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On the validity of asymmetric timeliness measures of accounting conservatism

Abstract

This study extends the asymmetric timeliness measure (ATM) framework described in Ball et al. (Journal of Accounting Research 51(5): 1071–1097, 2013a) to investigate the validity of tests for differences in conservative accounting practices across firms and time. This extension is important because that framework is not designed to measure or test for differences in conservatism, which is the explicit focus of nearly all conservatism research. This extension identifies three structural biases (which we refer to as the misclassification, contemporaneous income, and growth biases) inherent in the Basu (Journal of Accounting and Economics 24(1): 3–37, 1997) ATM. We show that correcting for the contemporaneous income bias results in a substantial reduction in ATM estimates. Additionally, the estimated magnitude of the contemporaneous income bias is so large that the typically reported significantly positive relationship between conservatism and leverage and the negative relationship between conservatism and size become insignificant after correcting the traditional ATM to control for this bias. Also, the positive relationship between conservatism and book-to-market ratio is attenuated significantly. Developing empirical controls for the misclassification and growth biases identified in our framework is problematic, but one or both are expected to be sufficiently large as to raise significant concerns about results of conservatism studies that rely on the ATM. Until methods to control for or eliminate all sources of bias are established, we suggest that future research use ATMs that focus only on conditionally conservative accruals or on alternative measures of conditional conservatism.

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Notes

  1. The BKN framework also includes a variable for accounting income noise.

  2. The good news and bad news labels are intended to distinguish between the accounting treatment for transactions subject to conservative accounting. In application, they are determined by the sign of returns.

  3. Research that examines the “one-regime setting” implicit in Basu (1997) and Ball et al. (2013a), finds that the ATM measure suffers from econometric problems, such as return endogeneity and sample truncation bias. Of particular interest, relying on the assumption that information (that may be unobservable to the researcher) has a causal relationship with returns and with earnings, Dietrich et al. (2007) shows that, except under very restrictive conditions, the asymmetric timeliness measure is biased because returns constitutes an endogenous variable in the earnings-returns relationship. Dietrich et al. (2007) also demonstrates that bad news and good news coefficients are affected by sample selection bias because an endogenous variable—stock returns—is used to form subsamples.

  4. For example, prior research uses ATM differences to evaluate differences in conservatism across firm characteristics (e.g., Khan and Watts 2009; Ramalingegowda & Yu 2012), across time (e.g., Givoly & Hayn 2000; Holthausen & Watts 2001; Sivakumar & Waymire 2003), and across countries (e.g., Pope & Walker 1999; Ball et al. 2000; Ball et al. 2003; Bushman & Piotroski2006). Other studies using the ATM in a two-regime setting examine: cost of equity (Francis et al. 2004; Lara et al. 2011), the information content of accounting numbers (Ryan & Zarowin, 2003), and the market-to-book ratio (Roychowdhury & Watts, 2007). In addition, studies use the ATM to assess the impact of conservatism on corporate actions, such as capital raising (Kim et al. 2013), acquisitions (Kravet, 2014), debt characteristics (Nikolaev, 2010), internal controls (Goh & Li, 2011), and earnings restatements (Ettredge et al. 2012). All of these studies implicitly incorporate a two-regime setting. For reviews of related research, see Watts (2003a), Watts (2003b), and Wang et al. (2009).

  5. Callen and Segal (2013) uses a different theoretical foundation to provide an alternative approach to estimate ATMs to test for differences in conditionally conservatism accounting across firms. This approach is unaffected by the structural biases that are the focus of this study and is discussed later in our analyses.

  6. Research typically finds R2s between earnings and returns of less than 20 percent.

  7. Other studies provide alternative explanations why ATMs could provide a false-positive result and raise concerns regarding the inferences of empirical tests of asymmetric timeliness. For instance, Dutta and Patatoukas (2017) demonstrates that positive ATMs can arise due to differences in expected returns and cash flow persistence. Also, Breuer and Windisch (2017) demonstrates that positive ATMs can arise due to short-run adjustment frictions and long-run investment behavior under uncertainty.

  8. Some studies use total returns and earnings. Ball et al. (2013a) and other studies use unexpected returns and unexpected earnings to remove effects that otherwise may induce bias in estimates of the earnings/return relationship. We sometimes omit “unexpected” or include it in parentheses to ease readability or to indicate that the statement applies to both measures.

  9. For example, consider two start-up firms that purchased assets with identical fair values at the start of the year. Firm A’s asset is accounted for using GAAP as applied to inventory using lower-of-cost-or-market; firm B’s asset is accounted for using GAAP as applied to an acquired brand. Assume further that, at the end of the year, the fair value of each asset declined by 10 percent, relative to the acquisition price. Because of differences in impairment accounting under GAAP, firm A is more likely to record an impairment loss than firm B.

  10. Basu (1997) provides intuition for accounting conservatism, but does not formally develop an empirical specification.

  11. See Appendix B for econometric proofs and intuition.

  12. Ball et al. (2013a) claims that, “under the null hypothesis of no conditional conservatism, the Basu coefficient is zero” (p. 1083). This “no conservatism” case is invoked through the condition that ωit = 0. In the generalized model that we consider, depicted in Eq. (12), this implies that p(y)ityit < cit = p(y)ityitcit = p(R)itRit < 0 = p(R)itRit ≥ 0 = 0. Notice that this condition is rather uninteresting as it eliminates yit, as those transactions then behave exactly as git transactions. We do not consider this case in detail as the hypothesis being tested in empirical research is not whether yit exists but rather whether symmetric recognition of yit exists under some non-zero recognition rule that leads to p(y)ityit < cit = p(y)ityitcit. In any event, the application of this extreme characterization results in ATM bias of \(\left [\frac {\sigma _{R,x}}{{\sigma _{R}^{2}}}\mid R_{it}<0\right ]-\left [\frac {\sigma _{R,x}}{{\sigma _{R}^{2}}}\mid R_{it}\geq 0\right ]\). Under this simplification and the generalized BKN framework, incorrect inferences can arise in empirical studies examining subsample differences in ATMs unless Condition #2 below is satisfied. In the Ball et al. (2013a) one-regime setting, this ATM bias is ruled out by further invoking a linearity assumption (discussed in more detail below) that makes the distributions and covariances of returns and its components equal across the bad and good news subsamples. In empirical work, this assumption will rarely, if ever, be satisfied. For instance, prior empirical studies demonstrate that the (truncated) variances of returns differ by a factor of ten across the two subsamples of returns greater than zero versus returns less than zero. Further, under the null hypothesis that p(y)ityit < 0 = p(y)ityit ≥ 0, only the assumption that p(y)it = ωit = 0 will lead the ATM bias to be zero. Other conditions will lead to non-zero and, more importantly, generally unpredictable bias.

  13. Misclassification bias also leads to other properly measured explanatory variables correlated with the misclassified dichotomous variable to be biased (i.e., Tennekoon & Rosenman2019).

  14. Notice that the relative importance of yit does not necessarily arise from accounting standards or managers being more or less conservative. The variation in yit across firms and time may also arise from changes in underlying macroeconomic, industry, and firm conditions. In addition, the variation in yit across firms and time may arise from the types of assets firms hold—e.g., gains and losses on the value of goodwill can only arise for firms that have undertaken acquisitions involving goodwill. Tests focused on changes in the application of conservative accounting rules, whether voluntary or mandatory (i.e., differences in cit across firms or time), will also be affected by changes in macroeconomic, industry, and firm conditions that do not arise from changes in conservative accounting rules. Whether this distinction poses a limitation in interpreting the ATM depends on the research question.

  15. Unlike our depiction, Ball et al. (2013a) suggests that variation in the components leads to interesting variation in empirical estimates of ATMs. For instance, Ball et al. (2013a) shows evidence that the “Basu asymmetric timeliness coefficient declines in the variance of growth options” (p. 1085). As Eq. (12) demonstrates, assuming that such variation is intended to be captured in empirical tests using the ATM, such evidence will obtain only under the extreme conditions that p(R)itRit < 0 = p(y)ityit < cit = 1 and p(R)itRit≥ 0 = p(y)ityitcit = 0 for all firms and time. For reasons discussed above, typical empirical settings would be highly unlikely to satisfy these conditions.

  16. Such a position would be inconsistent with the goal of ATMs capturing mandatory or voluntary differences in verifiability thresholds of losses relative to gains—the focus of prior conservatism research (e.g., Dyreng et al. 2017).

  17. See Appendix B for the derivation of the endogeneity bias, which arises from the use of Rit to estimate ATM coefficients.

  18. On Compustat, special items include unusual and nonrecurring items, including impairments, inventory write-downs when reported, litigation reserves, asset write-downs, receivable write-downs, bad debt expenses, provision for doubtful accounts, and other types of write-downs. Accordingly, OIBDP likely includes relatively few amounts that would be considered part of yit.

  19. Property impairments of oil and gas firms are included in cost of goods sold and are therefore included in OIBDP. In untabulated sensitivity tests, our later inferences are unchanged if we exclude firms from the oil and gas industry.

  20. OIBDP also may include the effect of transactions subject to accounting conservatism for which yit− 1 > cit− 1; however, the effect of these amounts is analogous to git− 1.

  21. As described in greater detail below, OtherIncome also might include a portion of xit.

  22. Evidence in Lawrence et al. (2013), however, indicates that leverage becomes insignificant if BMit− 1 rather than BMit, which has been used in prior research, is included as a control.

  23. For brevity, we do not show the regression specifications with the ATM interacted with BMit− 1, Leverageit− 1, and Sizeit− 1.

  24. The coefficients estimated using OIBDP and OtherIncome are not statistically significantly different.

  25. Conversely, income taxes may include the effect of xit to the extent that income taxes are based on amounts reported in OIBDP.

  26. Due to the inclusion of firm fixed effects, the ATM coefficient estimates for UOIBDPit and OtherIncomeit UOtherIncomeit do not exactly sum to the ATM coefficient for UIit.

  27. It is unclear whether authors of subsequent empirical work understand the implications of the identification issues underlying the ATM from guidance provided in Ball et al. (2013a). For instance, Ball et al. (2013a) makes limited reference to some of the identification issues we raise, stating that “the correlations and interactions between different information components are expected to have an effect on timely loss recognition empirically” (p. 1087). Ball et al. (2013a) concludes that controlling for these factors depends on the research objective of a study; however, the nature of the identification issues and how to control for such factors is left unaddressed. For reasons indicated above, controlling for these other factors or assuring that they are absent, is important for investigations that focus on two-regime tests of asymmetric timeliness for transactions subject to conditional conservatism. Moreover, even issues explicitly raised in Ball et al. (2013a) have been ignored in subsequent empirical work. For instance, Ball et al. (2013a) argues that the book-to-market ratio interacted with the ATM coefficient can be problematic, as the book-to-market ratio inadvertently varies with unrecorded growth options, git. Despite this guidance, the Khan and Watts (2009) measure of conservatism, which relies on the book-to-market ratio as a key determinant for firm-specific asymmetric timeliness, continues to be used without modification in subsequent empirical research (e.g., Goh et al. 2017). Moreover, the Ball et al. (2013b) suggestion of including firm fixed effects to mitigate bias in ATM measures will not eliminate the econometric issues we raise (i.e., misclassification and time-varying endogeneity biases).

  28. A solution for misclassification bias that is endogenous (e.g., firms’ degree of conservatism is based on economic incentives; see Watts (2003a) and Watts (2003b)) currently has no econometric solution (e.g., Nguimkeu et al. 2019). This is likely the case even if an instrumental variable can be found for measuring whether yit is less than cit. Thus research using an instrumental variable for returns to “solve” the returns endogeneity problem may not do so. For instance, Badia et al. (2017) measures news by using a fitted measure of annual share returns in a sensitivity analysis. Specifically, in the context of Canadian oil and gas firms’ reserve estimates, the study uses fitted returns from a regression of returns on oil and gas price index returns. Future research using instrumental variables to estimate ATMs must, as with any IVs, justify why the chosen IV is uncorrelated with xit and git but correlated with yit, and also how the approach solves misclassification bias that is endogenous.

  29. The discussion in Wooldridge (2013) is in the context of an unobservable control variable but applies equally to a variable of interest.

  30. To simplify notation, we sometimes suppress subscripts when they can be inferred from the context. In contrast, subscripts for p(y)it are not suppressed to emphasize that the probability or proportion of yit that will be captured in Iit based on its sign and magnitude, relative to the cutoff cit, can vary across firms and time.

  31. Note that Eq. (19) describes the estimable or “statistical” model rather than the structural model. See Wooldridge (2010) for greater discussion of the distinction between estimable and structural models.

  32. For all derivations that follow, recall for two random variables, say Z and W, that \(Z^{\prime }Z={\sigma _{Z}^{2}}\) and \(Z^{\prime }W=\sigma _{Z,W}.\)

  33. This conclusion follows conventional practice that an estimator \(\hat {T}\) is an unbiased estimator of T if \(E(\hat {T})=T\).

  34. Following conventional econometric terms, we define an explanatory variable as endogenous if it is correlated with the structural error term. For instance, “the usage in econometrics, while related to traditional definitions, is used broadly to describe any situation where an explanatory variable is correlated with the disturbance” (Wooldridge 2010, p. 54).

  35. The derivation relies on the Ball et al. (2013a) assumption that yit− 1, git− 1, εit, and εit− 1 are orthogonal to Rit.

  36. Although Ball et al. (2013a) does not allow for variation across firms, we include a subscript i in the variables and equations to facilitate comparisons with our notation.

  37. Ball et al. (2013a) uses plim(.) rather than E(.); we use E(.) as we are interested in bias rather than consistency of the

    coefficient estimates. The econometric issues are similar if we use plim(.).

  38. This expression, except for notational differences, is identical to Eq. (8) in Ball et al. (2013a).

  39. In contrast to this conclusion, Ball et al. (2013a) indicates that “it follows directly from result (5) that, for a correctly specified functional form, the least-squares estimation of (4) yields an unbiased conditional expectation. This is true irrespective of the distributional assumptions made with respect to It and Rt.” (p. 1079). In Ball et al. (2013a), (4) refers to \(I_{t}=\mu \left (R_{t}\right )+\varepsilon _{t}\). Note that this characterization in Ball et al. (2013a) assumes that returns and the structural error term are independent, which as demonstrated above occurs only in the extreme case of ωit = 0 and σR,x = 0.

  40. Ball et al. (2013a) claims that the assumption is invoked “to keep the analysis tractable” (p. 1075). However, the simplification is key to eliminating differential endogeneity bias.

  41. Importantly, managerial discretion over conservatism is not possible by simply “relabeling” certain types of accounting transactions from one category into another. As described in Ball et al. (2013a) (pp. 1077–1078), x, y, and g refer to specific types of accounting transactions. For example, x, y, and g refer to changes in the quantity of accounts receivable, tangible and intangible impairments, and cash flow realizations from unbooked growth options, respectively.

  42. The BKN framework assumes perfect classification (i.e., ωit = 1 when Rit < 0 and ωit = 0 when Rit ≥ 0), so differences in estimated ATMs across subsamples cannot be attributed to differences in the cutoff, cit, that determines the level of conservatism. Instead, under the BKN framework, differences in estimated ATMs across subsamples will reflect differences in return endogeneity as demonstrated above.

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Acknowledgments

We appreciate receiving comments and suggestions from Mirna Boghossian, Sam Bonsall, Farah Kabir, Kevin Koharki, Thaddeus Neururer, Syrena Shirley, Ian Tarrant, Jalal Sani, and Hal White. Professor Muller acknowledges financial support from the Robert and Sandra Poole Faculty Fellowship in Accounting.

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Appendices

Appendix A: Variable definitions

Variable Description
R i t The buy-and-hold annual return ending three months after fiscal year-end, computed using compounded monthly CRSP equity returns.
U R i t The unexpected buy-and-hold annual return ending three months after fiscal year-end, computed using compounded monthly CRSP equity returns. Unexpected returns are constructed using annual 5𝖷5 reference portfolios by sorting on size and book-to-market following Fama and French (1992) and Fama and French (1993). We then obtain unexpected returns by subtracting the expected return from Rit.
D R i t An indicator variable equal to one when Rit or URit is less than zero and equal to zero otherwise.
I i t Earnings (per share) excluding extraordinary items scaled by lagged share price. [EPSPX/LPRCC_F1]
U I i t Unexpected earnings, defined as the difference in earnings excluding extraordinary items (i.e., Iit - Iit− 1).
O I B D P i t Operating income before depreciation, defined as income before interest, taxes, depreciation, and non-operating items (i.e., extraordinary items, special items, and discontinued items), scaled by beginning of the year market value of equity. [OIBDP / (PRCC_F*CSHO)t− 1]
U O I B D P i t Unexpected operating income before depreciation, defined as the difference in operating income before deprecation (i.e., OIBDPit - OIBDPit− 1).
O t h e r I n c o m e i t Other reported annual earnings, defined as Iit less OIBDPit.
U O t h e r I n c o m e i t Unexpected other income, defined as the difference in other income (i.e., OtherIncomeit - OtherIncomeit− 1).
B M it− 1 The book-to-market ratio at the beginning of the fiscal year. [(CEQ+LT) /((PRCC_F*CSHO)+LT)t− 1]
L e v e r a g e it− 1 Firm leverage at the beginning of the fiscal year. [(DLTT+DLC) /(AT)t− 1]
S i z e it− 1 The natural logarithm of market value of equity at the beginning of the fiscal year. [ln(PRCC_F*CSHO)t− 1]
C C A i t “Funds from Operations - Other” scaled by beginning of the year market value of equity. [-FOPO / (PRCC_F*CSHO)t− 1]
U C C A i t (Scaled) unexpected special items (i.e., CCAit - CCAit− 1).
UI_bef_UCCAit UIit -UCCAit

Appendix B:: Econometrics of the earnings on returns regression coefficient

Research on accounting conservatism is inherently interested in testing the link between Iit and yit—that is, the relationship between earnings and transactions that are subject to asymmetric accounting recognition. Because yit is unobservable to researchers, Rit is used instead. In this appendix, we formally derive the econometric properties of the earnings on returns regression coefficient.

Because yit is unobservable to researchers, a “plug-in” solution that substitutes a proxy variable for the unobservable explanatory variable is used. The assumptions that must be met to obtain unbiased estimates are discussed in ?[ ()pp. 308–313]wooldridge2012introductory.Footnote 29 In the generalized BKN framework, yit is expressed using Eq. (3) and then substituted into Eq. (4). Ball et al. (2013a) performs an analogous substitution to form an estimable equation with the observable variables Iit and Rit, although this step is not shown in Ball et al. (2013a).

To demonstrate this, we start with Eq. (3):

$$ R_{it}=x_{it}+y_{it}+g_{it} $$

and solve for yit (the unobservable construct of interest to researchers) as:

$$ y_{it}=R_{it}-x_{it}-g_{it}. $$
(13)

This representation is of returns measuring yit with error of the following form:

$$ e_{it}=R_{it}-y_{it}=x_{it}+g_{it}. $$

Recall that researchers of asymmetric timeliness are interested in the estimation of the structural relationship between Iit and yit:

$$ I_{it}=\left[p(y)_{it}\right]y_{it}+u_{it}, $$
(14)

where

$$ u_{it}=x_{it}+\left[1-p(y)_{it-1}\right]y_{it-1}+g_{it-1}+\varepsilon_{it}-\varepsilon_{it-1}. $$
(15)

Because yit is unobservable, Eq. (14) cannot be estimated directly. Consistent with prior conservatism research, returns is used as a measure of good or bad news, resulting in the substitution of yit from Eq. (13) into Eq. (14) to obtain:

$$ \begin{array}{@{}rcl@{}} I_{it} & = & \left[p(y)_{it}\right](R_{it}-x_{it}-g_{it})+u_{it}. \end{array} $$
(16)

This can be simplified into the following structural equation:

$$ I_{it}=\left[p(y)_{it}\right]R_{it}+\upsilon_{it}, $$
(17)

where

$$ \begin{array}{@{}rcl@{}} \upsilon_{it} =\left[p(y)_{it}\right](-x_{it}-g_{it})+x_{it}+\left[1-p(y)_{it-1}\right]y_{it-1}+g_{it-1}+\varepsilon_{it}-\varepsilon_{it-1}. \end{array} $$
(18)

Equations (17) and (18) are the key to understanding why using returns as a proxy for yit leads to biased estimates. First, following Wooldridge (2010), the classical errors-in-variables assumption requires that the measurement error of the proxy variable not be correlated with the unobservable variable. Clearly, this assumption is violated, as eit(= xit + git) and yit are correlated based on the Ball et al. (2013a) assumptions that \(cov\left (x_{it},y_{it}\right )=\sigma _{x,y}>0\) and \(cov\left (y_{it},g_{it}\right )=\sigma _{y,g}>0\).Footnote 30 Second, even if ωit = 0 when news is sufficiently good and accordingly the errors-in-variables problem doesn’t arise (i.e., \(\left [p(y)_{it}\right ](-x_{it}-g_{it})=0\)), the structural error term, υit, will still be correlated with Rit, as both are determined by xit. (See Eqs. (18) and (3) above.)

Because the structural error term υit is not independent of Rit, the estimated slope coefficient \(\hat {p(y)_{it}}\) from an OLS regression of:Footnote 31

$$ I_{it}=\left[\hat{p(y)_{it}}\right]R_{it}+\hat{\xi}_{it} $$
(19)

will have the following expected value:Footnote 32

$$ \begin{array}{@{}rcl@{}} E\left[\hat{p(y)_{it}}\right] & = & E\left[\frac{\hat{\sigma}_{R,I}}{\hat{\sigma}_{R}^{2}}\right]=\left[\frac{\sigma_{R,({{\left[p(y)_{it}\right]}}R+\upsilon)}}{{\sigma_{R}^{2}}}\right] \\ & =&\left[\frac{\left[p(y)_{it}\right]\sigma_{R}^{2}}{{\sigma_{R}^{2}}}+\frac{\sigma_{R,\upsilon}}{{\sigma_{R}^{2}}}\right]=\left[\left[p(y)_{it}\right]+\frac{\sigma_{R,\upsilon}}{{\sigma_{R}^{2}}}\right]. \end{array} $$
(20)

Following conventional practice, our derivation substitutes the structural equation \(I=\left [p(y)_{it}\right ]R+\upsilon \) for I in σR,I to obtain an expression for the structural parameter p(y)it.

As can be seen in Eq. (20), \(\hat {p(y)_{it}}\) does not provide an unbiased estimate of p(y)it—the structural parameter linking Iit and yit—because σR,υ≠ 0.Footnote 33 Accordingly, Rit and υit are not independent, and R is endogenous, which leads to p(y)it (or ωt in the BKN framework) not being identified in a regression of earnings on returns.Footnote 34 An expansion of υit in Eq. (20) leads to the more general representation:Footnote 35

$$ \begin{array}{@{}rcl@{}} E\left[\hat{p(y)_{it}}\right]&= & E\left[\frac{\hat{\sigma}_{R,I}}{\hat{\sigma}_{R}^{2}}\right]=\left[\frac{\sigma_{R,(\left[p(y)_{it}\right]R+\upsilon)}}{{\sigma_{R}^{2}}}\right]\\ & =&\left[\frac{\left[p(y)_{it}\right]\sigma_{R}^{2}}{{\sigma_{R}^{2}}}+\frac{\sigma_{R,\left\{ \left( 1-\left[p(y)_{it}\right]\right)x_{it}-\left[p(y)_{it}\right]g_{it}+\left( 1-\left[p(y)_{it-1}\right]\right)y_{it-1}+g_{it-1}+\varepsilon_{it}-\varepsilon_{it-1}\right\} }}{{\sigma_{R}^{2}}}\right] \\ & =&\left[\left[p(y)_{it}\right]+\frac{\left( 1-\left[p(y)_{it}\right]\right)\sigma_{R,x}-\left[p(y)_{it}\right]\sigma_{R,g}}{{\sigma_{R}^{2}}}\right]. \end{array} $$
(21)

As Eq. (21) shows, empirical estimates of p(y)it will vary with the importance of \(\left (1-\left [p(y)_{it}\right ]\right )\sigma _{R,x}\) and \(\left [p(y)_{it}\right ]\sigma _{R,g}\) relative to \({\sigma _{R}^{2}}\). For the empirical estimate to be unbiased, \(\left (1-\left [p(y)_{it}\right ]\right )\sigma _{R,x}=0\) and \(\left [p(y)_{it}\right ]\sigma _{R,g}=0\), or alternatively, \(\left (1-\left [p(y)_{it}\right ]\right )\sigma _{R,x}=\left [p(y)_{it}\right ]\sigma _{R,g}\).

Appendix C: Clarification of prior claims in (Ball et al. 2013a)

Revisiting (Ball et al. 2013a) claims of addressing return endogeneity and sample truncation bias

Ball et al. (2013a) makes specific claims regarding return endogeneity and sample truncation bias in one-regime ATMs. Specifically, the study states:

A regression of earnings on returns fulfills its research objective of representing timeliness (p. 1079.)

When the research objective is to estimate the functional shape of the conditional expectation \(E\left (I\mid R\right )\), return is the correct independent variable, and conditioning on it does not induce bias (p. 1091).

We also address the Dietrich, Muller, and Riedl [2007] claim that return endogeneity and sample truncation lead to biased Basu regression estimates (p. 1074).

An important clarification is that the analysis in Ball et al. (2013a) confuses asymmetric timeliness and earnings timeliness. This is indicated in the first two statements that suggest that researchers are interested in the earnings timeliness of all components of returns, not just the timeliness of y—the focus of conservatism research. This alternative focus leads the analysis in Ball et al. (2013a) to provide only a statistical representation of the relationship between I and R, as no structural relationship exists between I and R in the BKN framework. This can clearly be seen in the path analysis depiction of the BKN framework in Fig. 1.

Fig. 1
figure 1

Path analysis of BKN framework. The variables in the figure are defined as: Rt is the total unexpected security return; t is the time subscript; xt is the portion of Rt that is contemporaneously captured in accounting income, It; yt is the portion of Rt that is not contemporaneously captured in It unless required by conservative accounting; gt is the portion of Rt that never is contemporaneously captured in It but always is incorporated with a lag; ωt is an indicator variable that takes the value of one when conservative accounting rules and practices lead to recognition of in period t; and εt is the noise in accounting earnings that reverses in the next period. All income variables are scaled by lagged share price

The research approach in Ball et al. (2013a) deviates from suggested research practices in accounting. For instance, Gow et al. (2016) advises:

An important point worth emphasizing is that the model-based causal reasoning is distinct from statistical reasoning. Suppose we observe data on x and y and make the strong assumption that we know causality is one-way. How do we distinguish between whether X causes Y or Y causes X? Statistics can help us determine whether X and Y are correlated, but correlations do not establish causality. Only with assumptions about causal relations between X, Y, and other variables (i.e., a theory) can we infer causality. (p. 482)

Because of the focus on “earnings timeliness”, rather than the the structural relationship between I and y, the Ball et al. (2013a) representation (shown below in Eq. (23)) is not useful for investigations that focus on ATMs. Regarding the last Ball et al. (2013a) statement, below we address claims about the validity of earnings on returns regressions and the effects on ATM estimates of conditioning on returns. Our focus is on the asymmetric timeliness of y in earnings, the (only) structural equation of interest; we also demonstrate why the statistical representations of earnings on returns regressions, including piece-wise regressions presented in Ball et al. (2013a), do not support the assertions above. We continue to use the two-regime framework in this section for notational convenience and for its generality.

(Ball et al. 2013a) claim of addressing return endogeneity

Regarding the claim in Ball et al. (2013a) of addressing return endogeneity, Eq. (21) shows that the estimated coefficient from a regression of earnings on returns does not provide an unbiased estimate of the extent to which earnings incorporates transactions that are subject to asymmetric accounting recognition. Recall that Eq. (21) takes the following form.

$$ \begin{array}{@{}rcl@{}} E\left[\hat{p(y)_{it}}\right]= \left[\left[p(y)_{it}\right]+\frac{\left( 1-\left[p(y)_{it}\right]\right)\sigma_{R,x}-\left[p(y)_{it}\right]\sigma_{R,g}}{{\sigma_{R}^{2}}}\right]. \end{array} $$

Unless both \(\left (1-\left [p(y)_{it}\right ]\right )\sigma _{R,x}=0\) and \(\left [p(y)_{it}\right ]\sigma _{R,g}=0\) (or alternatively, \(\left (1-\left [p(y)_{it}\right ]\right )\sigma _{R,x}=\left [p(y)_{it}\right ]\sigma _{R,g}\)), the coefficient estimate will be biased. Absent this, the bias cannot be signed, given the separate influence of σR,x and σR,g and the unknown value of p(y)it.

Ball et al. (2013a) does not consider this general case. Instead, a restriction that ωit = 0 (corresponding to \(\left [p(y)_{it}\right ]=0\) in our notation) is invoked.Footnote 36Ball et al. (2013a) refers to this as the “no-conservatism” condition when evaluating the properties of earnings on returns regression. Even under this condition, the estimated coefficient will be positive rather than 0 as illustrated below:

$$ \begin{array}{@{}rcl@{}} E\left[\hat{p(y)_{it}}\mid\omega_{it}=0\right] =E\left[\frac{\hat{\sigma}_{R,I}}{\hat{\sigma}_{R}^{2}}\right]=\left[\frac{\sigma_{R,x}}{{\sigma_{R}^{2}}}\right]. \end{array} $$
(22)

Consequently, when there are no transactions that face asymmetric accounting recognition, an OLS regression slope coefficient will be zero as expected only if xit = 0 (for all i,t). Stated differently, the estimated coefficient will be unbiased only if earnings and returns are orthogonal to each other—a rather uninteresting special case. This conclusion arises under the condition of the symmetric non-recognition of yit; that is, there is no recognition of transactions subject to accounting conservatism.

In contrast to our derivations, the analysis in Ball et al. (2013a):Footnote 37

  • begins with \(E\left [\frac {\hat {\sigma }_{R,I}}{\hat {\sigma }_{R}^{2}}\right ]\),

  • substitutes Iit = xit + yit− 1 + git− 1 + εitεit− 1 for Iit, setting ωityit = 0 by assumption, and

  • substitutes Rit = xit + yit + git for Rit.

These steps lead to the following characterization:Footnote 38

$$ \begin{array}{@{}rcl@{}} E\left[\hat{p(y)_{it}}\mid\omega_{it}=0\right] & = & E\left[\frac{\hat{\sigma}_{R,I}}{\hat{\sigma}_{R}^{2}}\right] \\ & =&E\left[\frac{\hat{\sigma}_{(x_{it}+y_{it}+g_{it}),(x_{it}+y_{it-1}+g_{it-1}+\varepsilon_{it}-\varepsilon_{it-1})}}{\hat{\sigma}_{\left( x_{t}+y_{t}+g_{t}\right)}^{2}}\right] \\ & =&\left[\frac{{\sigma_{x}^{2}}+\sigma_{x,y}+\sigma_{g,x}}{{\sigma_{x}^{2}}+2\sigma_{(x_{it},y_{it}+g_{it})}+\sigma_{(y_{it}+g_{it})}^{2}}\right]. \end{array} $$
(23)

Ball et al. (2013a) indicates that the properties of \(E\left [\hat {p(y)_{it}}\mid \omega _{it}=0\right ]\) in Eq. (23) are desirable, observing that, as the ratio of information incorporated into earnings this period increases (i.e., \({\sigma _{x}^{2}}\uparrow \)) relative to all other information (i.e., \(\sigma _{\left (y_{it}+g_{it}\right )}^{2}\)), \(E\left [\hat {p(y)_{it}}\mid \omega _{it}=0\right ]\) becomes larger. Consider, however, that in the extreme, if all news in returns is incorporated into earnings in the current period, then yit = 0 (for all i,t) and git = 0 (for all i,t), and therefore \(\sigma _{(x_{it},y_{it}+g_{it})}=0\) and \(\sigma _{(y_{it}+g_{it})}^{2}=0\). Eq. (23) reduces to:

$$ \begin{array}{@{}rcl@{}} E\left[\hat{p(y)_{it}}\mid\omega_{it}=0\right] & = & \left[\frac{{\sigma_{x}^{2}}}{{\sigma_{x}^{2}}}\right]=1. \end{array} $$
(24)

This derivation speaks to the timeliness of earnings, not the timeliness of yit.

Because the derivation in Eq. (23) focuses on the statistical properties of the relationship between earnings on returns, the analysis cannot speak to whether return endogeneity is problematic. This occurs as the bias in an estimator can only be evaluated relative to a structural parameter. As noted above, the BKN framework does not specify a structural equation between earnings and returns. More importantly, researchers investigating asymmetric timeliness are interested in the (asymmetric) timeliness of yit in earnings, which has the structural parameter p(y)it. With this objective in mind, reconsider Eq. (23); ωit = 0 by assumption; however, \(E\left [\hat {p(y)_{it}}\right ]{{\neq }}0\) leads to an inconsistency. This inconsistency occurs because the underlying structural relationship, \(I=\left [p(y)_{it}\right ]R+\upsilon \), which contains the structural coefficient, p(y)it, regarding how yit affects Iit, and the structural error term, υit, is not part of the derivation. In addition, the substitution of Rit = xit + yit + git for Rit obscures that the explanatory variable, Rit, in the regression of earnings on returns is endogenous, as it becomes omitted from the derivation.

The different focus in Ball et al. (2013a) has important implications. To see this, closely examine Eq. (22) versus Eq. (23) when ωit = 0. The equations are equivalent, as the numerators of both equations equal σR,x (i.e., in slightly different notation for the numerator for Eq. (23), \(\sigma _{x_{it},(x_{it}+y_{it}+g_{it})}\) equals σR,x, as Rit = xit + yit + git) and denominators of both equal \({\sigma _{R}^{2}}\) (i.e., in slightly different notation for the denominator for Eq. (23), \(\sigma _{(x_{t}+y_{t}+g_{t}),(x_{t}+y_{t}+g_{t})}\) equals \({\sigma _{R}^{2}}\)). Ball et al. (2013a) fails to point out that, if ωit = 0 (for all i,t), then a consistent estimator is zero because no relationship exists between Iit and yit (proxied by Rit); however, empirical estimates to the contrary will arise because σR,x > 0. That is, when yit does not determine Iit (i.e., the Ball et al. (2013a) “no-conservatism” condition), Ball et al. (2013a)’s Eq. (8) demonstrates the properties of the endogeneity bias that arise because the unobservable variable xit is in the error term and is positively correlated with Rit.Footnote 39

In summary, the Ball et al. (2013a) derivations demonstrate only the statistical properties of the slope coefficient from a regression of earnings onto returns and not of a structural relationship (i.e., Fig. 1 shows there is not a direct link between Iit and Rit). Researchers testing for asymmetric timeliness are fundamentally interested in the structural coefficient between Iit and yit. Because it focuses on the statistical relationship between earnings and returns, the Ball et al. (2013a) analysis cannot speak to whether the earnings on returns regression leads to biased estimates of the structural coefficient between Iit and yit. For these reasons, the derivations in Ball et al. (2013a) do not support the assertion that causal relationships between earnings and transactions subject to asymmetric accounting recognition are being tested in empirical tests of earnings on returns.

(Ball et al. 2013a) claim of addressing sample truncation bias

Regarding the claim in Ball et al. (2013a) of addressing sample truncation, as we demonstrate in Eq. (12), the ATM has the following properties:

$$ \begin{array}{@{}rcl@{}} ATM Bias_{it}&= & \left\{ \left[p(R)_{it}+\frac{\left( 1-p(R)_{it}\right)\sigma_{R,x}-p(R)_{it}\sigma_{R,g}}{{\sigma_{R}^{2}}}\mid R_{it}<0\right]-\left[p(y)_{it}\mid y_{it}<c_{it}\right]\right\} \\ & & -\left\{ \left[p(R)_{it}+\frac{\left( 1-p(R)_{it}\right)\sigma_{R,x}-p(R)_{it}\sigma_{R,g}}{{\sigma_{R}^{2}}}\mid R_{it}\geq0\right]-\left[p(y)_{it}\mid y_{it}\geq c_{it}\right]\right\} . \end{array} $$

Subsection 3.4 describes the two conditions under which the ATM will not suffer from differential endogeneity bias that is a function of truncated distributions. Neither condition is trivial.

How is it that Ball et al. (2013a) reaches the alternative conclusion that conditioning on returns does not induce bias? The analysis in Ball et al. (2013a) follows these steps:

  • begin with \(E\left [\frac {\hat {\sigma }_{R,I}}{\hat {\sigma }_{R}^{2}}\right ]\),

  • substitute \(I_{it}=x_{it}+\left [\omega _{it}\right ]y_{it}+\left [1-\omega _{it-1}\right ]y_{it-1}+g_{it-1}+\varepsilon _{it}-\varepsilon _{it-1}\) for Iit,

  • substitute Rit = xit + yit + git for Rit, and

  • assume that (i) ωit = 0 for all Rit, or alternatively, (ii) ωit = 1 when Rit < 0 and ωit = 0 when Rit ≥ 0.

This leads to the following characterizations of the bad and good news coefficients (see Ball et al. (2013a) Eqs. (A1) and (A2)):

$$ \begin{array}{@{}rcl@{}} E\left[\hat{\delta}_{1}^{bad}\right] & = & E\left[\frac{\hat{\sigma}_{R,I}}{\hat{\sigma}_{R}^{2}}\mid R_{it}<0\right] \\ & =&E\left[\frac{\hat{\sigma}_{(x_{it}+y_{it}+g_{it}),(x_{it}+\left[\omega_{it}\right]y_{it}+\left[1-\omega_{it-1}\right]y_{it-1}+g_{it-1}+\varepsilon_{it}-\varepsilon_{it-1})}}{\hat{\sigma}_{R}^{2}}\mid R_{it}<0\right] \\ & =&\left[\frac{\sigma_{x_{it},(x_{it}+y_{it}+g_{it})}+\sigma_{\left[\omega_{it}\right]y_{it},(x_{it}+y_{it}+g_{it})}}{{{\sigma}}_{R}^{2}}\mid R_{it}<0\right] \end{array} $$
(25)
$$ \begin{array}{@{}rcl@{}} E\left[\hat{\delta}_{1}^{good}\right] & = & E\left[\frac{\hat{\sigma}_{R,I}}{\hat{\sigma}_{R}^{2}}\mid R_{it}\geq0\right] \\ & =&E\left[\frac{\hat{\sigma}_{(x_{it}+y_{it}+g_{it}),(x_{it}+\left[\omega_{it}\right]y_{it}+\left[1-\omega_{it-1}\right]y_{it-1}+g_{it-1}+\varepsilon_{it}-\varepsilon_{it-1})}}{\hat{\sigma}_{R}^{2}}\mid R_{it}\geq0\right] \\ & =&\left[\frac{\sigma_{x_{it},(x_{it}+y_{it}+g_{it})}+\sigma_{\left[\omega_{it}\right]y_{it},(x_{it}+y_{it}+g_{it})}}{\hat{\sigma}_{R}^{2}}\mid R_{it}\geq0\right]. \end{array} $$
(26)

Ball et al. (2013a) then invokes a “linearity assumption,” which requires returns and all of its components to share the same variance-covariance matrix for subsamples partitioned based on the sign of returns. This leads to the ATM coefficient being represented as (see Ball et al. (2013a) Eq. (A3), and notice that the Ball et al. (2013a) linearity assumption equates \({\sigma _{R}^{2}}\mid R_{it}<0\) and \({\sigma _{R}^{2}}\mid R_{it}\geq 0\)):

$$ \begin{array}{@{}rcl@{}} & E\left[\hat{\delta}_{1}^{bad}\right]-E\left[\hat{\delta}_{1}^{good}\right]= & \frac{\left[\sigma_{\left[\omega_{it}\right]y,(x_{it}+y_{it}+g_{it})}\mid R_{it}<0\right]-\left[\sigma_{\left[\omega_{it}\right]y,(x_{it}+y_{it}+g_{it})}\mid R_{it}\geq0\right]}{{\sigma_{R}^{2}}\mid R_{it}\geq0}.\\ \end{array} $$
(27)

As Ball et al. (2013a) indicates, the Basu ATM will equal zero, if ωit = 0 for all Rit, and will be positive, if ωit = 1 when Rit < 0 and ωit = 0 when Rit ≥ 0. The first condition of no conservatism can be seen in Eq. (27) as ωit = 0. The second condition leads to Eq. (27) collapsing to:

$$ \begin{array}{@{}rcl@{}} & E\left[\hat{\delta}_{1}^{bad}\right]-E\left[\hat{\delta}_{1}^{good}\right]= & \frac{\left[\sigma_{y_{it},(x_{it}+y_{it}+g_{it})}\mid R_{it}<0\right]}{{\sigma_{R}^{2}}\mid R_{it}\geq0}. \end{array} $$
(28)

Note that the right-hand side of Eq. (28) portrays the statistical properties of the ATM rather than demonstrating whether it is unbiased, relative to a structural coefficient of interest. Specifically, as before with the Ball et al. (2013a) representation of the properties of the earnings on returns coefficient, the underlying structural relationship (using our notation) \(I=\left [p(y)_{it}\right ]R+\upsilon \), which contains the structural coefficient, p(y)it, regarding how yit affects Iit, and the structural error term, υit, is not part of the derivation. In addition, the substitution of Rit = xit + yit + git for Rit again obscures that the explanatory variable, Rit, in the regression of earnings on returns is endogenous, as it is omitted from the derivation.

Consider closely the properties of the Ball et al. (2013a) representation of the ATM. Under that representation, there is no sample truncation bias, because it is ruled out by the linearity assumption.Footnote 40 Specifically, the \(\sigma _{x_{it},(x_{it}+y_{it}+g_{it})}\) terms in Eqs. (25) and (26) demonstrate that differential sample truncation bias can exist across the bad and good news coefficients. For example, because \(\sigma _{x_{it},(x_{it}+y_{it}+g_{it})}\) equals σR,x, as Rit = xit + yit + git, differences in \(\left [\frac {\sigma _{R,x}}{{\sigma _{R}^{2}}}\mid R_{it}<0\right ]\) and \(\left [\frac {\sigma _{R,x}}{{\sigma _{R}^{2}}}\mid R_{it}\geq 0\right ]\) can exist. Ball et al. (2013a) rules out this possibility through the linearity assumption. We demonstrate this point in greater detail below.

Second, notice that differences in the application of conservative accounting methods through the use of different cutoffs arising from differences across mandatory accounting practices or by managerial discretion are not captured by the Ball et al. (2013a) representation. That is, by assumption ωit = 1 when Rit < 0 and ωit = 0 when Rit ≥ 0. This assumption guarantees perfect classification when using the sign of stock returns. As we demonstrate above, the assumption is restrictive and, under most conditions, is required for the differential biases for the bad and good news samples to perfectly offset. As this assumption guarantees that p(y)it must always equal either one or zero for the bad and good news subsamples respectively, we are unclear how recent empirical studies claim to be relying on the analysis in Ball et al. (2013a) but then move to empirically test for differences in the mandatory or voluntary application of conservative accounting practices.

Third, why will the ATM vary under the linearity and perfect classification assumptions in Ball et al. (2013a)? Closer examination of Eq. (28) indicates that the ATM should equal one by the assumptions that ωit = 1 when Rit < 0 and ωit = 0 when Rit ≥ 0. However, unless yit = Rit, the ATM will be downward biased. To separate ωit from the factors driving the bias, substitute yit = Ritxitgit and Rit = xit + yit + git in Eq. (28) to obtain:

$$ \begin{array}{@{}rcl@{}} & E\left[\hat{\delta}_{1}^{bad}\right]-E\left[\hat{\delta}_{1}^{good}\right]= & \left[\frac{\sigma_{\left[\omega_{it}\right]R_{it}-x_{it}-g_{it},R_{it}}}{{{\sigma}}_{R}^{2}}\mid R_{it}<0\right] \\ & & =\left[\omega_{it}-\frac{\sigma_{R,x}+\sigma_{R,g}}{{{\sigma}}_{R}^{2}}\mid R_{it}<0\right] \\ & & =\left[1-\frac{\sigma_{R,x}+\sigma_{R,g}}{{{\sigma}}_{R}^{2}}\mid R_{it}<0\right]. \end{array} $$
(29)

As can be seen, while the ATM will be positive as claimed in Ball et al. (2013a), there exists a downward bias that grows with the importance of x and g relative to y. That is, even though the ATM should equal one by the assumptions regarding ωit, the coefficient estimate for the ATM will vary, due to the relative importance of the three components of returns. Ball et al. (2013a) discusses how the ATM is affected by the importance of x and g relative to y (Section 4) but does not characterize their importance as confounding the interpretation of the timeliness of y, as the ATM should always equal one under the Ball et al. (2013a) formulation.Footnote 41

The bias, represented by the last term in Eq. (29), arises solely because of the endogeneity of returns. To see this, consider the more general ATM representation based on our Eq. (12):

$$ \begin{array}{@{}rcl@{}} E\left[\hat{\delta}_{1}^{bad}\right]-E\left[\hat{\delta}_{1}^{good}\right]&= & \left[\left\{ p(R)_{it}+\frac{\left( 1-p(R)_{it}\right)\sigma_{R,x}-p(R)_{it}\sigma_{R,g}}{{\sigma_{R}^{2}}}\mid R_{it}<0\right\} \right]\\ & & -\left[\left\{ p(R)_{it}+\frac{\left( 1-p(R)_{it}\right)\sigma_{R,x}-p(R)_{it}\sigma_{R,g}}{{\sigma_{R}^{2}}}\mid R_{it}<0\right\} \right]. \end{array} $$

Now, following the analysis in Ball et al. (2013a), invoke these two assumptions: (i) the linearity assumption and (ii) perfect classification assumption based on the sign of stock returns. This reduces the above equation to:

$$ \begin{array}{@{}rcl@{}} E\left[\hat{p(y)_{it}}\mid R_{it}<0\right]-E\left[\hat{p(y)_{it}}\mid R_{it}\geq0\right]&= & \left[1\right]+\left[\frac{-\sigma_{R,g}}{{\sigma_{R}^{2}}}\mid R_{it}<0\right]\\ & & -\left[0\right]-\left[\frac{\sigma_{R,x}}{{\sigma_{R}^{2}}}\mid R_{it}\geq0\right]\\ & =&\left[1-\frac{\sigma_{R,x}+\sigma_{R,g}}{{{\sigma}}_{R}^{2}}\mid R_{it}<0\right]. \end{array} $$

Here, the ATM is still a function of the remaining endogeneity bias, despite invoking the two assumptions in Ball et al. (2013a). In addition, the absence of either assumption leads to a much more complicated depiction of the validity concerns faced by the empirical researcher, as given in Eq. (12). Further, note that Ball et al. (2013a)’s linearity assumption is not a new insight regarding the required conditions for the ATM to be unbiased. Rather, the assumption essentially serves the same purpose as Dietrich et al. (2007)’s conditions (i)–(iii) to rule out possible bias in ATMs. Accordingly, requiring the linearity assumption to hold fails to justify Ball et al. (2013a)’s assertion that “conditioning on [returns] does not induce bias” while simultaneously invoking this condition to mitigate the effects of the biases. Thus the conclusion in Ball et al. (2013a) that the analysis in the study “contradicts the claims of Dietrich, Muller, and Riedl [2007]” (p. 1083) is unfounded. Instead, notwithstanding the restrictive assumptions that are invoked in Ball et al. (2013a) to obtain its derivations and inferences, the asymmetric timeliness test is still affected by the remaining endogeneity bias that is a function of truncated distributions. Finally, and most importantly, notice that invoking the two assumptions in Ball et al. (2013a) leads to an ATM measure that cannot be used to justify empirical tests intended to measure variation in the asymmetric recognition of yit.Footnote 42

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Dietrich, J.R., Muller, K.A. & Riedl, E.J. On the validity of asymmetric timeliness measures of accounting conservatism. Rev Account Stud (2022). https://doi.org/10.1007/s11142-022-09684-2

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  • DOI: https://doi.org/10.1007/s11142-022-09684-2

Keywords

  • Conservatism
  • Asymmetric timeliness
  • Contemporaneous income bias
  • Endogeneity

JEL Classification

  • G10
  • M41