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Asymmetric timeliness tests of accounting conservatism

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Abstract

Recent accounting research employs an asymmetric timeliness measure to test the hypothesis that reported accounting earnings are “conservative.” This research design regresses earnings on stock returns to examine whether “bad” news is incorporated into earnings on a more timely basis than “good” news. We identify properties of the asymmetric timeliness estimation procedure that will result in biases in the test statistics except under very restrictive conditions that are rarely met in typical empirical settings. Using data series that are devoid of asymmetric timeliness in reported earnings, we show how these biases result in evidence consistent with conservatism. We conclude that the biased test statistics inherent in the asymmetric timeliness research design preclude using this method to measure conservatism; that these biases are irresolvable as they originate in the test’s specification; and that studies employing asymmetric timeliness tests cannot be interpreted as providing evidence of conservatism.

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Fig. 1
Fig. 2
Fig. 3
Assume R it = βX it + λη it and β = λ = 1. X is distributed mean 0 and is symmetric. The distribution of η is symmetric and has mean 0. The covariance of X and η is zero. Asymmetric timeliness regressions of X onto R using samples formed on the sign of R results in identical coefficients of δ0 = 0.813 for the “good” news sample (i.e., R it  ≥ 0) and δ1 = 0.813 for the “bad” news sample (i.e., R it < 0). As illustrated in the second figure, sampling on the sign of R results in symmetric non-random sampling on η (i.e., the dots/triangles), and thus equality in the coefficients.

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Notes

  1. For example, see Basu (1997); Pope and Walker (1999); Ball, Kothari and Robin (2000); Ryan and Zarowin (2003); Sivakumar and Waymire (2003); and Beaver and Ryan (2005). Watts (2003) provides a recent summary of this literature.

  2. The “accounting earnings” information channel includes conventional earnings releases and other disclosures that convey information that is equivalent to accounting earnings. Ball and Brown (1968) provide evidence that information from the accounting earnings information channel is impounded into stock prices during the fiscal year even if annual accounting earnings are not disclosed until after the end of the year. The precise format of earnings disclosure is irrelevant.

  3. This characterization of the information channels as non-overlapping partitions simplifies exposition. The more general case in which earnings information may be communicated through an “other information” channel is described in the appendix.

  4. This development is consistent with theoretical accounting models of price formation (e.g., Garman & Ohlson, 1980), as well as prior empirical implementation of these models (e.g., Easton & Zmijewski, 1989). Further, note that Basu (1997) and others appear to rely on the causal relation of other information to stock returns (consistent with the value-relevance literature), but assume that accounting earnings are not a source of information in the formation of stock returns (at least during the return windows employed, i.e., fiscal year returns), or take no position regarding the source of “news” to the market. For instance, consider Basu’s intuition that returns can be used as a proxy for “news of interest, which reaches the market from sources other than earnings” (Basu, 1995, p. 25). In addition, Ryan and Zarowin (2003) similarly state: “Note that AM [accrual measurement] is silent as to whether accounting numbers convey new information to the market or are just associated with market values” (p. 7).

  5. Parameters θ, ω, and α are, in general, associated with each economic event. Parameter subscripts are suppressed to ease exposition.

  6. This assumption simplifies the specification without loss of generality.

  7. Although the characterization of link D appears to depend on the sign of Δv it , the link is constructed so as to present the portion of Δv it that is not communicated through the earnings channel. Alternatively, it could be viewed as an independent Δv it that would be communicated through earnings with a one-period delay (i.e., α = 1).

  8. Note, in the following derivations, we change notation from x (unscaled earnings) and z (unscaled non-earnings information) to X (earnings scaled by lagged price) and η (non-earnings information scaled by lagged price). We use the latter to maintain consistency with the conservatism literature.

  9. This follows from the identities \({\hbox{plim} \hat {\beta}^{\prime}=\hbox{plim} \left[\frac{\hat{\sigma}_{R, X}}{\hat{\sigma}_X^2}\right]}\) from (1.2) and σR,X = βσ 2 X + λσX,η from (1.1), and the assumption σX,η = 0. That is, \({\hbox{plim} \hat{\beta}^{\prime}=\hbox{plim} \left[\frac{\hat{\sigma}_{R, X}}{\hat{\sigma}_X^2}\right]=\left[\frac{\sigma_{R, X}}{\sigma_X^2}\right]=\left[\frac{\beta \sigma_X^2}{\sigma_X^2}+\frac{\lambda \sigma_{X,\eta}} {\sigma_X^2}\right]=\beta}.\) See Maddala (1992) for a discussion of large sample distribution theory.

  10. The Basu (1997) model assumes unexpected earnings and unexpected price changes, rather than earnings and raw price changes; we adopt the latter constructs for simplicity. Our choice also is consistent with the implementation by prior related research (e.g., Basu, 1997, Table 1, Panel A; Pope & Walker, 1999; Ball et al., 2000, Table 2; Givoly & Hayn, 2000; Ryan & Zarowin, 2003; Sivakumar & Waymire, 2003).

  11. In other contexts, the inverse of a reverse regression slope coefficient has been used as an upper bound estimate of the forward regression coefficient to address errors in variables problems; however, this approach is typically used when R 2 s are large (i.e., when the coefficient estimate bias is small).

  12. Basu (1997, ft. 7, p. 11) alternatively specifies the properties of “reverse” regression coefficients as: β2 = R 2 × [var(Earnings)/var(Returns)], where β in that study’s notation corresponds to δ in ours. Notice that the equation mathematically equals our (1.4), with the former expressing the properties of δ*δ rather than δ.

  13. Equivalently, the estimate will be upward biased unless R 2 = 1. Because regressions of earnings onto returns typically have low explanatory power (i.e., R 2s are generally below 15%), the estimated slope coefficient will not conform closely to interpretations regarding the permanent or transitory nature of earnings.

  14. Our Eqs. 1.5a and 1.5b are equivalent to stacking regressions using “good” and “bad” news samples, and thus are also equivalent to the typical implementation of the asymmetric timeliness test: \({X_{it} =\phi_0^{\rm good} +\phi_0^{\rm bad\_incr} {DR_{it}} +\phi_1^{\rm good} R_{it} +\phi_1^{\rm bad\_incr} R_{it} \ast {DR_{it}} +\varphi_{it}}\) (i.e., our Eq. 1.3a). Notice, the coefficients are related as: \({\phi_1^{\rm good} =\delta_0}\) and \({\phi_1^{\rm good} +\phi_1^{\rm bad\_incr} =\delta_1}.\)

  15. The same set of conditions provide for unbiased estimates of R 2. Using the identity \({\hbox{plim} (\hat{R}^2)=\left\{ \hbox{plim} (\hat{\delta}) \right\}\ast \left\{ \hbox{plim} (\hat{\beta}^{\prime}) \right\}},\) substituting in from Eqs. 1.7a and 1.7b, and considering the impact of sample truncation on \({\hbox{plim} (\hat{\beta}^{\prime})=\beta +\frac{\lambda \sigma_{X,\eta}}{\sigma_X^2}},\) the properties of estimated R 2s using the asymmetric timeliness research design for the “good” and “bad” news samples are:

    $$ \begin{aligned} &\hbox{plim} (\hat{R}_0^2)=\left\{ \beta \left[ \left. \frac{\sigma_X^2}{\sigma_R^2} \right|R_{it}\geq 0 \right]+\lambda \left[ \left. \left( \frac{\sigma_{X,\eta}}{\sigma_R^2} \right) \right|R_{it} \geq 0 \right] \right\}\ast \left\{ \beta +\lambda \left[ \left. \frac{\sigma_{X,\eta}}{\sigma_X^2} \right|R_{it} \geq 0 \right] \right\}\\ &\hbox{plim} (\hat{R}_1^2)=\left\{ \beta \left[ \left. \frac{\sigma_X^2}{\sigma_R^2} \right|R_{it} < 0 \right]+\lambda \left[ \left. \left( \frac{\sigma_{X,\eta}}{\sigma_R^2}\right) \right|R_{it} < 0 \right] \right\}\ast \left\{ \beta +\lambda \left[ \left. \frac{\sigma_{X,\eta}}{\sigma_X^2} \right|R_{it} < 0 \right] \right\} \end{aligned} $$

    As with the coefficient estimators, these estimators are likely to be equal only under restrictive conditions, as identified in (i)–(iii) above.

  16. Ball and Kothari (2006) also analyze the asymmetric timeliness model. Their model, which for simplicity ignores negative earnings, employs a permanent growth rate approach to model accounting income and price. They demonstrate that, under conditions substantially equivalent to those presented above, the regression model is econometrically well-specified under the null hypothesis that accounting is not conservative. Their study does not examine model specification under other conditions. As we show in Sect. 2, the sufficient conditions we identify in this section are unlikely to obtain. Thus, the extent to which asymmetric timeliness tests are affected by actual distributions is an empirical matter and is addressed in Sect. 2.

  17. This occurs as the ST bias (e.g., \({\left. \frac{\hat{\sigma}_{X,\eta}}{\hat{\sigma}_R^2} \right|R_{it} < 0})\) converges to its expected value as n increases. In small samples, differences will be observed as the sample covariance is scaled by n, whereas the sample variance is scaled by n−1.

  18. Prior conservatism studies (e.g., Ball et al., 2000) have interpreted the left-skewness of earnings scaled by lagged price as evidence of conservative accounting and supportive of the evidence found using the asymmetric timeliness regression. The supposition is that conservative accounting results in earnings incorporating large economic losses relatively rapidly, but incorporating economic gains gradually over time. However, recent research by Durtschi and Easton (2005) provide evidence that the left-skewness of earnings scaled by lagged price is attributable to deflation. Specifically, they demonstrate that the deflator (lagged price) is significantly lower for loss observations than for profit observations. This distorts the distribution, moving loss observations away from zero and profit observations towards zero. Further, they demonstrate that earnings per share—for which the deflator (number of shares outstanding) does not differ systematically across loss and profit observations—is right-skewed. This recent evidence is the opposite of an accounting conservatism prediction. Moreover, notice that findings of “aggressive” accounting obtains if the signs of the values for earnings (X) in Panel C of Fig. 3 are reversed to make earnings right-skewed. Consistent with this, we demonstrate later that the asymmetric timeliness research design provides evidence that earnings are “aggressive” when the scalar of lagged prices is replaced with shares outstanding (Panel D of Table 3).

  19. We focus on the period 1963–1990 for consistency with Basu (1997); we also report a later time period (1991–2001) for reference.

  20. To see this, assume that two partitioning variables exist: one that equals one when an (overall) unrealized economic gain occurs, zero otherwise, and another that equals one when an (overall) unrealized economic loss occurs, zero otherwise. Accountants viewing of the underlying transactions could in concept give rise to such partitioning variables. Now, if the intercept and slope coefficient for earnings were interacted with these two variables, then the resulting slope coefficients would capture the accounting asymmetric recognition of unrealized gains and losses (consistent with the Basu, 1997 notion of conservatism), respectively.

  21. We conduct several alternative simulations. First, because it is possible that within-year error terms may be correlated across firms (e.g., due to macroeconomic events), we also randomize error terms across (versus within) years. Second, we also replicate this simulation 1,000 times, using averaged coefficient estimates. Finally, to parallel the assumptions of our stylized model in Sect. 1, we also conduct a simulation wherein the coefficient from Eq. 1.1 (i.e., β) is set to 1. In all cases, the simulations provide evidence consistent with “conservatism,” though none should exist.

  22. We use all available observations from Compustat for the period 1963–1990, trimming observations at the 1% and 99% levels. In addition, observations with negative book value of owners’ equity at the beginning of year t are excluded.

  23. Note that Basu (1997) reveals (but does not discuss) similar results.

  24. We choose a statistical representation for convenience. Conceptually, this is equivalent to a projection of news onto accounting earnings, resulting in η as the component of all news that is orthogonal to accounting earnings. Alternatively, we could depict underlying economic events affecting both earnings and other information sources.

  25. This follows from substituting the identity \({\sigma_{R,\eta_X} =\lambda^\ast \sigma_{\eta_X}^2 +\lambda \sigma_{\eta_X,\eta}}\) from Eq. A.1 into the identity \({\hbox{plim} \hat{\beta}^{\prime}=\hbox{plim} \left[ \frac{\hat{\sigma}_{R,\eta_X}}{\hat{\sigma}_{\eta_X}^2} \right]}\) from Eq. A.3, and using the assumptions \({\sigma_{\eta_X}^2 =\sigma_X^2 =\sigma_1^2,\ \sigma_{R,\eta_X} =\sigma_{R,X}},\) and \({\sigma_{\eta_X,\eta} =0}.\) That is: \({\hbox{plim} \hat{\beta}^{\prime}=\hbox{plim} \left[\frac{\hat{\sigma}_{R,X}}{\hat{\sigma}_X^2}\right]=\left[ \frac{\sigma_{R,X}}{\sigma_X^2}\right]=\left[ \frac{\lambda^\ast \sigma_{\eta_X}^2}{\sigma_{\eta_X}^2}+\frac{\lambda \sigma_{\eta_X,\eta}}{\sigma_{\eta_X}^2} \right]=\lambda^\ast}.\)

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Acknowledgements

We gratefully acknowledge useful comments by and discussions with Sudipta Basu, Anne Beatty, Joe Comprix, Ilia Dichev, Peter Easton, Paul Fischer, Glen Hansen, Paul Healy, Steve Huddart, SP Kothari, Christian Leuz, Jim McKeown, Jim Ohlson, Joshua Rosett, Terry Shevlin, Doug Skinner, Richard Sloan, Monica Stefanescu, Ram Venkataraman, Ross Watts, Hal White, Dave Wright, and workshop participants at the 2003 Minnesota Empirical Accounting Conference and the following universities: Harvard, Iowa, Michigan, Ohio State, Penn State, and Tulane. Previous drafts of this manuscript were titled “Using Stock Returns to Determine ‘Bad’ versus ‘Good’ News to Examine the Conservatism of Accounting Earnings.”

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  1. Fisher College of Business, The Ohio State University, 2100 Neil Avenue, Columbus, OH, 43210, USA

    J. Richard Dietrich

  2. Smeal College of Business, The Pennsylvania State University, University Park, PA, 16802, USA

    Karl A. Muller III

  3. Harvard Business School, Soldiers Field, Boston, MA, 02163, USA

    Edward J. Riedl

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Appendix

Appendix

This appendix shows that econometric biases explain purported evidence of conservatism using the asymmetric timeliness research design under an alternative assumption that “other” (non-earnings) information sources provide new information to the market and that the disclosure of accounting earnings simply confirms information previously revealed during the period. Again, our attention is restricted to a setting in which conservatism does not exist.

Define R as stock returns, X as accounting earnings, η X as “other” information that is subsequently summarized in accounting earnings, and η as non-earnings information sources (all are scaled by lagged price). Assume the following market pricing function and statistical representation of earnings reflecting earnings-related information that preempts the release of accounting earnings during period t: Footnote 24

$$ R_{it} =\lambda^\ast \eta_{X,it} +\lambda \eta_{it} $$
(A.1)
$$ X_{it} \sim \eta_{X,it} $$
(A.2)

where λ* and λ are response coefficients for earnings-related information and non-earnings information, and subscripts i and t denote firms and time, respectively. For simplicity, further assume that λ* = λ = 1 (i.e., earnings-related and non-earnings information are completely transitory). We denote two response coefficients, λ* and λ, to distinguish the two types of information sources; however, both incorporate current period value changes via link D of Fig. 1. In addition, assume that X has mean μ1 and variance σ 21 ; η has mean μ2 and variance σ 22 ; and \({\sigma_{\eta_X, \eta} =\sigma_{X, \eta} =0}.\) As constructed, news that conveys earnings-related information that is subsequently summarized by earnings shares the same statistical properties as accounting earnings. Therefore, \({\sigma_{R,\eta_X} =\sigma_{R,X}}.\) The empirical implementation of this model, assuming only R and X are observable, results in the following (where \(\varepsilon\) is an error term representing (scaled) unobservable non-earnings information):

$$ R_{it} =\beta^{\prime}X_{it} +\varepsilon_{it} $$
(A.3)

The estimation of (A.3) will obtain an unbiased slope estimate of λ*. That is, \({\hbox{plim} (\hat{\beta}^{\prime})=\lambda^\ast}.\) Footnote 25

Notice, when Eq. A.3 or equivalently Eq. 1.2 is estimated, that the researcher is unable to discern whether \({\hat{\beta}^{\prime}=1}\) is attributable to stock price changes occurring due to the release of information from sources that preempted the release of accounting earnings (i.e., λ* = 1), due to the release of accounting earnings (i.e., β = 1), or some combination of the two. However, the empirical estimate of \({\hat{\beta}^{\prime}}\) nevertheless tells the researcher about the “measurement” of accounting earnings, such as the transitory/permanent nature of accounting earnings. Under the assumption of accounting earnings being transitory, \({\hbox{plim} \hat{\beta}^{\prime}=1}\) regardless of the underlying information link (i.e., accounting earnings release, or information that is correlated with accounting earnings).

The assumption that information sources, but not the release of accounting earnings, provide new information to the market results in the same empirical biases as described in Sect. 1. To see this, consider again the asymmetric timeliness regressions estimated using the “good” and “bad” news subsamples, respectively:

$$ \left. X_{it} =\delta_0 R_{it} +\xi_0 \right| R_{it} \geq 0\quad \hbox{(``Good'' news regression)}$$
(A.4a)
$$\left. X_{it} =\delta_1 R_{it} +\xi_1 \right| R_{it} < 0\quad \hbox{(``Bad'' news regression)}$$
(A.4b)

These statistical representations are, of course, equivalent to the statistical representations (1.5a) and (1.5b). Under this alternative assumption, the properties of \({\hbox{plim}(\hat{\delta}_0)}\) and \({\hbox{plim}(\hat{\delta}_1)}\) can be seen by substituting the identity \({\sigma_{R,\eta_X}=\lambda^\ast \sigma_{\eta_X}^2 +\lambda\sigma_{\eta_X,\eta}}\) from (A.1) into the identities \({\hbox{plim} (\hat{\delta}_0)=\hbox{plim} \left[ \left. \frac{\hat{\sigma}_{R,X}}{\hat{\sigma}_R^2} \right| R_{it} \geq 0 \right]}\) from (A4.a) and \({\hbox{plim}(\hat{\delta}_1)=\hbox{plim} \left[ \left. \frac{\hat{\sigma}_{R,X}}{\hat{\sigma}_R^2} \right|R_{it} < 0 \right]}\) from (A4.b), and using the assumptions \({\sigma_{\eta_X}^2 =\sigma_X^2 =\sigma_1^2,\ \sigma_{R,\eta_X} =\sigma_{R,X},\ \hbox{and}\ \sigma_{\eta_X,\eta}=0},\) to obtain:

$$ \begin{aligned} \hbox{plim}(\hat{\delta}_0)&=\hbox{plim} \left[ \left. \frac{\hat{\sigma}_{R,X}}{\hat{\sigma}_R^2}\right|R_{it} \geq 0 \right]=\left[ \left. \frac{\sigma_{R,X}}{\sigma_R^2} \right|R_{it}\geq 0 \right]\\ &=\lambda^\ast \left[ \left. \frac{\sigma_{\eta_X}^2}{\sigma_R^2} \right|R_{it} \geq 0 \right]+\lambda \left[ \left. \left( \frac{\sigma_{\eta_X,\eta}}{\sigma_R^2} \right) \right|R_{it} \geq 0 \right] \end{aligned}$$
(A.5a)
$$ \begin{aligned} \hbox{plim} (\hat{\delta}_1)&=\hbox{plim} \left[ \left. \frac{\hat{\sigma}_{R,X}}{\hat{\sigma}_R^2} \right|R_{it} < 0 \right]=\left[ \left. \frac{\sigma_{R,X}}{\sigma_R^2} \right|R_{it} < 0 \right] \\ &=\lambda^\ast \left[ \left. \frac{\sigma_{\eta_X }^2}{\sigma_R^2} \right|R_{it} < 0 \right]+\lambda \left[ \left. \left( \frac{\sigma_{\eta_X,\eta}}{\sigma_R^2} \right) \right|R_{it} < 0 \right] \end{aligned}$$
(A.5b)

As in Sect. 1, in general, the coefficient estimators will not be equal. This will occur because the conditional sample variance ratios (i.e., \({\left. \frac{\sigma_{\eta_X }^2}{\sigma_R^2} \right|R_{it}\geq 0}\) and \({\left. \frac{\sigma_{\eta_X}^2}{\sigma_R^2} \right|R_{it} < 0)}\) are unlikely to be equal except under restrictive conditions due to the non-random sampling resulting in the SVR bias being determined by truncated sample distributions (i.e., \({\lambda^\ast \frac{\sigma_{\eta_X}^2}{\sigma_R^2}-\lambda^\ast \left| R_{it} \geq 0 \right.}\) and \({\lambda^\ast \frac{\sigma_{\eta_X}^2}{\sigma_R^2}-\lambda^\ast \left| R_{it} < 0 \right.)}.\) This will also occur because the conditional covariances (i.e., \({\sigma_{\eta_X,\eta} \left| R_{it} \geq 0 \right.}\) and \({\sigma_{\eta_X,\eta } \left| R_{it} < 0 \right.)}\) need not be zero (or equal) even if the unconditional covariance (i.e., \({\sigma_{\eta_X,\eta}})\) is zero.

Accordingly, the SVR and ST biases associated with \({\hbox{plim}(\hat{\delta}_0)}\) and \({\hbox{plim} (\hat{\delta}_1)}\) are the same as those obtained under the earlier assumption of stock price changes occurring due to the release of accounting earnings. This occurs again as empirically \({\hbox{plim} (\hat{\delta}_0)}\) and \({\hbox{plim} (\hat{\delta}_1)}\) are the same regardless of why stock price changes occur—i.e., stock price changes occur due to the release of information from sources that preempted the release of accounting earnings (i.e., λ* = 1), due to the release of accounting earnings (i.e., β = 1), or some combination of the two. The biases for the estimated R 2s for the “good” and “bad” news samples are also the same as those obtained under the earlier assumption of stock price changes occurring due to the release of accounting earnings—simply replace β with λ*.

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Dietrich, J.R., Muller, K.A. & Riedl, E.J. Asymmetric timeliness tests of accounting conservatism. Rev Acc Stud 12, 95–124 (2007). https://doi.org/10.1007/s11142-006-9023-y

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