Numerological superstition and earnings management: evidence from China

Purpose – Anemerginglineofresearchexaminingtheroleofnumerologicalsuperstitioninthecapitalmarket shows that it has significant impact on investor behavior (Bhattacharya, Kuo, Lin, & Zhao, 2018; Hirshleifer, Jian, & Zhang 2018). However, to the authors ’ best knowledge, there is a dearth of evidence on whether numerological superstition affects corporate behavior. This study fills this void by examining the association between investors ’ numerological superstition and earnings management using Chinese data. Design/methodology/approach – Chinese culture views 6 and 8 as lucky numbers. Using Chinese publicly traded firms, the authors examine the relation between investors ’ numerological superstition and corporate financial reporting behavior. Findings – Theresultssuggestthatfirmsreportingluckyearnings-per-share(EPS)numbersendingwith6or 8 are more likely to engage in earnings management. These firms also raise more capital through seasoned equity offerings in the following year; however, they do not have more capital investments. Instead, their controllingshareholderssiphonasignificantamountofcapitalthroughrelatedpartytransactions.Overall,thefindingssuggestthatmanagerscolludewithcontrollingshareholderstomanageearningsbyexploitingthe superstitiousbeliefsofminorityshareholders. Originality/value – To the authors ’ best knowledge, there is a dearth of evidence on whether numerological superstition affects corporate behavior. This study fills this void by examining the association between investors ’ numerological superstition and earnings management using Chinese data.


Introduction
Superstition is common in many cultures and has been shown to have significant impact on human decision-making (Kramer & Block, 2008) [1].In particular, although without any scientific ground, numerological superstition is prevalent in both Western and Chinese cultures [2], [3].Accordingly, it is intriguing to understand the economic consequences of numerological superstitions.An emerging line of research examining the role of numerological superstition in the capital market shows that it has significant impact on investor behavior (Bhattacharya, Kuo, Lin, & Zhao, 2017;Hirshleifer, Jian, & Zhang, 2018;Bai, Xu, Yu, & Zurbruegg, 2020) [4].However, to our best knowledge, there is a dearth of evidence on whether numerological superstition affects corporate behavior.We fill this void by examining the association between investors' numerological superstition and earnings management using Chinese data.
Specifically, we investigate whether firms with earnings-per-share (EPS) ending with lucky numbers (i.e.our proxy for investors' numerological superstition) are more likely to engage in earnings management [5].The Chinese stock market is characterized by heightened information asymmetry between firms and external investors.Therefore, market participants, especially individual investors, have less reliable information available when making investment decisions (Hope, Wu, & Zhao, 2017;He, Wong, & Young, 2012;Jiang, Lee, & Yue, 2010;Ke, Rui, & Yu, 2012).Instead, they have to rely more on subjective judgments (Firth, Wang, & Wong, 2015).Accordingly, we conjecture that firms reporting lucky earnings numbers could be more likely to manage earnings for two reasons.First, a superstitious manager may believe that reporting lucky earnings numbers brings good luck to herself/ himself.Second, since minority shareholders in China are individual investors (Hong, Jiang, Wang, & Zhao, 2012) who are usually regarded as less rational (Fang & Peress, 2009;Gurun & Butler, 2012), a manager may collude with controlling shareholders to exploit minority shareholders' superstitious belief (Hirshleifer et al., 2018).By reporting lucky earnings numbers, the manager will help control shareholders' economic benefits.Both arguments suggest that managers have incentives to manage earnings to report lucky earnings number [6].
Our empirical analyses employ a sample of 22,370 firm-year observations of publicly traded firms in China from 2007 to 2016.If a firm's earnings-per-share (EPS) reported in the annual report ends with 6 or 8, we label it as a firm reporting lucky earnings numbers.To measure earnings management, we use both discretionary accruals and the incidence of subsequent accounting restatements.Our results show that firms with lucky earnings numbers have greater unsigned discretionary accruals and a higher probability of restatements.These inferences are robust to controlling for a number of common determinants of earnings management from the prior literature as well as year, industry or firm fixed effects.
To distinguish between the two aforementioned reasons why numerological superstition is related to earnings management, we perform a cross-sectional test by dividing the sample based on CEOs' education and zodiac year.CEOs with less education are expected to be more superstitious (i.e. have more beliefs without scientific grounding).In addition, it is widely believed in Chinese culture that a person is more likely to experience bad luck during her zodiac year, which occurs every 12 years since one's birth [7].Thus, it is possible that a manager in her zodiac year is more likely to report a lucky earning number to avoid bad luck.However, we fail to find any significant relation between lucky earnings number and earnings management in the subsample of CEOs with less education or in the one with CEOs in their zodiac years.This rules out the possibility that earnings management is due to manager's superstitious beliefs.Therefore, it is likely that mangers report lucky earnings numbers to take advantage of the superstitious beliefs of minority shareholders, which contributes to the positive association between lucky EPS numbers reporting and earnings management.
Next, we examine firms' future equity financing behavior after earnings management.If reporting lucky earnings numbers positively affects investors' perception of a firm, it would be easier to raise more capital from the stock market.This is indeed what we find.Our results show that firms with lucky EPS numbers are more likely to have seasoned equity offerings in the following year.In addition, the total amount of external equity raised is also greater for these firms.However, we document that they do not have more private placements to large controlling shareholders.
We also investigate how firms utilize the raised equity capital.If the maximization of firm value is the goal, managers will increase capital investment.But we fail to find that firms with Numerological superstition lucky EPS numbers have more capital investment after seasoned equity offerings.Instead, our results suggest that their controlling shareholders benefit from reporting lucky EPS numbers by expropriating minority shareholders.In China, controlling shareholders have strong influence over managers' career path (Jiang et al., 2010;Bradshaw, Liao, & Ma, 2019).As a result, managers often cater to the interest of controlling shareholders at the expense of minority shareholders.Jiang et al. (2010) find that controlling shareholders expropriate minority shareholders' wealth by siphoning funds from listed firms through transactions between related parties.Along this line, we find that firms with lucky EPS numbers have more future-related party transactions with controlling shareholders.Therefore, our evidence shows that controlling shareholders gain significant private control benefits when firms report lucky EPS numbers, which helps to explain the reason why firm managers engage in lucky EPS number reporting.
Finally, we provide a number of robustness checks.First, we show that discretionary accruals of firms reporting lucky EPS numbers are driven by earnings-increasing activities rather than earnings-decreasing activities.This is consistent with the argument that firms report lucky EPS numbers to optimistically bias investors' perception of firm value upwards.Second, our inferences stay the same when using alternative definition of lucky EPS numbers.Third, we perform falsification tests by examining firms with cash flows per share or shareholder equity per share ending with 6 or 8. Shareholder equity and cash flows are not directly affected by accruals manipulation, and as expected, we fail to find that these pseudolucky firms are more likely to manage earnings.Thus, the relation between lucky EPS numbers and earnings management is unlikely random.This is also consistent with the role of earnings as the main resource of firm-specific accounting information (e.g.Biddle, Seow, & Siegel, 1995;Liu, Nissim, & Thomas, 2002).
Our study contributes to the emerging line of literature on the implications of culture in the capital markets by providing the first evidence that numerological superstition is related to financial reporting quality.Prior research finds that superstitious beliefs significantly affect the trading behavior of individual investors in the stock market (Hirshleifer et al., 2018;Bhattacharya et al., 2017).However, those studies do not test whether mangers and controlling shareholders actually take advantage of individual investors' superstitious beliefs.Our findings suggest that as mangers realize that minority shareholders are superstitious, they intentionally exploit minority shareholders' superstitious beliefs by reporting lucky earnings numbers and controlling shareholders' benefit as a result through tunneling.This provides an explanation for why superstition negatively affects minority shareholders' welfare.
More broadly, our study also relates to the literature on how culture and social environment affect financial reporting behavior.Prior literature focuses on the role of religiosity and suggests that strong religious beliefs significantly curb earnings management and improve financial reporting quality in both the US and Chinese settings (e.g.McGuire, Omer, & Sharp, 2011;Bjornsen, Do, & Omer, 2019;Du, Wei, Lai, Du, & Pei, 2015;Cai, Li, & Tang, 2020).Our findings suggest that superstition, a key component of social and cultural environment, leads to more opportunistic manipulation behavior that benefits controlling shareholders at the expense of minority shareholders.
Finally, our results add to the literature examining tunneling by controlling shareholders in the Chinese market.For example, Jiang et al. (2010) document that controlling shareholders siphon a significant amount of funds through intercorporate loans.Our findings suggest earnings management could facilitate such tunneling behavior.Firms first engage in upward earnings management to achieve lucky EPS numbers and raise external capital through seasoned equity financing.Then, controlling shareholders further siphon the raised capital from the firms for their private benefits.

CAFR 25,3
The reminder of the paper proceeds as follows.Section 2 reviews related literature and develops the hypothesis.We present our research design, variable definition and sample selection in Section 3. Section 4 and Section 5 report results from our main empirical tests and additional analyses, respectively.Section 6 concludes.
2. Literature review and hypothesis 2.1 Superstition and culture Superstition is widespread in many cultures worldwide.Prior anthropology and psychology research suggest that superstition is a way people interpret uncertain events (e.g.Vyse, 1997;Burger & Lynn, 2005).The outcome of these uncertain events is determined by both factors controlled by people (e.g.effort, knowledge, experience) and random factors that are uncontrollable.Based on this theory, superstitious people attribute uncontrollable factors to luck.People with desire to control uncertain events are more likely to turn to superstition (Keinan, 2002).Therefore, superstitious behavior is more prevalent in times of high uncertainty.Supporting this view, Keinan (1994) finds that superstitious beliefs were stronger among Israeli citizens during the Gulf War.Similarly, Padgett and Jorgenson (1982) document more articles related to superstition in Germany popular periodicals in periods following high economic uncertainty.Another prominent example is that US President Reagan set his schedule with guidance from an astrologer following the attempted assassination of him in March 1981 (Vyse, 1997) [8].
A common superstitious behavior is belief in lucky and unlucky numbers.In Chinese culture, 6 and 8 are viewed as lucky numbers.Previous literature shows that numerological superstition has significant impact on business behavior in areas that are heavily affected by Chinese traditions.For instance, Simmons and Schindler (2003) finds that Chinese companies disproportionately use 8 in their product commercials.Block and Kramer (2009) document that Taiwanese consumers are willing to pay more for a package of 8 tennis balls than 10 [9].Agarwal et al. (2014) show that Singaporean Chinese pay a higher price for residential homes on the 8th floor [10].Similarly, in Hong Kong where the government sells new license numbers for motor vehicles by auction, Ng, Chong, and Du (2010) find that the price of license numbers ending with 8 is significantly higher than that of other numbers.
Prior research finds that numerological superstition influences investors' behavior as well.For example, Bhattacharya et al. (2017) document that investors in the Taiwanese stock market are more likely to lose money in trading when they submit limit orders at prices ending with 8.In addition, Hirshleifer et al. (2018) show that many Chinese IPO firms attempt to obtain lucky listing codes containing 6 and 8; more importantly, these firms gets better IPO pricing terms but have lower post-IPO stock price performance.Examining Chinese firms with unlucky listing codes, Bai et al. (2020) show that these firms have greater stock price crash risk [11].
Western Cultures also have superstitious behavior related to numbers.In the US, 13 is considered a symbol of bad luck.As a result, luxurious hotels in the US usually do not have the 13th floor.In contrast, many people think the number 7 is associated with good luck.Many businesses attempt to exploit such irrational beliefs.For example, on July 7, 2007, the Ritz Carlton Hotel in New York provided a wedding ceremony for the price of $77,777.The reception offered a seven-tier wedding case, and the wedding ring had 7 diamonds from Tiffany.

Hypothesis development
Prior literature has examined the effect of superstition in the capital market.An early study, Kolb and Rodriguez (1987), finds that the US stock market has lower returns on Friday the Numerological superstition 13th compared to other days.More recent studies in this area mostly focus on Asian markets.For instance, Hirshleifer et al. (2018) document that many Chinese IPO firms attempt to obtain lucky listing codes (i.e.those containing 6 or 8).The study shows that there is a mispricing of lucky listing codes around and after IPOs, and the results are attributable to unsophisticated investors who rely on superstition to guide their portfolio selection.Bhattacharya et al. (2017) identify a group of superstitious investors in the Taiwanese stock market based on their limit orders submissions.The evidence suggests that investors lose more money when they submit more limit orders at prices ending with 8. Thus, both studies imply that numerological superstition adversely affects investors.
In contrast, our study examines the relation between numerological superstition and corporate financial reporting behavior.We argue that firms have incentives to report lucky earnings numbers, as doing so may attract superstitious investors' attention and distort their perception of firm's valuation.As a result, firms can exploit investors' superstition and enjoy higher valuation in the stock market.More importantly, managers, whose career path depends on controlling shareholders to a considerable extent (Jiang et al., 2010;Bradshaw et al., 2019), often cater to the interest of controlling shareholders at the expense of minority shareholders.Accordingly, our hypothesis is formulated as follows: Hypothesis.Ceteris paribus, firms with lucky earnings numbers are more likely to engage in earnings management than other firms.

Data and empirical research design 3.1 Main variables
We employ two alternative measures of earnings management.The first one is the absolute values of discretionary accruals (Abs_Dac) calculated using the modified Jones model (Jones, 1991;Dechow, Sloan, & Sweeney, 1995) [12].
where TA is total accruals calculated by net income (NI) minus operating cash flow (OCF), and A denotes total assets.ΔSales and ΔReceivables represent changes in total sales and changes in account receivables, respectively.In addition, PPE denotes property, plant and equipment.We estimate this model by industry-years and require at least 10 observations for each industry-year.The residuals represent discretionary accruals (DAC), while Abs_Dac is the absolute values of discretionary accruals.For robustness check, we also consider several alternative measures, such as signed discretionary accruals and performance-matched abnormal discretionary accruals.
In addition to discretionary accruals, we use the incidence of accounting restatements as our second proxy for earnings management.Specifically, Restate is a dummy variable that equals to 1 if the firm's financial statements are restated in subsequent years, and 0 otherwise.
To identify firms with lucky earnings numbers (i.e.our proxy for investors' numerological superstition), we construct a dummy variable, Lucky EPS, which takes the value of 1 for firms with EPS ending in 6 and 8, and 0 otherwise.As discussed earlier, 6 and 8 are viewed as lucky numbers in the Chinese culture, and the last digit of EPS numbers is especially salient [13].We focus on the last digit of the EPS also because firms can more easily manipulate the last digit than other digits [14].

Regression model
To estimate the relation between lucky EPS numbers and earnings management, we begin by estimating model (1): CAFR 25,3 where i indexes firm and t indexes year.We cluster standard errors at the firm level [15].The dependent variable is either absolute discretionary accruals (Abs_Dac) or restatement (Restate).We estimate an OLS model when using Abs_Dac as the dependent variable.As Restate is a dummy variable, we adopt a Logit model for regressions using Restate as the dependent variable.The primary independent variable of interest is Lucky EPS.Our hypothesis predicts that firms with EPS ending with 6 or 8 are more likely to manage earnings, as evidenced by higher abnormal discretionary accruals and/or a greater probability of accounting restatements.Thus, the coefficient β 1 is expected to be positive.
We also include a vector of control variables in model ( 1) following prior literature (e.g.Yu, 2008;Fang, Huang, & Karpoff, 2016).They include firm size (Size), leverage (Lev), firm age (Age), market-to-book ratio (MB), sales growth (Grow), PP&E (PPE), ownership by the largest shareholder (TopShare), big-4 auditor (Big4Audit), loss indicator (Loss), analyst coverage (Coverage) and an indicator for firms that meet or just beat analyst earnings forecast (MBE).Furthermore, model (1) also includes year-fixed effects and firm-or industry-fixed effects.We provide detailed definition of these variables in the Appendix.

Sample selection
Our initial sample includes 27,877 observations of publicly traded firms in the Chinese stock markets from 2007 through 2016, excluding financial institutions defined based on the standard industry classification of the China Securities Regulatory Commission (henceforth CSRC).Our sample period starts from 2007 because China introduced a new accounting standard in 2007 to achieve convergence with the International Financial Reporting Standards (IFRS).We obtain financial data and stock return data for all listed Chinese firms from the China Stock Market & Accounting Research Database (CSMAR).We further manually collect information on restatement of financial report through the Giant Tide Information Net [16].Next, we remove firm-year observations with missing data on variables used in model ( 1) and observations with missing data to estimate the modified Jones model.Our final sample for the restatement tests consists of 19,719 firm-year observations.Further, after automatically removing the collinear observations, we have 19,592 firm-year observations when we use restatement as the dependent variable in Logit model with industry-fixed effect.

Descriptive statistics
In Table 1, we report summary statistics of our sample.The mean value of Abs_Dac is 0.070, and its median is 0.046.The mean value of Restate is 0.084, indicating that around 8.4% of annual reports in our sample are restated in subsequent periods.In addition, the mean of Lucky EPS takes the value of 0.198, which implies that around 20% of sample firms report EPS ending with 6 or 8.

Earnings management tests
In Table 2, we report the estimation results of model (1).In columns (1) and (3), we estimate the model after controlling for year-and industry-fixed effects.In column (1), where Abs_Dac is the dependent variable, the coefficient on Lucky EPS is positive (0.003) and significant at the 1% level.This indicates that, on average, firms with EPS ending with 6 or 8 have higher abnormal discretionary accruals than other firms, and thus they are more likely to engage in earnings management.In column (3), with Restate being the dependent variable, our Logit model estimation shows a significant and positive coefficient on Lucky EPS (0.260) with a marginal effect of 2.01%, implying that annual reports with EPS ending with 6 or 8 are more likely to be restated in subsequent years.These findings support our hypothesis and suggest that firms with EPS ending in 6 or 8 are more likely to manage earnings.In columns ( 2) and ( 4), to control for firm-level time-invariant omitted factors that may affect the tendency of earnings management, we further include firm-fixed effects instead of industry-fixed effects.The sample of the Logit model in column (4) reduces to 7,176 observations, because many firms never have restatements during our sample period and thus drop from the sample.The coefficients on Lucky EPS are still positive and significant in both columns.These results lend further support to our hypothesis and also mitigate concerns about time-insensitive omitted variables, such as corporate governance.
The coefficients on the control variables are consistent with prior literature (e.g.Fang et al., 2016).Specifically, earnings management is positively associated with leverage, growth and firm loss, while negatively associated with PPE.There is also some suggestive evidence on that high audit quality can curtail earnings management.

Additional analyses 5.1 CEO education and zodiac year
The results above are consistent with firms reporting a lucky EPS number are more likely to manage earnings.To shed light on possible underlying channels of our main findings, we conduct cross-sectional analyses based on several firm characteristics in this section.We report these results in Table 3.
Specifically, we first test the moderating roles of CEO characteristics.One explanation for the earnings management behavior to report EPS ending with 6 or 8 is that superstitious managers think a lucky earnings number can bring good luck to them and the firms.If so, the relation between EPS ending with 6 or 8 and earnings management should be driven by firms with more superstitious CEOs.We employ two measures of CEO superstition.The first measure, CEO_Zodiac, is constructed based on the traditional Chinese belief that one is more likely to have bad luck in his/her "zodiac year of birth."Zodiac year occurs every twelve years (3), we include year-and industry-fixed effects.In columns (2) and (4), we include year-and firm-fixed effects.Robust standard errors clustered at the firm level are reported in parentheses.Coefficients marked with *, ** and *** are significant at 10%, 5% and 1%, respectively Source(s): Table by   from birth and corresponds to the twelve-year cycle in Chinese astrology.Therefore, CEOs in their zodiac years may have stronger incentives to report a lucky number in order to bring about good fortunes.The second measure, HigherEdu, is an indicator for CEOs who received higher education.CEOs with higher education are expected to make decisions based on more scientific methods and thus be less superstitious [17].
In Panel A (Panel B), we interact Lucky EPS with CEO_Zodiac (Lucky EPS with HigherEdu).The first two columns (next two columns) report OLS regressions (Logit regressions) results, with discretionary accruals (restatements) as the dependent variable.As coefficients on interaction terms may be biased in Logit models, we also report linear probability regressions for the restatement test in the last two columns.Consistent with our main findings, the coefficients on Lucky EPS are consistently significant and positive.However, the coefficients on the interaction terms are insignificant across all the regressions.These findings are inconsistent with the argument that the superstitious earnings reporting behavior is due to CEO superstition.

Equity financing
Another explanation for our findings is that firms report lucky EPS numbers to exploit investors' superstitious beliefs for economic benefits.To understand the potential economic benefits that firms gain by reporting lucky earnings numbers, we consider the effect of EPS ending with 6 or 8 on firms' future equity financing behavior.Firms with EPS ending with 6 or 8 can attract investment from superstitious individual investors, which will, in turn, facilitate equity financing in the following period.
We employ three measures of external equity financing activities: (1) an indicator variable for firms with seasoned equity offerings in the following year (SEO), (2) the natural logarithm of one plus the amount of capital raised through seasoned equity offerings in the following  3) and ( 5), we include year-and industry-fixed effects.In columns ( 2), ( 4) and ( 6 The control variables in model ( 2) are the same as those in model ( 1).Logit models are used to estimate the effect of Lucky EPS on SEO and Private Place.An OLS model is alternatively used to analyze the effect of Lucky EPS on SEOscale.We report the regression results in Table 4.In columns (1) and (2) (columns (3) and ( 4)), the dependent variables are SEO (SEOscale).Our results show that there are positive and significant coefficients on Lucky EPS in all the four columns, indicating that firms with reported EPS ending with 6 or 8 have more seasoned equity offerings in the next year and also raise more capital.
In the last two columns, the dependent variable is Private Place.As discussed earlier, most Chinese firms are controlled by larger owners (i.e.controlling shareholders).Thus, managers are unlikely to use lucky EPS numbers to mislead this group of investors.Indeed, the coefficients on Lucky EPS in both columns are insignificant.This shows that lucky EPS numbers are associated with more seasoned equity financing activities but do not relate to private placements to controlling shareholders.

Capital investment
To investigate the intent of the seasoned equity offering, we examine how the capital raised through seasoned equity financing is used by firms.A firm with a lucky EPS number may use the raised equity capital to support a larger capital investment program.If so, firms with lucky EPS numbers are expected to have more capital investments.To test this, we estimate model (3): (3) In model ( 3), the dependent variable is change in capital investment in the following year scaled by total assets.We report the estimation results in Table 5.In the first two columns, we employ full sample, while the last two columns show the subsample of firms with seasoned equity offerings in the following year.For all the four columns, we include the same set of control variables as those in model (1).We find that the coefficients on Lucky EPS are insignificant in all columns.This suggests that firms with lucky EPS numbers do not seem to use the raised equity capital in their capital investments.

Controlling shareholder expropriation
Since evidence documented above shows that firms with lucky EPS numbers raise more capital in SEOs but do not have higher capital investors, in this subsection, we look into how these use the raised capital.Specifically, we examine whether controlling shareholders derive private benefits through expropriating additional capital raised in SEOs.Jiang et al. (2010) find that controlling shareholders siphon a significant amount of funds through related party transactions.For example, a public firm can lend funds to a related private firm that is solely owned by the public firm's controlling shareholder.These loans are rarely paid back and often end up being written off as bad debts.These loans are usually reported as "other receivables" on the balance sheet.Therefore, firm insiders can benefit from superstitions EPS reporting through turning funds obtained from SEOs to intercorporate loans for their own usages.To explore this explanation, we estimate the following model (model 4).3) and ( 5), we include year-and industry-fixed effects.In columns (2), ( 4) and ( 6), we include yearand firm-fixed effects.Robust standard errors clustered at the firm level are reported in parentheses.*, ** and *** indicate significance at 10%, 5% and 1%, respectively Source(s): Table by authors   Table 4.

Numerological superstition
where the dependent variable Tunnel is calculated as other receivables resulting from transactions related to major controlling shareholders (scaled by total sales).We include the same set of control variables as those in model (1).We report estimation results in Table 6, and they show that there are positive and significant coefficients on Lucky EPS in both columns.This suggests that firms with EPS endings with 6 or 8 have more intercorporate loans with related parties than other firms in the following year.Put differently, controlling shareholders benefits from reporting lucky earnings numbers by tunneling corporate resources at the cost of minority shareholders.

Robustness checks
We provide several tests to examine the robustness of our main findings in  3), we include year-and industry-fixed effects.In columns (2) and (4), we include year-and firmfixed effects.Robust standard errors clustered at the firm level are reported in parentheses.*, ** and *** indicate significance at 10%, 5% and 1%, respectively Source(s): Table by authors   Table 5.Corporate investment CAFR 25,3 discretionary accruals, implying that firms intentionally manipulate earnings to mislead superstitious investors.To provide further support on this, we examine the relation between EPS ending with 6 or 8 and positive vs. negative discretionary accruals in panel A. In columns (1) and (3), we include observations with positive discretionary accruals; while in columns ( 2) and (4), our observations include those with negative discretionary accruals only.In columns (1) to (4), we control for year-and industry-fixed effects.In the subsample of observations with positive discretionary accruals (columns (1) and (3)), our results show that the coefficient on Lucky EPS is positive and significant at the 1% level.In columns (2) and (4) in which the sample contains observations with negative discretionary accruals, the coefficient on Lucky EPS becomes insignificant at the conventional level.This indicates that firms with EPS ending with 6 or 8 manipulate earnings upward rather than downward based on Chinese superstition.Such findings are consistent with firms using superstitious earnings management behavior to positively manipulate investors' perceptions.

Numerological superstition
In panels B and C, we employ two alternative measures of lucky EPS numbers.As Hirshleifer et al. (2018) also consider 9 as a lucky number, we construct a variable, Lucky EPS 869, an indicator for firms with EPS ending with 6, 8 or 9.In addition, since 4 is usually considered an unlucky number in China, Lucky EPS 8694 is set to 1 if the last digit of the EPS is 6, 8 or 9, negative 1 if the last digit of EPS is 4, and 0 otherwise.Using both measures, we find results similar to those in Table 3.
In panel D, we conduct a set of falsification tests.Specifically, we consider whether other per-share measures have a similar relationship with abnormal discretional accruals and restatement.Apart from EPS, Chinese listed firms also disclose operating cash flows and total stockholders' equity in the annual report.However, as these measures are not directly related with firms' earnings, it is less likely individual investors will rely on them to make their investment decisions.We construct the following measures: Lucky Cashflow, an indicator variable equals to1 if the last digit of the year-end operating cash flows per share is 6 or 8; Lucky Equity, an indicator variable equals to 1 if the last digit of the year-end stockholders' equity per share is 6 or 8.We conjecture that if our story holds, we should not observe significant relationship between the last digit of per-share measures of these two variables and earnings management.This is indeed what we find.We find that Lucky Cashflow is negatively associated with the likelihood of restatement, and other main explanatory variables have no significant association with dependent variables.These results suggest that the reporting strategies of EPS play a prominent role in earnings manipulation, which are consistent with the view that earnings are the main resource of firm-specific accounting information (e.g.Biddle et al., 1995;Liu, Nissim, & Thomas, 2002).3) and ( 5), we include year-and industry-fixed effects.In columns (2), ( 4) and ( 6), we include year-and firm-fixed effects.CAFR 25,3

Conclusion
The Chinese culture views 6 and 8 as lucky numbers.This study examines the relation between numerological superstition and corporate financial reporting behavior using Chinese publicly traded firms.We show that firms with EPS ending with 6 or 8 are more likely to engage in earnings management, proxied by larger absolute discretionary accruals and a greater probability of accounting restatements, compared to other firms.Furthermore, our evidence suggests that firms with EPS ending with 6 or 8 raise more external equity capital in the following period, but they do not have more capital investments.We also find that these firms' controlling shareholders expropriate minority shareholders' wealth by tunneling funds through related-party transactions.Overall, our study suggests that in an environment with superstition culture and a large number of unsophisticated individual investors, firm mangers, colluding with controlling shareholders, manipulate earnings to exploit minority investors' superstitious beliefs for economic benefits.Our findings can help better understand how social and cultural environment affects firms' financial reporting behavior.

Notes
1. Superstition refers to psychological biases and irrational beliefs that are not based on reason.While some superstitious beliefs are results of personal experience, most of them are culture-dependent (Bhattacharya et al., 2017;Hirshleifer et al., 2018).
3. In the Chinese culture, 8 is viewed as a lucky number because its pronunciation sounds similar to that of the word "prosper"pronounced "faa," in both Mandarin and Cantonese Chinese.As evidence of such superstitious belief, the official starting time of the 2008 Beijing Summer Olympics Games is 8:08 PM on August 8, 2008 (https://www.mercurynews.com/2008/08/07/lucky-numberinspired-china-to-start-olympics-at-808-p-m-8808/).As another example, in 2016, a Hong Kong car license plate bearing a number ending with 8 was auctioned for a record HK$18.1 million (US$2.3 million) (https://theculturetrip.com/asia/china/hong-kong/articles/7-superstitions-that-still-shapethe-lives-of-hongkongers-today/).Similarly, 6 is also a lucky number, which means "smooth" in Chinese culture.This phenomenon has a long history.In I-Ching (易经), which was written more than 2,000 years ago and summarized the Yin-Yang knowledge in China, 6 is viewed as the symbol of yin.The hexagram of 6 yins is the symbol of "long" and "smooth" (https://baijiahao.baidu.com/s?id51591615806674923293&wfr5spider&for5pc).
4. Hirshleifer et al. (2018) find that Chinese firms with more lucky listing codes in IPO are priced higher, but they have lower post-IPO stock price performance.In addition, Bhattacharya et al., 2017 document that investors on the Taiwanese stock market lose more money when they submit more limit orders at prices ending with 8. Finally, Bai et al. (2020) find that Chinese firms with unlucky listing codes have greater crash risk, and argue that investors' overreaction to negative news from these firms is the mechanism through which superstition affects crash risk.
5. A stream of related literature finds that religion is negatively associated with the extent of earnings management or real earnings management using Chinese samples (Du et al., 2015;Cai, Li, & Tang, 2020).
6. Either argument leads to a positive association between lucky EPS number reporting and earnings management.As shown in our empirical tests later, our inferences support the second story after ruling out the first explanation.
Numerological superstition This table reports summary statistics of our primary test sample, including the number of observations, mean, median, standard deviation, bottom and top quartiles, respectively.Variable definitions are provided in the Appendix Source(s): Tableby authors This table examines the earnings management behavior by firms with EPS ending with 6 or 8.All variables are as defined in Table A1 in Appendix.The sample period is from 2007 to 2016.In columns (1) and authors This table estimates the cross-sectional differences in the earnings management behavior of firms reporting EPS ending with 6 or 8.All variables are as defined in the Appendix.The sample period is from 2007 to 2016.In columns (1), (

Table 3 .
Numerological superstition year (SEOscale) and (3) an indicator for firms that issue additional equity stocks to one of the largest ten shareholders through private placements in the following year (Private Place).
), we include year-and firm-fixed effects.Robust standard errors clustered at the firm level are reported in parentheses.*,** and *** indicate significance at 10%, 5% and 1%, respectively Source(s): Tableby authors This table examines firms' equity financing behavior in the following period when firms report EPS endings with 6 or 8.All variables are as defined in the Appendix.The sample period is from 2007 to 2016.In columns (1), (

Table 7 .
First, our main tests show that firms with reported EPS ending with 6 or 8 have greater absolute This table examines firms' investment behavior in the following period when firms report EPS endings with 6 or 8.All variables are as defined in the Appendix.The sample period is from 2007 to 2016.In columns (1) and ( This table examines the controlling shareholders' tunneling behavior when firms report EPS endings with 6 or 8.All variables are as defined in the Appendix.The sample period is from 2007 to 2016.In columns (1) and (3), we include year-and industry-fixed effects.In columns (2) and (4), we include year-and firm-fixed effects.Robust standard errors clustered at the firm level are reported in parentheses.*,** and *** indicate significance at 10%, 5% and 1%, respectively Source(s): Tableby authors

Table 7 .
This table provides falsification tests by defining lucky firms based on the last digit of cash flows per share and shareholders' equity per share.All variables are as defined in the Appendix.The sample period is from 2007 to 2016.In columns (1), (