Comment on “On estimating conditional conservatism” by Ball, Kothari, and Nikolaev

Panos N. Patatoukas University of California at Berkeley Haas School of Business [email protected] Jacob K. Thomas Yale University [email protected]

Current Version: May 18, 2011

Abstract: Ball, Kothari, and Nikolaev (2011) make two major claims in their recent working paper titled “On estimating conditional conservatism.” While they agree that the effect documented in Patatoukas and Thomas (2011) biases the conditional conservatism estimate proposed in Basu (1997), they claim that the source of bias is not scale effects but a non-linear relation between expected returns and expected earnings. More important, they propose a revised measure of conditional conservatism, which they claim should be unbiased, and recommend that it be used in future research. Our evidence contradicts both claims.

Comment on “On estimating conditional conservatism” by Ball, Kothari, and Nikolaev 1. INTRODUCTION Research findings in the conditional conservatism literature have seesawed between optimism and pessimism regarding the Basu (1997) measure. Dietrich et al. (2007) and Givoly et al. (2007) provide evidence and arguments which suggest that the measure is unreliable. Ball et al. (2010) dismiss those concerns and encourage use of the Basu measure. Patatoukas and Thomas (2011), referred to hereafter as PT, renew the call to avoid the Basu measure by showing substantial evidence of conditional conservatism in lagged earnings. Ball et al. (2011), referred to hereafter as BKN, agree that the PT evidence confirms bias in the Basu measure, but propose alternative measures that they claim are unbiased.1 BKN also dispute PT’s explanation for the lagged earnings result and offer a different explanation. Even though BKN is a recent working paper, as yet unpublished, the strong claims made therein merit investigation. We evaluate BKN and find evidence that contradicts BKN’s claims and conclusions. Our first, and more important, finding is that the three revised Basu measures proposed by BKN are biased. While those measures are designed to eliminate spurious evidence of differential timeliness in lagged earnings, they do not address the concerns in Dietrich et al. (2007) and Givoly et al. (2007). For example, using the methodology underlying Table 2 of Dietrich et al. (2007) we show that BKN’s revised measures find conditional conservatism in simulated data from which conditional conservatism has been scrubbed. This is a disappointing finding as researchers eagerly await a reliable measure of conditional conservatism.2

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PT and BKN can refer either to the studies or the authors of those studies, depending on the context. In the interim, researchers have resorted to ad hoc solutions, such as confirming that their results are not altered when they use different measures that are currently available. Consider, for example, Biddle et al. (2011), which uses four measures of conditional conservatism: a) minus one times the ratio of accumulated non-operating

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Second, our evidence contradicts the BKN explanation for the PT results, but provides additional support for the PT explanation. BKN claim that the PT result is due to a non-linear relation between expected returns and earnings, but do not probe the validity of their explanation.3 Our evidence contradicts their explanation. BKN also provide a separate explanation, based on time-series variation in return variances, to explain PT’s results on timeseries comovement among estimates of timeliness and the loss and return variance effects. Again, we find evidence inconsistent with this second BKN explanation PT’s explanation is that scale, which is positively related to price-deflated earnings and negatively related to return variance, is an omitted variable. We show that the BKN investigation of scale effects is biased against observing any such effects, because they use the dependent variable—inverse of share price—to form partitions. Their conclusion is reversed when we a) fix the bias in the BKN specification or b) use the BKN specification but consider variation in scale along dimensions other than share price. We recognize that details of disagreement between BKN and PT regarding explanations for the lagged earnings result are of little interest to most researchers using conditional conservatism measures; their main concern is the availability of a reliable measure. But for the hard core with inquiring minds, we lay it all out. 2. ARE BKN’S REVISED BASU MEASURES UNBIASED? The original Basu specifications, which are estimated on pooled data and described in Panels A and B of Table 1 in Basu (1997), are provided below in equations (1A) and (1B). Whereas the first specification is based on earnings and returns, the second specification is based

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accruals to total assets (adapted from Zhang (2008)); b) the ratio of the C score plus G score to G score (Khan and Watts (2009)); c) a CR ratio of unexpected current earnings to total earnings news (adapted from Callen et al. (2010)); and d) a factor score from a principal component analysis of the above three metrics. BKN assert that the improvement offered by their revised measures relies on controls for the non-linear relation between expected returns and expected earnings. In fact that improvement is based on controls for expected earnings and does not rely on relations between expected returns and earnings.

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on unexpected earnings and returns, where the corresponding cross-sectional means proxy for expected earnings and returns.4 (1A) ∑

(1B) where Xit = earnings per share reported by firm i in year t, Pit-1 = price per share for firm i at the end of year t-1, Rit = stock return for firm i in year t, ARit = stock return for firm i in year t minus equally-weighted market return for year t, Dit = 1 if ARit < 0, which represents bad news, and 0 otherwise, and n = number of firms in each cross-section. PT regress different measures (V) derived from current and lagged earnings and price on abnormal returns. Those regressions, described below as equation (1C), are based on the Basu specifications above which allow for coefficients to vary between good and bad news. To maintain consistency with the literature that follows Basu (1997), PT estimate annual crosssectional regressions and designate positive (negative) abnormal returns as good (bad) news.

(1C) As reported in the fourth row of Table 3, Panel A, of PT, the coefficient on β1 is 0.185 for current earnings (V=Xit/Pit-1), which suggests substantial evidence of conditional conservatism. However, the results reported in the third row for lagged earnings (V=Xit-1/Pit-1) show that the corresponding estimate of β1 is 0.116. Given that lagged earnings should exhibit no evidence of conditional conservatism, observing an estimate for lagged earnings that is about 60 percent as

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Whereas the cross-sectional mean used for expected earnings is based only on sample firms, the cross-sectional mean used for expected returns is based on all firms with available return data on CRSP.

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large as that for current earnings suggests that the Basu measure is associated with considerable upward bias. PT recommend that researchers a) heed the call of prior research to avoid the Basu measure, b) reevaluate inferences from prior evidence of cross-sectional and time-series variation based on the Basu measure, and c) be cautious when using any revised Basu measure that deals with the bias observed in lagged earnings. BKN assert that the PT lagged earnings result is caused by an asymmetric relation between expected earnings and expected returns that resembles the asymmetric relation between unexpected earnings and unexpected returns predicted by conditional conservatism. If the proxies for unexpected earnings and returns used in the original Basu specification contain elements of expected earnings and returns, respectively, estimates for conditional conservatism will be biased upward. BKN replace unexpected earnings in equation (1B) with three alternative measures that incorporate information contained in lagged earnings. Approach 1 estimates unexpected earnings as the residual (ζit) from cross-sectional regressions of price-deflated earnings on lagged values, estimated within each two-digit SIC Industry code (see equation (6) in BKN). Coefficients are allowed to vary between positive and negative lagged earnings as described by equation (2) below. 0

0

ζ

(2)

Approach 2 proposes two within-firm measures of unexpected earnings: a) first differences in earnings, deflated by lagged price ([Xit − Xit-1]/Pit-1), and b) price-deflated earnings for firm i and year t less firm i’s time-series mean value of price-deflated earnings. The first measure assumes that earnings follow a random walk process.5 The second measure assumes that 5

Lobo et al. (2008) also consider earnings differences, as a proxy for unexpected earnings.

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price-deflated earnings revert over time to a firm-specific mean, and is implemented by inserting firm-fixed effects, which effectively control for the firm-specific mean value of Xit/Pt-1. BKN claim that the conditional conservatism estimates based on these revised measures of unexpected earnings are unbiased and recommend that these revised measures be used in future research. They also recommend that inferences from prior research regarding crosssectional and time-series variation in conditional conservatism remain valid, given that similar, though considerably muted, results are observed for these revised measures. Differences in the recommendations and conclusions made by PT and BKN reflect the different weights the two papers assign to the concerns raised in Dietrich et al. (2007) and Givoly et al. (2007). Whereas BKN ignore those concerns when devising their revised measures, PT believe any revised measure should also address those concerns. Rather than investigate each potential source of error arising from those concerns, we focus on a simple procedure recommended by Dietrich et al. (2007). Before discussing that procedure, we believe it is useful to examine one of the reasons proposed in Ball et al. (2010) to dismiss the concerns raised in Dietrich et al. (2007). The discussion of bias in Dietrich et al. (2007) is framed in terms of endogeneity caused by returns reflecting information in reported earnings. Ball et al. (2010) conclude that “Return endogeneity simply is not important enough in practice to be a substantial issue.” The basis for this conclusion appears to be the results in Ball and Shivakumar (2008), which suggest that the average quarterly earnings announcement accounts for only about 2 percent of annual stock return variance. The Ball and Shivakumar (2008) metric, which is designed to measure the incremental return variance caused by earnings releases, is not the appropriate metric, however, to assess the

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validity of the Dietrich et al. (2007) concerns. We say so because Appendix A in Dietrich et al. (2007) shows that their bias remains as long as reported earnings reflects information that has already been incorporated in stock returns. In other words, any contemporaneous association between earnings and returns, as in Ball and Brown (1968) for example, is sufficient for the bias in Dietrich et al. (2007); there is no requirement that reported earnings cause stock returns. Returning to the procedure underlying Table 2 of Dietrich et al. (2007) we create simulated values of the regressor (unexpected returns) that are effectively scrambled across firmyears so the dependent variable (unexpected earnings) for each observation is no longer matched exactly with the corresponding regressor (see Easton,1998, for a related procedure). Our description provided below, which is taken for the most part directly from Dietrich et al. (2007), explains how to construct simulated returns that are scrubbed of evidence of conditional conservatism. We first estimate annual cross-sectional regressions, described below in equation (3), of market-adjusted stock returns on six variables (V) derived from current and lagged earnings and prices: a) current earnings (Xit/Pit-1), b) lagged earnings (Xit-1/Pit-1), c) inverse of price (1/Pit-1), d) earnings differences ((Xit − Xit)/Pit-1), e) unexpected earnings based on firm-fixed effects (Xit/Pit-1 − Effe[Xit/Pit-1]), and f) unexpected earnings based on industry relations between current and lagged earnings (Xit/Pit-1 − Eind[Xit/Pit-1]). The first three variables have been considered in PT and the last three variables are BKN’s measures of unexpected earnings described earlier.

(3) The estimated intercept (δ0) and slope (δ1) coefficients capture the average association between abnormal returns and each V. Because the coefficients are not allowed to vary across good and bad news firm-years in equation (3), any differences between the two sets of firm-years 6

will be captured by the estimated error term (τit). The error term also captures “other information”, an unobservable omitted variable, which is related to abnormal returns but unrelated to V. We then match the value of V for firm i during year t with a randomly selected (without replacement) error term for firm k during year t (τkt). Specifically, we compute predicted abnormal returns for firm i during year t, based on V and estimates of δ0 and δ1, and generate a simulated abnormal return by adding τkt, the randomly selected error term for firm k during year t. These simulated returns for firm i in year t will reflect the average relation with V, but will not reflect any differences in the relation between good and bad news firm-years because the error term associated with firm i for year t is not used to calculate the corresponding simulated return. We then regress the different variables (V) on simulated abnormal returns, based on equation (1C). For each simulation we obtain the time-series mean of the estimates from annual regressions, and then repeat the simulation over 100 trials to obtain a distribution for the timeseries mean coefficients. For comparison purposes, we also report the regressions based on actual, rather than simulated, abnormal returns. We consider three separate effects within these regressions estimated on actual and simulated returns: a) the potential presence of conditional conservatism in V, b) the potential for bias predicted by Dietrich et al. (2007) because of a linear association between abnormal returns and V, and c) the potential for bias documented by PT in lagged earnings because of associations between scale and (i) the variance of abnormal returns and (ii) V. For regressions based on actual returns, the first effect—presence of conditional conservatism—should be irrelevant for lagged earnings and inverse of price, but relevant for current earnings and the three BKN measures of unexpected earnings. But the first effect should

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not be observed for regressions based on simulated data for all six measures of V, as conditional conservatism is removed from simulated abnormal returns. The second effect—Dietrich et al. (2007) biases—should also be relevant for current earnings and the three BKN measures of unexpected earnings for the actual return regressions, because of the linear relation expected between those variables and abnormal returns. The second effect should, however, be much weaker for lagged earnings and inverse of price, for the actual return regressions. These predictions for the second effect also hold for simulated returns because the linear relations between abnormal returns and V are preserved in simulated returns. Finally, while the third effect—PT’s lagged earnings bias—is relevant for all six measures of V when we use actual abnormal returns, as shown in PT, it should not be observed for simulated abnormal returns because any relation between scale and return variance is removed by scrambling the error terms from equation (3) across observations. Under PT’s explanation, the return variance effect is necessary for the bias that is observed in conditional conservatism estimates for lagged earnings. To review, while the results based on actual returns will exhibit all three effects, the results based on simulated returns will only exhibit the second effect, which is the Dietrich et al. (2007) bias caused by any association that exists between abnormal returns and V. Although we discuss all three effects and different V measures, our focus is on the second effect and the three BKN measures. If the second effect is present (absent) for those three measures, estimates of β1 should be positive (zero) for those measures in the simulated returns regressions. The results based on actual and simulated abnormal returns are reported in Panels A and B of Table 1, respectively. For convenience, we use the same sample as in PT. As described in PT, estimates for conditional conservatism (β1) for current and lagged earnings in the first and

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second rows in Panel A (based on actual returns) equal 0.185 and 0.116, respectively. The corresponding estimate in the third row, based on inverse of price, indicates the return variance effect described in PT, where the average price per share decreases with the magnitude of positive and negative abnormal returns (ARit). Turning to the three BKN measures in the three bottom rows in Panel A, we find results similar to those reported in BKN. In each case, there is clear evidence of residual conditional conservatism, indicated by large positive estimates for β1. To determine whether those estimates for the three BKN measures are biased because of the second effect, described by Dietrich et al. (2007), we turn to the results for simulated returns reported in Panel B. In addition to the β0 and β1estimates from equation (1C), we also report in the right-most column the adjusted R2 values from equation (3) to indicate the level of association between abnormal returns and V. The higher the level of association, the greater the bias predicted by Dietrich et al. (2007). The estimated β1 coefficients in the bottom three rows, equal to 0.082, 0.125, and 0.170, suggest considerable bias for the three BKN measures.6 That is, while those measures might eliminate evidence of spurious conditional conservatism in lagged earnings they do not eliminate the bias predicted in Dietrich et al. (2007). This is our main finding from Table 1, because it suggests that BKN’s revised measures are not reliable. Given the positive association between those three measures and abnormal returns, indicated by the relatively high adjusted R2 values from equation (3), the “reverse” regressions of Basu (1997) will find evidence of conditional conservatism in data that should not exhibit any such tendency.

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The t-statistics associated with coefficients from the regressions of V on simulated returns are based on the distribution across the 100 trials of the time-series mean of the year-by-year coefficients in each trial. Given the procedures used to estimate simulated returns and the large sample sizes in each cross-section, these t-statistics tend to be very high.

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The results reported in the first three rows of Panel B in Table 1 are consistent with the bias predicted in Dietrich et al. (2007): V measures that are associated with abnormal returns will exhibit spurious evidence of conditional conservatism (indicated by positive estimates of β1) for simulated returns. The mean estimate of β1 equal to 0.233 reported in the first row reflects the strong positive association between returns and price-deflated earnings. Estimates of β1 close to zero for lagged earnings and inverse of price per share, reported in the second and third rows of Panel B, respectively, are expected given that they are only weakly associated with returns. The results in Panel B for lagged earnings and inverse of price contrast sharply with the results based on actual returns in Panel A, which indicate large positive and negative estimates for β1, respectively. This difference suggest that the Dietrich et al (2007) bias, which is highlighted by results based on simulated returns in Panel B, and the bias underlying the lagged earnings results in PT, which is observed for actual returns in Panel A, arise from different sources. We stress that this analysis does not represent a comprehensive investigation of all potential sources of bias associated with the revised BKN measures. Specifically, failing to observe bias for the three measures in Table 1, Panel B, when using simulated returns, does not provide conclusive proof that the BKN measure is unbiased. But observing a bias suggests that there is at least one source of bias associated with the BKN measure. 3. WHAT IS THE SOURCE OF THE PT BIAS? PT show that current returns are related to lagged earnings (deflated by lagged price) and that relation is positive for negative returns (i.e., bad news) but negative for positive returns (i.e., good news). PT suggest that this asymmetric relation can be explained by scale being an omitted correlated variable. Specifically, scale is positively related to lagged earnings, and scale is 10

negatively related to the variance of returns. The positive relation with lagged earnings is labeled the loss effect because it appears to be due to a negative relation between scale and the probability and magnitude of losses.7 The negative relation with return variance is labeled the return variance effect. While PT use price per share to illustrate the role of scale, they confirm that similar relations exist for other measures of scale. BKN dispute the role of scale, and suggest instead that PT’s lagged earnings results can be explained by a non-linear relation between expectations formed last year of earnings and returns for this year (Et-1[Xt] and Et-1[Rt]). In effect, whereas BKN believe the asymmetric relation between lagged earnings and returns is because of a non-linear relation between lagged earnings and the first moment of returns, PT believe the asymmetric relation arises because scale links lagged earnings to the variance or second moment of returns. While BKN offer the nonlinear relation as a general explanation, they offer an unrelated, second explanation based on time-series variation in abnormal return variances to explain PT’s time-series results. We show first in Section 3.1 why BKN’s explanation based on the non-linear relation between expected returns and earnings is not supported by the evidence. Next we show in Section 3.2 that PT’s time-series results are inconsistent with BKN’s second explanation, but consistent with time-series variation in PT’s scale effects. Finally, we show in Section 3.3 why the BKN analysis investigating whether scale is an omitted variable is biased against observing a scale effect, and how mitigating that bias reveals evidence of scale effects.

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That is, while the probability of observing positive earnings is positively related to scale, the magnitude of positive earnings is not. Also, PT document that this relation between scale and lagged earnings is a general one, because the same relation is also observed for current earnings and twice lagged earnings.

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3.1 Reexamination of BKN’s explanation for PT’s lagged earnings result BKN only provide tangential support for their claim that PT’s lagged earnings result can be explained by a non-linear relation between expected returns and expected earnings. The support they offer is a V-shaped relation between current E/P ratios and next period’s returns, described in their Figure 1B. While that relation is non-linear, it differs from the non-linearity underlying PT’s lagged earnings result: BKN highlight how the lagged-earnings/returns relation varies across earnings levels, whereas PT’s result describe how that relation varies across levels of returns. BKN do not test the validity of their explanation by considering unexpected earnings and unexpected abnormal returns in equation (1C), where expectations for earnings and returns are derived from empirical regularities shown or prediction models developed by BKN. To be more specific, BKN do incorporate earnings expectations from three different models, but they do not consider expectations for returns based on their Figure 1 B. We conduct a direct test of the BKN explanation by incorporating the non-linear relation between expected returns and expected returns implied by the non-linear relation between returns and lagged earnings (deflated by lagged price) provided in Figure 1B of BKN. Prior research (e.g., Desai et al. 2004) has shown that the two arms of the V-shaped relation meet near the point where lagged earnings is 0. If so, one convenient way to represent that non-linear relation is a regression of returns on lagged earnings estimated separately for positive and negative lagged earnings, as shown below in equation (4). The sign of lagged earnings is represented by the term LLDit-1, or lagged loss dummy, which takes on the value of 1(0) when lagged earnings is negative (positive). (4) 12

The error term (eit) from equation (4) is our proxy for unexpected returns or residual abnormal returns after controlling for the non-linear relation described in BKN’s Figure 1B. If this non-linear relation plays a role in explaining PT’s lagged earnings result, we expect to see two patterns. First, estimates of b1 from equation (4) for each year should co-move with estimates of β1 from equation (1C) estimated for lagged earnings. Differences across negative and positive earnings in regression of abnormal return on lagged earnings should be reflected in differences across positive and negative abnormal returns in regressions of lagged earnings on abnormal returns. Second, estimates of β1 from equation (1C) based on regressions of lagged earnings on residual abnormal returns should decline to zero and be unrelated to corresponding estimates of β1 derived from regressions of lagged earnings on abnormal returns. Evidence contradicting these two predictions from the BKN explanation based on a nonlinear relation between expected returns and expected earnings is reported in Panels A and B, respectively, of Figure 1. Time-series variation in estimates of b1 from equation (4), the dotted line in Panel A, appears unrelated to that for estimates of β1 from equation (1C) based on lagged earnings. And magnitudes of estimates of β1 based on residual abnormal returns, the dotted line in Panel B, are approximately the same as those for abnormal returns, not zero as implied by BKN’s explanation, and the two series show considerable covariation. To review, whereas BKN do not directly investigate their explanation for PT’s lagged earnings result, we investigate the non-linear relation underlying BKN’s explanation and find evidence contradicting their explanation. 3.2. Reexamination of BKN’s alternative explanation for PT’s time-series results Perhaps the strongest evidence provided by PT in support of the return variance and loss effects underlying their explanation is the time-series analysis described in Section VI of that 13

paper. There is remarkable comovement between the extent of bias in the Basu measure, indicated by the magnitude of β1 for lagged earnings, and the magnitude of the return variance effect. Also, while the return variance effect is necessary for the PT bias, it is not sufficient; PT show that the return variance effect has little impact when the loss effect is weak. Rather than investigate whether time-series variation in β1 for lagged earnings can be explained by time-series variation in the non-linear relation underlying their explanation, BKN offer a different explanation for PT’s time-series results. They claim that time-series covariation documented in PT between estimates of the return variance effect and β1 for lagged earnings— from equations (4) and (1C), respectively—is mechanically induced because the variance of the regressor, ARit, is common to both estimates. In essence, time-series covariation in the two sets of estimates is due not to corresponding variation in the numerator of the ratio representing the slopes (covariance of the dependent variable and the regressor) but due entirely to variation in the denominator (variance of the regressor). At first, this explanation seems odd since the variance of the regressor in a traditional ordinary least squares regression framework should not affect the estimated slope.8 BKN contend, however, that in this particular case “some time-series variation” in the variance of the regressor is unrelated to the dependent variable because it is “due to changes in macroeconomic conditions, cross-sectional variation in expected returns, or the presence of growth opportunities.” According to the BKN explanation, the slopes for good news (β0) and bad news (β0+β1) equation (1C) regressions of earnings on abnormal returns are biased toward zero during periods

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When the regressor is exogenous, sampling from a narrow or wide range of regressor values should not affect the slope estimate in a properly specified OLS regression.

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when the corresponding variance of returns is high due to factors unrelated to earnings.9 As a result, the differential timeliness estimate (β1) is also biased toward zero during such periods. The same mechanical bias will be noted in slopes for equation (1C) regressions based on lagged earnings and the inverse of lagged price (the return variance effect). A simple test of their explanation is to plot time-series variation in the estimated slopes as well as the corresponding numerators and denominators used to estimate those slopes. Given that much of the time-series variation in the differential timeliness measure is due to variation in the timeliness slope associated with bad news observations, we focus here on the bad news slope and its numerator and denominator. Also, given our interest in the lagged earnings regression, we restrict our analysis below to the slopes associated with that dependent variable. The results reported in Figure 2, Panel A plot time-series variation in the estimated slope for bad news firm-years (β0+β1) and the numerator, covariance between abnormal returns and price-deflated lagged earnings (Cov(ARt,Xt-1/Pt-1)). The results reported in Figure 2, Panel B describe time-series variation in β0+β1 and the denominator, variance of abnormal returns. To maintain consistency with the BKN analysis we use the inverse of the standard deviation (1/Std. dev. (ARt)) to describe variation in the denominator. Based on BKN’s explanation for PT’s timeseries results, the bad news slopes should co-move with the denominator in Panel B but be unrelated to the numerator in Panel A. The results in Figure 2 contradict both predictions. There is considerable comovement between the bad news slope and the numerator in Panel A, and there is little indication of comovement between the bad news slope and the denominator in Panel B. In fact, the two series in Panel B appear to be negatively related during the early years in the sample period. 9

Including return components to the regressor that are unrelated to the dependent variable effectively creates measurement error in the regressor which results in slope estimates that are biased toward zero.

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Rather than consider both the numerator and denominator effects, BKN focus only on the denominator effect. Their plot for the bad news subsample, reported in their Figure 2, Panel B, mirrors the corresponding plot we constructed for our sample in our Figure 2, Panel B. And yet they conclude that “It is clear from the graph that the inverse standard deviations also exhibit pronounced co-movement with the regression model slope coefficients.” Again, we see very little comovement between the two series in the BKN plots, and the two series are clearly moving in opposite directions early in their sample period: the inverse of standard deviation series declines from about 10 in the mid 1960’s to about 5 in the mid 1980’s whereas their estimates of β0+β1 increase from 0 to about 0.2. While the evidence reported here and in BKN contradicts BKN’s alternative explanation for PT’s time-series results, PT’s explanation is supported strongly by the evidence reported in PT. The results reported in Panel B of Figure 5 in PT suggest considerable comovement between estimates of the return variance effect and β0+β1. More important, that covariation is dampened when the loss effect is small, between 1963 and 1975, as predicted by PT. 3.3 Reexamination of BKN evidence against scale as an explanation for PT’s lagged earnings results We consider finally the evidence described in Section 4.3 and Figure 3 of BKN, which investigates regressions based on equation (1C), for both current and lagged earnings, estimated separately across 50 partitions based on price per share. That evidence appears to show that while the loss and return variance effects are almost zero in each of the 50 partitions, the estimate of β1 is clearly positive for both the current and lagged earnings specifications. Observing spurious evidence of conditional conservatism, indicated by the positive value of β1 for lagged

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earnings, even when the loss and return variance effects are suppressed suggests that those two effects are unrelated to PT’s lagged earnings result. BKN’s conclusion that the PT explanation is invalid relies critically on their methodology suppressing the return variance and loss effects within their price partitions. We provide three reasons why that is not the case. First, at a conceptual level the return variance and loss effects should not be diminished by forming partitions based on price. As described in Panel A (B) of Figure 1 in PT, mean values of price-deflated lagged earnings (return variance) increase with (decline with) price per share. Given that share price is the exogenous regressor for both effects, estimates of the slope in a properly specified OLS regression should not be affected by the range over which the regressor is sampled from.10 Second, the specifications used by BKN will, however, result in estimates of the two effects that are biased severely toward zero, because the dependent variables in those specifications is price per share, which is the same variable used to form partitions. Third, when using the BKN specification on alternative measures of scale, rather than share price, we find evidence of both effects remaining quite strong in the price partitions. While PT use price per share to illustrate the scale effect, they show that the return variance and loss effects are also related to other measures of scale. The regressions used in BKN to estimate the loss and return variance effects are as follows: (5) (6)

10

See Section 3.2 and footnote 7 for the same point in a different context.

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Because the partitions are effectively based on the inverse of lagged share price (Pit-1), which is the dependent variable in both regressions, the slope estimates—β0 and β1 in equation (5) and γ1 in equation (6)—are biased toward zero. And because BKN use 50 partitions, the bias is so severe that the estimates are approximately zero. Figure 3 illustrates the extent of bias for 50 partitions using the dependent variable (Y) in simulated data that is derived for the case where the true slope is 1. Because variation in the dependent variable is limited to lie within a very narrow range for each partition, the slope is almost 0.11 Accordingly, it is not surprising that BKN find zero slopes for β1 and γ1 in equations (5) and (6), respectively. But because those estimates are biased toward zero, BKN should not conclude that the return variance and loss effects have been removed within each partition. To illustrate our third reason to doubt BKN’s conclusion about the irrelevance of loss and return variance effects, we repeat the regressions described by equations (5) and (6) by replacing price per share with two other measures of scale: book value of equity per share and total assets per share. As in BKN, the partitions are based on share price. To keep matters simple, we form 10 portfolios, based on deciles of price per share, rather than 50 portfolios.12 The results reported in Panel A of Figure 4 show that the return variance effect, indicated by the incremental slope on bad news (β1 from equation (5)), is not removed within the price per share partitions. Estimates of β1 for the other two scale variables are clearly non-zero. The estimates based on book value per share are larger in magnitude than those for total assets per share. Also, magnitudes for both sets of estimates decline with share price as noted in PT and other prior research. As expected, estimates of β1 based on price per share remain close to zero,

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The two extreme partitions which are open at one end are associated with more variation which increases slightly the estimated slopes. We confirm that similar results are observed for 50 partitions.

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as in BKN, because of the severe bias toward zero caused by using price partitions when the dependent variable is also price. The results reported in Panel B of Figure 4 confirm that the loss effect, indicated by the slope on lagged earnings (γ1 from equation (6)), is not removed by forming price per share partitions. Whereas the estimates of γ1 for price per share are biased toward zero, the corresponding estimates for book value of equity per share and total assets per share are clearly negative for all price deciles. Unlike the results in Panel A, which indicated that the return variance effect was greater for low price deciles, the loss effect remains constant across price deciles when scale is measured by book value of equity per share, whereas it increases with price when scale is measured by total assets per share. The overall bias for the Basu measure based on regressions of lagged earnings is an interaction of the return variance and loss effects. As that overall effect indicates that the bias is greater for low price firms, we infer that the impact of the return variance effect dominates the interaction. In sum, the results in Section 3.3 suggest that the BKN analysis based on price partitions should not be viewed as contradicting PT’s explanation for their lagged earnings result, which posits that scale is an omitted variable. Even though there is very little variation in price within those partitions, the return variance and loss effects remain within each partition. Given that those effects remain, it is not surprising that lagged earnings continues to be associated with spurious evidence of conditional conservatism within the narrow price partitions. 4. CONCLUDING REMARKS PT renew the call in prior research to avoid the Basu measure and reevaluate prior results based on the Basu measure (e.g., evidence of cross-sectional and time-series variation). They also recommend that future research avoid using the Basu measure even if the bias they 19

document is adjusted for, because of the other sources of bias mentioned in Dietrich et al. (2007) and Givoly et al. (2007). BKN believe PT’s position is excessively alarmist, because they find that a) spurious evidence of differential timeliness in lagged earnings is easily eliminated and b) the prior results continue to hold for the revised measures they propose. The evidence presented here suggests that BKN are excessively optimistic about the reliability of their revised measure of conditional conservatism. We show here that there is indeed some residual bias in the revised BKN measure of conditional conservatism, which renders that measure unreliable. But we caution that the methodology we use is not comprehensive and does not identify all possible biases associated with the revised BKN measure. A serious effort to address each of the sources of bias discussed in the literature will increase confidence in the reliability of the measure of conditional conservatism that emerges. The second claim in BKN is that the PT bias is not due to the explanation provided in PT but due to a non-linear relation between expected returns and expected earnings. This claim is of less import than the first claim, because the recommendations made by PT are not contingent on the validity of their explanation. Nevertheless, our evidence contradicts this second claim too. We find that BKN’s investigation of the PT explanation is biased against finding support for that explanation. Correcting for that bias reveals evidence consistent with the PT explanation. Our investigation of BKN’s explanation provides evidence inconsistent with that explanation. Also, an alternative explanation provided by BKN for time-series covariation between estimates of conditional conservatism and estimates of the return variance and loss effects is not supported by the evidence. We believe this time-series covariation is the strongest evidence in support of the PT explanation for why the Basu measure indicates spurious evidence of conditional conservatism for lagged earnings.

20

Table 1: Annual regressions of unexpected earnings on actual and simulated returns This table provides results of annual regressions of different variables (V) on abnormal returns (ARit): V=α0+α1Dit+ β0ARit+β1ARit*Dit+εit, based on data from Patatoukas and Thomas (2011). The variables considered are: a) the level of earnings (Xit) which is the measure used in Basu (1997), b) lagged earnings (Xit-1), c) inverse of lagged price per share (1/Pit-1), d) the first difference in earnings (Xit−Xit-1), e) unexpected earnings based on introducing firm fixed effects to the Basu model, which effectively subtracts the time-series mean of Xit/Pit-1 for firm i from each Xit/Pit-1, and f) unexpected earnings based on equation (2) regressions of Xit/Pit-1 on Xit-1/Pit-1 within 2digit SIC industry codes. The last three values are proxies for unexpected earnings proposed in Ball et al. (2011) The variables used are derived from the following variables (described for firm i in year t). Xit is earnings per share before extraordinary items, Pit is price per share at the fiscal year-end, and Rit is the return from the beginning of the fourth month of the current fiscal year to the end of the third month of the next fiscal year. ARit equals Rit minus Rmt, where Rmt is the return for the CRSP equally-weighted market index over the 12 month period corresponding to Rit.. Dit =1 when ARit is < 0, and =0 otherwise, representing bad and good news, respectively. The results in Panel A are based on actual returns, and the first three rows have been reported in Patatoukas and Thomas (2011). The results in Panel B are based on simulated values of ARit computed as follows. We first estimate the regression ARit=δ0+δ1V+τit in each year to get estimates of the slope (δ0) and intercept (δ1) for each measure V. Next, we estimate a predicted value of ARit for firm i in year t, based on V and estimates of δ0 and δ1, and then compute a simulated abnormal return by adding a randomly selected (without replacement) error term of firm k during year t (τkt). The simulated return for firm i in year t will reflect the average relation with V, but will not reflect any differential relation between V and ARit across good and bad news firms (based on simulated returns being positive and negative, respectively). The estimates of β1 in Panel B will be zero (positive) if the bias predicted by Dietrich et al. (2007) is absent (present). Observing positive estimates of β1 in the bottom three rows suggests that the measures of conditional conservatism proposed in Ball et al. (2011) contain the bias predicted in Dietrich et al. (2007).

Panel A: Regressions based on actual returns.

β0

Variable (V) Xit/Pit-1 Xit-1/Pit-1 1/Pit-1

β1

Coefficient

0.019

0.185

t-statistic

3.20***

15.33***

Coefficient

-0.035

0.116

t-statistic

-8.22***

12.66***

0.073

-0.160

10.89***

-11.14***

0.054

0.069

10.16***

9,79***

Coefficient t-statistic

(Xit− Xit-1)/Pit-1

Coefficient

Xit/Pit-1 − Effe[Xit/Pit-1]

Coefficient

0.039

0.058

t-statistic

8.16***

7.49***

Xit/Pit-1 − Eind[Xit/Pit-1]

Coefficient

0.040

0.104

t-statistic

8.08***

12.08***

t-statistic

21

Panel B: Regressions based on simulated returns. Mean Estimates (across 100 trials)

Variable (V)

β0

β1

Coefficient

0.013

0.233

t-statistic

118.81***

1087.25***

Coefficient

0.003

0.024

t-statistic

21.70***

77.83***

Coefficient

0.002

0.003

t-statistic

10.82***

9.41***

(Xit− Xit-1)/Pit-1

Coefficient

0.047

0.082

t-statistic

288.24***

336.33***

Xit/Pit-1 − Effe[Xit/Pit-1]

Coefficient

0.016

0.125

t-statistic

119.26***

585.39***

Xit/Pit-1 − Eind[Xit/Pit-1]

Coefficient

0.021

0.170

t-statistic

195.18***

810.76***

Xit/Pit-1 Xit-1/Pit-1 1/Pit-1

22

Adj. R2 from regression of ARit on V 10% 1% 2% 8% 7% 10%

Figure 1. Asymmetric relation between lagged earnings and unexpected returns, adjusted for the non-linear relation between lagged earnings and expected returns. Ball, Kothari, and Nikolaev (2011) claim that the spurious evidence of conditional conservatism observed in Patatoukas and Thomas (2011) for lagged earnings is due to a non-linear relation between expected earnings and expected returns. Based on the non-linear relation in Figure 1B in Ball, Kothari, and Nikolaev (2011), we estimate residual abnormal returns (Residual ARit) as the residual from the following regression of abnormal returns (ARit) on lagged earnings, deflated by lagged price, estimated separately for positive and negative lagged earnings (indicated by values of LLDit-1 equal to 0 and 1, respectively): ARit= a0 + a1LLDit-1 + b0Xit-1/Pit-1 + b1Xit-1/Pit-1*LLDit-1 + eit. We then estimate differential timeliness (β1) based on regressing lagged earnings on residual abnormal returns, separately for positive and negative residual abnormal returns as follows. Xit-1/Pit-1 = α0+α1Dit+ β0*eit+β1*eit*Dit+εit. In Panels A and B below, we compare estimates of b1 and β1, respectively, with estimates of β1 from regressions of lagged earnings on abnormal (market-adjusted) returns, rather than residual abnormal returns (see Patatoukas and Thomas, 2011). If the claim in Ball, Kothari, and Nikolaev (2011) holds, we expect to see in Panel A covariation between estimates of b1 and estimates of β1 from regressions of lagged earnings on abnormal returns. In Panel B, however, we expect to see no variation in estimates of β1 from regressions of lagged earnings on residual abnormal returns. Variables are defined as follows (described for firm i in year t). Xit is earnings per share before extraordinary items, Pit is price per share at the fiscal year-end, and Rit is the return from the beginning of the fourth month of the current fiscal year to the end of the third month of the next fiscal year. ARit equals Rit minus Rmt, where Rmt is the return for the CRSP equally-weighted market index over the 12 month period corresponding to Rit.. Dit =1 when ARit is < 0, and =0 otherwise, representing bad and good news, respectively. When the regressor is unexpected returns (URit), Dit =1 when URit is < 0, and =0 otherwise, representing bad and good news, respectively.

Panel A: Time-series variation in estimates of the differential lagged earnings/returns relation between positive and negative lagged earnings (b1) and the differential lagged earnings/returns relation between positive and negative abnormal returns (β1) 3

0.3

b1 for ARt on Xt‐1/ Pt‐1

2

0.3

1 0

0.2

‐1 ‐2

0.2

‐3 0.1

‐4 ‐5

0.1

β1 for  Xt‐1/ Pt‐1 on ARt

‐6

0.0

23

2005

2003

2001

1999

1997

1995

1993

1991

1989

1987

1985

1983

1981

1979

1977

1975

1973

1971

1969

1967

1965

1963

‐7

Panel B: Time-series variation in estimates of the differential lagged earnings/returns relation (β1) between positive and negative abnormal returns, based on abnormal returns and residual abnormal returns. 0.450

β1 for Xt‐1/ Pt‐1 & residual ARt‐1

0.400 0.350 0.300 0.250

β1 for  Xt‐1/ Pt‐1 &  ARt‐1

0.200 0.150 0.100 0.050

24

2005

2003

2001

1999

1997

1995

1993

1991

1989

1987

1985

1983

1981

1979

1977

1975

1973

1971

1969

1967

1965

‐0.050

1963

0.000

Figure 2. Time-series variation in the estimated timeliness for bad news subsample. Ball, Kothari, and Nikolaev (2011) claim that time-series variation in estimates of differential timeliness for lagged earnings observed in Patatoukas and Thomas (2011) is due to time-series variation in the standard deviation of abnormal returns, rather than variation in the return variance and loss effects. The plots below describe year-by-year variation in Cov(ARt,Xt-1/Pt-1) and 1/Std. dev. (ARt) in Panels A and B, respectively. These two variables represent the numerator and denominator of the timeliness estimate (β0+β1) for the bad news subsample (indicated by negative abnormal returns), based on regressing lagged earnings on abnormal returns, separately for positive and negative residual abnormal returns as follows. Xit-1/Pit-1 = α0+α1Dit+ β0*ARit+β1*ARit*Dit+εit. Variables are defined as follows (described for firm i in year t). Xit is earnings per share before extraordinary items, Pit is price per share at the fiscal year-end, and Rit is the return from the beginning of the fourth month of the current fiscal year to the end of the third month of the next fiscal year. ARit equals Rit minus Rmt, where Rmt is the return for the CRSP equally-weighted market index over the 12 month period corresponding to Rit.. Dit =1 when ARit is < 0, and =0 otherwise, representing bad and good news, respectively. If the claim in Ball, Kothari, and Nikolaev (2011) holds, we expect to see estimates of β0+β1 to not vary with Cov (ARt,Xt-1/Pt-1) in Panel A, but vary positively with 1/Std. dev. (ARt) in Panel B.

Panel A: Time-series variation in Cov(ARt,Xt-1/Pt-1) and the timeliness estimate (β0+β1) for the bad news subsample. 0.20

0.008 0.007 0.006

0.15

β0+β1 for Xt‐1/Pt‐1

0.005 0.004

0.10

0.003 0.002

0.05

0.001

Cov (ARt,Xt‐1/Pt‐1) 0.000

‐0.05

for bad news subsample (ARt < 0)

25

2005

2003

2001

1999

1997

1995

1993

1991

1989

1987

1985

1983

1981

1979

1977

1975

1973

1971

1969

1967

1965

1963

0.00

‐0.001 ‐0.002

Panel B: Time-series variation in 1/Std. dev. (ARt) and the timeliness estimate (β0+β1) for the bad news subsample. 0.20

10

1/Std. Dev (ARt)

9

0.15

8 7

0.10

6 5

0.05

4 3

β0+β1 for Xt‐1/Pt‐1 2005

2003

2001

1999

1997

1995

1993

1991

1989

1987

1985

1983

1981

1979

1977

1975

1973

1971

1969

1967

1965

2 1963

0.00

1

for bad news subsample (ARt < 0) 0

‐0.05

26

Figure 3. Bias in slope estimate induced by partitioning along dependent variable Below is a plot of the mean estimated slope coefficient (b) based on simulated data, designed to show that the estimate is very close to zero for 50 partitions based on the dependent variable (Y). The data are simulated to generate values of Y from the regression Y = a + b*X + e, where a, and b equal 1, and X and e are sampled from Normal distributions with unit variance and means of 1 and 0, respectively. The coefficients a and b are estimated for each trial from a simulated sample of 100,000 observations and the process is repeated for 1,000 trials. 1.20 1.00 0.80 0.60 Estimated Slope 0.40

Actual Slope

0.20 0.00

27

49

47

45

43

41

39

37

35

33

31

29

27

25

23

21

19

15

13

11

9

7

5

3

1

17

Partitions based on Y

‐0.20

Figure 4. Impact of variation in alternative measures of scale within share price partitions The plots below consider the impact of using alternative measures of scale to determine whether the return variance and loss effects described in Patatoukas and Thomas (2011) are observed within partitions based on share price. As price is used to form partitions as well as be the dependent variables in equations (5) and (6) designed to determine the magnitude of return variance and loss effects, respectively, estimates of the slopes β1 and γ1 from those two regressions will be biased toward zero (see Figure 3). However, replacing price per share with other measures of scale should reduce that bias. Panel A is a plot of the mean estimated slope coefficient for bad news (β1), for regressions designed to identify the return variance effect. The inverse of three lagged scale variables (1/Sit-1) is regressed on abnormal returns (ARit), with separate slopes allowed for positive and negative returns as follows. 1/Sit-1 t=α0+α1Dit+ β0ARit+β1ARit*Dit+εit. The three lagged scale variables are price per share (Pit-1), total assets per share (TAit-1), and book value of equity per share (BEit-1). A similar analysis is conducted for the loss effect based on the regression 1/Sit-1 t=γ0+γ1Xit-1/Pit-1+ωit. Panel B is a plot of the mean estimated slope coefficients (γ1). Variables are defined as follows (described for firm i in year t). Xit is earnings per share before extraordinary items, Pit is price per share at the fiscal year-end, and Rit is the return from the beginning of the fourth month of the current fiscal year to the end of the third month of the next fiscal year. ARit equals Rit minus Rmt, where Rmt is the return for the CRSP equally-weighted market index over the 12 month period corresponding to Rit.. Dit =1 when ARit is < 0, and =0 otherwise, representing bad and good news, respectively.

Panel A: Return variance effect across price deciles based on alternative measures of scale. β1 for 1/Pt‐1

0.1 0.0 ‐0.1 ‐0.2

β1 for 1/TAt‐1

‐0.3

β1 for 1/BEt‐1

‐0.4 ‐0.5

Deciles of Pt‐1

‐0.6 1

2

3

4

5

6

28

7

8

9

10

Panel B: Loss effect across price deciles based on alternative measures of scale. γ1 for 1/Pt‐1

0.1

Deciles of Pt‐1

0.0 ‐0.1

1

2

3

4

5

6

7

8

9

10

‐0.2

γ1 for 1/TAt‐1

‐0.3 ‐0.4 ‐0.5 ‐0.6

γ1 for 1/BEt‐1

‐0.7 ‐0.8

29

REFERENCES Ball, R., and Brown, P., 1968. An empirical evaluation of accounting income numbers, Journal of Accounting Research 6, 159-177. Ball, R., S.P. Kothari, and V.A. Nikolaev, 2011. On estimating conditional conservatism. Working paper, University of Chicago. Ball, R., S.P. Kothari, and V.A. Nikolaev, 2010. Econometrics of the Basu asymmetric timeliness coefficient and accounting conservatism. Working paper, University of Chicago. Ball, R., Shivakumar, L., 2008. How much new information is there in earnings? Journal of Accounting Research 46, 975-1016. Basu, S., 1997. The conservatism principle and the asymmetric timeliness of earnings. Journal of Accounting and Economics 24, 3-37. Biddle, G.C., M. L. Z. Ma, and F. M. Song, 2011. Accounting Conservatism and Bankruptcy Risk. Working paper, University of Hong Kong. Callen, J. L., Chen, F., Dou, Y. and Xin, B., 2010. Information Asymmetry and the Debt Contracting Demand for Accounting Conservatism. Working paper, University of Toronto. Desai, H., S. Rajgopal, and M. Venkatachalam, 2004. Value-glamour and accruals mispricing: One anomaly or two? The Accounting Review 79, 355-386. Dietrich, D., K. Muller, and E. Riedl. 2007. Asymmetric timeliness tests of accounting conservatism. Review of Accounting Studies 12, 95-124. Easton, P. D., 1998. Discussion of revalued financial, tangible, and intangible assets: Association with share prices and non-market-based value estimates. Journal of Accounting Research, 36, 235–247. Givoly, D., C. Hayn, and A. Natarajan, 2007. Measuring reporting conservatism. The Accounting Review 82, 65-106. Khan, M., and R. Watts. 2009. Estimation and empirical properties of a firm-year measure of accounting conservatism. Journal of Accounting and Economics 48, 132-150. Lobo, G.J., K. Parthasarathy, and S. Sivaramakrishnan. 2008. Growth, managerial reporting behavior, and accounting conservatism. Working paper, University of Houston. Patatoukas, P.N., and J. K. Thomas, 2011. More evidence of bias in differential timeliness estimates of conditional conservatism. The Accounting Review, Forthcoming. Zhang, J., 2008. The Contracting Benefits of Accounting Conservatism to Lenders and Borrowers. Journal of Accounting and Economics 45, 27–54.

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