Identifying accounting conservatism in the presence of skewness

Since Ball and Brown (1968), the financial accounting literature has studied the association between annual earnings and stock returns. It is well known that accounting earnings lack timeliness (i.e., prices lead earnings), because generally accepted accounting principles (GAAP) trade-off relevance and timeliness of financial statement information in favor of reliability and verifiability (e.g., Dechow 1994; Collins et al. 1994; Kothari et al. 2010). Basu (1997) predicts that conditionally conservative conventions that underlie the accounting measurement process are the source of a state-dependent positive correlation between earnings and returns. Using firms’ stock returns to measure news, Basu (1997) shows that the contemporaneous sensitivity of earnings to negative returns is two to six times higher than the sensitivity of earnings to positive returns. The incremental coefficient on negative returns in a piecewise-linear regression of scaled earnings on contemporaneous stock returns is known as the asymmetric timeliness (AT) coefficient and is the most widely used measure for assessing the degree of conservatism.¹

In this paper, we analyze the construct validity of Basu’s (1997) AT coefficient as a measure of accounting conservatism in the presence of skewed returns and earnings.² This investigation is important because several studies cast doubt on the validity of the AT coefficient as a measure of conditional conservatism for reasons attributable to the conditional variance of stock returns. Most notably, Dietrich et al. (2007) addresses the so-called sample truncation bias resulting from dividing the sample based on an endogenous variable (i.e., returns), while Patatoukas and Thomas (2011, 2016) and Dutta and Patatoukas (2017) argue that the AT coefficient is biased because of higher-order moments in the distribution of returns.³ Moreover, several papers modify the Basu (1997) model on a relatively ad hoc basis and provide defence for the AT coefficient as a valid measure of conditional conservatism (Ryan 2006; Ball et al. 2013a, b; Collins et al. 2014; Badia et al. 2021). Given this background, the purpose of this paper is to clarify the exact conditions under which the AT coefficient fails to identify accounting conservatism in the presence of skewness.

We begin our analysis by analytical assessment of the Basu (1997) model in the presence of skewness in data. To facilitate tractability, we take as our starting point that both earnings and returns are measured using their unexpected components, meaning that the earnings-returns relation is formulated entirely in terms of news (Ball et al. 2013a, b). We next perform extensive simulations to assess the individual and joint impacts of return skewness, earnings skewness, and return endogeneity on the validity of the AT coefficient. In doing so, we discuss the validity of arguments for and against using the AT coefficient as a measure of accounting conservatism. We make three main findings from our simulations. First, we document that the AT coefficient is a valid measure of conservatism when returns are a strictly exogenous variable. Specifically, when we simulate earnings as a linear function of exogenously realized returns, we do not find a spurious AT coefficient, even in the presence of skewness. This result follows from the well-known fact that unbiasedness of the OLS estimator does not require the variables to be Normally distributed, but it does require the independent variables to be exogenous (see Greene 2000). Given the concerns surrounding return skewness,⁴ we point out that different return variances between good and bad news subsamples do not per se lead to biased estimates of accounting conservatism.

Second, our simulations demonstrate that the adverse effect of skewness on the AT coefficient occurs when stock returns are an endogenous variable in the regression model such that partition into positive and negative return samples is non-random. In other words, when we endogenize returns by specifying returns as a function of exogenous earnings, or when we generate earnings and returns simultaneously (i.e., both are endogenous), we do find a spurious AT coefficient when the variables are skewed. We also study the latent variable model by Ball et al. (2013a), where earnings and returns are jointly realized as functions of unobservable components. Specifically, when the latent components are skewed, the AT coefficient is typically nonzero and significant, even in the absence of conservatism. A positive AT coefficient therefore does not necessarily identify conservatism. Since a strict exogeneity assumption of annual returns with respect to annual earnings is empirically unrealistic, the joint effect of endogeneity and skewness is of major concern for the measurement of conservatism as first proposed by Dietrich et al (2007).

Third, and consistent with our analytical predictions, we find that not only the positive skewness of returns but also the negative skewness of earnings can generate a spurious positive AT coefficient that is unrelated to conditional accounting conservatism. This is a novel finding. While negative earnings skewness is itself a predicted consequence of conservatism, it is certainly possible that cross-sectional differences in earnings skewness exist for reasons other than accounting conservatism (e.g., “big bath” accounting), thereby leading to misleading variation in the AT coefficient.

We also provide compelling evidence that simple skew-reducing transformations of the data and outlier-robust estimators do not resolve the issue. Within the Ball et al. (2013a, b) latent-variable framework, we illustrate that it is not possible to “fix” the AT measure by a logarithmic or rank transformation of the data. Skewness of the underlying components causes the relation between earnings and returns to be inherently nonlinear, which does not disappear when the observed returns and earnings are ex-post transformed to remove the skewness. This nonlinear relation between earnings and returns induces a nonzero AT coefficient while the underlying data generating process is free of accounting conservatism, even after skew-reducing transformations have been applied to the data. Asymmetry in the distributions of returns and earnings is generally a sign of nonlinearity in the underlying latent factors of returns and skewness (e.g., Ball et al. 2013a; Hemmer and Labro 2019; and Breuer and Windisch 2019). Adjusting for skewness ex-post using logarithmic and rank transformations, or by using outlier-robust estimators as suggested by Kim and Ohlson (2018), does not remove this underlying nonlinearity.⁵ As a result, we find that spurious AT coefficients appear even after applying these transformations.

Empirically, we investigate cross-sectional variation in return skewness, earnings skewness, and asymmetric timeliness. Consistent with our analytical predictions, the empirical AT coefficients are strongly correlated to the skewness coefficients of unexpected earnings and unexpected returns.⁶ Following Khan and Watts (2009), Ball et al. (2013b), and Patatoukas and Thomas (2016), the firm-specific characteristics that we consider are beginning-of-period size and the market-to-book ratio (MTB), because conservatism is expected to vary with these characteristics.⁷ Specifically, we construct deciles by independently sorting US firms on size and MTB, after which we estimate Basu’s (1997) AT coefficient for each decile. When sorting firms on size, it appears that cross-sectional variation in asymmetric timeliness coefficients coincides with variation in return and earnings skewness. When sorting on the MTB ratio, we find that the differences in skewness are not significant, such that variation in the AT coefficient provides stronger evidence for cross-sectional variation in conservatism. In addition, Basu’s (1997) AT coefficient indicates asymmetry in the timeliness of (unexpected) earnings and accruals, but also of cash flows. We take this as further evidence of spurious asymmetric timeliness, since cash flows are not subject to conservative reporting (e.g., Dietrich et al. 2007; Collins et al. 2014; Dutta and Patatoukas 2017).

Taken together, our analytical, numerical, and empirical results contribute to the literature by showing that the AT coefficient is significantly distorted in the presence of skewness, such that inferences based on estimated AT coefficients may be misleading. Concerning the distribution of earnings and accruals, we cannot rule out a “reverse causality” explanation, in which the skewness of observed earnings or accruals is by itself the result of accounting conservatism (Basu 1995; Ball et al. 2000; Givoly and Hayn 2000; Ball and Shivakumar 2005; Peek et al. 2010; Dutta and Patatoukas 2017).⁸ We can, however, safely assume that return skewness is unrelated to conservatism, and therefore contaminates the AT coefficient as a measure of conservatism. We stress that the OLS estimator of the AT coefficient is not statistically biased. The estimator correctly indicates asymmetry (or nonlinearity) in the earnings-returns relation. While conservatism plausibly contributes to this asymmetric relation, there may be several other factors contributing as showed by prior studies (see fn. 3). In other words, the relation between earnings and returns is not necessarily linear in the absence of conservative accounting. We therefore conclude that, without controlling for these other sources of asymmetry, the AT coefficient does not reliably identify conditional conservatism in the presence of return skewness.

The following section provides an analytical background of the Basu (1997) model and demonstrates the potentially adverse effects of the skewness of earnings and returns on the AT measure. In Sect. 3, we conduct a simulation exercise to demonstrate the properties of the AT measure under different assumptions regarding the distribution and endogeneity of both returns and earnings. In Sect. 4, we examine the effect of skewness within the Ball et al. (2013a) latent variable framework and test the effect of skew reducing transformations. Section 5 presents empirical results. Concluding remarks are provided in the final section of the paper.

In this section, we provide an overview of the Basu (1997) model and demonstrate analytically how skewness in earnings and returns can lead to nonzero values of the asymmetric timeliness (AT) coefficient, even without the presence of conditional conservatism. The Basu (1997) model is represented by the following equation:where i and t are firm and year subscripts, respectively; I denotes price-deflated unexpected earnings per share; R denotes unexpected stock returns; D is an indicator variable that takes a value of 1 when \(R<E\left[R\right]\) (expected return), and 0 otherwise. \({\beta }_{1}\) is the AT coefficient, which measures the asymmetry in the relation between earnings and returns.

The AT coefficient can be equivalently obtained by estimating the simple regressionseparately for subsamples of observations with \(R<0\) and \(R\ge 0\), and taking the difference between the slope estimates:

The OLS estimator of \(\beta\) in Eq. (2) is equal to:where \({\sigma }_{R}\) is the standard deviation of returns; \({\sigma }_{I}\) is the standard deviation of earnings; and \({\rho }_{R,I}\) is the correlation coefficient between returns and earnings. Using this notation, the AT coefficient and Eq. (3) can be expressed as follows:

In Eq. (5), it becomes evident that both positive skewness of returns and negative skewness of earnings can result in a positive AT coefficient.⁹ When returns are positively skewed, it follows from the definition of skewness that:

When returns are positively skewed, the standard deviation of returns for observations above the mean (R ≥ 0) is expected to be higher than that for observations below the mean (R < 0). As a result, the first term of Eq. (5) is larger than the second term, given a positive correlation between earnings and returns. Therefore, even in the absence of conditional conservatism, the OLS estimator \({\widehat{\beta }}_{1}\) can be positive due to positive return skewness. However, it is important to note that the OLS estimator does not require variables to follow a normal distribution. In the subsequent section, we demonstrate through simulations that skewness of returns does not always lead to a nonzero AT coefficient because the assumption of fixed values for \({\sigma }_{I}\) and \({\rho }_{R,I}\) may not hold. Specifically, if returns are specified as strictly exogenous, any difference in \({\sigma }_{R}\) (Eq. 6) is offset by simultaneous differences in \({\sigma }_{I}\) and \({\rho }_{R,I}\), resulting in a zero AT coefficient (Eq. 5).

Furthermore, we demonstrate that negative skewness of earnings can also generate a spurious positive estimate of the AT coefficient under empirically plausible conditions. When earnings are negatively skewed and positively correlated with returns (even in the absence of conditional conservatism), dividing the sample into subsamples of relatively high (low) returns coincides with subsamples of relatively high (low) earnings. Thus, when earnings are negatively skewed, it follows that:

As a result, the standard deviation of earnings for a subsample of low returns paired with relatively high earnings (I ≥ 0) is expected to be higher than the standard deviation for a subsample of high returns paired with relatively low earnings (I < 0). Assuming fixed values for \({\sigma }_{R}\) and \({\rho }_{R,I}\), the first term of Eq. (5) becomes larger than the second term due to the numerator being larger in the first term. Consequently, the OLS estimator \({\widehat{\beta }}_{1}\) in the Basu model Eq. 1) can be positive in the presence of negative earnings skewness, even without conditional conservatism.

This section highlights the analytical foundation of the Basu model and its implications for the estimation of the AT coefficient. By considering the skewness of returns and earnings, we demonstrate how positive and negative skewness can lead to spurious positive estimates of the AT coefficient, regardless of conditional conservatism.

In this section, we present the results of a simulation exercise aimed at illustrating the concepts discussed earlier. The simulation involves generating observations of two correlated variables and examining the circumstances under which a spurious nonzero asymmetric timeliness (AT) coefficient arises. While referred to as "returns" and "earnings," these variables are not meant to replicate real-world properties but rather to evaluate the AT estimator's characteristics when analyzing the relationship between correlated skewed variables without considering accounting conservatism. Earnings are assumed to be a linear function of returns, with returns treated as an exogenous variable and earnings generated endogenously using a combination of returns and an independently and identically distributed (i.i.d.) innovation term. The simulation allows us to assess the behavior of the AT estimator in the absence of conditional conservatism and investigate situations where positive skewness in returns or negative skewness in earnings can lead to a positive AT coefficient.

Data generating process 1: Earnings are a linear function of returns

For simplicity, and without loss of generalization, we assume that both R and the innovation term \(\epsilon\) have mean zero and standard deviation one. We calibrate the parameters \({\gamma }_{1}=0\) and \({\gamma }_{2}=0.6\), indicating a positive linear relation between returns and earnings. We simulate N = 1000 observations of R and \(\epsilon\) from a Normal distribution, such that neither R nor \(\epsilon\) are skewed. We then estimate the Basu model (Eq. 1) on the simulated data, repeating this process 10,000 times (r = 10,000). The results, presented in the first column of Table 1, show the sample averages and standard deviations of the estimated coefficients. The table also includes additional statistics on the simulated distribution of returns and earnings. As expected, given the linear specification between R and I, both the coefficient on the dummy term and the AT coefficient on the interaction term are not significantly different from zero.

We generate three additional simulated samples by: (i) transforming R into a right (positively) skewed variable; (ii) transforming \(\epsilon\) into a left (negatively) skewed variable; and (iii) transforming both R and \(\epsilon\) into right and left skewed variables, respectively. Skewed variables are sampled from the skew-normal distribution introduced by Azzalini (2013), allowing for a straightforward comparison of samples with varying degrees of skewness while keeping other distribution properties constant.¹⁰ Columns 2–4 of Table 1 report the estimated coefficients of the Basu models using skew-transformed simulated data. As the results in Table 1 indicate, the AT coefficient \({\beta }_{1}\) remains insignificant even if R is right-skewed and/or \(\epsilon\) is left-skewed. This finding demonstrates that skewness of the underlying variables alone does not introduce bias in the AT coefficient when the data generating process specifies earnings as a linear function of returns. This aligns with the expectation that the unbiasedness and consistency of the OLS estimator rely on the exogeneity of the independent variables (R and \(\epsilon\) being uncorrelated), rather than assuming non-skewed normally distributed data (e.g. Greene 2000). This aligns with the expectation that the unbiasedness and consistency of the OLS estimator rely on the exogeneity of the independent variables (R and \(\epsilon\) being uncorrelated), rather than assuming non-skewed normally distributed data. However, it is important to note that the assumption made in the previous section, where \({\sigma }_{I}\) and \({\rho }_{R,I}\) were considered fixed values across positive and negative return samples, does not hold in our simulation exercise, as shown in the second column of Table 1. In this simulation, the higher variance of returns in the positive sample (indicative of positive skewness) is offset by a higher variance of earnings and a higher correlation between earnings and returns in positive return samples. Consequently, the relationship between earnings and returns remains linear, and the expected value of the AT coefficient (Eq. 5) remains zero, despite the underlying skewness.

Next, we explore the scenario where returns are specified as a linear function of earnings. This situation corresponds to the case described by Dietrich et al. (2007), where the Basu regression model reverses a structural equation. In this setup, returns, which serve as the independent variable in the Basu regression, are considered endogenous and depend on earnings:

Data generating process 2: Returns are a linear function of earnings

In a similar manner to the previous data generating process, we calibrate \({\theta }_{1}=0\) and \({\theta }_{2}=0.6\). We conduct the same simulation exercise by generating simulated samples of N = 1000 observations of R, ω, and I under both Normal and skewed distributions. We estimate the Basu model (Eq. 1) using the simulated data and report the sample averages and standard deviations of the r = 10,000 estimated coefficients in Table 2. In the absence of skewness (first column), the AT coefficient remains insignificant. However, when I and/or ω exhibit skewness, a spurious significant AT coefficient emerges. This simulation result confirms the prediction made by Dietrich et al. (2007): the AT coefficient is a biased measure of conditional conservatism when the sample is truncated based on the endogenous sign of returns. Notably, this sample truncation bias arises only in the presence of skewness, as demonstrated by our simulations.

Finally, we consider the case where R is not specified as a linear function of I or vice versa. Instead, we simulate values of R and I simultaneously from a joint distribution, such that both R and I are endogenous.

Data generating process 3: Earnings and returns are jointly distributed

As before, we simulate a sample of N = 1000 observations of R and I, and estimate the Basu model (Eq. 1), on the sample of simulated data. The first column of Table 3 reports the regression results when the data is simulated from a Multivariate Normal distribution. As expected, since the relation between R and I is linear, the coefficient on the dummy term and the AT coefficient on the interaction term are not significantly different from zero.

We proceed by transforming R and/or I into positively and negatively skewed variables, respectively. The results in Table 3 demonstrate that when R is right-skewed and/or I is left-skewed, the AT coefficient \({\beta }_{1}\) becomes positive and significant. Importantly, this outcome arises even in the absence of any structure associated with accounting conservatism in the data-generating process. Therefore, the significant AT coefficient observed in these cases can be attributed to the asymmetry resulting from skewness rather than conditional conservatism.

Figure 1 illustrates the relationship between simulated observations of R and I, based on data generating process 3. In Panel A, where both R and I follow a Normal distribution, no evidence of conservatism is observed, as expected. However, when positive skewness is introduced to R, the Basu regression line exhibits a positive slope, resulting in a "kink" in Panel B. Similarly, in Panel C, where earnings are negatively skewed, a weaker kink is observed. The most pronounced kink occurs in Panel D, where both returns are positively skewed and earnings are negatively skewed. It is important to note that these kinks, which may mistakenly be interpreted as evidence of accounting conservatism, are solely due to the presence of skewness rather than actual conservatism. The dashed line represents a simple regression of I on R over the entire sample.

The simulation results presented in this section demonstrate that skewness can lead to a spurious nonzero AT coefficient in the absence of accounting conservatism, except when returns are strictly exogenous. In cases where returns are strictly exogenous, the AT coefficient remains zero regardless of the skewness of the underlying variables, as shown in Table 1. However, when returns are endogenous (Tables 2 and 3) and the underlying variables (R or I) exhibit skewness, the AT coefficient becomes nonzero, potentially misleadingly suggesting the presence of accounting conservatism. The combination of skewness and endogeneity of returns represents a significant empirical scenario, as both returns and earnings commonly exhibit skewness. On the other hand, assuming strict exogeneity of returns (where returns occur independently from earnings) is unrealistic when estimating regression (1), as acknowledged by various recent studies such as Ball et al. (2013a) and Dutta and Patatoukas (2017). In the next section, we explore the impact of skewness in the latent factors that determine both earnings and returns on the AT coefficient.

This paper examines the construct validity of the AT coefficient as a measure of conditional conservatism in the presence of skewed returns and earnings. Through simulations, we find that the AT coefficient is only insensitive to skewness when returns are strictly exogenous, which is empirically unrealistic. When considering the Ball et al. (2013a) latent factor model, we observe that skewness of the underlying factors significantly impacts the AT coefficient. However, skewness alone is not sufficient to generate a spurious AT coefficient, as endogeneity of returns plays a crucial role. Various econometric adjustments and transformations do not eliminate the adverse impact of skewness on the AT coefficient. Empirically, we find cross-sectional variation in asymmetric timeliness across deciles based on market capitalization and the MTB ratio. The AT coefficient is higher for large firms and value firms. The observation that the high AT coefficient for large firms may not be attributed to conservatism due to the presence of high return skewness and low earnings skewness highlights the complexity of interpreting the results. However, the higher AT coefficient for value firms, particularly stemming from the accrual component of earnings, provides stronger evidence of conservatism. This finding suggests that conservative reporting practices are more prevalent in value firms and contribute to the observed asymmetry in the relation between earnings and returns.

Overall, our analysis highlights the significance of considering other economic explanations and confounding factors when interpreting the AT coefficient. We emphasize the need to form groups with similar skewness properties for comparative analysis, as this can provide more meaningful insights into the degree of asymmetric timeliness in financial reporting. Moreover, we believe that investigating specific mechanisms at both the firm and institutional level that induce conservatism in financial reporting is an important avenue for future research. Understanding the factors and drivers that contribute to the observed patterns of conservatism can enhance our knowledge of financial reporting practices and their implications.