4.1 Testing for cross-horizon forecast error predictability
Studies have examined whether analyst forecasts efficiently use information by regressing forecast error on the forecast for the same horizon (DeBondt and Thaler
1990; Keane and Runkle
1998)—for example, by regressing the current year’s forecast error on the current year’s forecast. Coefficients above (below) zero provide evidence that analysts underweight (overweight) the information incorporated into the forecast.
5 We adjust this methodology to test whether analysts efficiently use the information they incorporate into forecasts at
any horizon. Specifically, we regress forecast error on earnings forecasts from a variety of horizons, allowing us to assess whether analysts assign Bayesian or non-Bayesian weights to information in their own forecasts at other horizons. Evidence that a different horizon’s earnings forecast has a positive (negative) coefficient would suggest that analysts underweight (overweight) the information in that horizon’s forecast. We interpret the R-squared as the amount analysts can reduce forecast bias by more efficiently weighting the information they have collected and incorporated into their own forecasts. Because accuracy incentives decrease with horizon, we expect forecast bias can be reduced by placing greater weight on the shorter horizon forecasts and less weight on the longer horizon forecasts. We estimate the following model.
$$ FE={\beta}_0+{\beta}_1 FORE(Shorter)+{\beta}_2 FORE(Contemporaneous)+{\beta}_3 FORE(Longer)+\varepsilon $$
(1)
FE is the analyst’s forecast error and is calculated as the firm’s actual earnings per share less the analyst’s forecasted earnings per share scaled by price. We study forecast errors at five horizons: the four quarterly forecasts of the current year (
FE(Q1), FE(Q2), FE(Q3), FE(Q4)), and next year’s annual forecast (
FE(YRt+1)). Consistent with studies on forecast efficiency, we control for the contemporaneous forecast, but we are primarily interested in the forecasts at shorter and longer horizons.
FORE(Contemporaneous) is the analyst’s forecast of earnings per share for the same horizon as the forecast error in the dependent variable.
FORE(Shorter) is the sum of the shorter horizon earnings per share forecasts.
FORE(Longer) is the sum of the longer horizon earnings per share forecasts. For instance, when the dependent variable is
FE(Q3),
FORE(Contemporaneous) is the third quarter forecast,
FORE(Shorter) is the sum of the first and second quarter forecasts, and
FORE(Longer) is the sum of the fourth quarter and next year’s forecasts. All of the forecast variables are scaled by price. Again, the forecasts used to calculate each of the above variables are all made on the same day to hold the analyst’s information set constant (Kang et al.
1994).
The results from estimating Eq. (
1) are reported in Table
2. In column (1), we regress the first quarter forecast error on a contemporaneous forecast (the first quarter forecast) and a longer horizon forecast (the sum of the second, third, and fourth quarter forecasts as well as next year’s forecast). We observe no forecast error predictability as both of the independent variables have insignificant coefficients and the adjusted R-squared is very low at 0.0001. In column (2), we regress the second quarter forecast error on a shorter horizon forecast (the first quarter forecast), a contemporaneous forecast (the second quarter forecast), and a longer horizon forecast (the sum of the third and fourth quarter forecasts as well as next year’s forecast). The coefficient on the shorter horizon forecast is significantly positive, whereas the coefficient on the longer horizon forecast is significantly negative. Thus the second quarter forecast bias could decrease by placing greater weight on the information in the shorter horizon forecast and less weight on the information in the longer horizon forecasts. We observe similar results in columns (3) to (5) where the dependent variable is the third quarter, fourth quarter, and next year’s forecast error, respectively. In each column, the shorter horizon forecast loads positively, and the longer horizon forecast loads negatively. Further, the predictability of forecast error increases with horizon, as evidenced by the adjusted R-squared increasing monotonically with horizon, from 0.037 at the second quarter horizon to 0.104 at the next year horizon.
6Table 2
Testing for Cross-Horizon Forecast Error Predictability
FORE(Shorter) | | 0.1592*** | 0.1393*** | 0.1464*** | 0.6207*** |
| | (12.7094) | (11.3024) | (9.3435) | (10.8635) |
FORE(Contemporaneous) | −0.0061 | −0.1355*** | −0.1550*** | −0.1794*** | −0.8199*** |
| (−1.3317) | (−6.9062) | (−7.9184) | (−10.1349) | (−13.3631) |
FORE(Longer) | 0.0011 | −0.0101*** | −0.0436*** | −0.1009*** | |
| (1.1895) | (−3.0337) | (−6.1504) | (−7.3597) | |
CONS | 0.0004*** | 0.0008*** | 0.0013*** | 0.0013*** | 0.0079*** |
| (5.5826) | (7.3765) | (7.7775) | (4.9005) | (6.7361) |
Observations | 166,030 | 166,030 | 166,030 | 166,030 | 166,030 |
Adjusted R2 | 0.0001 | 0.0367 | 0.0641 | 0.0778 | 0.1035 |
There are several important takeaways from these analyses. First, analysts’ own forecasts from other horizons do not predict forecast error at the current quarter’s forecast horizon. This suggests the shorter horizon of the forecast disciplines the analyst to incorporate information efficiently. However, we begin to observe forecast inefficiency at the second quarter horizon, and it increases monotonically at longer horizons. We observe shorter horizon forecasts are positively associated with forecast error, while longer horizon forecasts are negatively associated with forecast error.
4.2 Measuring the ability of other horizon forecasts to explain current year forecast error
Next, we examine the ability of other horizon forecasts to explain current year forecast error and contrast the predictability with other sources of predictable error identified in the literature. We focus on current year forecast error predictability, because (i) it is a commonly used horizon to forecast earnings by both academics and practitioners (i.e., Martin et al.
2018; Call et al.
2021) and (ii) the strong forecast error predictability for the third and fourth quarters in Table
2 suggests we can plausibly explain a significant proportion of forecast error at the annual horizon.
7 We regress the current year forecast error on the first quarter forecast, the remainder of the current year forecast, and next year’s forecast via the following model.
$$ FE\left({YR}_t\right)={\beta}_0+{\beta}_1 FORE\left({Q}_1\right)+{\beta}_2 FORE\left({Q}_{2- 4}\right)+{\beta}_3 FORE\left({YR}_{t+ 1}\right)+\varepsilon . $$
(2)
FE(YRt) is the analyst’s current year forecast error.
FORE(Q1) is the first quarter forecast,
FORE(Q2–4) is the remainder of the current year forecast (i.e., quarters two through four), and
FORE(YRt+1) is next year’s forecast.
8
The results from estimating Eq. (
2) using the detail file sample are reported in Panel A of Table
3. To present a baseline specification, column (1) reports the results from regressing current year forecast error on the current year forecast, similar to prior forecast efficiency studies (DeBondt and Thaler
1990; Keane and Runkle
1998). The coefficient on the current year forecast is negative and significant, but the model explains minimal variation in forecast error as evidenced by the adjusted R-squared of 0.004. In other words, the traditional approach to detect forecast inefficiency, by regressing forecast error on earnings forecasts for the same horizon, explains little of the error in the current year’s forecast (DeBondt and Thaler
1990; Keane and Runkle
1998).
Table 3
Cross-Horizon Forecast Error Predictability
Panel A: Detail File |
FORE(YRt) | −0.0387*** | | | | |
| (−4.3395) | | | | |
FORE(Q1) | | 0.6691*** | | 0.5155*** | 0.5814*** |
| | (12.8813) | | (9.6217) | (8.1096) |
FORE(Q2–4) | | −0.0842*** | | −0.1336*** | −0.2661*** |
| | (−2.6139) | | (−3.9286) | (−9.8370) |
FORE(YRt + 1) | | −0.1715*** | | −0.1239*** | −0.0807*** |
| | (−5.8713) | | (−5.0498) | (−3.9491) |
ACCRUALS+ | | | −0.0594*** | −0.0323*** | −0.0047 |
| | | (−6.0734) | (−3.3985) | (−0.6952) |
ACCRUALS− | | | 0.0175* | −0.0079 | −0.0166** |
| | | (1.6639) | (−0.7516) | (−2.1474) |
AG | | | −0.0040*** | −0.0049*** | −0.0016*** |
| | | (−6.4097) | (−7.2153) | (−3.4926) |
NODIV | | | −0.0023*** | −0.0026*** | 0.0016** |
| | | (−3.7913) | (−4.7211) | (2.4239) |
DIV | | | −0.0077 | −0.0305 | 0.0103 |
| | | (−0.3624) | (−1.5687) | (0.5280) |
BTM | | | −0.0041*** | −0.0029*** | −0.0059*** |
| | | (−3.3106) | (−2.8645) | (−2.8912) |
PRC | | | 0.0000*** | 0.0000*** | −0.0001*** |
| | | (5.1567) | (3.8476) | (−4.5874) |
ACT(YRt-1)+ | | | −0.0702*** | −0.0068 | −0.0756*** |
| | | (−4.5697) | (−0.3266) | (−3.9194) |
ACT(YRt-1)− | | | −0.0067*** | −0.0088*** | −0.0022 |
| | | (−6.4623) | (−6.6664) | (−1.5948) |
RETPRE | | | 0.0066*** | 0.0062*** | 0.0040*** |
| | | (8.1497) | (7.2031) | (5.6605) |
FE(YRt-1) | | | 0.4409*** | 0.3726*** | 0.2280*** |
| | | (8.9222) | (7.3518) | (6.7295) |
CONS | −0.0024*** | 0.0042*** | 0.0030*** | 0.0085*** | 0.0142*** |
| (−3.1703) | (8.1702) | (2.8836) | (9.0878) | (9.1807) |
Observations | 166,030 | 166,030 | 166,030 | 166,030 | 166,030 |
Adjusted R2 | 0.0041 | 0.0647 | 0.0619 | 0.1054 | 0.3223 |
Out of Sample Adjusted R2 | 0.0014 | 0.0546 | 0.0457 | 0.0836 | NA |
Panel B: Consensus File |
FORE(YRt) | −0.0528*** | | | | |
| (−5.2571) | | | | |
FORE(Q1) | | 0.8867*** | | 0.6559*** | 0.8710*** |
| | (16.0396) | | (13.3663) | (12.2787) |
FORE(Q2–4) | | 0.0080 | | −0.0817** | −0.2699*** |
| | (0.2869) | | (−2.5986) | (−7.8975) |
FORE(YRt + 1) | | −0.3380*** | | −0.2224*** | −0.1227*** |
| | (−12.5360) | | (−11.0711) | (−4.7704) |
ACCRUALS+ | | | −0.0614*** | −0.0337*** | −0.0199*** |
| | | (−8.6521) | (−5.6520) | (−3.4922) |
ACCRUALS− | | | 0.0162* | −0.0132* | −0.0180*** |
| | | (1.9355) | (−1.8890) | (−2.8560) |
AG | | | −0.0049*** | −0.0060*** | −0.0026*** |
| | | (−9.1472) | (−10.4367) | (−5.3458) |
NODIV | | | −0.0016*** | −0.0020*** | 0.0044*** |
| | | (−3.0729) | (−4.3077) | (5.1311) |
DIV | | | 0.0486*** | −0.0077 | 0.0342* |
| | | (2.7177) | (−0.5334) | (1.8709) |
BTM | | | −0.0062*** | −0.0025* | −0.0059*** |
| | | (−3.5770) | (−1.7849) | (−2.8778) |
PRC | | | 0.0001*** | 0.0001*** | −0.0000*** |
| | | (11.2820) | (9.3183) | (−2.6261) |
ACT(YRt-1)+ | | | −0.1281*** | −0.0422* | −0.1266*** |
| | | (−6.7510) | (−1.7636) | (−7.5485) |
ACT(YRt-1)− | | | −0.0103*** | −0.0114*** | −0.0018 |
| | | (−8.3827) | (−8.0521) | (−1.2346) |
RETPRE | | | 0.0077*** | 0.0065*** | 0.0056*** |
| | | (8.7669) | (7.4573) | (8.7284) |
FE(YRt-1) | | | 0.5538*** | 0.4351*** | 0.2863*** |
| | | (9.1360) | (7.2012) | (5.8168) |
CONS | −0.0066*** | 0.0054*** | −0.0000 | 0.0078*** | 0.0107*** |
| (−8.3096) | (7.4018) | (−0.0491) | (8.6524) | (7.8001) |
Observations | 54,073 | 54,073 | 54,073 | 54,073 | 54,073 |
Adjusted R2 | 0.0054 | 0.1046 | 0.1067 | 0.1587 | 0.3102 |
Out of Sample Adjusted R2 | 0.0078 | 0.1016 | 0.0988 | 0.1427 | NA |
Column (2) reports the results from estimating Eq. (
2) without control variables. The coefficient on the first quarter (next year) forecast is significantly positive (significantly negative). This suggests, in the current year forecast, the analyst underweights (overweights) the information included in the shorter (longer) horizon forecasts. The model substantially increases forecast error predictability as evidenced by the adjusted R-squared of 0.065.
9
In column (3), we regress the current year forecast error on a series of firm characteristics that studies have shown to predict forecast error, to compare the power of the forecast inefficiency we document to models used in the literature. The control variables follow both So (
2013) and Larocque (
2013). Following So (
2013), we include controls for prior earnings, accruals, asset growth, dividends, book to market, and price.
ACT[YRt-1]+ is the prior year earnings per share scaled by price when positive and zero otherwise.
ACT[YRt-1]− is an indicator variable set equal to one when the prior year earnings per share scaled by price is negative and zero otherwise.
ACCRUALS is the change in current assets minus the change in cash and cash equivalents minus the change in current liabilities plus the change in current debt, scaled by beginning market value of equity.
ACCRUALS+ (
ACCRUALS−) is equal to
ACCRUALS when
ACCRUALS is positive (negative) and zero otherwise.
AG is asset growth.
DIV is dividends scaled by beginning market value of equity and
NODIV is an indicator set equal to one if no dividends were paid and zero otherwise.
BTM is the book value of common equity scaled by the market value of equity.
PRC is the share price the day before the forecasts are issued. Following Larocque (
2013), we also control for past forecast error and past returns.
FE(YRt-1) is the prior year forecast error, and
RETPRE is the 12 month market-adjusted return ending the month before the forecast date. Specific variable definitions are reported in Appendix A, and descriptive statistics are reported in Table
1. The adjusted R-squared of 0.062 in column (3) resembles the adjusted R-squared of 0.065 in column (2). Thus the forecast inefficiency we document predicts a similar level of the current year’s forecast error, relative to an extensive set of firm characteristics used in prior studies.
In column (4), we estimate a model combining the forecast characteristics and other horizon forecasts to examine whether the two models predict similar errors. The incremental R-squared from adding forecast characteristics to the forecast inefficiency model is 0.041. To measure the ability of the forecast inefficiency we document to explain the predictable errors from firm characteristics, we compute the ratio of the incremental R-squared (from incorporating firm characteristics into the forecast inefficiency model) to the R-squared of the model with just the firm characteristics included. We find roughly 34% of the information explained by firm characteristics is also explained by analysts’ forecasts at other horizons (1–0.041/0.062). Finally, in column (5), we include firm and quarter fixed effects, to ensure our results are not driven by time or firm-invariant characteristics. In both columns, the coefficient on the first quarter forecast remains significantly positive, and the coefficient on next year’s forecast remains significantly negative.
10
Importantly, we also demonstrate out of sample forecast bias reductions to more fully ensure all of the information used to adjust the forecasts would be available at the time the forecasts are issued. To do so, we estimate rolling, out-of-sample regressions for each of the specifications in Panel A of Table
3 (except column 5, because this specification includes fixed effects). For each year
t in the sample, we estimate the regression using the prior three years of data (years
t-3 to
t-1). We then use the coefficients from these regressions to determine the predicted forecast error in year
t. Finally, we report the out of sample adjusted R-squared values to gauge the level of forecast bias reduction on an out of sample basis. Similar to the in-sample values, the out-of-sample adjusted R-squared is larger in column (2) than in column (3) (0.055 versus 0.046, respectively), and the difference is even larger on a percentage basis.
In Panel B of Table
3, we conduct a similar set of tests using consensus analyst forecasts rather than individual analyst forecasts. These analyses have several purposes. First, they allow us to assess whether identifying forecast inefficiency yields significant improvements in the consensus forecast, which is more commonly used in the literature to predict earnings because of its greater accuracy (Bradshaw et al.
2012). Second, they allow us to assuage concerns that the results are not generalizable beyond the restrictive sample used in the detail file analyses (which requires the same analyst to forecast earnings at five horizons for the same firm on the same day).
In column (2), using the consensus file sample, we document higher forecast error predictability than in the detail file sample, inconsistent with idiosyncratic errors leading to forecast inefficiency. Specifically, the coefficient on the first quarter forecast increases from 0.669 in the detail file to 0.887 in the consensus file, the coefficient on next year’s forecast decreases from −0.172 to −0.338, and the adjusted R-squared increases from 0.065 to 0.105. Contrasting the forecast inefficiency model in column (2) with the firm characteristic model in column (3), both models continue to predict similar levels of forecast error (adjusted R-squared of 0.105 versus 0.107). In column (4), we see that adding the firm characteristics increases the R-squared only 5.4%, relative to the model including only forecasts at other horizons, so the information in other forecasts explains nearly 50% of the error predicted by firm characteristics (1–0.054/0.107). In column (5), we again include year and quarter fixed effects. In both columns, the coefficient on the first quarter forecast remains significantly positive, and the coefficient on next year’s forecast remains significantly negative. Overall, information from forecasts at other horizons explains much of the error predicted by firm characteristics, which is consistent with analysts processing the information that predicts errors in at least one horizon’s forecast.
4.3 Analyst optimism and forecast inefficiency
In this section, we examine how optimism affects the forecast inefficiency documented in the prior section. Analysts have incentives to issue optimistically biased longer horizon forecasts (Kang et al.
1994; Ke and Yu
2006; Jackson
2005), because doing so stimulates trading volume and enhances their access to firm managers by catering to the reporting preferences of those managers. In contrast, we expect analysts have strong reputational incentives to provide an accurate forecast for shorter horizon forecasts, given the proximity of the earnings realization. We thus suspect that optimism will lead to greater inefficiency and greater forecast re-weighting in the presence of more optimistic forecasts (i.e., incrementally more weight on the first quarter forecast and incrementally less weight on next year’s forecast). We test this via the following model.
$$ FE\left({YR}_t\right)={\beta}_0+{\beta}_1 FORE\left({Q}_1\right)+{\beta}_2 FORE\left({Q}_{2- 4}\right)+{\beta}_3 FORE\left({YR}_{t+ 1}\right)+{\beta}_4 OPTIMISM+{\beta}_5 FORE\left({Q}_1\right)\ast OPTIMISM+{\beta}_6 FORE\left({YR}_{t+ 1}\right)\ast OPTIMISM+\varepsilon . $$
(3)
We use two proxies to capture distinct aspects of optimism (
OPTIMISM). First, we use past firm news, because analysts are incentivized to incorporate (not incorporate) negative firm news into their shorter (longer) horizon forecasts.
11 We measure past news by multiplying prior returns compounded over the 12 months ending the month before the forecast by negative one, percentile ranking the variable, and rescaling the variable between zero and one (
NEWS). The lowest (highest) values of
NEWS represent firm-years with the most positive (negative) past returns. Second, we use analysts’ share price target optimism as a measure of the observed optimism, because (i) analysts are incentivized to issue optimistic price targets to generate trading commissions and (ii) analysts’ price targets convey little information about future price changes (e.g., Bradshaw et al.
2013). We measure share price target optimism as the share price target on the I/B/E/S consensus file, divided by the outstanding share price, minus one. We then percentile rank the variable and rescale it between zero and one (
SPT). The lowest (highest) values of
SPT represent firm-years with the least (greatest) share price target optimism.
NEWS captures analysts’ incentives for optimism, whereas
SPT captures analysts’ realized optimism.
We interact each optimism variable with the shortest horizon forecast (the current year’s first quarter forecast) and the longest horizon forecast (next year’s annual forecast).
12 The coefficients on the main effects of the forecasts can be interpreted as the re-weighting effect when analyst optimism is weakest, and the coefficients on the interaction terms can be interpreted as the incremental re-weighting effect when analyst optimism is strongest. The main effects on the optimism proxies capture their relations with forecast bias, but our interest is in the effect of optimism on forecast inefficiency (thus the interactions).
In column (1) of Table
4, we report the results from estimating eq. (3), using the optimism proxy
NEWS. Consistent with prior research, we find a significantly negative coefficient on the main effect of
NEWS (i.e., analysts underreact to past news). We also find a significantly positive coefficient on
FORE(Q1)*NEWS and a significantly negative coefficient on
FORE(YRt+1)*NEWS. The model incorporating both accuracy incentives related to horizon and the variation in those incentives associated with recent public information predicts 13.6% of forecast error. In column (2) of Table
4, we report the results from estimating eq. (3), using the optimism proxy
SPT. The main effect on
SPT loads with a significantly negative coefficient, suggesting analysts are consistent in their optimism across both types of forecasts. More importantly, its interaction with
FORE(Q1) is significantly positive, and its interaction with
FORE(YRt+1) is significantly negative. As predicted, these results suggest that incrementally more (less) weight should be placed on the shorter (longer) horizon forecast when analyst optimism is greater.
Table 4
Incentives for Optimism & Cross-Horizon Forecast Error Predictability
FORE(Q1) | 0.4097*** | 0.4570*** | 0.2408** | 0.2425*** | 0.3029*** | 0.1243 |
| (6.0052) | (3.9256) | (2.2912) | (3.2599) | (2.7096) | (1.0647) |
FORE(Q2–4) | −0.0189 | −0.0425 | −0.0470 | −0.0948*** | −0.0932* | −0.0966** |
| (−0.6935) | (−1.0338) | (−1.1145) | (−2.9620) | (−1.9854) | (−2.0144) |
FORE(YRt + 1) | −0.0981*** | −0.0286 | 0.0674 | −0.0354 | 0.0390 | 0.1080*** |
| (−3.4364) | (−0.6587) | (1.5756) | (−1.3049) | (1.0169) | (2.7849) |
NEWS | −0.0041** | | −0.0053*** | −0.0004 | | −0.0024 |
| (−2.1969) | | (−2.9759) | (−0.1866) | | (−0.9883) |
NEWS*FORE(Q1) | 0.6472*** | | 0.3698*** | 0.6410*** | | 0.3371** |
| (6.6168) | | (2.7433) | (6.7235) | | (2.5580) |
NEWS*FORE(YRt + 1) | −0.3155*** | | −0.1725*** | −0.2909*** | | −0.1533*** |
| (−9.9874) | | (−4.3912) | (−9.7925) | | (−3.9863) |
SPT | | −0.0052*** | −0.0037** | | 0.0004 | −0.0004 |
| | (−2.8117) | (−2.2209) | | (0.2217) | (−0.2706) |
SPT*FORE(Q1) | | 0.3160** | 0.2677 | | 0.3844** | 0.3441** |
| | (2.1142) | (1.5925) | | (2.5187) | (2.0908) |
SPT*FORE(YRt + 1) | | −0.2536*** | −0.2273*** | | −0.2731*** | −0.2437*** |
| | (−6.3332) | (−5.3683) | | (−7.1028) | (−5.8622) |
CONS | 0.0051*** | 0.0030*** | 0.0041*** | 0.0070*** | 0.0037*** | 0.0052*** |
| (6.1723) | (3.0466) | (3.4800) | (5.0898) | (3.7608) | (3.1217) |
Controls | No | No | No | Yes | Yes | Yes |
Observations | 54,073 | 35,509 | 35,509 | 54,073 | 35,509 | 35,509 |
Adjusted R2 | 0.1364 | 0.0991 | 0.1132 | 0.1705 | 0.1305 | 0.1348 |
In column (3), we combine both sets of interactions and find the interactions with both
NEWS and
SPT remain significant. Moreover, the main effect on the first quarter forecast reduces from 0.887 (in Table
3 Panel B column 2) to 0.241, and the main effect on next year’s forecast becomes insignificantly positive. Thus, when optimism is lowest, we find little evidence of forecast inefficiency.
In columns (4) to (6), we include the firm characteristics from Table
3 to document two main findings. First, after including this series of control variables, the interactions from columns (1) to (3) remain significant. Second, including the interactions, which identify when analysts have incentives to use information less efficiently, substantially attenuates the forecast error predictability from firm characteristics. We measure the ability of our model to explain the predictable forecast errors from firm characteristics as the ratio of the incremental R-squared (the increase in R-squared attributable to incorporating firm characteristics to a model that already includes the forecast variables and interactions) to the R-squared from a model that includes only forecast characteristics. The model that includes the
NEWS interactions explains 68% of the forecast error predictability from firm characteristics.
13 When estimating our most extensive model including both
NEWS and
SPT, the incremental R-squared from including firm characteristics is only 2.2% (column (6) versus column (3)), suggesting our most extensive forecast inefficiency model explains 80% of the predictable errors from firm characteristics.
Overall, we conclude that accuracy incentives drive forecast inefficiency and that forecast inefficiency explains a substantial portion of the predictable errors in firm characteristics. Thus we argue that incentives likely explain the majority of the cross-section of predictable forecast errors.
14
4.4 Do market expectations adjust for the predictability of forecast errors?
In the next set of analyses, we test whether market expectations adjust for predictable errors. Specifically, we test whether unexpected earnings computed using analyst forecasts adjusted for forecast inefficiency have a stronger association with future returns than published analyst forecasts (Gu and Wu
2003; Hughes et al.
2008). The strength of the association between earnings surprises and future returns should allow us to identify the model the market uses to compute expected earnings. This is because measurement error in the calculation of the earnings surprise will bias the regression coefficient toward zero and generate a smaller R-squared value. If market expectations adjust for predictable errors, removing the predictable errors from the earnings surprise would increase the coefficient estimate on the earnings surprise as well as the R-squared value. We examine whether an adjusted forecast better represents the market’s expectations of earnings, relative to the unadjusted forecast, by estimating the following set of equations.
$$ RET={\beta}_0+{\beta}_1 FE{\left({YR}_t\right)}_{UNADJ}+\varepsilon . $$
(4a)
$$ RET={\theta}_0+{\theta}_1 FE{\left({YR}_t\right)}_{ADJ}+\varepsilon . $$
(4b)
The dependent variable is either market adjusted returns over the 12 months beginning the first month after the first-quarter earnings announcement (RETPOST) or market-adjusted returns over the three days surrounding the current fiscal-year earnings announcement (RETEA).
FE(YRt)UNADJ is the current-year forecast error calculated using analysts’ published forecasts, and
FE(YRt)ADJ is the current-year forecast error adjusted for predictable errors. We compare the unadjusted forecast error to the forecast error adjusted for three sources of predictable errors. First, we adjust for predictable errors from analysts’ own forecasts.
FE(YRt)ADJ-FORECASTS is the adjusted forecast error, calculated as
FE(YRt)UNADJ less the predicted forecast error from estimating column (2) in Panel B of Table
3. Second, we adjust for predictable errors from firm characteristics.
FE(YRt)ADJ-CONTROLS is the adjusted forecast error, calculated as
FE(YRt)UNADJ less the predicted forecast error from estimating column (3) in Panel B of Table
3. The control variables are measured as of year t-1 to avoid look ahead bias. Third, we adjust for predictable errors from both sources.
FE(YRt)ADJ-BOTH is the adjusted forecast error, calculated as
FE(YRt)UNADJ less the predicted forecast error from estimating column (4) in Panel B of Table
3. If the adjusted forecast better represents the market’s expectations of earnings, we expect it to have a stronger association with future returns. Thus the coefficient
θ1 would be significantly greater than the coefficient
β1 (and the R-squared would significantly increase). We calculate the predicted component of forecast error on an out-of-sample basis, using the same methodology wherein we calculated the out of sample R-squared values in Table
3. Specifically, we regress the first stage model on years
t-3 to
t-1 and then use the coefficient estimates on the data in year
t to calculate predicted forecast error.
Table
5 reports the results from estimating eqs. (4a) and (4b). Panel A reports descriptive statistics. Panel B reports the results for the long-window returns. In column (2), the coefficient on the earnings surprise adjusted for forecasts at other horizons is significantly greater than the coefficient on the earnings surprise computed using published forecasts in column (1). The difference is statistically significant at the 1% level. Further, the adjusted R-squared increases by roughly 21% from 0.061 to 0.074. A Vuong (
1989) test, which compares R-squared values, indicates this difference is statistically significant at the 1% level.
Table 5
Do Adjusted Forecasts Better Approximate the Market’s Expectation of Earnings?
Panel A: Descriptive Statistics |
Variable | N | Mean | StdDev | Min | P25 | Median | P75 | Max |
RETPOST | 53,536 | −0.0008 | 0.4261 | −0.8356 | −0.2592 | −0.0432 | 0.1852 | 1.7091 |
RETEA | 53,536 | 0.0029 | 0.0864 | −0.2515 | −0.0427 | 0.0013 | 0.0470 | 0.2733 |
FE(YRt)UNADJ | 53,536 | −0.0089 | 0.0359 | −0.1956 | −0.0140 | −0.0010 | 0.0047 | 0.0830 |
FE(YRt)ADJ-FORECASTS | 53,536 | 0.0007 | 0.0341 | −0.2457 | −0.0063 | 0.0039 | 0.0132 | 0.2405 |
FE(YRt)ADJ-CONTROLS | 53,536 | 0.0008 | 0.0343 | −0.2180 | −0.0078 | 0.0029 | 0.0141 | 0.1824 |
FE(YRt)ADJ-BOTH | 53,536 | 0.0007 | 0.0335 | −0.2410 | −0.0083 | 0.0019 | 0.0131 | 0.2157 |
Panel B: Long-Run Return ERC Tests |
| (1) | (2) | | (3) | (4) |
| RETPOST | RETPOST | | RETPOST | RETPOST |
FE(YRt)UNADJ | 2.9408*** | | | |
| (18.8512) | | | |
FE(YRt)ADJ-FORECASTS | | 3.4054*** | | | |
| | (20.6695) | | | |
FE(YRt)ADJ-CONTROLS | | | 3.1933*** | |
| | | (20.8426) | |
FE(YRt)ADJ-BOTH | | | | 3.4100*** |
| | | | (21.0290) |
CONS | 0.0255** | −0.0031 | | −0.0035 | −0.0031 |
| (2.3539) | (−0.2883) | | (−0.3246) | (−0.2862) |
Coef = UNADJ | | p-val = 0.0000 | | p-val = 0.0024 | p-val = 0.0000 |
Coef = ADJ-CONTROLS | | p-val = 0.0002 | | | p-val = 0.0000 |
Coef = ADJ-FORECASTS | | | | p-val = 0.9219 |
Observations | 53,536 | 53,536 | | 53,536 | 53,536 |
R2 | 0.0614 | 0.0744 | | 0.0661 | 0.0717 |
Panel C: Earnings Announcement Return ERC Tests |
| (1) | (2) | (3) | (4) |
| RETEA | RETEA | RETEA | RETEA |
FE(YRt)UNADJ | 0.1335*** | | | |
| (8.9678) | | | |
FE(YRt)ADJ-FORECASTS | | 0.1682*** | | |
| | (9.8660) | | |
FE(YRt)ADJ-CONTROLS | | | 0.1508*** | |
| | | (9.8604) | |
FE(YRt)ADJ-BOTH | | | | 0.1687*** |
| | | | (10.2036) |
CONS | 0.0041*** | 0.0028*** | 0.0027*** | 0.0028*** |
| (6.4351) | (4.3654) | (4.2475) | (4.2929) |
Coef = UNADJ | | p-val = 0.0000 | p-val = 0.0343 | p-val = 0.0001 |
Coef = ADJ-CONTROLS | | p-val = 0.0270 | | p-val = 0.0000 |
Coef = ADJ-FORECASTS | | | | p-val = 0.9395 |
Observations | 53,536 | 53,536 | 53,536 | 53,536 |
R2 | 0.0031 | 0.0044 | 0.0036 | 0.0043 |
In column (3), we benchmark this improvement against that obtained by adjusting the earnings surprise using firm characteristics and lagged news variables (i.e., the regression model used to estimate column (3) in Panel B of Table
3). Consistent with prior research (e.g., Larocque
2013), we find these adjustments substantially improve explanatory power, relative to the unadjusted forecasts. However, the improvement is lower than that obtained by using the adjustment for other horizon forecasts in column (2).
In column (4), we adjust the earnings surprise using the combination of both firm characteristics and other horizon forecasts. As expected, the coefficient on the adjusted earnings surprise is significantly larger than the coefficient on the unadjusted earnings surprise. More importantly, the coefficient on this adjusted earnings surprise is significantly larger than the coefficient adjusted for firm characteristics only (column (3)), but it is not significantly different from the coefficient adjusted for other horizon forecasts only (column (2)). Thus adding the other horizon forecasts to the firm characteristic model improves its explanatory power, but adding the firm characteristics to the other horizon forecast model does not. Untabulated Vuong (
1989) tests yield similar inferences as the F-tests.
In Panel B of Table
5, we obtain similar results estimating earnings response coefficients using returns over the three-day window centered on the current fiscal year’s earnings announcement. Earnings surprises adjusted using other horizon forecasts have larger earnings response coefficients than both unadjusted forecasts and forecasts adjusted using a series of firm characteristics.
15
4.5 Do analysts issue longer-horizon forecasts less frequently in response to bad news?
Two assumptions underlying our analyses are that (i) analysts’ accuracy incentives decrease with horizon and (ii) analysts’ incentives for optimism increase with horizon. Although prior findings are consistent with these assumptions, in this section, we provide evidence on both assumptions by examining the frequency of forecast issuances. While forecast accuracy is a complex process, the issuance of a forecast has an intuitive link to effort. Evidence that analysts exert less effort to forecast longer horizon earnings and that this becomes stronger with greater incentives for optimism would support our assumptions. This analysis also contributes to prior research that finds analysts selectively respond to good news (McNichols and O’Brien
1997; Scherbina
2008) by showing the decision to forecast varies with horizon. That is, longer (shorter) horizon forecasts are more responsive to good (bad) news (Berger et al.
2019).
16
We first present descriptive statistics in Table
6, Panel A. Like the previous analysis, the sample is limited to forecasts issued between the prior fiscal year’s earnings announcement and the first fiscal quarter’s earnings announcement. We also require market-adjusted returns from CRSP. We see that analysts issue more forecasts for the current year horizon than the next year horizon (before the log transformation, 7.8 versus 6.6 forecasts, respectively). For the quarterly forecasts, analysts issue more forecasts for the first (i.e., current) quarter than each of the next three quarters (before the log transformation, 6.4 forecasts for the first quarter versus 5.4, 5.3, and 5.5 forecasts for the second, third, and fourth quarters, respectively). These findings suggest that analyst effort declines with horizon, which is consistent with our assumption that accuracy incentives decline with horizon.
Table 6
Analyst Forecast Frequency
Panel A: Descriptive Statistics |
Variable | N | Mean | StdDev | Min | P25 | Median | P75 | Max |
RETQTR | 120,023 | 0.0091 | 0.2034 | −0.5246 | −0.1009 | −0.0009 | 0.1029 | 0.7556 |
RETEAt-1 | 120,023 | 0.0020 | 0.0759 | −0.2400 | −0.0337 | 0.0011 | 0.0379 | 0.2443 |
#FORE(YRt) | 120,023 | 1.7452 | 0.9233 | 0.0000 | 1.0986 | 1.6094 | 2.3979 | 3.8918 |
#FORE(YRt + 1) | 120,023 | 1.5932 | 0.9438 | 0.0000 | 0.6931 | 1.6094 | 2.3026 | 3.7377 |
#FORE(Q1) | 120,023 | 1.5562 | 0.9481 | 0.0000 | 0.6931 | 1.6094 | 2.1972 | 3.7377 |
#FORE(Q2) | 120,023 | 1.3704 | 0.9677 | 0.0000 | 0.6931 | 1.3863 | 2.0794 | 3.6376 |
#FORE(Q3) | 120,023 | 1.3646 | 0.9644 | 0.0000 | 0.6931 | 1.3863 | 2.0794 | 3.6376 |
#FORE(Q4) | 120,023 | 1.3788 | 0.9774 | 10.0000 | 0.6931 | 1.3863 | 2.0794 | 3.6636 |
Panel B: Quarterly Return Regression Analyses |
| (1) | (2) | (3) | (4) | (5) | (6) |
| #FORE(YRt) | #FORE(YRt + 1) | #FORE(Q1) | #FORE(Q2) | #FORE(Q3) | #FORE(Q4) |
RETQTR | −0.1214*** | 0.0245* | −0.0737*** | −0.0079** | 0.0004 | 0.0171** |
| (−7.2156) | (1.7655) | (−7.1091) | (−2.1293) | (0.0933) | (2.4457) |
#FORE(YRt) | | 0.7520*** | | | | |
| | (59.1379) | | | | |
#FORE(YRt + 1) | 0.7454*** | | | | | |
| (48.4270) | | | | | |
#FORE(Q1) | | | | 0.1250*** | 0.0492*** | 0.1147*** |
| | | | (17.7332) | (6.9964) | (5.7194) |
#FORE(Q2) | | | 0.3763*** | | 0.5643*** | 0.3379*** |
| | | (30.3502) | | (19.9673) | (38.4675) |
#FORE(Q3) | | | 0.1629*** | 0.6204*** | | 0.5412*** |
| | | (7.1735) | (27.3093) | | (36.6135) |
#FORE(Q4) | | | 0.2574*** | 0.2521*** | 0.3672*** | |
| | | (8.2931) | (13.2560) | (13.7700) | |
CONS | 0.5588*** | 0.2806*** | 0.4639*** | −0.0182*** | 0.0082 | −0.0014 |
| (19.7052) | (13.4537) | (16.9631) | (−2.9665) | (0.7718) | (−0.0732) |
Fixed Effects | Firm | Firm | Firm | Firm | Firm | Firm |
Observations | 120,023 | 120,023 | 120,023 | 120,023 | 120,023 | 120,023 |
Adjusted R2 | 0.8191 | 0.8253 | 0.8799 | 0.9617 | 0.9649 | 0.9497 |
Panel C: Earnings Announcement Return Regression Analyses |
| (1) | (2) | (3) | (4) | (5) | (6) |
| #FORE(YRt) | #FORE(YRt;+1) | #FORE(Q1) | #FORE(Q2) | #FORE(Q3) | #FORE(Q4) |
RETEAt-1 | −0.2173*** | 0.0795*** | −0.0797*** | −0.0492*** | −0.0039 | 0.0671*** |
| (−11.1117) | (4.5146) | (−4.4386) | (−6.4858) | (−0.5045) | (6.1408) |
#FORE(YRt) | | 0.7518*** | | | | |
| | (59.1189) | | | | |
#FORE(YRt+1) | 0.7467*** | | | | | |
| (48.7045) | | | | | |
#FORE(Q1) | | | | 0.1250*** | 0.0492*** | 0.1144*** |
| | | | (17.7089) | (7.0093) | (5.7329) |
#FORE(Q2) | | | 0.3770*** | | 0.5643*** | 0.3382*** |
| | | (30.3379) | | (19.9606) | (38.5487) |
#FORE(Q3) | | | 0.1631*** | 0.6202*** | | 0.5411*** |
| | | (7.1990) | (27.2875) | | (36.6643) |
#FORE(Q4) | | | 0.2575*** | 0.2523*** | 0.3673*** | |
| | | (8.3357) | (13.2531) | (13.7622) | |
CONS | 0.5559*** | 0.2810*** | 0.4622*** | −0.0181*** | 0.0083 | −0.0013 |
| (19.7020) | (13.5540) | (16.9222) | (−2.9679) | (0.7830) | (−0.0676) |
Fixed Effects | Firm | Firm | Firm | Firm | Firm | Firm |
Observations | 120,023 | 120,023 | 120,023 | 120,023 | 120,023 | 120,023 |
Adjusted R2 | 0.8187 | 0.8254 | 0.8797 | 0.9617 | 0.9649 | 0.9497 |
Next, we regress the log of the number of forecasts during a firm-quarter on market-adjusted returns (calculated during the quarter and at the prior year earnings announcement) while controlling for other horizon forecasts and firm fixed effects. We measure the number of forecasts for both longer and shorter horizons. Our use of market-adjusted returns as well as firm fixed effects removes time-invariant and economy-wide shocks that affect both returns and the information analysts respond to. We use returns to measure news because it provides a comprehensive measure of firm news. We control for revisions to other forecasts, because this allows us to control for the average response to news and examine which horizon analysts intensively map information into. We estimate the following model.
$$ Log\left(\# Forecasts\right)={\beta}_0+{\beta}_1\ Returns+{\beta}_k\ Log\left(\# Other\ Horizon\ Forecasts\right)+\sum Firm\ Fixed\ Effects+\varepsilon . $$
(5)
If analysts respond more to negative (positive) news in their shorter (longer) horizon forecasts, we expect a smaller coefficient (
β1) when the dependent variable is the number of shorter horizon forecasts and a larger coefficient when the dependent variable is the number of longer horizon forecasts. We present the results from estimating eq. (5) in Table
6, Panels B and C. Our main result is that analysts revise shorter horizon forecasts relatively more in response to negative news and longer horizon forecasts relatively more in response to positive news.
In Panel B, the returns are measured over the corresponding quarter. In column (1), the dependent variable is the log of the number of current fiscal year forecasts, and we control for the number of forecasts for the next fiscal year. We find that returns in this specification load with a significantly negative coefficient, suggesting that forecasts of current year earnings are more responsive to negative news. In column (2), the dependent variable is the log of the number of next fiscal year forecasts, and we find a significantly positive coefficient, suggesting that forecasts of next year earnings respond more to positive news.
In columns (3) through (6), we estimate a similar set of equations, except our dependent variables and control variables are forecasts for the four quarterly forecasts of the current year’s earnings. Specifically, in column (3), the dependent variable is the number of current quarter forecasts, and the control variables include the number of forecasts issued for the subsequent three quarters. We find a significantly negative coefficient on returns, consistent with the number of forecasts issued for one quarter ahead being more sensitive to negative news. In column (4), we replace the dependent variable with the number of next quarter forecasts and use the number of forecasts issued at all other quarterly horizons as control variables. We find the coefficient on returns remains significantly negative, although it is smaller in magnitude than in column (3). In columns (5) and (6), the coefficient on returns continues to monotonically increase as the forecast horizon lengthens. In column (6), we find a significantly positive coefficient on returns, suggesting that, relative to shorter horizon forecasts, longer horizon forecasts are more sensitive to positive news.
Finally, in Panel C, we re-estimate eq. (5), using as our independent variable of interest market-adjusted returns over the three-day window centered on the prior year earnings announcement. Because earnings announcement returns tend to be driven by public information, this allows clean identification of how the sign of news influences analysts’ responses to information (eliminating concerns of reverse causation, such as the analyst forecasting causing returns during the quarter). Similar to Panel B, we find (i) significantly negative coefficients on the shortest horizon forecasts (in both annual and quarterly forecast regressions), (ii) significantly positive coefficients on the longest horizon forecasts, and (iii) monotonic increases in the coefficient on returns as the horizon lengthens. Collectively, these results support our contention that analysts’ incentives for optimism increase with the forecast horizon.