Earnings quality and the heterogeneous relation between earnings and stock returns

We adopt a heterogeneous regime switching method to examine the informativeness of accounting earnings for stock returns. We identify two distinct time-series regimes in terms of the relation between earnings and returns. In the low volatility regime (typical of bull markets), earnings are moderately informative for stock returns. But in high volatility market conditions (typical of financial crisis), earnings are strongly related to returns. Our evidence suggests that earnings are more informative to investors when uncertainty and risk is high which is consistent with the idea that during market downturns investors rely more on fundamental information about the firm. Next, we identify groups of firms that follow similar regime dynamics. We find that the importance of accounting earnings for returns in each of the market regimes varies across firms: certain firms spend more time in a regime where their earnings are highly relevant to returns, and other firms spend more time in a regime where earnings are moderately relevant to returns. We also show that firms with poorer accrual quality have a greater probability of belonging to the high volatility regime.


Introduction
Accounting and finance have a long tradition of studying the relation between accounting earnings and stock market returns. This interest is driven by the importance of earnings to investment decisions and to the prediction of returns. In their asset allocation decisions, investors form expectations about the firm's future cash flows and the risk associated with these cash flows (Fama 1970). As earnings contain information about the stream of cash flows, investors use earnings information to revise their expectations about future flows and this leads to a revision of stock prices. In other words, earnings are useful for stock price formation. Prior studies have focused on explaining the time series variation or the cross-sectional variation in the earnings-return relation. We propose to study both the temporal and cross-sectional variation in the relation between earnings, earnings changes and returns using an extension of the regime switching methodology introduced by Hamilton (1989): the heterogeneous regime switching methodology. The heterogeneous regime switching method can be summarized as follows. First, we estimate the time series variation in the earnings-returns relation for the sample firms for the period 1997-2010. The estimation method allows us to identify breaks in the time series of earnings-returns and to characterize each regime. As a result, we are able to let the data generating process determine the regime rather than identifying the breaks ex-ante which would be subjective. Second, each firm is assigned to a group (or cluster) based on how long it stays in one regime and the likelihood of switching to the other regime. Thus, the model is dynamic as it allows firms to switch between regimes across time.
We identify two regimes. The low volatility regime corresponds to periods of low return volatility and a moderate association between earnings and returns. Both earnings and earnings changes are positively associated with returns but the magnitude of the earnings coefficients is smaller than in the other regime. The high volatility regime represents periods of high volatility in returns with earnings and earnings changes strongly associated with returns. This result is consistent with the idea that in periods of high price instability, such as financial crises, information about earnings is more important to investors than in ''normal'' periods. During bear market conditions, investors become more risk averse and fly from stocks with high levels of uncertainty about fundamental value (Lang and Maffett 2011). As financial information lessens uncertainty about the firm's fundamental value and reduces risk perception, earnings become more important for investors (Lang and Maffett 2011). In other words, investors rely more on earnings information during market downturns because other information is more likely to reflect speculation and noise.
Next we identify the firms with similar regime dynamics, i.e. firms that spend similar time in each regime and have a similar probability of switching. We find two clusters of firms. Firms in the first cluster have stable dynamics, i.e. they start and remain in the low volatility regime throughout most of the sample period. Conversely, firms in the second cluster spend more time in the high volatility regime and also have a higher probability of transition to the other regime. We then investigate the properties of accounting information in the two groups of firms. Our aim is to explore whether the quality of financial information, and of other firm fundamentals, is associated with the firms' regime dynamics. We find that firms with a greater likelihood of being in the high volatility regime (firms in cluster two) have poorer information quality, measured in terms of accrual quality and smoothness. During market downturns, earnings are more unstable due to unexpected losses, impairments, and other unusual transactions. The volatility between earnings and cash flows increases, resulting in poor accrual quality. Regarding other firm-specific characteristics, we find that smaller firms, firms with poor performance, lower market-tobook ratio, and growing firms are more likely to be in the high volatility earnings-returns regime.
Our study contributes to the accounting and finance literature in two ways. First, we complement prior research that studied the informativeness of earnings (e.g., Collins and Kothari 1989;Easton et al. 1992;Collins et al. 2009;Balachandran and Mohanram 2011;Freeman et al. 2011) by considering that the earnings-returns relation entails both timeseries variation and cross-sectional variation. Prior literature found that the usefulness of earnings to returns varies through time, but it does not consider that the time variation affects individual firms differently. We add to the literature by showing that certain firms spend more time in a setting where their earnings are highly relevant to stock returns, and other firms spend more time in a setting where earnings are moderately relevant to stock returns. Further, we show that these settings represent periods of high uncertainty in stock markets, and periods of calm in stock markets, respectively. Second, we add to prior research by confirming the link between firm fundamental accounting information and the type of earnings-returns relation of the firm. Specifically, we find an association between earnings quality measures and the group that the firm belongs to in terms of the earningsreturns relation. Our findings highlight the link between the finance perspective that identifies stock market cycles, and the accounting perspective that focuses on the importance of accounting earnings for stock price formation.
The remainder of the paper is organized as follows. Section 2 reviews prior literature. Section 3 presents the heterogeneous regime switching model. Section 4 describes the sample and the data, and presents descriptive results. Section 5 reports the estimation results of the heterogeneous regime switching model. Section 6 discusses the link between cluster affiliation and earnings quality. Section 7 concludes.

Prior literature
The idea that earnings convey useful information for stock returns has long been established by academics (Ball and Brown 1968;Beaver 1968;Watts and Zimmerman 1986). It relies on three important theoretical links developed by Watts and Zimmerman (1986) and Beaver (1998). First, current accounting earnings provide information about expected future earnings. Second, current and expected earnings help predict the firm's stream of future cash flows. Third, stock prices represent the present value of expected future cash flows. The view that earnings are useful to investors has also been endorsed by accounting standard setters around the world. For example, both the FASB (Financial Accounting Standards Board) in the US and the IASB (International Accounting Standard Board) define the primary objective of financial reporting as the provision of information that is useful to capital providers in making decisions about allocating resources to the firm (International Accounting Standards Board 2010; Financial Accounting Standards Board 2010). The decision-usefulness criterion that guides the preparation of earnings information makes earnings the widely accepted measure of firm performance. Consequently, earnings-based valuation models are commonly used by academics, practitioners and investors. 1 The seminal work of Ball and Brown (1968) and Easton and Harris (1991) introduced a model that evaluates the information usefulness of earnings for returns. The model explains the contemporaneous relation between returns and current earnings and changes in earnings. Earnings provide investors with useful information if the earnings variables in the model exhibit a considerable explanatory power. 2 The large body of literature examining the contemporaneous relation between earnings and returns shows that earnings contain relevant information for stock returns (e.g. Collins and Kothari 1989;Lipe 1990;Lipe and Kormendi 1994;Easton et al. 1992;Strong 1993;Lamont 1998;Firth et al. 2008;Barth et al. 2013;Chen and Tiras 2015). The literature also documents considerable time variation in the usefulness of earnings, with many studies reporting a decline in usefulness. Lev (1987) is one of the first studies showing that both the slope coefficient estimates and the explanatory power of earnings for stock returns decreased over time. Subsequently, Collins et al. (1997), Lev and Zarowin (1999), and Francis and Schipper (1999) also found evidence of a decline in the usefulness of earnings. Lev and Zarowin (1999) ascribe the apparent decline in earnings informativeness to the failure of the accounting system to recognize business innovation (i.e. R&D investment) in a timely manner. Collins et al. (1997) and Francis and Schipper (1999) find that the decrease in the value relevance of earnings is compensated by the increase in the value relevance of book value and hence conclude that the usefulness of the accounting system as a whole has not declined. However, Brown et al. (1999) argue that scale factors influence this result. After controlling for scale effects they find that in fact the usefulness of earnings has deteriorated over time. Studies analyzing more recent periods of time also show a decline in the usefulness of earnings to investors (Ryan and Zarowin 2003;Core et al. 2003;Kothari and Shanken 2003;Dontoh et al. 2004;Balachandran and Mohanram 2011). The idea that earnings have lost their usefulness has prompted research on the factors driving the decline. One perspective suggests that the efficiency of information processing of stock prices has changed over time. An increase in return volatility linked to non-informed trading hampers the ability of returns to reflect fundamental earnings information (Dontoh et al. 2004). The other view claims that the problem lies with the loss of quality of accounting earnings, i.e. the loss of ability to reflect future cash flows. 3 Several reasons are given for the decline in earnings quality. First, reported earnings do not reflect the richness of information on voluntary corporate disclosures (Lundholm and Myers 2002). Second, the increasing abundance of concurrent disclosures, e.g. conference calls and pro-forma disclosure preempts the information content of earnings (Amir and Lev 1996;Collins et al. 2009). Third, complex accounting issues such as fair value measurements and intangible recognition can reduce the association of earnings with stock returns (Lev and Zarowin 1999;Balachandran and Mohanram 2011). Rajgopal and Venkatachalam (2011) provide evidence consistent with the view that earnings have lost quality over time. They show that the increase in stock return volatility in the US is associated with a decline in the quality of earnings, and that association persists over time. The explanation is that poor earnings quality causes noisier earnings leading to dispersion in investors' belief in the firm's future cash flows. At the same time financial analysts resort more to other sources of information because they view earnings as a weak information signal. This in turn generates more volatility as 2 In this paper we take the common view that value relevance is a direct measure of the usefulness of earnings to stock returns (Joos and Lang 1994;Collins et al. 1997;Francis and Schipper 1999;Lev and Zarowin 1999;Barth et al. 2001;Francis et al. 2004). Other ways of assessing the usefulness of earnings include: market reaction to earnings announcements (Ball and Brown 1968;Beaver 1968), correlation between earnings and cash flows (Lev et al. 2010), and reliability of earnings-based models (Dechow et al. 1999;Francis et al. 2000). 3 For example, Kim et al. (2012) use portfolio tests and find that accounting earnings are not more useful for investors than cash flows or working capital.
analysts use diverse sources of information and investors follow different analysts. The recent and growing literature on the consequences of the international adoption of IFRS has also raised concerns about the informativeness of IFRS-based earnings for investors (for recent reviews about the information properties of IFRS earnings, see Leuz and Wysocki (2016) and Brown (2013)). The weak enforcement structures in place in some jurisdictions, the difficult implementation of certain IFRS concepts such as the fair value measurement, and scope for management discretionary choices have been noted as factors that can impair the usefulness of accounting information for investors.
If problems with the quality of accounting earnings explain the decline in the returnsearnings relation over time, then we should also expect cross-sectional variation in that relation because accounting quality is a function of the firm's activities (Dechow et al. 2010). Amir and Lev (1996) and Core et al. (2003) find that earnings are less related with returns in intangible-intensive firms, Frank (2002) reports lower value relevance of earnings in high-growth firms, Burgstahler et al. (2006) show that firms with higher book-tax alignment have lower earnings quality. Further, manager incentives also vary across firms leading to differences in the discretion that managers apply in the preparation and disclosure of earnings. For example Kraft et al. (2014) find that managers and other senior officers engage in accrual earnings management before trading on their own stock.
To summarize, variation in the usefulness of earnings for returns across firms reflects differences in underlying fundamental aspects of the business and in the quality of the accounting system to portray current and future performance. Givoly and Hayn (2000) investigate temporal variation in earnings, cash flows and accruals and address this point. They argue that if time variation in earnings follows the same time-trend as the stream of cash flows (which captures fundamental performance that is not affected by the accounting system), then accounting earnings simply reflect changes in fundamental performance and there are no structural changes in the quality of the accounting system over time. Their results do not confirm this hypothesis. They find that the decline in profitability does not result from a decrease in the underlying cash flows of the firm, but derives from changes in the relation between cash flows and earnings. In other words, a change in accounting accruals. This finding suggests that the ability of the accounting system to capture economic change as captured by accruals is important to explain the time variation in the usefulness of earnings for stock returns. Similarly, studies investigating the cross-sectional relative explanatory power of accruals and cash flows (e.g. Livnat and Zarowin 1990;Dechow 1994) show that accruals have information usefulness beyond that of cash flows. In a similar vein, Ryan and Zarowin (2003) report that the time series decline in the usefulness of earnings is explained by changes in the accrual component of earnings. They conclude that the decline is attributable to the quality of accounting not to the change in the economic conditions of the firms. Studies such as Givoly and Hayn (2000) and Ryan and Zarowin (2003) use accounting conservatism to infer about the quality of the accounting system. Other studies rely on other properties of accounting notably the quality of accruals. 4 Prior studies investigating time variation in the usefulness of earnings typically estimate the earnings-returns model one period at a time, year by year or by groups of years, or simply add a time variable to the model (Strong 1993;Collins et al. 1997;Ryan and Zarowin 2003;Balachandran and Mohanram 2011;Rajgopal and Venkatachalam 2011). But that approach is incomplete for various reasons. First, it fails to consider that time variation in earnings usefulness does not affect all firms similarly. Second, the partition of time in years or groups of years is subjective and lacks theoretical support. The time a firm experiences high or low correlation between earnings and returns does not necessarily coincide with calendar years. Third, although prior studies control for time variation, they do not model or explain that variation. The heterogeneous regime switching methodology provides support for the identification of breaks in the earnings-returns relation, and identify groups of firms with similar regime dynamics. That is, we complement prior literature by modeling the time component of the relation between earnings and returns. But more importantly and differently from prior studies, our method allows firms to experience periods when earnings are more correlated with returns and periods where earnings are less correlated with returns.

The heterogeneous regime switching model
This study applies a novel framework based on the regime switching model (RSM) introduced by Hamilton (1989) to study the relation between earnings and returns. Regime switching models can be very useful in economic data modeling because they allow for non-linear stationary processes which are typical in economic problems. They have become very popular in economics and finance as they capture breaks (or discontinuities) in the business cycle (e.g. Krolzig 2001;Tan and Mathews 2010) and in the behavior of economic time series. These discontinuities are typical in the time series of returns where periods of low return volatility and high prices are followed by periods of high return volatility and low prices. For this reason regime switching models have been used in finance to characterize stock market cycles (Bekaert and Harvey 1995; Ang and Bekaert 2002;Aktas et al. 2007;Hwang et al. 2007;Zhu and Zhu 2013). The regime-switching approach was also used to model other economic research problems. Recent examples include Tang and Chang (2015) who use a switching regression model to classify firms into strong and weak governance, and Paeglis and Veeren (2013) who model the speed at which venture capitalists exit a firm after its IPO. Our approach differs from the one adopted in these studies in that we not only estimate the regimes but we also allow for firm heterogeneity. The existence of a low and high volatility regime in stock market returns (i.e. boom and downturn market conditions) is widely recognized in the finance literature. What our method adds to the literature is the possibility that the importance of accounting earnings to stock returns in each of the regimes varies across firms. That is, we identify clusters of firms with different regime dynamics. While identifying regimes the model simultaneously ''tracks'' the relation between earnings and returns for each firm and tries to identify firms that behave in the same manner; i.e., firms that spend a similar time in each regime. These arguments are in line with research documenting differences across firms in the earnings response coefficients (e.g., Freeman et al. 2011;Beneish and Harvey 1998). Our method constitutes an innovation in the implementation of regime switching models which typically only estimate the existence of regimes in time series. As we model not only the time series but also the cross-sectional variation in each regime, we apply a heterogeneous regime-switching model. Based on the evidence that the earnings-returns relation can be affected by heterogeneity in firm conditions, we assume more than one latent Markov process that is characterized by a transition probability between each of the regimes. The HRSM-Heterogeneous Regime-Switching Model (Dias et al. 2008;Ramos et al. 2011) enables the statistical estimation of regime-switching models based on the similarity of the dynamics associated with each homogeneous group of firms (or clusters). The HRSM can also be viewed as an extension of the hybrid model introduced by Dias and Ramos (2014), which estimates a panel regime switching model and based on the posterior probabilities the heuristic clustering identifies the hierarchical structure of the stock market. The HRSM estimates clusters and regimes simultaneously. A model with S clusters is denominated HRSM-S. In other words, we identify distinct groups of firms in terms of earnings-returns relation following Markov chains with distinct probabilities of transition from one regime at time t À 1 to another regime at time t. Next we explain the HRSM-S model.
Let R it represent the compounded stock return of firm i at quarter t, where i 2 f1; . . .; ng and t 2 f1; . . .; Tg. Let f ðR i ; uÞ be the probability density function associated with the returns for firm i. The HRSM-S (S being the number of groups or clusters associated with this application) is given by: The right-hand side of Eq. (1) indicates that the underlying model architecture is typical of a mixture model consisting of the time-constant latent variable w and T realizations of the time-varying latent variable z t . In this context, the observed data density f ðR i ; uÞ is obtained by marginalizing over the latent variables. Furthermore, the term f ðw i ; z i1 ; . . .; z iT Þ of Eq. (1) can be further transformed into: where f ðw i Þ essentially represents the probability of a given firm belonging to a given latent class or cluster w, with multinomial parameter k w ¼ PðW i ¼ wÞ, f ðz i1 jw i Þ represents the initial-regime probability and f ðz it jz i;tÀ1 ; w i Þ represents the latent transition probability. Moreover, the observed return depends only on the regime applicable at that specific time point, i.e., response R it is independent of returns at other moments (this is known as the local independence assumption). Simultaneously, the said observed return value is also independent of latent states at other times. These assumptions can be formulated as follows: where the probability density that a particular observed stock return value at time t conditional on the regime in place at that chronological point-f ðR it jz it Þ-is assumed to have the specification of a univariate Gaussian density function. We consider the following regression structure that explains stock returns as a function of earnings and earnings changes (plus industry and quarter indicators): R it is the compounded quarterly returns of firm i at quarter t calculated as logðP it =P i;tÀ1 Þ and vector x it contains the independent variables ðE it ; DE it ; IND i1 ; . . .; IND i7 ; Q i1 ; . . .; Q i4 Þ. E it is quarterly earnings per share scaled by price at the beginning of the quarter. DE it is change in quarterly earnings per share from quarter t À 1 to quarter t, scaled by price at the beginning of the quarter. 5 We include IND ir , a set of industry indicators based on the onedigit standard industry classification (SIC) industry r, as industry is likely to affect the relation between earnings and prices (e.g., Kuo 2017). We also add quarter indicators (Q iq ). Industry 3 (industrials and electronics) and quarter 1 are the reference categories, thus h 3k ¼ 0 and k 1k ¼ 0. The model is heteroskedastic as the variance of returns depends on the regime: The full model is depicted in Fig. 1. The figure shows that conditional on the covariates (e.g., industry and quarter indicators), this model takes longitudinal and cross-sectional heterogeneity into account through regimes and clusters, respectively. Latent variables (regimes and clusters) are depicted as circles, whereas squares represent observed variables.
The parameters of the model are estimated using the maximum likelihood method. The Expectation-Maximization (EM) algorithm can subsequently be employed to solve the maximization of the log-likelihood function. Nevertheless, it should be pointed out that the application of the EM algorithm requires both a lengthy computational effort and a cumbersome computer storage capacity. Therefore, the application of this algorithm is often impractical, if not impossible. To circumvent this operational problem, a special variant of the EM algorithm-the Baum-Welch (BM) algorithm-has been advanced in the literature, enabling the above-mentioned maximization problem to be more easily solved (Dias et al. 2008). Furthermore, the choice of the appropriate number of latent classes S is traditionally based on the analysis of statistical information criteria. We use the BIC criterion (Schwarz 1978), and we identify the most appropriate value of S when the value of BIC is at its minimum.

Sample, data and descriptive results
In the empirical analysis we use quarterly data from 1997 to 2010. The sample comprises US firms from the interception of Compustat and CRSP databases, and with complete financial and return data. As in prior studies, we eliminate cases with negative book values. The final sample includes 2140 firms with 60 quarters of returns and earnings data. Table 1 presents descriptive statistics for the returns and earnings variables by industry. During the sample period the average (median) compounded stock return is 0.004 (0.025), but there is a substantial variation in returns both within and across industry. The agricultural, mining and construction industry has the highest returns, whereas the financial sector exhibits the lowest returns. The average earnings-to-lagged price ratio is 0.042 but there is also cross-industry and cross-firm heterogeneity. The large standard deviations in returns and earnings suggest that accounting earnings and stock returns (and thus the earnings-returns relation) are affected by firm-specific conditions. We explore how firm specific conditions explain heterogeneity in the earnings-returns relation in Sect. 6. Figure 2 plots the time variation in the correlation between returns and earnings, and between returns and changes in earnings. The volatility in the earnings-returns correlation is evident, with periods of high positive correlation followed by periods of low and negative correlation. The three peaks of large negative correlations correspond to important stock market crashes: the 1998-1999 Asian crisis and Russian ruble crisis, the 2002-2003 internet bubble crash, and the most recent financial crisis in 2008-2009. In periods of dramatic decline in stock markets, accounting earnings are more strongly correlated with returns, albeit negatively. This is because reliable information about firm fundamentals becomes more important to investors when uncertainty is high and concerns about the firm's future cash flows are more acute (Lang and Maffett 2011;Lang et al. 2012).

Returns
Covariates X i1 X i2 X i3 X iT Fig. 1 The heterogeneous regime switching model 5 Results of the estimation of the heterogeneous regime switching model Table 2 presents the estimation results of the heterogeneous regime switching model. The results indicate a dual returns-earnings regime characterized by low return volatility and high return volatility. These two regimes are in line with the finance literature that identifies periods of low volatility in stock markets (boom periods) and periods of low volatility in stock markets (downturn periods). In the low volatility regime, the level of returns is positive and the return variance is relatively low (0.010). In such bull market conditions earnings and earnings changes are moderately useful in explaining returns. That is, in good times investors are likely to use other sources of information besides information about accounting earnings to make investment decisions (e.g. news from the press and other nonfinancial information). In contrast, fundamental earnings information becomes more important when uncertainty and volatility are high. The high volatility regime in our model mimics the characteristics of the market in a bear state or in a crash: negative stock returns (represented by the negative intercept) and high return volatility (the variance is 0.101). In this regime the coefficients of earnings and earnings changes are more important in explaining stock returns than in the low volatility regime which implies that earnings information is more useful to investors in depressed stock markets. The negative coefficient of earnings in the high volatility regime reflects the high prevalence of losses in periods where stock returns are negative. Hayn (1995) finds a similar result when she considers losses and profits separately: for periods of losses the earnings level variable is negative in almost all yearly regressions. Negative shocks to returns lead to large return volatility (French et al. 1987;Schwert 1989;Edwards et al. 2003;Schwert 2011). The large volatility is explained by three phenomena: high uncertainty about the firm's future cash flows, high risk perception, and Fig. 2 The correlation between returns and earnings, and returns and earnings changes. This figure shows correlation coefficients between returns and earnings (R / E) and returns and earnings changes (R=DE) for a sample of 2140 US firms for 60 quarters from 1997 Q1 to 2010 Q4. R it is compounded quarterly returns. E it is earnings per share scaled by price at the beginning of the quarter. DE it is the quarterly change in earnings per share, scaled by price at the beginning of the quarter general decline in prices and asset liquidity. Fundamental financial information about the business can help attenuate uncertainty and risk perception resulting in investors relying more on earnings information when markets are depressed. A recent study by Leung et al. (2014), entitled ''Predictability of bank stock returns during the recent financial crisis'', investigates bank holdings during the recent financial crisis and concludes that banks' fundamental information, including earnings, was the major criterion used by investors to make investment decisions in the crisis period. Similarly, Lang and Maffett (2011) contend that transparent financial information lessens the uncertainty about the firm's fundamental value which is particularly pronounced during market downturns. In such periods, financial information becomes more important because of the ''flight to quality'' behavior where investors become more risk averse and flee from stocks with high levels of uncertainty on fundamental value (Lang and Maffett 2011). This view is also proposed by the Securities and Exchange Committee (SEC). In a speech on the role of accounting in preventing financial crises, the SEC Chief Accountant concludes ''when pressures are highest, and investor confidence has the greatest potential to be shaken by uncertainty, the importance of transparent, objectively audited financial reporting to investors, and an independent and objective system to establish standards for such reporting, are necessary and critical components to both short term and long term success''. 6 Next, we describe the dynamics of the two regimes across latent classes (Table 3). The BIC criterion indicates that the sample firms can be clustered into two groups with distinct dynamics. 7 The groups or clusters are estimated based on the firm's similarity in terms of the likelihood of being in each regime and likelihood of switching to the other regime. Firms in cluster one have a large total probability of being in the low volatility regime (the probability of being in the low volatility regime is 0.890 whereas the probability of being 6 Regarding the industry and quarter indicators included in the model (not tabulated) we find the following results. In the high volatility regime, industries 1 (agriculture), 4 (transportation and communication) and 7 (services) are significantly different from industry 3 (industrial and electronics), and quarter 2 is significantly different from quarter 1. In the low volatility regime, industries 1 and 6 (finance) are significantly different from industry 3, and quarters 2 and 3 are significantly different from quarter 1. 7 Results on model selection are available from the authors upon request. We also experimented other solutions in terms of number of regimes and clusters. However, based on the BIC selection criterion, we conclude that a model with two regimes and two clusters is the best. The solution with two regimes is in line with the finance literature that suggests stock markets alternate between boom and downturn periods. This way the two regime solution has the advantage of allowing simple economic interpretation of the results. in the high volatility regime is only 0.110). Further, most firms in cluster one start in a low volatility regime (the initial probability is 0.929) and stay in that regime. The probabilities of transition between regimes are relatively low but distinct between clusters. The transition probability from the low to the high volatility regime is approximately two times larger in cluster two (0.145) than in cluster one (0.061). On the other hand, the probability of transition from the high to the low volatility regime is larger in cluster one (0.489) than in cluster two (0.128). The mean sojourn time measures the expected time that a firm takes to move out of a given regime. Firms in cluster one take 16.4 quarters to move out of the low volatility regime, but take only 2 quarters to move out of the high volatility regime. Firms in cluster two are less sticky to return regimes. They have a larger total probability of being in the high volatility return regime and a larger sojourn time in that regime. The different dynamics of the two groups of firms is quite visible in Fig. 3. The figure represents the probability of being in the high volatility regime for firms in each cluster. The darker the mark, the higher the probability of the firm spending time in the high volatility regime. The difference between the two clusters of firms is striking. Cluster two is represented by much darker marks than cluster one. This graphical result confirms that firms in the two clusters have very different behavior in their earnings-returns relation. The informativeness of earnings for returns in periods of boom or downturn in market returns is not the same for all firms. Thus, simply dividing the periods of time in subperiods of bull and bear market conditions and assuming that earnings will be associated with returns in the same way for all firms in each sub-period is problematic. Our evidence highlights that one should consider that the informativeness of earnings varies both through time and across firms. Table 4 shows the industry classification of firms by cluster. The finance sector is the most represented sector in cluster one (36.2% of cluster one firms) while the industrials and electronics is the most represented sector in cluster two (37.2% of cluster two firms). The majority of firms in industries 2 (basic manufacturing), 4 (transportation and communication), and 6 (finance) fall into cluster one in terms of the returns-earnings dynamics. But most firms in industry 1 (agricultural, mining and construction), industry 3 (industrial and electronics), industry 5 (wholesale trade), and 7 (services) are classified into cluster two. This table reports estimates of the initial probability in the regime and the transition probability between regimes for firms in each cluster. The sample includes US 2140 firms with 60 quarters of data from 1997 Q1 to 2010 Q4

The association between firm clustering and earnings quality
This section explores the association between the quality of financial information and firms' fundamental characteristics and the cross-sectional heterogeneity in the earnings-returns relation. We draw on prior research documenting that the returnsearnings relation is associated with the quality of accounting earnings (e.g., Cahan et al. 2009). To that end, we estimate the following probit model where the probability (p) of firm i being in cluster two versus being in cluster one is given by the probit-link function Uð:Þ:

Measurement of variables
The variable Cluster takes the value of one if the firm is assigned to cluster two (firms that stay longer in the high volatility regime), and zero if it is assigned to cluster one (firms that stay longer in the low volatility regime). To measure earnings quality, we use (3) four measures that rely solely on accounting numbers. 8 We use three measures that capture the properties of accounting accruals: the standard deviation, and the absolute value of the residuals of the Dechow and Dichev (2002) model, and earnings smoothness. The fourth variable is persistence, which solely captures the time series variation in earnings. These variables have been extensively used in prior research to capture the quality of earnings and they vary substantially across firms. The measures are defined so that higher values imply lower earnings quality. Next we explain how the measures are calculated. Accruals Accruals measures are based on the Dechow and Dichev (2002) model relating total current accruals (TCA) to lagged, current, and future cash flows from operations (CFO).
where TCA is total current accruals measured as the quarterly change in current assets minus the quarterly change in current liabilities, minus the quarterly change in cash, plus the quarterly change in short-term debt. All variables are scaled by lagged total assets. The first accrual quality measure (AccrualQ1) is the standard deviation of e it over the eight-quarter rolling window, and the second measure (AccrualQ2) is the absolute value of e it . Accruals models are widely used in the accounting and finance literature to measure accounting quality (e.g., Francis et al. 2004;Dechow et al. 2010;Alam et al. 2015;Kim et al. 2013;Francis et al. 2016;Jaggi et al. 2015).
Persistence is the slope coefficient estimate (b 1 ) from an autoregressive model of order one for quarterly earnings per share (E), i.e.
Smoothness is the ratio of firm's standard deviation of net income before extraordinary items to its standard deviation of cash flows from operations, both scaled by lagged total assets (r NI =r CFO ), calculated over eight-quarter rolling windows.
We include in the analysis the following firm fundamentals that are likely to affect firm cluster membership, or in other words are likely to affect the cross-sectional variation in the earnings-returns relation. Size defined as the log of total assets, leverage calculated as the ratio of long-term debt to total assets, intangibility measured as the ratio of intangible assets to total assets, operating performance calculated as the ratio of operating profit to sales, market-to-book ratio defined as the market value of equity to the book value of equity, and sales growth defined as the change in quarterly sales divided by previous quarter sales. 9 As the assignment of firms to the clusters is time-invariant, we need to reduce the data to one single observation for each firm. Therefore, we use the firm median for each of the variables. 10 We also add industry fixed effects to the model to account for time invariant industry differences in cluster composition. Table 5 reports summary statistics by cluster for the variables used to estimate the probit model. On average, firms in cluster one have higher accrual quality. Firms in this cluster are on average larger, more leveraged, have positive operating profit, and a higher market-8 To avoid bias due to the use of earnings in the returns regime switching model, we do not estimate measures of earnings quality that rely on stock returns. This way we ensure there is no mechanical relation between the regime switching model and the earnings quality models. 9 Another relevant firm fundamental that is not included in the model is cash flow volatility (standard deviation of cash flow from operation scaled by total assets over the eight quarter window). We do not include it in the tabulated results because Compustat does not report cash flow from operations for several sample firms and thus including the variable would reduce considerably the number of observations. When we re-estimate the model including cash flow volatility we obtain the same results for earnings quality and find that cash flow volatility is higher for cluster 2 firms but only in the persistence and smoothness models. 10 Using the mean values yields similar results.

Empirical results
to-book ratio. Table 6 presents correlation coefficients. The correlations are generally small. The largest correlations are between accrual variables and size, and between accrual variables and leverage.
In Table 7 we present the results of estimating the probability of a firm being assigned to cluster two versus being assigned to cluster one taking into account earnings quality and other firm fundamentals. The final sample is reduced to 2128 firms because of missing values for some of the control variables. The most interesting result is the positive association between accruals-based measures of earnings quality and the probability of the firm following the dynamics of cluster two. The positive and significant coefficient for the accruals measures indicates that firms that are more likely to be in the high volatility regime experience higher volatility in accruals; i.e., poor accounting quality. For Accru-alQ1 (AccrualQ2), a unit decrease in accrual quality is associated with an increase in the Smoothness is the ratio of the standard deviation of net income before extraordinary items to the standard deviation of cash flows from operations both scaled by lagged total assets; Size is the log of total assets; Leverage is the ratio of long-term debt to total assets; Intangibility is the ratio of intangible assets to total assets; Operating performance is the ratio of operating profit to sales; Market-to-book is the ratio of the market value of equity to the book value of equity; and Sales growth is the change in quarterly sales divided by previous quarter sales. The sample includes 2128 US firms with 60 quarters of data from 1997 Q1 to 2010 Q4 Table 6 Correlations AQ1 AQ2 Pers. Smooth.

Size
Lev.
Int.  Firm fundamental variables are: Size measured as the log of total assets; Leverage measured as the ratio of long-term debt to total assets; Intangibility measured as the ratio of intangible assets to total assets; Operating performance measured as the ratio of operating profit to sales; Market-to-book measured as the ratio of the market value of equity to the book value of equity; Sales growth measured as the change in quarterly sales divided by previous quarter sales. The independent variables are the median values for each firm in the sample period. Robust standard-errors are presented in parenthesis below the coefficient estimates. Average marginal effects are presented at the right-side of the coefficient estimates The symbols ***, **, * indicate statistical significance at the 1, 5 and 10% levels, respectively. The sample includes 2,128 US firms with 60 quarters of data from 1997 Q1 to 2010 Q4 probability of the firm being assigned to cluster two by 30.8% (20.3%). The result is consistent with prior findings that return volatility and poor quality of accruals are positively associated (Rajgopal and Venkatachalam 2011). This is when there is more volatility in the earnings-return relation; abnormal accruals are also more volatile, which indicates poor accounting quality. One explanation for this result is that when stock markets are more volatile, cash flows, which reflect market conditions immediately, also become more volatile. Consequently the relation between cash flows and accounting earnings becomes noisier, i.e. abnormal accruals and the smoothness ratio increases and thus accounting quality deteriorates. Another interpretation is that sooner or later market instability leads to earnings volatility because the firm needs to impair certain assets, create provisions, and recognize other non-recurring transactions. Again, the instability in earnings will negatively affect accrual quality. We find similar results for smoothness, a measure that also captures the relation between earnings and cash flows. However, we do not find an association between earnings persistence and cluster affiliation. This is not surprising because persistence merely reflects how past earnings predict contemporaneous earnings but it is not informative about the link between earnings and cash flows. Regarding other firm specific characteristics, we note that smaller firms, firms with poorer operating performance, and lower market-to-book are more likely to follow cluster two dynamics than cluster one dynamics. This profile is characteristic of a young and fastgrowing firm. Younger firms are more likely to experience higher earnings-returns volatility because they are not yet established businesses and there is more uncertainty about their accounting information. Overall the empirical analysis suggests that crosssectional variation in earnings quality captured by accruals is associated with the likelihood of firms experiencing high volatility in terms of earnings-returns.

Conclusion
The degree to which accounting earnings provides useful information for stock markets is of considerable interest to businesses, investors and regulators. Accounting earnings is an important piece of information because it influences investors' expectations about the firm's future prospects. A number of academic studies document a decline in the usefulness of earnings for returns and suggest that increased return volatility and deterioration in the quality of the accounting system explain the decline. We add to that debate by investigating how a firm-level variation in the quality of earnings is related to both the time-series and cross-sectional variation in the earnings-returns relation. To do that, we adopt a heterogeneous regime switching methodology that allows us to model both the intertemporal and cross-sectional variation in the relation between earnings and stock returns. We show that the relation between earnings and returns in periods of boom and downturn market conditions varies across firms. Certain firms spend more time in a setting where their earnings are highly relevant to stock returns (high volatility regime), and other firms spend more time in a setting where earnings are moderately relevant to stock returns (low volatility regime).
We next link the dynamics of the firms in terms of the periods they spend in the high or low volatility regimes to measures of earnings quality. We find that firms with poor earnings quality, measured as accrual quality and smoothness, have a greater probability of spending more time in a high volatility earnings-returns regime. Although our study does not address causality, we believe that we provide an important result by showing that the quality of financial information is linked to the time series properties of the informativeness of earnings for stock returns.