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Conservatism measures that control for the effects of economic rents on stock returns

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Abstract

Recent studies show that regression-based estimates of accounting conservatism reflect both differences in the asymmetric recognition of bad news and differences in asset composition. In particular, a firm’s market value and returns reflect both assets-in-place and expected future rents, while book values tend to reflect only assets-in-place. We propose two tests that remove the effect of asset composition on cross-sectional comparisons of accounting conservatism. First, a test based on a ratio of regression coefficients allows for valid cross-sectional comparisons of conservatism relative to overall news recognition. Second, in some cases, researchers can separately identify and make cross-sectional comparisons of the fraction of good news recognized and the fraction of bad news recognized. The estimates in this second scenario use a regression of earnings on returns interacted with a book-to-market ratio. We validate our model by deriving and testing several predictions based on it.

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Notes

  1. See Guay and Verrecchia (2006) for a discussion of the importance of distinguishing between estimates of a firm’s bad news recognition versus its recognition of bad news relative to good news.

  2. See the contemporaneous paper by Ball et al. (2009) for an alternative econometric model.

  3. This assumption relates to Roychowdhury and Watts’ (2007) development of Watts’ (2003a) framework in which accounting attempts to represent the value of a firm’s separable assets.

  4. We searched articles in Contemporary Accounting Research, Journal of Accounting and Economics, Journal of Accounting Research, Review of Accounting Studies, and The Accounting Review through March 2012.

  5. We show that controlling for lagged earnings yields statistically significant coefficients on positive earnings in earnings/returns regressions, which is important for using a ratio to infer conservatism.

  6. Although not modeled here, current earnings could also recognize a portion of prior unrecognized changes in separable assets and realized rents. The exclusion of these elements from the model does not affect our inferences because we assume the current recognition of prior returns is uncorrelated with current returns. Our more elaborate econometric model available from the authors does incorporate these additional elements.

  7. This does not eliminate the need to have a fairly precise measure of the coefficient on positive returns. The Appendix discusses the Fieller method procedure for computing confidence intervals for ratios of regression coefficients. The regression coefficients must be statistically significant in order to have bounded confidence intervals. For example, a 95 % confidence interval requires that the regression coefficients be significant at the 5 % level. This implies that the ratios will be statistically insignificant in settings where the asymmetric timeliness coefficient is statistically insignificant, such as Eng and Lin (2012) examination of Chinese cross-listing firms.

  8. Although this prediction is not immediately obvious, the derivation is available from the authors upon request.

  9. Another approach to estimating asymmetric timeliness in the absence of market return data is to measure the frequency of large negative net income (e.g. Barth et al. 2008; Elbannan 2011).

  10. The market-to-book ratio reflects both asymmetric timeliness and ex ante conservatism.

  11. Our analysis in the next section shows that the typical Basu (1997) framework produces estimates of β 2 near zero. However, including additional controls to better measure unexpected earnings and unexpected returns often results in a positive coefficient on positive returns.

  12. Pope and Walker (1999) do not assess the statistical significance of their ratio measures.

  13. We use earnings per share from continuing operations, but note there is no consistency in the literature. Of the 36 studies that use returns in their measurement of conservatism, 18 use earnings per share from continuing operations, 10 use earnings per share, 4 use both, and 4 do not provide enough detail to determine which measure they used.

  14. This evidence must be viewed as consistent with P2, but not as conclusive. This is because multiplying returns by any number between zero and one will tend to generate larger coefficients. The interpretation of the estimates rests on their derivation from our econometric model. If the book-to-market ratio is unrelated to the structural construct λ, then its interaction with returns when estimating (7) can be viewed as a source of bias. For the specification to be totally invalid would require the book-to-market ratio to be totally unrelated to the portion of firm value due to separable net assets, which seems unlikely; however, the book-to-market ratio is an imperfect measure of λ and therefore does yield some estimation bias as we noted earlier.

  15. The difference in coefficient results relative to Kwon et al. (2006) may be due to differences in sample construction.

  16. The number of observations is reduced in these tests due to the variable restrictions necessary to estimate the Shu (2000) model.

  17. Untabulated analysis shows that the mean (median) beginning book-to-market ratio of high litigation firms is 0.560 (0.447) versus 0.781 (0.626) for the non-high litigation firms.

  18. We also recognize that economic circumstances affect the implementation of standards and cause variation in conservatism measures across time. Our model explicitly allows this. However, as Givoly et al. (2007) point out, the variation across time may partially be due to poor estimation in years with few negative news observations.

  19. Measures of ex ante conservatism, including Easton and Pae’s (2004) measures of conservatism due to positive NPV projects and rules and Penman and Zhang’s (2002) ‘hidden reserves’ measure, should not necessarily be correlated with the AT ratio.

  20. The market-to-book ratio is also impacted by ex ante conservatism since ex ante conservatism excludes rents from book values and can also understate separable assets via, for example, accelerated depreciation.

  21. For the AT coefficients, discretionary accruals, and the persistence coefficient the null to test significance is zero. For the ratios and book-to-market the null to test significance is one, and for the CR rank significance is tested relative to a null of three.

  22. Also see Staiger, Stock and Watson (1997) for an example application of this approach.

  23. If d′β < 0 the second inequality is reversed, but (A2) still determines the confidence interval.

  24. See Buonaccorsi (1979) and Zerbe’s (1978) response for a discussion that a 2 > 0 implies \( a_{1}^{2} - a_{0} a_{2} > 0 \), and a discussion of the confidence interval when a 2 < 0.

  25. For example, if the ratio’s denominator is the jth regressor β j , then \( a_{2} = (\varvec{\beta}_{j}^{2} /\hat{\varvec{\sigma }}_{jj}^{2} - t_{\alpha /2}^{2} )\hat{\varvec{\sigma }}_{jj}^{2} \) so that \( a_{2} < 0 \)and the confidence interval is unbounded if β j is insignificant based on a two-tailed test with significance α.

  26. We computed the confidence intervals using the regFieller.ado Stata program available on Judson Caskey’s website: http://webspace.utexas.edu/jc2279/www/data.html.

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Acknowledgments

We thank an anonymous referee, David Aboody, Sudipta Basu, Peter Demerjian, Carla Hayn, Jack Hughes, Steve Matsunaga, Karl Muller, Eddie Riedl and workshop participants at AAA FARS 2009 Mid-Year Meeeting, Pennsylvania State University, UCLA and University of Southern California for their helpful comments. This paper was previously titled “On the estimation of the asymmetric timeliness of earnings: Inference and bias corrections.”

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Authors and Affiliations

  1. McCombs School of Business, University of Texas, Austin, 1 University Station, B6400, Austin, TX, 78712, USA

    Judson A. Caskey

  2. Lundquist College of Business, University of Oregon, Eugene, OR, 97403, USA

    Kyle Peterson

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  1. Judson A. Caskey
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Correspondence to Kyle Peterson.

Appendix

Appendix

This appendix describes the construction of confidence intervals for ratios of regression coefficients based on Fieller’s Theorem (Fieller 1954) as implemented in Zerbe (1978).Footnote 22 The confidence intervals are based on transforming a hypothesis for the ratio to an equivalent linear hypothesis. Given a value k, a vector β of p estimated coefficients and vectors n and d, the ratio \( \varvec{n}^{\prime } \varvec{\beta /d}^{\prime } \varvec{\beta > k} \) if and only if \( \varvec{n}^{\prime }\varvec{\beta}/\varvec{kd}^{\prime }\varvec{\beta}> 0 \).Footnote 23 Given estimated coefficients \( \hat{\varvec{\beta }} \) and covariance matrix \( \hat{\varvec{\Upsigma }} \) , a t-statistic for the inequality is:

$$ T = (\varvec{n}^{\prime } \hat{\varvec{\beta }} - \varvec{kd}^{\prime } \hat{\varvec{\beta }})/\sqrt {\varvec{n}^{\prime } \hat{\varvec{\Upsigma}}\varvec{n} - 2k\varvec{n}^{\prime } \hat{\varvec{\Upsigma}}\varvec{d} + k^{2} \varvec{d}^{\prime } \hat{\varvec{\Upsigma}}\varvec{d}} . $$
(9)

Given a confidence level α, sample size N and critical t-statistic t α/2 with N − p degrees of freedom such that P(−t α/2 < T < t α/2) = 1 − α, the confidence intervals on the ratio level k solve:

$$ a_{0} + 2a_{1} k + a_{2} k^{2} \le 0, $$
(10)
$$ a_{0} = (\varvec{n}^{\prime }\varvec{\beta})^{2} - t_{\alpha /2}^{2} \varvec{n}^{\prime } \hat{\varvec{\Upsigma}}\varvec{n}\quad a_{1} = t_{\alpha /2}^{2} \varvec{n}^{\prime } \hat{\varvec{\Upsigma}}\varvec{d} - (\varvec{n}^{\prime }\varvec{\beta})(\varvec{d}^{\prime }\varvec{\beta})\quad a_{2} = (\varvec{d}^{\prime }\varvec{\beta})^{2} - t_{\alpha /2}^{2} \varvec{d}^{\prime } \hat{\varvec{\Upsigma}}\varvec{d} $$
(11)

If a 2 > 0, then the 1 − α confidence interval for the ratio is \( ( - a_{1} \pm \sqrt {a_{1}^{2} - a_{0} a_{2} } )/a_{2} \).Footnote 24 If a 2 < 0 then the confidence interval is unbounded.Footnote 25 In this case, if \( a_{1}^{2} - a_{0} a_{2} < 0 \), then the confidence interval is the entire real line. If a 2 < 0 and \( a_{1}^{2} - a_{0} a_{2} > 0 \), then the confidence interval is the complement of \( ( - a_{1} \pm \sqrt {a_{1}^{2} - a_{0} a_{2} } )/a_{2} \).Footnote 26

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Caskey, J.A., Peterson, K. Conservatism measures that control for the effects of economic rents on stock returns. Rev Quant Finan Acc 42, 731–756 (2014). https://doi.org/10.1007/s11156-013-0360-1

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