Identifying accounting conservatism in the presence of skewness

Abstract

The asymmetric timeliness (AT) coefficient as a measure of accounting conservatism has been subject to much debate. We clarify the conditions under which the AT coefficient identifies accounting conservatism in the presence of skewness. Specifically, using an extensive simulation-based approach, we examine the joint impact of return skewness, earnings skewness, and return endogeneity. We show that skewness of returns and earnings distorts the AT coefficient as a measure of conservatism when returns are endogenous. While earnings skewness is a predicted consequence of conditional conservatism, return skewness is arguably unrelated to conservative reporting and cannot be tackled by simple skew reducing transformations or outlier-robust estimators. Empirically, we analyze AT and skewness of firms sorted on size and MTB, highlighting the importance of constant skewness across groups for accurate comparisons of accounting conservatism.

1 Introduction

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.

2 Analytical background

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:

$${I}_{it}={\alpha }_{0}+{{\alpha }_{1}D}_{it}+{\beta }_{0}{R}_{it}+{\beta }_{1}{{R}_{it}\times D}_{it}+{\varepsilon }_{it},$$

(1)

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 regression

$${I}_{it}=\alpha +\beta {R}_{it}+{\varepsilon }_{it}$$

(2)

separately for subsamples of observations with $R<0$ and $R\ge 0$, and taking the difference between the slope estimates:

$$E\left[ {\hat{\beta }_{1} } \right] = E\left[ {\hat{\beta }|R < 0} \right] - E\left[ {\hat{\beta }|R \ge 0} \right].$$

(3)

The OLS estimator of $\beta$ in Eq. (2) is equal to:

$$\widehat{\beta }=\frac{Cov(R,I)}{Var(R)}=\frac{{\sigma }_{R}{\sigma }_{I}{\rho }_{R,I}}{{\sigma }_{R}^{2}}=\frac{{\sigma }_{I}{\rho }_{R,I}}{{\sigma }_{R}},$$

(4)

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:

$$E\left[{\widehat{\beta }}_{1}\right]=E\left[\frac{\left({\sigma }_{I|R<0}\right)\left({\rho }_{I,R|R<0}\right)}{\left({\sigma }_{R|R<0}\right)}\right]-E\left[\frac{\left({\sigma }_{I|R\ge 0}\right)\left({\rho }_{I,R|R\ge 0}\right)}{\left({\sigma }_{R|R\ge 0}\right)}\right].$$

(5)

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:

$${\sigma }_{R|R\ge 0}\ge {\sigma }_{R|R<0}.$$

(6)

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:

$${\sigma }_{I|R\ge 0}\approx {\sigma }_{I|I\ge 0}<{\sigma }_{I|I<0}\approx {\sigma }_{I|R<0}.$$

(7)

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.

3 Simulation results

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

$${R}_{i} \sim i.i.d.\left(\mathrm{0,1}\right)$$

$${\epsilon }_{i} \sim i.i.d.\left(\mathrm{0,1}\right)$$

$${I}_{i}={\gamma }_{1}+{\gamma }_{2}{R}_{i}+{\epsilon }_{i}$$

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.

Table 1 Simulation results—Earnings as a linear function of Returns

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

$${I}_{i} \sim i.i.d.\left(\mathrm{0,1}\right)$$

$${\omega }_{i} \sim i.i.d.\left(\mathrm{0,1}\right)$$

$${R}_{i}={\theta }_{1}+{\theta }_{2}{I}_{i}+{\omega }_{i}$$

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.

Table 2 Simulation results—Returns as a linear function of Earnings

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

$$\left[\begin{array}{c}{R}_{i}\\ {I}_{i}\end{array}\right] \sim i.i.d.\left(\left[\begin{array}{c}0\\ 0\end{array}\right],\left[\begin{array}{cc}1& \rho \\ \rho & 1\end{array}\right]\right)$$

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.

Table 3 Simulation results—Earnings and Returns jointly distributed

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.

Fig. 1

Basu (1997) regressions on simulated data. This figure plots N = 1000 simulated observations of unexpected earnings (I) and unexpected returns (R) with the corresponding simple regression (dashed line) and a piecewise-linear Basu (1997) regression (solid line). In Panel A, I and R are Multivariate Normally distributed, with a correlation of 0.6 (data generating process 3). In Panel B, I is Normally distributed and R is right-skewed. In Panel C, I is left-skewed and R is Normally distributed. In Panel D, both I and R are left- and right-skewed, respectively

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.

4 Skewness and asymmetric timeliness in a latent factor model

4.1 Ball et al. (2013a) model of accounting income recognition

In this section, we discuss the accounting income recognition model proposed by Ball et al. (2013a).¹¹ The model distinguishes four unobserved (latent) components that capture the key characteristics of income recognition as practiced. The purpose of this section is to simulate artificial returns and earnings based on the Ball et al. (2013a) model and a modified version that excludes accounting conservatism. The goal of the model is not to match all empirical properties of returns and earnings, but rather to generate artificial returns and earnings from underlying latent factors with different distributional properties. This simulation approach thus allows for comparisons between firms with different levels of skewness in returns and earnings and between conservative and non-conservative firms, facilitating a strict comparison that would be challenging using empirical data and bootstrapping methods.¹²

The relation between unexpected returns (${R}_{it}$) and unexpected earnings (${I}_{it}$) in the Ball et al. (2013a) model is described by Eqs. (8) and (9):

$${R}_{it}={x}_{it}+{y}_{it}+{g}_{it}$$

(8)

$${I}_{it}={x}_{it}+{w}_{it}{y}_{it}+\left(1-{w}_{it-1}\right){y}_{it-1}+{g}_{it-1}+{\varepsilon }_{it}-{\varepsilon }_{it-1},$$

(9)

where the subscripts i and t denote firm and year, respectively. Returns consist of three unobserved information components ${x}_{it}$, ${y}_{it},$ and ${g}_{it}$. The information component ${x}_{it}$ is incorporated into accounting income contemporaneously. The second information component ${y}_{it}$ is subject to conditional conservatism. It is incorporated into accounting income contemporaneously or with a lag, depending on its state. When ${y}_{it}$ is negative, it is reported immediately in accounting income (${w}_{it}=1$ if ${y}_{it}<0$), while reporting ${y}_{it}$ is delayed to the next period during positive states (${w}_{it}=0 \mathrm{if }{y}_{it}\ge 0$).¹³ The third information component ${g}_{it}$ is always incorporated into accounting income with delay. The fourth component ${\varepsilon }_{it}$ is an accounting error that is reversed in the next period.

Without loss of generalizations, we assume that the unobserved components${x}_{i,t}$, ${y}_{i,t},$ ${g}_{i,t},$ and ${\varepsilon }_{i,t}$ have mean zero and are serially uncorrelated. However, we do allow, following Ball et al. (2013a), for a positive contemporaneous correlation ρ between ${x}_{it} , {y}_{it},$ and${g}_{it}$. Given these properties, the covariance between I and R, conditional on a negative state (${w}_{it}=1$), is:

$$\begin{aligned} \sigma_{RI|w = 1} & = Cov\left( {\left( {x_{it} + y_{it} + g_{it} } \right),\left( {x_{it} + y_{it} + \left( {1 - w_{it - 1} } \right)y_{it - 1} + g_{it - 1} + \varepsilon_{it} - \varepsilon_{it - 1} } \right)|w_{it} = 1} \right) \\ & = Cov\left( {\left( {x_{it} + y_{it} + g_{it} } \right),\left( {x_{it} + y_{it} } \right)|w_{it} = 1} \right) \\ & = \sigma_{x|w = 1}^{2} + \sigma_{y|w = 1}^{2} + 2\sigma_{xy|w = 1} + \sigma_{xg|w = 1} + \sigma_{yg|w = 1} , \\ \end{aligned}$$

(10)

while the covariance between I and R, conditional on a positive state ($w_{it} = 0$), is:

$$\begin{aligned} \sigma_{RI|w = 0} & = Cov\left( {\left( {x_{it} + y_{it} + g_{it} } \right),\left( {x_{it} + \left( {1 - w_{it - 1} } \right)y_{it - 1} + g_{it - 1} + \varepsilon_{it} - \varepsilon_{it - 1} } \right)|w_{it} = 1} \right) \\ & = Cov\left( {\left( {x_{it} + y_{it} + g_{it} } \right),x_{it} |w_{it} = 1} \right) \\ & = \sigma_{x|w = 0}^{2} + \sigma_{xy|w = 0} + \sigma_{xg|w = 0} . \\ \end{aligned}$$

(11)

Ball et al (2013a) assume that the unobserved components x, y, and g follow a symmetric (non-skewed) distribution. In this case, since ${\sigma }_{A|w=1}={\sigma }_{A|w=0}$ for $A\in \left\{x,y,g,xy,xg,yg\right\}$, it follows that ${\sigma }_{RI|w=1}-{\sigma }_{RI|w=0}={\sigma }_{y}^{2}+{\sigma }_{yg}$, which is a strictly positive number implying that ${\sigma }_{RI|w=1}\ge {\sigma }_{RI|w=0}$. In the absence of conservative reporting, (i.e. when the component y is not included in the model), the difference between ${\sigma }_{RI|w=1}$ and ${\sigma }_{RI|w=0}$ reduces to zero. In summary, conservative accounting practice causes the covariance between returns and earnings to be higher in negative states than in positive states. Given this result, the asymmetric timeliness coefficient ${\beta }_{1}$ in Eq. (1) is expected to be positive in the presence of conservatism and zero in the absence of conservatism.¹⁴ However, this result depends crucially on the assumption that x, y, and g follow a symmetric distribution. When these components are skewed, such that ${\sigma }_{A|w=1}\ne {\sigma }_{A|w=0}$, the inequality ${\sigma }_{RI|w=1}\ge {\sigma }_{RI|w=0}$ is not necessarily valid, and hence the sign of ${\beta }_{1}$ is unclear.

We illustrate this insight by a simulation exercise. We simulate the components $x, y, g$, and $\varepsilon$ for a cross-section of N = 1000 firms with t = 2 time-series observations per firm. For each firm i, we thus draw eight random numbers $\left({x}_{i0}, {x}_{i1}, {y}_{i0},{y}_{i1},{g}_{i0},{g}_{i1},{\varepsilon }_{i0},{\varepsilon }_{i1}\right)$ from a Multivariate Standard Normal (i.e. non-skewed) distribution. From these simulated random numbers, we compute ${R}_{i1} \mathrm{and} {I}_{i1},$ implied by Eqs. (8)–(9), respectively, for each firm i. We also use the simulated variables $\left({x}_{i0}, {x}_{i1}, {g}_{i0},{g}_{i1},{\varepsilon }_{i0},{\varepsilon }_{i1}\right)$ to generate returns and earnings from a restricted specification of the model that does not feature accounting conservatism. This model is equal to the model by Ball et al. (Eqs. 8–9), with the difference that the term y is excluded from the model:

$${R}_{it}={x}_{it}+{g}_{it}$$

(12)

$${I}_{it}={x}_{it}+{g}_{it-1}+{\varepsilon }_{it}-{\varepsilon }_{it-1}.$$

(13)

We then use the simulated samples of N observations of earnings and returns to estimate the coefficients of the Basu (1997) regression Eq. (1), both in the presence and absence of conservatism.

This process is repeated r = 10,000 times, and we report the means of the 10,000 estimates in Table 4. We consider four different values of the correlation ρ between x, y, and g ($\rho \in \left\{0, 0.2, 0.5, 0.8\right\}$). The top panel of Table 4 shows that in the presence of conservatism, the mean of the estimated AT coefficients (${\beta }_{1}$) is indeed positive and significant. In the absence of conservatism (right panel), the mean of the estimated AT coefficients (${\beta }_{1}$) is, as expected, insignificant and close to zero. With Normally-distributed data, the AT coefficient thus correctly identifies conservatism.

Table 4 Simulation of the Ball et al. (2013a) model

We repeat this experiment after transforming the Standard Normally distributed variables x, y, and g into right-skewed variables, using the same transformation as in Sect. 3, based on the Skew-Normal distribution by Azzalini (2003). This transformation of the underlying components x, y, and g induces skewness of the realized earnings and returns. The results are reported in the lower three panels of Table 4. After allowing the unobserved components of returns and earnings to be skewed, the mean AT coefficients ${\beta }_{1}$ remain significant, but they are no longer uniformly positive. Hence, even if the data are generated by a model that features accounting conservatism, the Basu regression could indicate negative rather than positive asymmetric timeliness, due to the non-symmetric distribution of the underlying components.

Using the restricted model that is free of conservatism Eqs. (12)–(13), a statistically significant AT coefficients (${\beta }_{1}$) appears once we introduce skewness to the latent variables x and g. This constitutes a clear example of “spurious conservatism”, in which the statistical distribution of the underlying components leads to an asymmetric relation between returns and earnings, which may be interpreted incorrectly as accounting conservatism. The results in Table 4 further indicate that skewness does not only affect the AT coefficient (${\beta }_{1}$), but also the estimated individual effect of the positive-return dummy variable (${\alpha }_{1}$) is spuriously different from zero in the presence of skewness.

The final column of Table 4 presents the difference between the estimated AT coefficient in the presence and absence of conservatism. Importantly, this difference is consistently positive across all cases. Specifically, when keeping skewness constant, introducing conservatism into the model leads to an increase in the estimated AT coefficient. This finding confirms that the Basu regression has the ability to distinguish between firms with and without conservative accounting practices, given that returns and earnings in both groups exhibit similar skewness properties.

In such a scenario where the skewness properties are comparable, the variation in the AT coefficient across groups provides stronger evidence of accounting conservatism, as it is not driven by differences in skewness alone. However, in practice, achieving similar skewness properties between the two groups can be challenging due to significant cross-sectional differences in the skewness of earnings and returns. In the next section, we compare empirical AT coefficients across firms sorted based on market capitalization and market-to-book ratio, further exploring this issue.

It is worth noting that the skewness of the simulated earnings, as reported in Table 4, does not appear to be influenced by the presence of conservatism. The skewness coefficients of earnings vary based on the skewness and correlations of the underlying components, but there is no systematic difference observed between the full model (left panel) and the restricted model without conservatism (right panel). This finding contrasts with the arguments made by Ball and Shivakumar (2005) and Givoly and Hayn (2000), who propose that negative earnings skewness may be a result of accounting conservatism. Within the framework of the Ball et al. (2013a) model, it seems that conservatism does not have a direct effect on earnings skewness. The variation in skewness appears to be primarily driven by the characteristics of the underlying components in the model rather than the presence or absence of conservatism.¹⁵

4.2 Skew-reducing transformations

A tempting solution to address the skewness-induced component of the asymmetric timeliness (AT) coefficient is to transform the variables. For instance, a logarithmic transformation can reduce right skewness, while a rank transformation can eliminate both positive and negative skewness from a variable. We apply both of these transformations to the simulated observations of returns (R) and earnings (I) before estimating the Basu model (Eq. 1). However, the resulting AT coefficients, as shown in Table 5, indicate that these data transformations do not resolve the issue at hand.

Table 5 Skew-reducing transformations

Even when using log and rank transformed data, we consistently observe that the AT coefficient varies with the distributional properties of the latent factors in our simulation. Consequently, the AT coefficient does not exhibit a consistent positive relationship with conservatism when it is present, and it often remains significantly different from zero even in the absence of conservatism. The reason these data transformations do not help in identifying conservatism is that the skewness originates from the latent factors (x, y, and g) in our model. The skewness of these latent factors not only affects the skewness of the observable variables (R and I) but also introduces inherent nonlinearity in the relationship between these variables. Merely removing the univariate skewness from R and I post-transformation does not eliminate the nonlinearity in the relationship between them. This nonlinearity, which is unrelated to accounting conservatism in our simulation, leads to a statistically significant AT coefficient even if the variables in the regression are transformed to reduce skewness.

Table 5 also shows that the AT coefficient does not identify conservatism when the model is estimated using the Theil (1950)–Sen (1968) (TS) estimator, which mitigates the impact of outlier observations. Contrary to suggestions made by Kim and Ohlson (2018), the TS estimator does not resolve the issue of the spurious AT coefficient caused by skewness, as the asymmetry in the earnings-returns relationship extends beyond the distribution's tails. Therefore, the TS estimator does not offer a solution to address the nonlinearity and asymmetry induced by skewness, preventing the reliable identification of accounting conservatism using the AT coefficient.

Finally, Table 5 presents the difference in R-squared values, denoted as ΔR² = R²₍₋₎− R²₍₊₎, which represents the disparity between the R-squared obtained from regressing earnings on returns in the subsamples of negative and positive news. This measure is relevant to Basu's (1997) hypothesis, suggesting that conservative reporting leads to a stronger relationship between earnings and returns, resulting in a higher R-squared during periods of bad news. However, the findings in Table 5 indicate that the differential R-squared is also influenced by skewness. While ΔR² generally demonstrates higher values in the presence of conservatism (Panel A), it does not necessarily equal zero in the absence of conservatism (Panel B). These results align with the simulation outcomes presented in Tables 1, 2, and 3, which show that the correlation (ρ) between earnings and returns is not consistent across positive and negative news samples. Consequently, the squared correlation, or R-squared, can vary between positive and negative news states for reasons unrelated to conservative reporting.

5 Empirical results

5.1 Sample construction and variable definitions

The empirical data for this study are obtained from the intersection of annual Compustat and monthly Center for Research in Security Prices (CRSP) files.¹⁶ Annual returns are computed by cumulating monthly returns starting from the fourth month after the firm’s fiscal year end. We follow the prior literature in eliminating utilities (SIC 4900-4999) and all financial services companies (SIC 6000-6999). Following Patatoukas and Thomas (2016) and Collins et al. (2014), we also delete firm years with missing data to compute returns, earnings, MTB ratio, firm size (market capitalization), and leverage. We calculate cash flows and accruals using the cash flow statement approach, which restricts the sample period to 1988–2020 (T = 33). We exclude firm years with lagged share price less than $1 from our sample. The final sample includes 12,658 distinct firms and a total of 109,452 firm-year observations.

Patatoukas and Thomas (2011) identified a significant AT coefficient for price-deflated lagged earnings per share and highlighted that lagged earnings cannot be linked to current news. Ball et al. (2013b) attribute this bias to a nonlinear correlation between the expected components of earnings and returns. Building on the recommendation by Ball et al. (2013b), we employ fixed-effect panel regressions for observed returns ($R$) and market capitalization-deflated earnings ($\widetilde{I}$) in order to derive unexpected returns and earnings¹⁷:

$${\widetilde{R}}_{it}={\alpha }_{i}^{R}+{\gamma }_{t}^{R}+{\varepsilon }_{it}^{R}$$

(14)

$${\widetilde{I}}_{it}={\alpha }_{i}^{I}+{\gamma }_{t}^{I}+{\varepsilon }_{it}^{I},$$

(15)

in which ${\alpha }_{i}$ and ${\gamma }_{t}$ are firm- and year-fixed effects, respectively. In our empirical analysis below, we proxy unexpected returns and earnings by the residuals from the above regressions, i.e., ${R}_{it}={\varepsilon }_{it}^{R}$ and ${I}_{it}={\varepsilon }_{it}^{I}$.¹⁸

In addition to earnings, we also examine accruals and cash flows separately. Basu (1997) highlights that accruals allow accountants to recognize negative news regarding future cash flows in an asymmetrically timely manner. Collins et al. (2014) further argue that the inclusion of operating cash flows in tests of conditional conservatism introduces noise or bias due to differential verification thresholds for recognizing unrealized gains versus losses. Hence, they recommend using accruals-based estimates of the AT coefficient. Dutta and Patatoukas (2017) demonstrate that estimating the AT coefficient using accruals instead of earnings leads to an increase in expected returns and asymmetry in the distribution of returns, while decreasing cash flow persistence, which are non-accounting factors. In line with Patatoukas and Thomas (2016), we compute unexpected accruals. Similarly, we calculate unexpected components of observed variables as follows:

$${\widetilde{Y}}_{it}={\alpha }_{i}^{Y}+{\gamma }_{t}^{Y}+{\varepsilon }_{it}^{Y},$$

(16)

where ${\widetilde{Y}}_{it}$ is replaced by market capitalization-deflated accruals and cash flows in two separate regressions. We denote the resulting residuals as unexpected accruals (${ACC}_{it})$ and unexpected cash flows (${CFO}_{it})$.

Table 6 reports descriptive statistics. Due to the removal of fixed effects (Eqs. 14–16), the mean values of our unexpected variables are zero by construction. The mean value of the indicator variable for negative unexpected returns (D) is 0.558, which is comparable to Dutta and Patatoukas (0.577). As expected, unexpected returns (R) and unexpected cash flows (CFO) exhibit positive skewness (1.474 and 2.198, respectively), while unexpected earnings (I) and unexpected accruals (ACC) exhibit negative skewness (− 2.139 and − 2.547, respectively).

Table 6 Descriptive statistics

5.2 Empirical results

Previous studies have demonstrated a correlation between AT estimates and book-to-market ratio as well as firm size (Khan and Watts 2009; Ball et al. 2013b). In this section, we explore whether within-sample cross-sectional skewness coefficients are related to cross-sectional AT coefficient estimates. To investigate this, we divide the sample within each year into deciles by sorting firms independently based on two firm characteristics: market capitalization (Size) and the market-to-book ratio (MTB), both measured at the beginning of the period. Table 6 provides summary statistics for Size and MTB, along with the corresponding analysis.

Table 7 reports the time-series averages of the cross-sectional skewness coefficients of unexpected returns (first column) and earnings (second column) within each Size (Panel A) and MTB (Panel B) decile. The third column of Table 7 reports estimated AT coefficients for each decile. Estimates are obtained following the Fama–MacBeth (1973) approach: in each year, we use the observations of unexpected returns and earnings for all firms in a decile to estimate the cross-sectional regression Eq. (1). The reported coefficients are the time-series means of the annual cross-sectional AT coefficients ($\widehat{{\beta }_{1}}$) within each Size and MTB decile.¹⁹

Table 7 Empirical AT coefficients and skewness

Panel A of Table 7 shows that the estimated AT coefficients (third column) are positive and significant for all Size deciles. There is a clear decreasing pattern in the AT coefficients when moving up in the Size distribution, with the difference between the small and large decile being highly significant. At the same time, return skewness also shows a significant negative correlation with firm size, while earnings skewness coefficients are negatively correlated with size: the cross-sectional skewness of returns (earnings) is significantly higher (lower) within the small stock deciles than within the large stock decile. Given the results in earlier sections, it is thus plausible that cross-sectional variation in the AT coefficient across Size deciles merely reflects cross-sectional variation in skewness, which may be unrelated to conditional conservatism.

Comparing across MTB deciles (Panel B of Table 7), we see a different pattern. The AT coefficient is significantly higher for value stocks than for growth stocks. However, the correlation of the AT coefficients with return skewness and earnings skewness is clearly weaker than for the Size deciles. Panel B shows that the difference in return skewness value stocks and growth stocks is not statistically significant and the pattern from decile 1 to 10 is far from monotonic.²⁰ Similarly, we do not find significant differences in earnings skewness between growth and value stocks. The higher AT coefficient for value firms is thus unlikely to reflect differences in distributional properties and can be interpreted as evidence supporting the hypothesis that value firms are more conservative in reporting than growth firms.

Comparing our regression results to the simulation findings presented in the previous section, we observe that the differences between value and growth stocks (Table 7B) exhibit a similar qualitative pattern to the differences observed between panel A (conservatism) and panel B (no conservatism) within each row in Table 4. Value and growth stocks display similar skewness characteristics, allowing us to interpret the higher AT coefficient for value stocks as evidence of conservative reporting. However, when comparing small and large stocks (Table 7A), we observe considerable variations in skewness properties, just as within panel A or panel B of Table 4. Consequently, we cannot conclusively determine whether the higher AT coefficient for small stocks reflects conditional conservatism or differences in skewness.

5.3 Accruals and cash flows

To assess cross-sectional variation in the AT coefficient, we extend our analysis to examine the accruals and cash flows components of earnings individually. We anticipate that conservative reporting will result in an asymmetric relationship between accruals and returns, while the relationship between cash flows and returns is expected to be symmetric and unaffected by conservatism.

The final two columns of Table 7 present the AT coefficients for Size and MTB deciles, estimated using unexpected accruals and unexpected cash flows, respectively, instead of unexpected earnings. We observe that, across both Size and MTB deciles, the AT coefficients tend to be higher for accruals compared to cash flows. This pattern aligns with the notion of conservative reporting affecting accruals asymmetrically but not cash flows. However, it is important to consider that this difference in AT coefficients could also be influenced by the inherent skewness of cash flows and accruals. Table 6 illustrates that accruals exhibit strong negative skewness, similar to earnings, while cash flows display slight positive skewness. Furthermore, we note the presence of significantly positive AT coefficients for cash flows within certain Size and MTB deciles. Since cash flow reporting is not subject to conservative accounting, these positive AT coefficients must stem from factors other than conservatism. In fact, a positive AT coefficient for cash flows aligns with the predictions of return skewness in the model proposed by Dutta and Patatoukas (2017).

In summary, our empirical analysis highlights the complexity of drawing conclusions about the extent of accounting conservatism due to the influence of skewness on estimated AT coefficients. We find that, within the Size dimension, the cross-sectional variation in AT coefficients is strongly associated with variations in return skewness and earnings skewness. Consequently, the observed differences in asymmetric timeliness cannot be solely attributed to conservative accounting practices. However, when considering value and growth firms, which exhibit similar skewness characteristics, the relatively higher AT coefficient for value firms can be interpreted as indicative of accounting conservatism. Thus, it is essential to consider the interplay between skewness and AT coefficients when examining the presence of conservatism in financial reporting.

6 Conclusions

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.