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Are forecasts of corporate profits rational? A note and further evidence
Journal of Empirical Finance 11 (2004) 617 – 626 www.elsevier.com/locate/econbase
Are forecasts of corporate profits rational? A note and further evidence Ahmed M. El-Galfy*, William P. Forbes Loughborough Business School, Loughborough University, Ashley Road, Loughborough, Leicestershire, LE11 3TU, UK Available online 11 June 2004
Abstract This paper revisits the claim by Keane and Runkle [J. Polit. Econ. 106 (1998) 768] that analyst forecasts of corporate profits may be rational, despite claims to the contrary by De Bondt and Thaler [Am. Econ. Rev. 80 (1990) 52] and others. We replicate the Keane and Runkle’s [J. Polit. Econ. 106 (1998) 768] research method and test some of the underlying assumptions in their modelling strategy. Specifically, we examine two key assumptions, the independence of forecast errors across time and the failure of forecast errors to spillover industrial boundaries. We find strong evidence of autocorrelation and interindustry forecast error spillovers. Our findings prompt us to extend Keane and Runkle’s tests to a revised General Method of Moments (GMM) estimate of model parameters as well as standard errors. Our revised GMM estimates employ two instruments designed to capture the impact of autocorrelation and spillover effects. These revised estimates suggest analyst forecasts of earnings are not rational with respect to publicly available information. D 2004 Elsevier B.V. All rights reserved. Keywords: Forecasts; Corporate profits; Industry
This paper revisits the claim by Keane and Runkle (1998) (henceforth KR) that analyst forecasts of earnings-per-share (henceforth EPS) are rational, despite evidence to the contrary by earlier researchers, notably De Bondt and Thaler (1990).1 KR claim that apparent overreaction in analyst forecasts results from a failure to correct for contemporaneous cross-correlation in forecast errors. They propose a correction to regression coefficient standard errors based on the General Method of Moments (GMM) * Corresponding author. Tel.: +44-141-330-6853. E-mail address: [email protected] (A.M. El-Galfy). 1 Empirical evidence to support ‘‘overreaction’’ in both stock prices and earning forecasts is reviewed in De Bondt (2000). 0927-5398/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jempfin.2004.04.004
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estimator of Hansen (1982). This correction is then used in combination with traditional OLS regression coefficient estimates. Furthermore, KR examine the effect of shocks to earnings in the form of special items, which analysts may find either hard to predict or unworthy of prediction. Analysts often focus upon core earnings (see Penman, 2001). KR’s conclusion in favour of the rationality of earning forecasts further depends on their treatment of large special items. While we do not make this issue the central thrust of our discussion, we do control for it.
1. The Keane and Runkle tests Let the forecast of company j’s EPS made by analyst n at time t be denoted tEPSn,t+1j. KR test whether such a forecast is rational in the Muthian sense (Muth, 1961). This requires that the forecast of EPS at time period t, be equal to its mathematical expectation. Whether analysts might rationally misrepresent their true expectation of earnings is an important question but not one easily encompassed by the KR framework (c.f. Morgan and Stocken, 2003; Lim, 1999), i.e., j t EPSn;tþ1
¼ EðEPSjtþ1 j In;t Þ
ð1Þ
where EPStj+ 1 is the actual EPS of firm j in period t + 1, In,t is the set of information available to analyst n, in quarter, and, finally, E is the mathematical expectation operator. For any single analyst, n, an appropriate test of rationality is undertaken by testing restrictions on the regression j EPSjtþ1 ¼ a0 þ a1t EPSjn;tþ1 þ a2 Xn;t þ en;tþ1
ð2Þ
where Xn,t is any information available to analyst n at time t that might be useful in predicting tEPStj+ 1. Unbiasedness requires a0 = 0, a1 = 1 in Eq. (2), whereas efficiency of analyst n’s forecasts additionally requires a2 = 0. KR point out that problems may arise when regressions of the form of Eq. (2) are used j on data for many firms and many analysts. In particular, the error term, en,t + 1 in Eq. (2) may display contemporaneous cross-correlation across analysts following the same, or related, firms. Or alternatively across firms in the same industry. KR consider a particular structure of cross-sectional dependence, across N analysts, following J firms, during T quarters, and reestimate Eq. (2) adjusting the standard errors of a1 and a2 accordingly. Here contemporaneous forecasts are those issued for the same quarter’s earnings, irrespective of how close in time they are issued. To allow the pattern of contemporaneous cross-correlation KR consider, let the forecast variance in regression Eq. (2) be described as follows:
j j Eðen;tþ1 ; en;tþ1þs Þ¼
8 < a; if s ¼ 0; :
0; if s p 0
ð3Þ
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Dependence of current forecast errors on past errors is ruled out, consistent with the assumption that agents learn fully from past mistakes. Similarly, cross-sectional dependence in the forecast errors of two analysts, n and m, following the same firm j, can be described by the equation: 8 < c; if s ¼ 0; m p n; j j Eðen;tþ1 ; em;tþ1þs Þ¼ ð4Þ : 0; if s p 0 We might expect forecast errors for two analysts following the same firm to be related, i.e., c>0, because difficulties in forecasting EPS for a particular firm are likely to be shared by all N analysts following that firm. Similarly, a single analyst following two firms subject to a common ‘‘shock’’ is likely to make similar errors. KR describe the propagation of forecast errors across firms as follows: 8 < b; if s ¼ 0; j; lVJ ; j p l j l Eðen;tþ1 ; en;tþ1þs Þ¼ ð5Þ : 0; if s p 0 Finally, systematic forecast errors might be expected to propagate across firms and across analysts. Such a propagation process is described by KR using the equation:
j l ; em;tþ1þs Þ¼ Eðe n;tþ1
8 < d;
if s ¼ 0; j; lVJ ; j p lm; nVN ; m p n
:
if s p 0
0;
ð6Þ
KR make some assumptions which impose a ranking on the magnitude of estimated contemporaneous cross-correlations (see the Appendix to their paper). First, KR assume that some shocks to expectations are firm-specific; such shocks being expected to cancel out across firms. This implies b < a. Similarly, KR assume each analyst has firm-specific private information which allows him to reduce his forecast error. This implies c>d. Some analysts may have more information than others, and hence the degree to which c exceeds d will vary across analysts. KR state that they do not consider possible autocorrelation in forecast errors because they restrict their sample to forecasts issued after the prior quarter’s EPS is known. Rational agents fully incorporate the effect of errors made in forecasting last quarter’s EPS into forecasts of next quarter’s EPS. We investigate the validity of this assumption below. In order to estimate the variance and covariances required by the GMM estimator we rank by firm, analyst, and earnings quarter ( J N T) as follows: 1 : 1 EPS1;1þk
: : T EPS1
2 : 1;T þ1 1 EPS1;1þk
: : T EPSJ
: : : 1 EPS1
1;Tþ1
: : : T EPSJ
2;1þk
N ;T þ1
ð7Þ
and then proceed to construct the variance– covariance matrix 6, where 6 is a JNT 2 block diagonal matrix with E on its principal diagonal and a matrix F elsewhere. The matrix E itself is JT 2 block diagonal matrix with a matrix A on the principal diagonal and a matrix
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B elsewhere and F is also a JT 2 block diagonal matrix with a matrix C on the principal diagonal and a matrix D elsewhere. Finally, the matrices A, B, C and D are T 2 matrices which are products of a T 2 identity matrix and the estimated variance term aˆ, and three the covariance terms bˆ, cˆ and dˆ given by aˆ ¼
T X J X N 1 X j eˆ n;tþ1 ; eˆ j TJN t¼1 j¼1 n¼1 n;tþ1
bˆ ¼
T X J X J X N X 1 j eˆ n;tþ1 eˆ j TJ ðJ 1ÞN t¼1 j¼1 l ¼1 n¼1 n;tþ1 j p1
cˆ ¼
T X J X N X N X 1 j eˆ m;tþ1 eˆ j TJN ðN 1Þ t¼1 j¼1 n¼1 m ¼ 1 n;tþ1 m pn
dˆ ¼
T X J X J X N X N X 1 þ 1ˆelm;tþ1 eˆ j TJ ðJ 1ÞN ðN 1Þ t¼1 j¼1 l ¼ 1 n¼1 m ¼ 1 n;tþ1 jp l
ð8Þ
m pn
Given the assumptions KR make about the structure of errors in Eq. (2) the estimator of the variance used to construct coefficient standard errors, for hypothesis testing, is given by. ˆ 1 ½XVX 1 V ðbˆ GMM Þ ¼ ½XVX ðX XXÞ
ð9Þ
2. The data We now outline the sample criteria used by KR and give some idea what the resulting sample of forecasts from the United States for the years 1983 –1997 look like. We construct our sample to match as closely as possible that of the original KR study. We begin with a data set of all forecasts of quarterly EPS listed on the I/B/E/S detailed History file CD for November 2002. The original population of 1,605,823 forecasts of quarterly EPS for the sample period is issued by 7,155 analysts for 10,468 different companies. Additional data on stock prices and Special Items in earnings are taken from the Chicago Center for Research on Security Prices CD and COMPUSTAT respectively. Special Items are defined by COMPUSTAT to be unusual, or nonrecurring items, including the write down of assets, calculated before tax payments. All variables in reported regressions are scaled by beginning of period (here each quarter) price. KR impose data restrictions which we list in Table 1. Table 1 also illustrates the cumulative impact of the KR sample criteria on our data. Note that less than a quarter of the companies reported in the I/B/E/S database remain on the tape for more than 25 separate quarters and attract more than one hundred forecasts. This implies that three quarters of firms receive a fairly sparse, or episodic, coverage by analysts.
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Table 1 Attrition of population of forecasts as sample criteria are sequentially imposed Criterion
No. of firms
No. of analysts
No. of observations
1 2 3 4 5 6 7
10,468 1836 2168 1465 1465 1465 1326
11,987 6387 6344 5937 5487 3259 3177
2,172,839 1,110,320 1,175,993 833,515 580,413 555,243 289,699
1. Selects only forecasts of quarterly EPS for US companies in the years 1983 – 1997, from firms with at least 100 forecasts distributed over at least 25 different quarters, 2. Selects only forecasts from firms in industries which have three companies or more meeting sample criteria 1 and 2 above, 3. Selects only forecasts for companies with December year ends, 4. Selects only forecasts for primary, as opposed to diluted, EPS, 5. Selects only forecasts made by analysts who issued forecasts in five separate quarters or more, 6. Selects only forecasts made at least seven days after the announcement of the prior quarter’s EPS.
First quarter forecasts constitute about half the population, but the sample is fairly evenly balanced, with a slight skew towards fourth quarter forecasts. This outcome reflects the requirement that the previous quarter’s earnings have been publicly known for 7 days. As expected, the sample criteria skew sample firms towards more intensely covered stocks, with median coverage rising from 44 analysts to 153. This aspect of the sample may bias the results in favour of the conclusion that analysts are rational. Fig. 1 shows the path of mean actual and forecast EPS. Two mild recessions occur in the period, centered upon 1986 and 1991. Fig. 2 plots special items over the sample period. Fig. 2 suggests that sudden asset write-downs may indeed explain the uneven path of EPS. If analysts seek to predict ‘‘core’’ earnings, a failure to predict asset write-downs
Fig. 1. Mean actual and forecast EPS for sample firms 1983 – 1997.
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Fig. 2. Mean special item provision for sample firms 1983 – 1997.
does not imply that analysts are irrational. Since we employ KR’s sample criteria on a far longer period, we inevitably end up with far more qualifying industries. We therefore concentrate our discussion of the regression-based tests upon three large industries with the most forecasts available, oil, chemicals and electrical utilities.
3. Results Table 2 present OLS results for rationality regressions, of the type presented in Eq. (2), excluding other sources of information (i.e., setting a2 = 0), for the three most populous industries in our sample. The results suggest only mild evidence of overreaction during the sample period. Only one industry shows substantial evidence of overreaction, Electrical Table 2 OLS regression tests of rationality Industry
a0
Oil Chemicals Electrical utilities
0.03 ( 5.43) 0.03 (4.49) 0.2 (26.81)
a1 1.09 (92.19) 0.96 (89.37) 0.57 (47.45)
R2
White
0.28 0.37 0.16
5.14* 2.44 10.51*
EPSjtþ1 ¼ a0 þ a1t EPSjn;tþ1 where t-values are given in parenthesis under regression coefficients. Note a2 is set equal to zero here. White denotes White’s (1980) test for heteroskedasticity. This is based on the retrieved squared residual from Eq. (2) in the text. It replaces the OLS estimate of the coefficient variance rI with the principal diagonal of the variance – covariance matrix XVXðXdiagðe2i ÞXÞðXVXÞ1 where ei = yi-Xib. * Significance at the 95% confidence interval.
ð10Þ
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Utilities, while the Oil industry results indicate insignificant underreaction to recent earnings information. The need to correct standard errors in order to conclude analyst forecasts are on average rational is not clear from these results because overreaction/ underreaction varies widely across industries. 3.1. Autocorrelation of forecast errors A requirement of the structure of the variance –covariance matrix structure advanced by KR is that forecast errors are independent across time. We examine this assumption in Table 3. We find a convincing rejection of this assumption, suggesting an alternative estimator allowing for serial correlation, such as that outlined by Newey and West (1999) may be more appropriate than the KR structure. While forecast error dependence decline throughout the year they remain both statistically and economically significant. 3.2. Independence of forecast errors across industries A further implied assumption of the KR estimation framework is that forecast error dependence is largely captured at the intraindustry level. This seems implausible given recent evidence that analysts struggle to interpret macroeconomic data (Chopra, 1998). Table 4 gives a Pearson correlation coefficient matrix between the forecast errors made in six major industries and those in the rest of the economy. Some correlations are intuitive, such as that between banking and insurance, or oil, and electrical utilities. Other correlations are not self-evident. Little doubt of the presence of industrial and macroeconomic spillovers remains however once we analyse the data in this way. Our results cast doubt on KR’s original tests and suggest revisions may be needed. 3.3. GMM and corrections for cross-sectional dependence We now follow KR’s method of estimating regressions of actual earnings on forecasts by OLS and GMM and we delete observations with extreme special items. As mentioned, KR consider a number of possible instruments for analysts’ forecasts individually. These are the forecast for firm j, of EPS last quarter by the same analyst n (X1), the previous
Table 3 Correlation in forecast errors across quarterly data for three industries in our sample Industry
1st lag
2nd lag
3rd lag
4th lag
Oil Chemicals Electrical utilities Banking Drugs Insurance Average
0.6 (0.02) 0.68 (0.01) 0.72 (0.04) 0.46 (0.02) 0.65 (0.03) 0.57 (0.01) 0.61
0.25 (0.02) 0.42 (0.01) 0.6 (0.06) 0.28 (0.02) 0.41 (0.04) 0.47 (0.01) 0.41
0.09 (0.02) 0.26 (0.26) 0.55 (0.07) 0.2 (0.02) 0.45 (0.05) 0.35 (0.02) 0.32
0.01 (0.03) 0.2 (0.01) 0.52 (0.07) 0.12 (0.02) 0.19 (0.05) 0.29 (0.02) 0.22
The analysis is based on consensus quarterly forecast errors in each industry. Standard errors are given below correlation coefficients in parentheses.
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Table 4 Pearson correlation coefficients between the errors in the six most populous industries Industry Oil Chemicals Electrical utilities Banking Drugs Insurance
Oil Chemicals 0.03 (0.7)
Electrical utilities Banking 0.18 (0) 0.06 ( 0.4)
Drugs
0.01 (0.9) 0.02 0.39 (0) 0.15 0.00 (1) 0.18 0.26
Insurance
Rest of economy
(0.7) 0.04 (0.6) 0.081 (0.3) (0.1) 0.01 (0.9) 0.042 (0.6) (0.0) 0.17 (0) 0.14 (0.1) (0) 0.01 (0.2) 0 (0.9) 0.03 (0.7) 0.2 (0) 0.084 (0.3)
Number reported in brackets, below the Pearson correlations, are significance levels.
quarter’s EPS for the same firm j (X2), the lagged forecast error made by analyst n in forecasting firm j’s EPS in the previous quarter (X3), and finally, the average forecast error made by all analysts following firm j in forecasting firm j’s EPS in the previous quarter (X4). Following KR, we denote an extreme special item observation as one more than four standard deviations away from the sample mean for the industry. Using our new extended data set the original KR conclusion, accepting their research method is placed in doubt. Table 5 gives OLS estimates of Eq. (2) where the value of actual EPS in the same quarter last year (At4) and the mean lagged forecast error for all firms in company j’s industry, excluding company j, in the relevant quarter (FEi p j) are both included in the other information vector, X. Our first instrument is a variant of KR’s original X2, the lagged actual for the previous quarter. While we regard the same quarter’s earnings last year as the more natural choice, little difference in results emerges by using KR’s original variable. Our second instrument is X4, included to capture intraindustry cross-sectional dependence in forecast errors. Table 5 shows that the analyst forecasts for three industries are inefficient with respect to both prior earnings outcomes and the lagged forecast error made in predicting the earnings of other firms in the same industry. This dependence of actual earnings, and j hence the regression equation error term, en,t +1, on past earning outcomes and the mean lagged forecast error of analysts following other firms makes them inappropriate instruments for entry into a GMM regression. Recall a good instrument is highly correlated with the variable it proxies for (forecasted earnings) but uncorrelated with the estimation error j from the regression, en,t + 1. Neither prior earnings, nor the lagged average forecast error predicting other firm earnings in the same industry fulfil this requirement. Table 5 OLS estimates including instruments in the overreaction regression equation Industry
a0
Oil Chemicals Electrical utilities
0.01 ( 2.89) 0.45 (9.94) 0.41 (6.53)
a1 0.86 (68.91) 0.78 (100.94) 0.35 (32.58)
a2At4 0.68 (40.28) 0.17 (34.34) 0.55 (67.89)
a2FEi p j 0.68 (2.12) 0.24 ( 7.92) 0.32 ( 9.49)
The instruments are the same quarter’s earnings-per-share last year (At4) and the lagged mean forecast error for the other firms in the j’ the firm’s industry, excluding company j (FEi p j) j j j ¼ a0 þ a1t EPSn;tþ1 þ a2 Xn;t þ en;tþ1 EPStþ1
The numbers in brackets below coefficients are t-values.
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Table 6 GMM estimates with FEi p j, the average forecast error for forecasts made for other firms earnings in j’s industry excluding j itself, and At4 is the coefficient on the same quarter’s earnings last year for firm j as instruments j j j j ¼ a0 þ a1t EPSn;tþ1 þ en;tþ1 and EPSn;tþ1 is instrumented for by FEi p j and At4 and a0 is the GMM EPStþ1 regression intercept, a1 is the slope coefficient on the earnings forecast in the GMM regression and a * denotes significance of the Wald test a the 95% confidence interval Industry
a0
Oil Chemicals Electrical utilities
0.76 ( 13.76) 0.16 ( 13.76) 0.31 (5.89)
a1 3.34 (20.23) 1.36 (41.45) 0.42 (4.29)
Wald a1 = 1
Wald a1 = 1, a0 = 0
240.33* 166.17* 34.86*
197.67* 124.31* 33.24*
We present Wald tests of the rationality restrictions which are the asymptotic equivalents of t and F tests in the OLS rationality regressions.
Despite this, we follow the logic of KR’s research method in Table 6 and allow both At4 and FEi p j to enter as instruments in a GMM regression. Recall in KR’s original paper only one instrument is considered at a time. Our results unambiguously reject rationality. The joint hypothesis that a0 = 0 and a1 = 1 is strongly rejected. A correction to remove observations with special items lying outside the four standard deviation boundaries, undertaken by KR, has little effect upon the reported results of either the OLS or GMM regressions we report. Furthermore, deletion of post-1990 data, to more closely approximate the original KR study, produces substantially weaker but qualitatively similar results.
4. Conclusion We revisit claims made by Keane and Runkle (1998) that analysts’ forecasts of earnings-per-share are rational. Our findings cast doubt on KR’s conclusions and the appropriateness of KR’s correction to the standard errors used in regression-based tests. KR ignore autocorrelation in forecast errors and the impact of forecast errors propagating over industrial boundaries. This paper also extends KR’s original work to a larger sample of companies over a longer and more recent time period. Our new estimates contradict the rationality of analyst earnings forecasts. While the instruments chosen by KR seem invalid for their stated purpose, even their use does not yield results supportive of analyst rationality.
Acknowledgements El –Galfy thanks the Egyptian Ministry of Education and Cairo University for funding his research. Forbes thanks the RijksUniversiteit Groningen for hospitality during his sabbatical year. We wish to thank our colleagues at Glasgow for helpful comments and support. Thanks to First Call, part of Thomson Financial, and especially Pamela Grant for providing data on analyst forecasts. We also thank John O’Hanlon, Peter Pope, Martien Lubberink and Martin Walker for helpful advice and guidance. We owe a special word of
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thanks to Turalay Kenc and Fathalla Rehan for help and advice upon the econometric methods used.
References Chopra, V., 1998. Why so much error in analyst’s forecasts? Financial Analysts Journal 54, 10 – 17. De Bondt, W.F.M., 2000. The pyschology of underreaction and overreaction in world equity markets. In: Keim, D.B., Ziemba, W.T. (Eds.), Publications of the Newton Institute, vol. 9. Cambridge Univ. Press, Cambridge, pp. 65 – 81. De Bondt, W.F.M., Thaler, R.H., 1990. Do security analysts overreact? American Economic Review 80, 52 – 57. Hansen, L.P., 1982. Large sample properties of generalized method of moments estimators. Econometrica 50, 1029 – 1054. Keane, M.P., Runkle, D.E., 1998. Are financial analysts forecasts of corporate profits rational? Journal of Political Economy 106, 768 – 805. Lim, T., 1999. Rationality and analysts forecast bias. Journal of Finance 56, 369 – 385. Morgan, J., Stocken, P., 2003. An analysis of stock recommendations. Rand Journal of Economics 34, 183 – 203. Muth, J.F., 1961. Rational expectations and the theory of stock price movements. Econometrica 29, 315 – 335. Newey, W., West, K., 1999. A simple positive definite heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703 – 708. Penman, S., 2001. Financial Statement Analysis and Security Valuation. McGraw-Hill, New York. White, H., 1980. A heteroskedasticity-consistent covariance estimator and direct test for heteroskedasticity. Econometrica 48, 817 – 838.
Are forecasts of corporate profits rational? A note and further evidence Ahmed M. El-Galfy*, William P. Forbes Loughborough Business School, Loughborough University, Ashley Road, Loughborough, Leicestershire, LE11 3TU, UK Available online 11 June 2004
Abstract This paper revisits the claim by Keane and Runkle [J. Polit. Econ. 106 (1998) 768] that analyst forecasts of corporate profits may be rational, despite claims to the contrary by De Bondt and Thaler [Am. Econ. Rev. 80 (1990) 52] and others. We replicate the Keane and Runkle’s [J. Polit. Econ. 106 (1998) 768] research method and test some of the underlying assumptions in their modelling strategy. Specifically, we examine two key assumptions, the independence of forecast errors across time and the failure of forecast errors to spillover industrial boundaries. We find strong evidence of autocorrelation and interindustry forecast error spillovers. Our findings prompt us to extend Keane and Runkle’s tests to a revised General Method of Moments (GMM) estimate of model parameters as well as standard errors. Our revised GMM estimates employ two instruments designed to capture the impact of autocorrelation and spillover effects. These revised estimates suggest analyst forecasts of earnings are not rational with respect to publicly available information. D 2004 Elsevier B.V. All rights reserved. Keywords: Forecasts; Corporate profits; Industry
This paper revisits the claim by Keane and Runkle (1998) (henceforth KR) that analyst forecasts of earnings-per-share (henceforth EPS) are rational, despite evidence to the contrary by earlier researchers, notably De Bondt and Thaler (1990).1 KR claim that apparent overreaction in analyst forecasts results from a failure to correct for contemporaneous cross-correlation in forecast errors. They propose a correction to regression coefficient standard errors based on the General Method of Moments (GMM) * Corresponding author. Tel.: +44-141-330-6853. E-mail address: [email protected] (A.M. El-Galfy). 1 Empirical evidence to support ‘‘overreaction’’ in both stock prices and earning forecasts is reviewed in De Bondt (2000). 0927-5398/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jempfin.2004.04.004
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A.M. El-Galfy, W.P. Forbes / Journal of Empirical Finance 11 (2004) 617–626
estimator of Hansen (1982). This correction is then used in combination with traditional OLS regression coefficient estimates. Furthermore, KR examine the effect of shocks to earnings in the form of special items, which analysts may find either hard to predict or unworthy of prediction. Analysts often focus upon core earnings (see Penman, 2001). KR’s conclusion in favour of the rationality of earning forecasts further depends on their treatment of large special items. While we do not make this issue the central thrust of our discussion, we do control for it.
1. The Keane and Runkle tests Let the forecast of company j’s EPS made by analyst n at time t be denoted tEPSn,t+1j. KR test whether such a forecast is rational in the Muthian sense (Muth, 1961). This requires that the forecast of EPS at time period t, be equal to its mathematical expectation. Whether analysts might rationally misrepresent their true expectation of earnings is an important question but not one easily encompassed by the KR framework (c.f. Morgan and Stocken, 2003; Lim, 1999), i.e., j t EPSn;tþ1
¼ EðEPSjtþ1 j In;t Þ
ð1Þ
where EPStj+ 1 is the actual EPS of firm j in period t + 1, In,t is the set of information available to analyst n, in quarter, and, finally, E is the mathematical expectation operator. For any single analyst, n, an appropriate test of rationality is undertaken by testing restrictions on the regression j EPSjtþ1 ¼ a0 þ a1t EPSjn;tþ1 þ a2 Xn;t þ en;tþ1
ð2Þ
where Xn,t is any information available to analyst n at time t that might be useful in predicting tEPStj+ 1. Unbiasedness requires a0 = 0, a1 = 1 in Eq. (2), whereas efficiency of analyst n’s forecasts additionally requires a2 = 0. KR point out that problems may arise when regressions of the form of Eq. (2) are used j on data for many firms and many analysts. In particular, the error term, en,t + 1 in Eq. (2) may display contemporaneous cross-correlation across analysts following the same, or related, firms. Or alternatively across firms in the same industry. KR consider a particular structure of cross-sectional dependence, across N analysts, following J firms, during T quarters, and reestimate Eq. (2) adjusting the standard errors of a1 and a2 accordingly. Here contemporaneous forecasts are those issued for the same quarter’s earnings, irrespective of how close in time they are issued. To allow the pattern of contemporaneous cross-correlation KR consider, let the forecast variance in regression Eq. (2) be described as follows:
j j Eðen;tþ1 ; en;tþ1þs Þ¼
8 < a; if s ¼ 0; :
0; if s p 0
ð3Þ
A.M. El-Galfy, W.P. Forbes / Journal of Empirical Finance 11 (2004) 617–626
619
Dependence of current forecast errors on past errors is ruled out, consistent with the assumption that agents learn fully from past mistakes. Similarly, cross-sectional dependence in the forecast errors of two analysts, n and m, following the same firm j, can be described by the equation: 8 < c; if s ¼ 0; m p n; j j Eðen;tþ1 ; em;tþ1þs Þ¼ ð4Þ : 0; if s p 0 We might expect forecast errors for two analysts following the same firm to be related, i.e., c>0, because difficulties in forecasting EPS for a particular firm are likely to be shared by all N analysts following that firm. Similarly, a single analyst following two firms subject to a common ‘‘shock’’ is likely to make similar errors. KR describe the propagation of forecast errors across firms as follows: 8 < b; if s ¼ 0; j; lVJ ; j p l j l Eðen;tþ1 ; en;tþ1þs Þ¼ ð5Þ : 0; if s p 0 Finally, systematic forecast errors might be expected to propagate across firms and across analysts. Such a propagation process is described by KR using the equation:
j l ; em;tþ1þs Þ¼ Eðe n;tþ1
8 < d;
if s ¼ 0; j; lVJ ; j p lm; nVN ; m p n
:
if s p 0
0;
ð6Þ
KR make some assumptions which impose a ranking on the magnitude of estimated contemporaneous cross-correlations (see the Appendix to their paper). First, KR assume that some shocks to expectations are firm-specific; such shocks being expected to cancel out across firms. This implies b < a. Similarly, KR assume each analyst has firm-specific private information which allows him to reduce his forecast error. This implies c>d. Some analysts may have more information than others, and hence the degree to which c exceeds d will vary across analysts. KR state that they do not consider possible autocorrelation in forecast errors because they restrict their sample to forecasts issued after the prior quarter’s EPS is known. Rational agents fully incorporate the effect of errors made in forecasting last quarter’s EPS into forecasts of next quarter’s EPS. We investigate the validity of this assumption below. In order to estimate the variance and covariances required by the GMM estimator we rank by firm, analyst, and earnings quarter ( J N T) as follows: 1 : 1 EPS1;1þk
: : T EPS1
2 : 1;T þ1 1 EPS1;1þk
: : T EPSJ
: : : 1 EPS1
1;Tþ1
: : : T EPSJ
2;1þk
N ;T þ1
ð7Þ
and then proceed to construct the variance– covariance matrix 6, where 6 is a JNT 2 block diagonal matrix with E on its principal diagonal and a matrix F elsewhere. The matrix E itself is JT 2 block diagonal matrix with a matrix A on the principal diagonal and a matrix
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B elsewhere and F is also a JT 2 block diagonal matrix with a matrix C on the principal diagonal and a matrix D elsewhere. Finally, the matrices A, B, C and D are T 2 matrices which are products of a T 2 identity matrix and the estimated variance term aˆ, and three the covariance terms bˆ, cˆ and dˆ given by aˆ ¼
T X J X N 1 X j eˆ n;tþ1 ; eˆ j TJN t¼1 j¼1 n¼1 n;tþ1
bˆ ¼
T X J X J X N X 1 j eˆ n;tþ1 eˆ j TJ ðJ 1ÞN t¼1 j¼1 l ¼1 n¼1 n;tþ1 j p1
cˆ ¼
T X J X N X N X 1 j eˆ m;tþ1 eˆ j TJN ðN 1Þ t¼1 j¼1 n¼1 m ¼ 1 n;tþ1 m pn
dˆ ¼
T X J X J X N X N X 1 þ 1ˆelm;tþ1 eˆ j TJ ðJ 1ÞN ðN 1Þ t¼1 j¼1 l ¼ 1 n¼1 m ¼ 1 n;tþ1 jp l
ð8Þ
m pn
Given the assumptions KR make about the structure of errors in Eq. (2) the estimator of the variance used to construct coefficient standard errors, for hypothesis testing, is given by. ˆ 1 ½XVX 1 V ðbˆ GMM Þ ¼ ½XVX ðX XXÞ
ð9Þ
2. The data We now outline the sample criteria used by KR and give some idea what the resulting sample of forecasts from the United States for the years 1983 –1997 look like. We construct our sample to match as closely as possible that of the original KR study. We begin with a data set of all forecasts of quarterly EPS listed on the I/B/E/S detailed History file CD for November 2002. The original population of 1,605,823 forecasts of quarterly EPS for the sample period is issued by 7,155 analysts for 10,468 different companies. Additional data on stock prices and Special Items in earnings are taken from the Chicago Center for Research on Security Prices CD and COMPUSTAT respectively. Special Items are defined by COMPUSTAT to be unusual, or nonrecurring items, including the write down of assets, calculated before tax payments. All variables in reported regressions are scaled by beginning of period (here each quarter) price. KR impose data restrictions which we list in Table 1. Table 1 also illustrates the cumulative impact of the KR sample criteria on our data. Note that less than a quarter of the companies reported in the I/B/E/S database remain on the tape for more than 25 separate quarters and attract more than one hundred forecasts. This implies that three quarters of firms receive a fairly sparse, or episodic, coverage by analysts.
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Table 1 Attrition of population of forecasts as sample criteria are sequentially imposed Criterion
No. of firms
No. of analysts
No. of observations
1 2 3 4 5 6 7
10,468 1836 2168 1465 1465 1465 1326
11,987 6387 6344 5937 5487 3259 3177
2,172,839 1,110,320 1,175,993 833,515 580,413 555,243 289,699
1. Selects only forecasts of quarterly EPS for US companies in the years 1983 – 1997, from firms with at least 100 forecasts distributed over at least 25 different quarters, 2. Selects only forecasts from firms in industries which have three companies or more meeting sample criteria 1 and 2 above, 3. Selects only forecasts for companies with December year ends, 4. Selects only forecasts for primary, as opposed to diluted, EPS, 5. Selects only forecasts made by analysts who issued forecasts in five separate quarters or more, 6. Selects only forecasts made at least seven days after the announcement of the prior quarter’s EPS.
First quarter forecasts constitute about half the population, but the sample is fairly evenly balanced, with a slight skew towards fourth quarter forecasts. This outcome reflects the requirement that the previous quarter’s earnings have been publicly known for 7 days. As expected, the sample criteria skew sample firms towards more intensely covered stocks, with median coverage rising from 44 analysts to 153. This aspect of the sample may bias the results in favour of the conclusion that analysts are rational. Fig. 1 shows the path of mean actual and forecast EPS. Two mild recessions occur in the period, centered upon 1986 and 1991. Fig. 2 plots special items over the sample period. Fig. 2 suggests that sudden asset write-downs may indeed explain the uneven path of EPS. If analysts seek to predict ‘‘core’’ earnings, a failure to predict asset write-downs
Fig. 1. Mean actual and forecast EPS for sample firms 1983 – 1997.
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Fig. 2. Mean special item provision for sample firms 1983 – 1997.
does not imply that analysts are irrational. Since we employ KR’s sample criteria on a far longer period, we inevitably end up with far more qualifying industries. We therefore concentrate our discussion of the regression-based tests upon three large industries with the most forecasts available, oil, chemicals and electrical utilities.
3. Results Table 2 present OLS results for rationality regressions, of the type presented in Eq. (2), excluding other sources of information (i.e., setting a2 = 0), for the three most populous industries in our sample. The results suggest only mild evidence of overreaction during the sample period. Only one industry shows substantial evidence of overreaction, Electrical Table 2 OLS regression tests of rationality Industry
a0
Oil Chemicals Electrical utilities
0.03 ( 5.43) 0.03 (4.49) 0.2 (26.81)
a1 1.09 (92.19) 0.96 (89.37) 0.57 (47.45)
R2
White
0.28 0.37 0.16
5.14* 2.44 10.51*
EPSjtþ1 ¼ a0 þ a1t EPSjn;tþ1 where t-values are given in parenthesis under regression coefficients. Note a2 is set equal to zero here. White denotes White’s (1980) test for heteroskedasticity. This is based on the retrieved squared residual from Eq. (2) in the text. It replaces the OLS estimate of the coefficient variance rI with the principal diagonal of the variance – covariance matrix XVXðXdiagðe2i ÞXÞðXVXÞ1 where ei = yi-Xib. * Significance at the 95% confidence interval.
ð10Þ
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Utilities, while the Oil industry results indicate insignificant underreaction to recent earnings information. The need to correct standard errors in order to conclude analyst forecasts are on average rational is not clear from these results because overreaction/ underreaction varies widely across industries. 3.1. Autocorrelation of forecast errors A requirement of the structure of the variance –covariance matrix structure advanced by KR is that forecast errors are independent across time. We examine this assumption in Table 3. We find a convincing rejection of this assumption, suggesting an alternative estimator allowing for serial correlation, such as that outlined by Newey and West (1999) may be more appropriate than the KR structure. While forecast error dependence decline throughout the year they remain both statistically and economically significant. 3.2. Independence of forecast errors across industries A further implied assumption of the KR estimation framework is that forecast error dependence is largely captured at the intraindustry level. This seems implausible given recent evidence that analysts struggle to interpret macroeconomic data (Chopra, 1998). Table 4 gives a Pearson correlation coefficient matrix between the forecast errors made in six major industries and those in the rest of the economy. Some correlations are intuitive, such as that between banking and insurance, or oil, and electrical utilities. Other correlations are not self-evident. Little doubt of the presence of industrial and macroeconomic spillovers remains however once we analyse the data in this way. Our results cast doubt on KR’s original tests and suggest revisions may be needed. 3.3. GMM and corrections for cross-sectional dependence We now follow KR’s method of estimating regressions of actual earnings on forecasts by OLS and GMM and we delete observations with extreme special items. As mentioned, KR consider a number of possible instruments for analysts’ forecasts individually. These are the forecast for firm j, of EPS last quarter by the same analyst n (X1), the previous
Table 3 Correlation in forecast errors across quarterly data for three industries in our sample Industry
1st lag
2nd lag
3rd lag
4th lag
Oil Chemicals Electrical utilities Banking Drugs Insurance Average
0.6 (0.02) 0.68 (0.01) 0.72 (0.04) 0.46 (0.02) 0.65 (0.03) 0.57 (0.01) 0.61
0.25 (0.02) 0.42 (0.01) 0.6 (0.06) 0.28 (0.02) 0.41 (0.04) 0.47 (0.01) 0.41
0.09 (0.02) 0.26 (0.26) 0.55 (0.07) 0.2 (0.02) 0.45 (0.05) 0.35 (0.02) 0.32
0.01 (0.03) 0.2 (0.01) 0.52 (0.07) 0.12 (0.02) 0.19 (0.05) 0.29 (0.02) 0.22
The analysis is based on consensus quarterly forecast errors in each industry. Standard errors are given below correlation coefficients in parentheses.
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Table 4 Pearson correlation coefficients between the errors in the six most populous industries Industry Oil Chemicals Electrical utilities Banking Drugs Insurance
Oil Chemicals 0.03 (0.7)
Electrical utilities Banking 0.18 (0) 0.06 ( 0.4)
Drugs
0.01 (0.9) 0.02 0.39 (0) 0.15 0.00 (1) 0.18 0.26
Insurance
Rest of economy
(0.7) 0.04 (0.6) 0.081 (0.3) (0.1) 0.01 (0.9) 0.042 (0.6) (0.0) 0.17 (0) 0.14 (0.1) (0) 0.01 (0.2) 0 (0.9) 0.03 (0.7) 0.2 (0) 0.084 (0.3)
Number reported in brackets, below the Pearson correlations, are significance levels.
quarter’s EPS for the same firm j (X2), the lagged forecast error made by analyst n in forecasting firm j’s EPS in the previous quarter (X3), and finally, the average forecast error made by all analysts following firm j in forecasting firm j’s EPS in the previous quarter (X4). Following KR, we denote an extreme special item observation as one more than four standard deviations away from the sample mean for the industry. Using our new extended data set the original KR conclusion, accepting their research method is placed in doubt. Table 5 gives OLS estimates of Eq. (2) where the value of actual EPS in the same quarter last year (At4) and the mean lagged forecast error for all firms in company j’s industry, excluding company j, in the relevant quarter (FEi p j) are both included in the other information vector, X. Our first instrument is a variant of KR’s original X2, the lagged actual for the previous quarter. While we regard the same quarter’s earnings last year as the more natural choice, little difference in results emerges by using KR’s original variable. Our second instrument is X4, included to capture intraindustry cross-sectional dependence in forecast errors. Table 5 shows that the analyst forecasts for three industries are inefficient with respect to both prior earnings outcomes and the lagged forecast error made in predicting the earnings of other firms in the same industry. This dependence of actual earnings, and j hence the regression equation error term, en,t +1, on past earning outcomes and the mean lagged forecast error of analysts following other firms makes them inappropriate instruments for entry into a GMM regression. Recall a good instrument is highly correlated with the variable it proxies for (forecasted earnings) but uncorrelated with the estimation error j from the regression, en,t + 1. Neither prior earnings, nor the lagged average forecast error predicting other firm earnings in the same industry fulfil this requirement. Table 5 OLS estimates including instruments in the overreaction regression equation Industry
a0
Oil Chemicals Electrical utilities
0.01 ( 2.89) 0.45 (9.94) 0.41 (6.53)
a1 0.86 (68.91) 0.78 (100.94) 0.35 (32.58)
a2At4 0.68 (40.28) 0.17 (34.34) 0.55 (67.89)
a2FEi p j 0.68 (2.12) 0.24 ( 7.92) 0.32 ( 9.49)
The instruments are the same quarter’s earnings-per-share last year (At4) and the lagged mean forecast error for the other firms in the j’ the firm’s industry, excluding company j (FEi p j) j j j ¼ a0 þ a1t EPSn;tþ1 þ a2 Xn;t þ en;tþ1 EPStþ1
The numbers in brackets below coefficients are t-values.
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Table 6 GMM estimates with FEi p j, the average forecast error for forecasts made for other firms earnings in j’s industry excluding j itself, and At4 is the coefficient on the same quarter’s earnings last year for firm j as instruments j j j j ¼ a0 þ a1t EPSn;tþ1 þ en;tþ1 and EPSn;tþ1 is instrumented for by FEi p j and At4 and a0 is the GMM EPStþ1 regression intercept, a1 is the slope coefficient on the earnings forecast in the GMM regression and a * denotes significance of the Wald test a the 95% confidence interval Industry
a0
Oil Chemicals Electrical utilities
0.76 ( 13.76) 0.16 ( 13.76) 0.31 (5.89)
a1 3.34 (20.23) 1.36 (41.45) 0.42 (4.29)
Wald a1 = 1
Wald a1 = 1, a0 = 0
240.33* 166.17* 34.86*
197.67* 124.31* 33.24*
We present Wald tests of the rationality restrictions which are the asymptotic equivalents of t and F tests in the OLS rationality regressions.
Despite this, we follow the logic of KR’s research method in Table 6 and allow both At4 and FEi p j to enter as instruments in a GMM regression. Recall in KR’s original paper only one instrument is considered at a time. Our results unambiguously reject rationality. The joint hypothesis that a0 = 0 and a1 = 1 is strongly rejected. A correction to remove observations with special items lying outside the four standard deviation boundaries, undertaken by KR, has little effect upon the reported results of either the OLS or GMM regressions we report. Furthermore, deletion of post-1990 data, to more closely approximate the original KR study, produces substantially weaker but qualitatively similar results.
4. Conclusion We revisit claims made by Keane and Runkle (1998) that analysts’ forecasts of earnings-per-share are rational. Our findings cast doubt on KR’s conclusions and the appropriateness of KR’s correction to the standard errors used in regression-based tests. KR ignore autocorrelation in forecast errors and the impact of forecast errors propagating over industrial boundaries. This paper also extends KR’s original work to a larger sample of companies over a longer and more recent time period. Our new estimates contradict the rationality of analyst earnings forecasts. While the instruments chosen by KR seem invalid for their stated purpose, even their use does not yield results supportive of analyst rationality.
Acknowledgements El –Galfy thanks the Egyptian Ministry of Education and Cairo University for funding his research. Forbes thanks the RijksUniversiteit Groningen for hospitality during his sabbatical year. We wish to thank our colleagues at Glasgow for helpful comments and support. Thanks to First Call, part of Thomson Financial, and especially Pamela Grant for providing data on analyst forecasts. We also thank John O’Hanlon, Peter Pope, Martien Lubberink and Martin Walker for helpful advice and guidance. We owe a special word of
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thanks to Turalay Kenc and Fathalla Rehan for help and advice upon the econometric methods used.
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