate of v(x ; y ) = E[ ajx ; y; g () ; b()] is very intractable and conjugate prior distribution families that improve tractability do not exist. Instead of assuming that clients make a such a di¢cult calculation, we will instead assume that they use an econometric estimation approach that is consistent but not necessarily e¢cient, with the ine¢ciency coming from the incorporation of the information from the prior distribution in an approximate rather than a fully Bayesian way. We will describe an equlibrium in which clients do econometric estimation that anticipates consistent exaggeration and then show that consistent exaggeration is in fact optimal for the analysts.4 This ex3 If we relaxed this assumption, agents would face an additional incentive for limiting the un- certainty regarding their exaggeration strategy, since uncertainty about exaggeration creates a gap between a = V ar[E (yj jsj ; C j )] and v = V ar[E ( yj jx j )]. Relative to the solution described below, the agent would choose an exaggeration factor slightly closer to their clients’ prior expectation of exaggeration. 4 Actually, a consistent-exaggeration equilibrium will be the only equilibrium whenever ¸ > 0 . To 7 ercise can be viewed as the derivation of an Bayesian equilibrium in which clients are constrained by bounded rationality and thus use an unbiased and tractable but less e¢cient estimation approach. Alternatively, it can be viewed as merely an analysis of the incentives created for analysts if clients estimate their ability using a particular econometric procedure. We proceed by specifying the clients’ estimator of analyst ability, solving the analyst’s problem given the clients’ valuation rule, and verifying that consistentexaggeration forecasting is an equilibrium. Clients’ problem If analysts follow the consistent-exaggeration forecasting rule described above, they will issue forecasts such that: p ( s ¡ Cj ) » N (0; a) p+§ j p = b¢ (sj ¡ Cj ) » N (0; b2 a) p+§ E(yj jsj ; Cj ) = xj yj = b¡1 xj + "j "j = yj ¡ E(yj js j; C j) . As a result, xj and yj are distributed joint normally: 2 3 2 3 ¡1 ba 6 yj 7 6 a + V + (§ + p) 7 4 5 » N (0; 4 5). 2a xj ba b Note that a is the information content of the analyst’s forecasts V ar[ E(yj jxj )]; clients are therefore trying to estimate a. see this consider an alternative equilbrium where clients expect an analyst to exaggerate by b ¢ f (j ) , where f varies predictably from observation to observation. In this case, the …rst-order condition in b (12) below will be b = [E (b CL ) + f ¡ 1 ¸][E (¯ CL )2 ¡ °¯ 2 + ¸ ]¡1 , so the analyst will choose a lower ¯ 0 b when f is high and vice versa, i.e. will choose a strategy closer to consistent exaggeration than they are expected to. It follows that a consistent exaggeration is the only equilibrium (when clients deviate from Bayesian estimation as described above). 8 Given the regression-like setup, it will be convenient to discuss ¯ = b¡1 as the change in the expectation of y for a given change in x. A natural set of estimators for ¯ = b¡1 and a are the classical statistical estimators that are used to estimate exaggeration and forecast information content in Zitzewitz (2001): PJ j b CL = P=1 xjyj ¯ J 2 j =1 xj P ( J=1 xjyj )2 2 j b d a bCL = ¯ CL ¢ V ar(xj ) = . P ( J ¡ 1) J=1 x2 j j (7) (8) These estimators are consistent and unbiased, but they are ine¢cient if clients have prior information about a or b(a; ¸). A client can improve the e¢ciency of an estimate of a by averaging the observed bCL with the mean of her prior distribution. In a d addition, since the estimate bCL is likely to be noisier than the estimate V ar(xj ), ¯ especially when V is high, clients can improve on the e¢ciency of their estimate b by constructing their b with an average of the observed ¯ CL and ¯ 0, client’s prior a expectation of b¡1 given the distribution g (a; ¸) and the function b(a; ¸) . We therefore assume that clients estimate analysts’ ability as: b2 d (¯ CL + ° ¢ ¯ 2) ¢ V ar (xj ) + ± ¢ a0 0 a bP = , 1+°+± (9) where ± is the weight given the prior expectation of ability and ° > 0 is the weight placed on ¯ 0. The ° term in (9) captures an important feature of any optimal estimator, namely that prior information about exaggeration should be relied on when estimates of exaggeration are noisy. Equation (9) is similar in structure to a maximum-likelihood estimator of ability; an analysis of the maximum likelihood estimator in Appendix A yields some intuitive predictions about the determinants of ° . The weight ° placed b on ¯0 should be higher when the estimate ¯ is noisier i.e. when earnings realizations are noisier (and V is higher) or when the number of observations J is low.5 5 We can also think of ° as capturing the potential for exaggeration to signal high or low ability. 9 Analyst’s problem Analysts choose their xj to maximize their expectation of a bP ¡ ¸ ¢ M SE , their clients’ estimation of their forecast value plus their incentive for absolute accuracy. If clients use the estimation approach outlined above, the analyst’s problem is: P PJ PJ ( J=1 xj yj )2 x2 (yj ¡ xj )2 j j max E[ + °¯2 j=1 ¡ ¸E [ j=1, PJ 0 x (J ¡ 1) (J ¡ 1) (J ¡ 1) j =1 x2 j (10) where the expectations are the analyst’s before y is realized. The …rst-order condition for each xj is:6 xj = b b E (yj ¯ CL) + E (yj) ¢ ¸ E (¯ CL ) + ¸ = E(yj ) ¢ . 2 b b E(¯ CL)2 ¡ °¯ 2 + ¸ E(¯ CL) ¡ °¯2 + ¸ 0 0 (11) So a consistent-exaggeration strategy of the type assumed above is in fact optimal. The analyst chooses b such that: ¯ =b ¡1 E (b CL)2 ¡ °¯2 + ¸ ¯ 0 = . b ¯ CL + ¸ (12) From (7) above we can see that rational expectations on the part of the analyst imply that E (b CL ) = ¯ . This condition together with (8) implies the following ¯ relationships between accuracy incentives (¸), the weight placed on ¯ 0 (° ), and exaggeration ( ¯): ² When ° = 0 (no prior information about ¯) and ¸ = 0 (no incentive for accuracy), any value of ¯ is possible. This is a cheap talk result: if there is no incentive for absolute accuracy, any language is as good as the next so long as the clients do not have prior beliefs about ¯ . When the distribution g( a; ¸ ) and the function b (a; ¸) are such that the priors on a and b (a; ¸ ) are positively (negatively) correlated, then exaggeration signals low (high) ability. Clients can account for this in their estimation by lowering (raising) ° relative to its value when the priors on a and b (a; ¸ ) are uncorrelated. 6 Although it might appear that this simpli…cation was made using the incorrect assumption that 2 b b E (yj b C L) = E (y j ) ¢ b CL and E (¯ CL ) = E (¯ CL )2 , actually, the two cross terms exactly cancel. ¯ ¯ 10 ² When ° = 0 and ¸ > 0, ¯ = 1. Adding even a small incentive for absolute accuracy to the cheap talk situation makes unbiased forecasting optimal. ² When ° > 0 and ¸ · °¯2 , ¯ = 0 and agents exaggerate by an in…nite factor. 0 With no or a limited incentive for absolute accuracy and with clients placing some weight on their prior belief, analysts can always increase estimates of their ability by exaggerating more. Analysts essentially report a binary forecast (i.e., above or below the consensus) and cannot credibly communicate the strength of their beliefs.7 ² When ° > 0 and ¸ > °¯ 2, ¯ = ¸¡1(¸ ¡ °¯ 2) < 1. Some exaggeration occurs, 0 0 but it is limited to a …nite amount by the incentive for absolute accuracy. As this incentive increases, the amount of exaggeration decreases. Likewise, as J decreases or random variable realizations become noisier and thus clients rely more on their prior beliefs about ¯0 , exaggeration increases.8 2.2 Three-period model In the two-period model above, the analyst makes all J forecasts before seeing any of the realizations. In this section, we analyze how an analyst’s past forecasting performance a¤ects her future exaggeration. We extend the model by assuming that agents observe the realizations of the …rst J variables and then forecast a second group 7 8 This result is similar to the in…nite exaggeration result in Ottaviani and Sorensen (2000). Notice that, given the estimation approach assumed above, b( a; ¸) is a function of only ¸ . This implies that when clients’ prior beliefs g (a; ¸) imply that a and ¸ are uncorrelated, then exaggeration will signal neither high or low ability. If instead clients’ believe that high-ability agents face more (less) exogenous incentives to exaggerate, then exaggeration will signal high (low) ability. When ability (a) and exogenous incentives to exaggerate (¸ ) are more positively correlated, exaggeration signals high ability and ° and the equilibrium amount of exaggeration increase. 11 of K variables. Clients expect consistent exaggeration within a group of random variables, but not necessarily across groups. Clients estimate ability as before, except that they allow for di¤erent exaggeration in the two sets of observations: P P +K ( J=1 wxj yj + J=J +1 xjyj )2 j j a bP = (1 + ° + ±)¡1 PJ PJ +K 2 2 2 j=1 w xj + j=J +1 xj PJ PJ +K 2 2 °¯ 2 ± j=1 xj + j=J +1 xj 0 + + ¢ a0 1 +° + ± (J + K ¡ 1) 1+°+± bJ ¯ w= E (¯K j b J ) ¯ where ¯J and ¯ K refer to the ¯ for the …rst J and the second K random variables, respectively. The weight w is the ratio between the observed exaggeration in the …rst set and the clients’ expectation of exaggeration in the second set of random b variables, conditional on the observed ¯ J . The …rst order condition for the agent when forecasting the second set of variables reduces to: ¯K = b¯ wE(¯ JK j bJ )2 ¡ °¯ 2 + ¸ 0 , b JK jb J ) + ¸ wE (¯ ¯ (13) where b JK is the exaggeration factor estimated across both sets of observations, which ¯ will be an average of w ¡1b J and ¯ K . ¯ Proposition 1 Equation (13) implies that agents will choose a ¯ K that is between b the one-period optimal ¯ 1 = ¸¡1 (¸ ¡ °¯ 2) and their client’s expectation E(¯ K j¯ J ): 0 Proof. In Appendix B Agents who have had bad luck in the past and realized a lower b J than the ¯J ¯ they intended will choose a lower ¯ K . This can be interpreted as the agents who have had bad luck in the past and are thus under-rated will exaggerate more in order to increase the relative weight of the later observations.9 9 This prediction that under-rated agents should exaggerate more is also made by a di¤erent model in Graham (1999). 12 3 Testing predictions of the model The model in section 2 has three cross-sectional predictions about when we should expect more exaggeration. Agents should exaggerate more when they are underrated by their clients, when earnings realizations are expected to be noisy, and when they expect to make a limited number of future forecasts. In this section of the paper we test these predictions using the I/B/E/S analyst earnings forecast dataset and the methodology for measuring exaggeration outlined in Zitzewitz (2001). 10 Speci…cally, we estimate the average exaggeration coe¢cient for a speci…c group of forecasts using the regression A ¡ C = ® + ¯ (F ¡ C ) + " (14) as in the classical estimator described in section 2.1.2, where A is the I/B/E/S actual earnings for a given …rm-quarter combination, F is a forecast of earnings, and C is an econometric expectation of earnings based on prior forecasts for that …rm-quarter.11 We test the predictions for how exaggeration should vary with a speci…c variable by interacting the right-hand side of (14) with the variable of interest. As Zitzewitz (2001) shows, the regression in (14) produces an unbiased estimate of the inverse of the exaggeration factor, ¯ = b¡1, because the error term is the analyst’s 10 As Zitzewitz (2001) argues, inferring exaggeration or herding from forecast dispersion, a popular methodology (e.g., Hong, Kubik, and Solomon, 2000), is problematic in that it does not control for forecast information content. In other words, a forecaster can forecast close to the consensus for two reasons: 1) if she is herding, but also 2) if she does not have very much independent private information. Since the amount of independent private information many vary with our cross-sectional variables, we use the methodology in Zitzewitz (2001) which controls for it. 11 The exaggeration measurement methodology, including the methodology for measuring C , is described in more detail in Zitzewitz (2001). A non-econometric methodology for estimating C (such as using the mean of all outstanding or the most recent forecasts) can be substituted without materially a¤ecting the results. All earnings variables are normalized by the share price. 13 expectational error at time of forecasting, " = A ¡ E (Aj s; C ), and expectational errors must be mean zero with respect to all variables known at time of forecasting, including F ¡ C . In order for interaction versions of this regression to be valid, the analyst’s expectational error must be mean zero with respect to the interaction variable as well. This must be true for all variables that are known at time of forecasting, but for variables that incorporate the econometricians knowledge of the future, we will need to verify that the orthogonality condition still holds. 3.1 Under-rated analysts Since it is impossible to directly observe which analysts have true ability that is higher than their measured ability, we are forced to use our knowledge of the future to help identify under-rated analysts. In particular, we divide analysts with a given past forecast information content into those whose performance eventually rises and those whose performance falls and assume that, on average, the analysts whose performance rises were under-rated in the past. Speci…cally, we rank analysts with at least 50 past forecasts based on two variables: their past forecast information content from observation 1 to j ¡ 1 and the di¤erence between their past information content and their information content from observation j + 1 to j +50 (or fewer if the analyst leaves the sample). We then interact these rankings with the right-hand side of equation (14). Table 1 presents the results of such an interaction regression. The results suggest that under-rated analysts exaggerate more, whether or not past performance is controlled for. The results also do not change if we control for the analyst’s career length or the size of their brokerage, both of which have signi…cant positive e¤ects on ¯ . In constructing this test, we took two steps to avoid violating the orthogonality condition discussed above. First, we used di¤erent observations to measure perfor14 mance improvement (observations j + 1 to j + 50) and exaggeration (observation j ). This is important since if an analyst “gets lucky” and gets surprised in the direction of their deviation from the consensus (i.e., A ¡ E and F ¡ C positively correlated), ¯ will be overestimated, exaggeration will be underestimated, and analyst performance will be overestimated. Using di¤erent observations avoids this potential problem. Second, we used bCL = ¯ 2V ar(x) as our performance measure, a measure that is a robust to exaggeration, so even if exaggeration in observation j were correlated with exaggeration in observations j + 1 to j + 50 or 1 to j ¡ 1, this would not create a correlation with our measure of the change in performance. 3.2 Expected earnings uncertainty We test for whether analysts exaggerate more when earnings are uncertain using a two-step process (Table 2). In the …rst step, we predict the average absolute earnings surprise (actual less consensus) for a particular …rm-quarter based on market cap, the standard deviation of prior outstanding forecasts, and the prior average absolute earnings surprise for the …rm in question. We hypothesize and …nd that average absolute earnings surprise is higher for small-cap …rms, when past forecasts are dispersed, and for …rms for which average earnings surprise has been large in the past. In the second step, we test the e¤ect of expected earnings surprise on ¯ using an interaction regression, …nding that there is signi…cantly more exaggeration when predicted absolute earnings surprise is higher. Notice that in this analysis all of the interaction variables are known at time of forecasting; thus the orthogonality condition should be satis…ed. 3.3 Expected career length The prediction that analysts should exaggerate less when they expect to make more future forecasts is more di¢cult to test. We can use the actual number of future 15 forecasts as our interaction variable, and when we do this, we …nd less exaggeration by analysts who make more future forecasts (Table 3, Panel A). A problem with this analysis, however, is that analysts who have good luck should both survive longer and have measured exaggeration that is less than what they intended. An alternative approach is to use variables that are known at time of forecasting that predict an analyst’s longevity. Probit regressions that predict an analyst’s leaving the sample and not returning for at least 2 years after a given forecast …nd longer survival is expected for analysts who have made a large number of past forecasts, analysts who work at larger (usually the more prestigous) brokerages, and analysts who have had better forecast accuracy in the past (Table 3, Panel B).12 In Table 1, we found that analysts with more forecasting experience and analysts at larger brokerage …rms exaggerated less. The probit regressions suggest that one potential explanation for this result is that these analysts have longer expected careers, and the optimal exaggeration rate for these analysts is lower. Alternative explanations exist, however. Analysts may become less overcon…dent in their own information or better calibrated with experience. In the model we assumed that analysts’ utility is linear in the market valuation of their forecasts; if the concavity of analyst’s incentives varies with brokerage size or career length, this may also explain the results. Inexperienced analysts may face greater outside options and thus more convex incentives (i.e., they can gamble and then leave if it does work out), and this may explain their greater exaggeration. Analysts at larger …rms may be given more concave incentives by their …rm to reduce exaggeration, such as a risk of getting …red 12 Forecast information content, in turn, does not appear to play a role in predicting exits from the I/B/E/S sample. One potential explanation for this result is that analysts can leave the I/B/E/S sample for either good reasons (moving to lucrative proprietary researcg positions) or bad reasons (getting …red). We do …nd that for analysts who stay in the profession, forecast information content helps explain which analysts are ranked highly by Institutional Investor (Zitzewitz, 2001, Table 7). 16 for deviating from the consensus and being wrong that is not fully compensated by the reward for deviating from the consensus and being right. A model in which …rms have a collective reputation for exaggeration might predict this, since larger …rms will make more forecasts in the future than smaller …rms and thus would prefer that their analysts exaggerate less. In summary, the empirical evidence that is available is consistent with the prediction that analysts who expect to make more future forecasts should exaggerate less, but alternative explanations for the results exist. 4 Conclusion The evidence presented in Zitzewitz (2001) suggests that there are persistent di¤erences in analyst’s exaggeration factors and forecast information content and that the best predictor of the future value of an analyst’s forecasts is the value of her past forecasts. This suggests that potential clients should use an analyst’s track record to determine how much to pay her. This paper investigates the incentives for exaggeration created by clients attempting to learn ability from forecasting record in a …nancial market environment where forecasts are valuable for their new information content. We …nd that career concerns can create an incentive for agents to exaggerate, or overweight their private information. This incentive exists because high-ability analysts have viewpoints that are more di¤erent from the consensus on average and since potential clients learn more quickly about an analyst’s average di¤erence with the consensus than about whether she is exaggerating. The equilibrium exaggeration rate is …nite so long as there is a su¢ciently large external incentive for absolute forecast accuracy. The model also predicts that agents should exaggerate more when earnings are expected to be noisy, when they expect to make a limited number of 17 future forecasts, or when they are under-rated by the market, and we …nd that these predictions are consistent with the equity analyst forecast data. Although the evidence in the paper is for equity analysts, the issues examined in this paper potentially apply to other opinion-producing agents. A large number of agents produce opinions that can be thought of as forecasts of random variables. Especially when the actions taken based on the opinions are strategic substitutes, the value of privileged access to an opinion depends on its information content relative to the consensus. Whenever the realized values of random variables are noisy, agents will learn more quickly about the average di¤erence between an agent’s opinion and the consensus that they will about whether the agent is exaggerating, an the agent will be able to raise estimates of her ability by exaggerating. This incentive to exaggerate will be greater when the realization of the random variable is expected to be more noisy, which makes exaggeration harder to detect, when the agent expects to leave the profession soon, or when the agent perceives that she is under-rated by the market. These predictions, together with the empirical support for them in the analyst data, are potentially useful for consumers attempting to account for exaggerate in their interpretation of opinions or for …rms attempting to reduce exaggeration in the incentives they design for opinion-producers. A Maximum likelihood estimation In this appendix we assume that rather than calculating expectations for a and b, clients calculate maximum likelihood estimates. We can think about combining the prior distribution g (a; ¸) and the function b(a; ¸) into a prior on a and ¯ = b¡1, which we will call f (a; ¯). For tractability, we will also assume that the prior distribution g (a; ¸) is such that the distribution f (a; ¯ ) is concave in logs for both variables, i.e. d2 ln f ( a;¯ ) da2 · 0 and d2 ln f (a;¯ ) d¯ 2 · 0 8x, a condition that is satis…ed by the normal 18 and chi-squared distributions, for example. We also assume that V = V ar(yj jxj ) is known. Given these assumptions, the log likelihood function is: ln L(x; y; a; ¯ ) = J X J ln Á ( j=1 X ¯xj y ¡x ¯ )+ ln Á( j 1=2j ) + ln[ f (a; ¯ )], a1=2 V j=1 where Á (¢) is the standard normal p.d.f. The maximum likelihood estimators of a and b satisfy the conditions: a bMLE bMLE ¯ PJ fa(bMLE ; bMLE ) b3=2 a ¯ a = + ¢ MLE b J J f (bMLE; ¯ MLE) a PJ V ¡1 j=1 xjyj f¯ (bMLE ; b MLE ) a ¯ V = (1 + ) [ PJ + ¢ PJ. a bMLE x2 f (bMLE; b MLE ) a ¯ x2 j=1 j j =1 j b2 ¯ MLE We have assumed that fa f 2 j =1 xj is monotonically decreasing in a, so the second term in the expression for a will be positive (negative) when a is less (greater) than the mode of the prior distribution. The maximum likelihood estimate of a will thus be 2 d between b MLE V ar(xj ) and the mode of the prior. The …rst factor in the maximum ¯ likelihood estimate of ¯ induces a bias toward zero that is a artifact of our taking a maximum likelihood approach to estimation. Ignoring this factor, the maximum likelihood estimate of ¯ will be between b OLS and the mode of the prior, with more ¯ weight being placed on the prior when V is large. Thus the MLE is similar in structure to the estimating approach assumed in (9): b2 d (¯ CL + ° ¢ ¯ 2) ¢ V ar (xj ) + ± ¢ a0 0 a bP = . 1+°+± The estimate of ¯ is some weighted average of the observed ¯ CL and the mean of the prior distribution ¯ 0. Ability is estimated in turn as some weighted average of b2 d ¯ MLEV ar(xj ) and the mean of the prior distribution. The weight placed on the prior belief about exaggeration, ° , is increasing in V and decreasing in J , i.e. it is higher when realizations are noisy or when the number of observations is small. 19 B Proof of Proposition 1 b We know that E (b JK j¯ J ) is between w¡1 bJ and ¯ K . Since w ¡1 bJ = E (¯ Kj b J ), this ¯ ¯ ¯ ¯ bb implies that ¯K will be above E(¯ JK j¯ J ) when it is above client’s expectation based b on the observed bJ . If we de…ne 4¯ = ¯K ¡ E (b JK j¯ J ), we can rewrite the …rst ¯ ¯ order condition as E( bJK j bJ ) + 4¯ = ¯¯ E (bJK j b J ) = ¯¯ ¯K ¯K b wE (b JK j¯ J )2 ¡ °¯ 2 + ¸ ¯ 0 bJK j¯ J ) + ¸ b wE(¯ ¸(1 ¡ 4¯ ) ¡ °¯2 0 ¸ + w ¢ 4¯ 2 2 bJ Kj b J ) + 4¯ = ¸ ¡ °¯0 + w (4¯) = E (¯ ¯ ¸ + w ¢ 4¯ bJK j bJ ) ¢ 4¯ wE(¯ ¯ = ¯1 ¡ . ¸ If we de…ne ¯1 = ¸¡1(¸ ¡ °¯ 2) to be the optimal one-period beta, we can multiply 0 both sides of the above expression by ¸¡1(¸ + w ¢ 4¯ )to get: ¯K = ¯1 ¡ bb wE(¯ JK j¯ J ) ¢ 4¯ ¸ This implies that ¯ K is less than ¯ 1 if and only if it is greater than E (bJK j b J ) and ¯¯ E (¯K j b J ). ¯ 20 References Avery, Christopher N. and Judith A. Chevalier, “Herding Over the Career,” Economics Letters, 1999, 63, 327–333. Banerjee, Abhijit, “A Simple Model of Herd Behavior,” Quarterly Journal of Economics, 1992, 107, 797–817. Bikchandani, Sushil, David Hirshleifer, and Ivo Welch, “A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades,” Journal of Political Economy, 1992, 100, 992–1026. Brandenburger, Adam and Ben Polak, “When Managers Cover Their Posteriors: Making Decisions the Market Wants to See,” RAND Journal of Economics, 1996, 27, 523–541. Chevalier, Judith A. and Glenn D. Ellison, “Risk Taking by Mutual Funds as a Response to Incentives,” Journal of Political Economy, 1997, 105, 1167–1200. and , “Career Concerns of Mutual Fund Managers,” Quarterly Journal of Economics, 1999, 114, 389–432. Cooper, Rick A., Theodore E. Day, and Craig M. Lewis, “Following the Leader: A Study of Individual Analysts Earnings Forecasts,” 1999. Vanderbilt University Mimeo. E¢nger, Matthias R. and Mattias K. Polborn, “Herding and Anti-herding: a model of reputational di¤erentiation,” 2000. University of Munich Mimeo. Ehrbeck, T. and R. Waldmann, “Why Are Professional Forecasts Biased? Agency Versus Behavioral Explanations,” Quarterly Journal of Economics, 1996, 111, 21–40. 21 Fama, Eugene, “Agency Problems and the Theory of the Firm,” Journal of Political Economy, 1980, 88, 288–307. Gibbons, Robert and Kevin J. Murphy, “Optimal Incentive Contracts in the Presence of Career Concerns: Theory and Evidence,” Journal of Political Economy, 1992, 100, 468–505. Graham, J. R., “Herding among Investment Newsletters,” Journal of Finance, 1999, 54, 237–268. Holmstrom, Bengt, “Managerial Incentive Problems: A Dynamic Perspective,” Review of Economic Studies, 1999, 66, 169–182. and Joan Ricart i Costa, “Managerial Incentives and Capital Management,” Quarterly Journal of Economics, 1986, 101, 835–860. Hong, Harrison, Je¤rey D. Kubik, and Amit Solomon, “Security Analysts’ Career Concerns and Herding of Earnings Forecasts,” RAND Journal of Economics, 2000, 31, 121–144. Klein, Benjamin and Keith B. Le-er, “The Role of Market Forces in Assuring Contractual Performance,” Journal of Political Economy, 1981, 89, 615–641. Kutsoati, E. and D. Bernhardt, “Can Relative Performance Evaluation Explain Analysts’ Forecasts of Earnings,” 1999. Tufts University Mimeo. Laster, David, Paul Bennett, and In Sun Geoum, “Rational Bias in Macroeconomic Forecasts,” Quarterly Journal of Economics, 1999, 114, 293–318. Nelson, Philip, “Advertising as Information,” Journal of Political Economy, 1974, 82, 729–754. 22 Ottaviani, Marco and Peter Sorensen, “Professional Advice,” 2000. University College London Mimeo. Prendergast, Canice and Lars Stole, “Impetuous Youngsters and Jaded OldTimers: Acquiring a Reputation for Learning,” Journal of Political Economy, 1996, 104, 1105–1134. Scharfstein, David and Jeremy Stein, “Herd Behavior and Investment,” American Economic Review, 1990, 80, 465–479. Schmalensee, Richard, “A Model of Advertising and Product Quality,” Journal of Political Economy, 1978, 86, 485–503. Shapiro, Carl, “Optimal Pricing of Experience Goods,” Bell Journal of Economics, 1983, 14, 497–507. Trueman, Brett, “Analyst Forecasts and Herding Behavior,” Review of Financial Studies, 1994, 7, 97–124. Welch, Ivo, “Herding Among Security Analysts,” 1999. UCLA Mimeo. Zitzewitz, Eric, “Measuring herding and exaggeration by equity analysts,” 2001. MIT Mimeo. Zweibel, J., “Corporate Conservativism and Relative Performance Compensation,” Journal of Political Economy, 1992, 103, 1–25. 23 Table 1. Exaggeration by under or over-rated analysts Dependent variable: (ACT - CONS) This table reports interaction coefficients from a version of equation (14) with the variables listed interacted with the righthand side. Regressions also include (FOR - CONS) and the interaction variables. Regressions include forecasts made by analysts with at least 50 past forecasts in the 1993-99. The UNDER and INFO variables are rankings, scaled to 0 to 1, of the analyst based on past performance and performance change over the next 50 forecasts, respectively. Spec. 1 2 3 4 5 6 7 8 Obs. 329,401 329,401 329,401 329,401 329,401 329,401 329,401 329,401 Variable defintions ACT FOR CONS UNDER INFO FNUM BROKSIZE Notes: 1. UNDER Coeff. S.E. -0.458 0.141 -0.503 0.133 -0.503 0.130 -0.519 0.133 Interactions with (FOR - CONS) INFO FNUM/100 Coeff. S.E. Coeff. S.E. -0.156 -0.140 -0.198 -0.029 0.120 0.117 0.112 0.136 -0.046 0.141 0.048 0.045 0.046 0.046 0.016 0.016 0.018 0.018 LN(BROKSIZE) Coeff. S.E. 0.092 0.084 0.082 0.087 0.084 0.035 0.038 0.041 0.037 0.040 Actual earnings per share Analyst's forecast of earnings per share Prior expectation of earnings per share, as estimated in Table 3 Ranking based on change in analyst forecast value over the next 50 forecasts, scaled 0 to 1. Ranking of analyst's historical forecast value, scaled 0 to 1. Forecast number in analyst's career Number of analysts at analyst's brokerage Standard errors are heteroskedasticity robust and adjusted for clustering within firm-quarter combinations. Table 2. Exaggeration and uncertainty The effect of expected earnings uncertainty is examined by predicting the absolute earnings surprise for a firm-quarter combination based on its market cap, the standard deviation of price-normalized forecasts, and past earnings surprise for the firm, and average earnings surprise in the prior 90 days. We then interact predicted earnings surprise with the right-hand side of (2) to measure the effect on exaggeration. The negative interaction coefficient reported implies more exaggeration when expected earnings surprise is high. Coeff. First stage regression Dependent variable: Abs(ACT - CONS) Indepdent variables: Ln(Market Cap) Ln(SD-Price ratio) Avg past abs(ACT - CONS) for firm Avg abs(ACT - CONS) in quarter Second stage Interaction coefficient from exaggeration regression Predicted abs. forecast error S.E. -0.0184 0.0092 0.710 0.136 0.0009 0.0004 0.015 0.007 -0.059 0.022 Notes: 1. Standard errors are heteroskedasticity robust and adjusted for clustering within firmquarter combinations. Standard error in second stage is adjusted for the use of a predicted value on the right-hand side. Table 3. Exaggeration and expected future forecasts In panel A, the right hand side of (14) is interacted with the actual number of future forecasts an analyst makes between the current forecast and the end of 1999. Forecasts for the years 1993-97 and for analysts who have already made 50 forecasts are included in the sample. In Panel B, exit from the I/B/E/S sample (defined as making a final forecast and not reappearing in the sample for 2 years) is predicted for each forecast in the 1993-97 period. Past average relative forecast ranking is the average of a 0-1 ranking of analysts' relative forecast accuracy for each firm-quarter in which they forecast. Panel A. Interaction regression with actual future forecasts Dependent variable: actual earnings less consensus Forecast less consensus (FOR - CONS)*(Actual future forecasts/100) Constant (in basis points) Actual future forecasts/100 (in basis points) Observations Coeff. S.E. 0.251 0.067 0.117 0.037 -0.159 0.202 -0.134 0.140 198,909 Panel B. Probit regression predicting exit from sample Forecasts in career/100 Ln(Analysts at brokerage) Ln(Forecast information content) Observations Coeff. S.E. -0.251 0.014 -0.090 0.010 0.001 0.003 334,388 ...
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