Long-term market reactions to earnings restatements.

Xu, Tan ; Jin, John Jongdae ; Li, Diane 等

INTRODUCTION

Ever since recent accounting scandal ignited by Enron fiasco, earnings restatements due to accounting irregularities (11) draw significant attention from public in academia and practice. Since accounting irregularities are intentional misrepresentations of accounting information by the reporting entity, earnings restatements due to these (hereafter called earnings restatements) do have different connotations to the capital market than other earnings information releases. First, earnings restatements may increase the uncertainty of the reporting entity because they usually cause class action lawsuits, management shuffle, restructuring, and even bankruptcy. Secondly, earnings restatements impair the information quality of the reporting entity because restating firm's information may not be as reliable to investment public as it used to be prior to the earnings restatement. Then, these higher uncertainty and lower information quality can increase the risk premium and stock return volatility of the restating firms (See Aboody (2005), Francis (2005), and Li (2005)), which may reflect that it is more difficult and time consuming for the capital market to response to restating firms' information release after the earnings restatements. Thus, how efficiently the capital market reacts to information release of the restating firms can be a valuable research question. As a way of addressing this question, the long-run stock price behavior of the restating firms after the restatements will be examined in this study.

Prior studies on the post-announcement stock price performance of earning restatement such as Hirschey et al. (2003), General Accounting Office (GAO) (2002), and Wu (2002) document negative abnormal stock returns of the restating firms in the months following the restatement announcement, which is contradictory to the efficient market hypothesis predicting no abnormal returns. All these studies exclusively used the Cumulative Abnormal Returns (CAR) approach to measure stock price performance. Hirschey et al. (2003) use the market-adjusted, the market-model adjusted and the mean-adjusted CAR approaches. GAO (2002) uses the market-adjusted CAR approach. Wu (2002) uses the [beta]- and size- adjusted CAR approach. For example, Wu (2002) observes over 10 percent negative CAR in the year following the announcement. She suggests two potential explanations: some firms fail to provide restated number at the same time as restatement announcements and leave the issue unconcluded; and investors keep revising their beliefs according to information received subsequently. Taken at face value, this evidence is consistent with the notion that market under-reacts to earning restatements.

However, the CAR approach does not provide a precise picture of long-term stock performance due to its embedded structural problem of simple summation of periodic abnormal returns rather than compounding of them and its cross-sectional dependence problem. And recent studies suggest that the results of long-run abnormal returns should be interpreted with caution because the abnormal return metrics are severely mis-specified. Misspecification of abnormal stock returns can cause some methods to detect spurious anomalies. Although various methodologies have been proposed to measure long-run stock price performance, each and every methodology has some sort of measurement problem or problems. And it is hard to identify the best methodology addressing these measurement problems, either. Thus, among those various methodologies, the three most popular and sound methodologies are used in this study to measure long-term stock price performance of restating firms after the earnings restatements. Those are the CAR, the buy-and-hold abnormal return (BHAR), and the calendar time portfolio approaches.

Thus, the purpose of this paper is to examine the long-term stock price behavior of restating firms using the above mentioned three major methodologies for measuring long-term stock returns. Our empirical results suggest that stocks of restating firms do not underperform or outperform the market in the year following the announcement day, supporting the efficient market hypothesis.

The remainder of this paper is organized as follows. Literature on methodologies for long-term stock returns is discussed in the next section that is followed by selection of sample firms and their data. Empirical tests using the above-mentioned three approaches and their results are presented and discussed in the following section. Conclusions are addressed in the final section.

LITERATURE REVIEW

Although there is substantial variation in the measures and test statistics of abnormal returns, there are three major approaches to measure the long term stock price performance: the cumulative abnormal return (CAR) approach, buy-and-hold abnormal return (BHAR) approach, and the calendar time portfolio approach. In the CAR approach, the abnormal performance is measured by the sum of either the daily or monthly abnormal returns over time (e.g., DeBondt and Thaler, 1985). The daily or monthly abnormal return is the difference between the actual return and a benchmark return, such as the predicted return estimated by the market model, the return of a reference portfolio or the return of a control firm. Beginning with Ritter (1991), the mean BHAR has become the most popular estimator of long-run abnormal returns (Mitchell and Stafford, 2000). In this approach, the abnormal performance is measured by the buy-and-hold return (BHR) differential between the sample firm and a benchmark. The BHR is calculated by compounding the daily or monthly returns over the post-event period. The calendar time portfolio approach requires first forming a portfolio at the beginning of each calendar month containing firms that had an event within the last one-, three-, or five-year (depending on the purpose of the study) and then calculating their mean return. The monthly returns of the portfolios are then regressed on Fama and French's (1993) three factors. The abnormal performance over the post-event period is measured by the intercept term of the model. Jaffe (1974), Mandelker (1974), Fama (1998), and Desai et al. (2002) use various forms of the calendar time portfolio approach. Fama (1998) suggests that the heteroskedasticity of the portfolio's abnormal return caused by the changes in number of stocks in the portfolio over time can be solved by using the weighted least square (WLS) technique: i.e., using the number of stocks in the portfolio as the weight when running the regression.

The benchmark used to estimate the abnormal returns varies in many studies. A benchmark can be the return of a reference portfolio. The value-weighted and equal-weighted CRSP market indices are two conventional reference portfolios. Reference portfolios can also be the size, the book-to-market (BM) ratio, or [beta] matched portfolios. To form these portfolios, researchers first divides all the NYSE/ASE, and NASDAQ stocks into deciles by size, BM ratio, or [beta] in June or December each year. The number of deciles varies in different studies. Some studies, e.g., Barber and Lyon (1997), divide firms into 50 deciles (10 size deciles by 5 BM ratio deciles). The return for each decile is calculated by averaging the returns of all stocks in the decile. Thus, a size-adjusted abnormal return is the return of the sample firm minus the average return of all the firms in the same size decile. Since firms might change deciles only once a year, the benchmark returns is equivalent to investing in an equal weighted decile portfolio with monthly rebalancing. A benchmark can also be the return of the control firm. The control firm is the firm that has similar characteristics as that of the sample firm. One way to identify the control firm is by first finding all firms with a market value between 70% and 130% of that of the sample firm; among the firms in this set, a firm that has BM ratio closest to that of the sample firm is finally selected as the control firm. Another type of benchmark is derived from a variety of asset-pricing models, such as the market model and the Fama and French (1993) three-factor model. The intercept term in these models represents the abnormal return. Nevertheless, Ball et al. (1995) document that many popular asset-pricing models are misspecified and, thus, may cause problems when using them to measure long-run stock price performance.

Lyon et al. (1999), Fama (1998), and Barber and Lyon (1997) have discussed how different types of misspecification can cause biases in various measures of long-run abnormal performance. These measurement biases are: 1) the new listing bias. It arises because sample firms generally have a long post-event history of returns while the reference portfolio constitutes new firms that begin trading subsequent to the event month. Since new firms concentrate in small growth stocks that historically have lower returns than the market (Brav and Gompers, 1997), the return of the reference portfolio is artificially depressed relative to the sample firms. Thus, comparing the return of the sample firms with the benchmark return yields positively biased test statistics, i.e., making it more likely to reject the null hypothesis of zero abnormal returns. On the other hand, if newly listed firms outperform the market, the test statistics will be downwardly biased; 2) the rebalancing bias. It arises since the return of a reference portfolio is calculated by compounding the equal weighted returns in each period while the returns of sample firms are compounded without rebalancing. The monthly rebalancing means that, at the beginning of each period, stocks that rose during the prior period (day or month) are reassigned the same weight as those dropped during the prior period. This is equivalent to the strategy of selling a portion of the past winners and buying past losers. Since past winners empirically outperform past losers in the intermediate term due to momentum (Jegadeesh and Titman, 1993), the long-run return of the reference portfolio is inflated relative to the sample firms, leading to a positive bias in measuring the long-run return of the sample firms. The magnitude of the rebalancing bias is more pronounced when using daily, rather than monthly, returns (Canina et al. 1996). The CAR approach is not subject to this bias since CAR is the sum of the difference between the returns of the sample firms and the market index; 3) the skewness bias. It arises because the long-run BHAR is positively skewed. When the test statistic is calculated by dividing the mean BHAR by the cross-sectional standard deviation of the sample firms, the positive skewness leads to a negatively biased test statistic. The skewness bias is less serious in CAR approach because the monthly returns of sample firms are summed rather than compounded; 4) the cross-sectional dependence. It inflates test statistics because the number of sample firms overstates the number of independent observations. Two types of cross-sectional dependence are calendar clustering (e.g., many firms have the same event during the same day or month) and overlapping return calculations (e.g., a firm has the same event twice or more during the event period, say, one year). The calendar clustering might be driven by certain fundamental forces, while the overlapping return might be driven by the firm characters. In both cases, the observations are not independent. While both the CAR and BHAR approaches suffer from this problem, the calendar-time portfolio approach eliminates this problem since the returns on sample firms are aggregated into the return of a single portfolio; 5) the bad model problem. Because all models for expected returns fail to completely describe the systematic patterns in average returns during any sample period (Fama, 1998), the estimate of the expected returns cannot be accurate, leading to spurious abnormal return which grows with the return horizon and eventually becomes statistically significant. The bad model problem is most acute with BHAR approach since the measurement error grows fast with compounding returns.

Fama (1998) prefers the CAR approach to the BHAR approach in testing market efficiency because the former is less susceptible to misspecification, which is more severe when compounding daily or monthly returns. Nevertheless, Barber and Lyon (1997) and Lyon et al. (1999) show that the statistical problems of BHAR can be attenuated using elaborate techniques. Although the improved methods of BHAR produce inferences no more reliable than the simpler CAR method, the BHAR approach precisely measures investor experience and can answer the question of whether sample firms earn abnormal returns over a particular horizon of analysis. On the other hand, the CAR approach should be used to answer a slightly different question: do sample firms persistently earn abnormal monthly returns? Although the question is related, the CAR is a biased estimator of BHAR. Thus, they do not recommend the CAR approach; Barber and Lyon (1997) prefer BHAR with the control firm method to BHAR with the reference portfolio method since the former alleviates the new listing bias, the rebalancing bias, and the skewness bias; moreover, the matching firm method can be extended to include more firm characteristics, such as momentum, in addition to the firm size and BM ratio. Kothari and Warner (1997) find that parametric test statistics, such as the BHAR with market model, or three-factor model, do not satisfy the assumptions of zero mean and unit normality. They suggest using the BHAR in conjunction with the pseudoportfolio approach proposed by Ikenberry et al. (1995) might reduce the misspecification problem. Lyon et al. (1999) advocate two approaches: 1) the BHAR approach using a carefully constructed reference portfolio, such as the bootstrapped skewness-adjusted t-statistic or the pseudoportfolio approach; and 2) the calendar time portfolio approach. Mitchell and Stafford (2000) compare the measurement biases in these two approaches and suggest that the cross-sectional dependence problem is more severe than the violation of normality. The bootstrapping procedure assumes cross-sectional dependence and, thus, is not reliable. They recommend the calendar-time portfolio approach that assumes normality. Fama (1998) strongly advocates the calendar-time portfolio approach since: 1) monthly returns are less susceptible to the bad model problem; 2) it accounts for the cross-sectional dependence problem; and 3) the estimator is better approximated by the normal distribution, allowing for classical statistical inference. Nevertheless, the calendar-time portfolio approach does not reflect investors' experience and has low power to detect abnormal performance since it averages over months of "hot" and "cold" event activity (Loughran and Ritter, 2000).

The results of long-run abnormal return might also be influenced by the low-priced stock effect. Conrad and Kaul (1993) and Ball et al. (1995) report that most of DeBondt and Thaler's (1985) long-run overreaction findings can be attributed to a combination of bid-ask effect and the low-price effect, rather than prior return. Although Loughran and Ritter (1996) question the methodology used in both studies, the impact of low-price stocks might be important when the sample firms are extremely low-priced since micro-structure problems, such as larger bid-ask spread, might decrease market participants' ability to capitalize on and hence cause the mis-valuation of these stocks.

Furthermore, recent empirical studies increasingly consider the momentum effect (2) when measuring long-run performance (e.g., Desai et al., 2002). Several studies document that restating firms experienced stock price decline in the six months before restatement announcement (e.g., Hirschey et al., 2003; Wu, 2002), none has control for the momentum effect when measuring the long-run performance.

In sum, there are various methodological problems in all three major approaches to measure long-run stock performance. But there is no panacea for all the above problems and no consensus on which approach is the best in measuring long-run stock performance. Thus, it is necessary to use all three major approaches such as CAR approach, the BHAR approach and the calendar-time portfolio approach to obtain more robust evidence on how the capital market responses to earnings restatements.

SAMPLE DESCRIPTION

A list of earnings restatements due to accounting irregularities announced during January 1997 through December 2002 is obtained from GAO. According to GAO's (2002) report, it is the most comprehensive sample during that period and contains 919 earnings restatements announced by 845 public companies. The accounting and stock returns data are drawn from COMPUSTAT and CRSP, respectively. The sample period almost covers the stock market run-up during the late 1990s and its collapse after March 2000. It is the period when the number and magnitude of earnings restatement surge to historic high, providing us a large number of observations. In this period, the public concern on corporate governance grew, leading to the passage of Sarbanes-Oxley Act in July 2002. There is no shift in legal regime during the sample period. We exclude earnings restatements announced by American Depository Receipts (ADRs) firms because they subject to different supervisory requirements.

Comparisons between characteristics of the restating firms and those of all COMPUSTAT firms are presented in Table 1. To measure the statistical significance of the difference between restating firms and all firms, a nonparametric test called Wilcoxon test was conducted, because the test avoids the problems caused by skewness and outliners. Since earnings restatements are unevenly distributed across industries (Beasley et al., 2000) and the average size, Book to Market (BM) ratio, and leverage vary from industry to industry; it might be more meaningful to use the industry-adjusted indicators. Industry-adjusted variables are calculated by subtracting the industry median value from the raw value of the variables. We identify companies in the same industry by matching their 4-digit historical SIC codes in the fiscal year when earnings restatement was announced. The reason to use the historical SIC code rather than the current SIC code is that some firms might change their industry after the sample period, making current SIC code an imprecise proxy for industry sector in the sample period. The earlier the event day the more severe the problem is.

Table 1 show that the raw BM ratios of restating firms are lower than those of all firms in 5 out of 6 sample years (1997, 1998, 1999, 2001, & 2002) and the entire sample period. But the differences are not statistically significant in any year. The industry adjusted-BM ratios of restating firms, however, are higher than the industry mean in all 6 testing years. And the differences are statistically significant in 3 out of 6 sample years (1999, 2000, & 2002) and the whole sample period. This discrepancy may suggest that restating firms concentrate in industries with more growth opportunities (the lower BM ratio than the overall) but they have less growth opportunities or are considered riskier than their peers (higher BM ratios than the industry mean).

Restating firms are larger in size: the mean market value of the restating firms is significantly larger than that of all COMPUSTAT firms in 4 out of 6 sample years (1999, 2000, 2001, & 2002) and the whole sample period. Our result is different from the previous results that suggest that restating firms concentrate in small firms (e.g., Beasley et al., 2000). This discrepancy might be due to a significant increase in the number of large restating firms during the sample period. The industry-adjusted market value of the restating firms are significantly higher than zero in 5 out of 6 sample years (1998, 1999, 2000, 2001, & 2002) and the whole sample period, indicating that restating firms are larger than their peers in the same industry.

Restating firms also have a lower leverage in terms of the ratio of total debt to total assets but the difference is significant in year 1977 and for the whole sample period, only, indicating restating firms have lower leverage ratios than the all COMPUSTAT firms. And the industry-adjusted leverage is significantly higher than zero in 5 out of 6 years (1997, 1998, 1999, 2000, & 2001) and the whole sample period, indicating that restating firms do have higher leverage ratios than the industry average.

Some companies restated the same financial statement more than once, making the second announcement less informative. To reduce this noise, only the first announcement in the sample is kept if a company announces restatement more than once within the same fiscal year. To isolate the effect of earnings restatement from other factors, companies that announce earnings figure or guidance, or bankruptcy over the (-5, 5) event-date window are excluded. The information on earnings or earnings guidance announcement and bankruptcy announcement is collected from the U.S. news in the Factiva database around the event day of each firm. Stocks selling below one dollar (so-called penny stocks) before earnings restatement are excluded because they have wide bid-ask spreads, high commissions, low liquidity (Conrad and Kaul, 1993) and higher delisting risks. After these procedures, the final sample includes 542 restating firms but the number of observations varies in different tests depending on data availability.

Table 2 shows that sample firms have average CAR of -7.40 percent and -9.05 percent over the (-1, 1) and (-5, 5) windows, respectively, both of which are statistically significant. None of daily abnormal returns are statistically significant from day 2 after the announcement of restatements in terms of the standardized cross-sectional (SCS) test (t-statistic) and the generalized sign test (Z-statistic).

Corhay and Rad (1996) show that since stock returns series generally exhibit time-varying volatility, a market model accounting for generalized autoregressive conditional heteroskedastic (GARCH) effects produces more efficient estimators of abnormal returns than a market model estimated using the ordinary least squares (OLS) method. Thus, we also estimate the abnormal returns using market model with the GARCH (1, 1) procedure. Results from the GARCH-adjusted technique presented in Table 3 are similar to those from the conventional CAR. The GARCH-adjusted average CARs are -7.42 percent and -8.96 percent in the (-1, 1) and (-5, 5) windows, respectively, both of which are statistically significant. None of daily abnormal returns are statistically significant from the day 2 after the announcement of restatements in terms of the standardized cross-sectional (SCS) test (t-statistic) and the generalized sign test (Z-statistic).

In sum, the results in Table 2 and Table 3 suggest that the short term impact of earnings restatement announcements on stock prices seems to fade away by the day 1 after the announcement because none of daily abnormal returns are statistically significant from the day 2 after the announcement of restatements in terms of the standardized cross-sectional (SCS) test (t-statistic) and the generalized sign test (Z-statistic). Thus, it is reasonable to observe abnormal stock returns from day 2 after the announcement to measure the long-term stock performance of restating firms, which is used in this study.

EMPIRICAL TESTS AND RESULTS

Three approaches used in this study to measure the stock price performance of restating firms over the one year period and six months period following earnings restatement announcements are the CAR approach, the BHAR approach, and the calendar-time approach. The one-year post-announcement period extends from the 2nd day through 255th day following the announcement date, while the six-month post-announcement period extends from the 2nd day through 128th day after the announcement date. It is assumed that each month has 21 trading days except in the sixth and twelfth month when there are assumed be 22 trading days to complete the six-month and twelve-month event-day window.

CAR Approach

To compare with the prior studies on long-term stock performance of restating firms, the conventional CAR are estimated, first. Precision-weighted CAR advocated by Cowan (2002) are also estimated to control for the variance of stock returns. The abnormal returns are the error terms in the market model in which the CRSP equal-weighted market index and the value-weighted market index are used as the market returns. The estimation period is from 300 days to 66 days before the announcement date. The SCS test introduced by Boehmer et al. (1991) and the generalized sign test advocated by Cowan (1992) are performed to test the statistical significance of CAR.

The conventional and precision-weighted CAR of restating firms over the post-announcement period and test statistics are shown in Table 4. The results suggest that restating firms do not have significant abnormal performance over either the six months period or the one year period following the announcement of earnings restatements. Of the twelve months following earnings restatement, restating firms have significant abnormal return only in the month 1 using the SCS test, indicating that there are significantly negative abnormal returns during the first month after the announcement. But this may be because the short-term effect of the earnings restatement announcement on stock prices does not fade away by the first day following the announcement. There are no significant abnormal stock returns observed in any other months, the six month period, and the one year period. This indicates that the capital market prices the stocks of restating firms efficiently in spite of added uncertainties about the restating firms by earnings restatements, supporting the efficient market hypothesis.

Regarding the general sign test, only month 4, month 6, and month 8 show statistically significant z-values, indicating that there are significantly more restating firms with positive abnormal returns than restating firms with negative abnormal returns in those three months. There are no significant z-values observed in any other months than those three months, the six month period, and the one year period. This also indicates that overall the capital market performs efficiently in pricing stocks of restating firms in spite of added uncertainties about the restating firms by earnings restatements, supporting the efficient market hypothesis.

Figure 1 plots the mean, median, and precision-weighted CAR from the 63 days before to 252 days after earnings restatement. The result is in line with the findings that restating firms on average experience negative price drift before earnings restatement and no significant price drift over the long horizon following the announcement of earnings restatements.

In sum, the results from CAR approach presented in Table 4 and Figure 1 suggest that the capital market performs efficiently in pricing stocks of restating firms in spite of added uncertainties about the restating firms due to earnings restatements, supporting the efficient market hypothesis.

BHAR Approach

The measure of abnormal performance in the BHAR approach is the average BHAR. First, for each restating firm, the monthly return is calculated by compounding the daily returns in that month; then these monthly returns are compounded to calculate the six-month or one-year buy-and-hold returns (BHRs). By compounding the monthly returns rather than directly compounding all the daily returns in the holding period, we alleviate the bad model problem. Each restating firm's BHAR is the difference between its BHR and the equal weighted CRSP market index within the holding period. The cross-sectional test is performed to test the significance of the six-month or one-year BHAR. To alleviate the misspecification problem in using daily returns, the average abnormal returns of each month and the holding period are tested using the bootstrapped approach along with the skewness-adjusted t test. If a firm is delisted within the holding period, it is assumed that the stock is sold at the end of the last trading day and the proceeds are reinvested in the rest of the stocks in the portfolio equally in the next trading day.

[FIGURE 1 OMITTED]

BHAR's of restating firms calculated by compounding monthly returns data are presented in the Panel A of Table 5. The results show that restating firms have significantly negative abnormal returns of 9.97 percent and 16.93 percent in the six-month and one-year post-announcement periods, respectively. This indicates that the restating firms' stocks under-perform the market over the six month period and one year period following the announcement of earnings restatements, inconsistent with the efficient market hypothesis.

BHAR's calculated by compounding daily returns with bootstrapped approach are presented in Panel B of Table 5.3 Mean BHAR's over the six month and the one year periods are -16.39% and -64.03%, respectively, both of which are statistically significant. This also indicates that the restating firms' stocks under-perform the market over the holding periods, consistent with the under-reaction hypothesis but not with the efficient market hypothesis. Restating firms under-perform the market by 3.16 % in the first month on average. The generalized sign test shows that there are significantly more restating firms with negative BHAR than restating firms with positive BHAR over the six month and the one year holding periods. This may also implies that restating firms under-perform the market over the holding periods, inconsistent with the efficient hypothesis.

The six-month and one-year BHAR's in Panel B are much more negative than those in Panel A, which may support the notion that misspecification problem can be more severe when compounding daily returns than compounding monthly returns.

In sum, results from BHAR approach presented in Table 5 suggest that restating firms under-perform the market over the six month period and the one year period following the announcements of earnings restatements, consistent with the under reaction hypothesis but not with the efficient market hypothesis. However, it is premature to draw any inferences or make any conclusion based these results, because the effects of firm specific characteristics on stock returns are not controlled for in this BHAR Approach. Considering various firm characteristics of sample restating firms such as BM ratio, market value, and momentum shown in Table 1, it is necessary to control over these firm characteristics to obtain more meaningful and reliable test statistics.

For this control purpose, the BHAR approach with the control firm method advocated by Barber and Lyon (1997) is adopted in this study. Under this method, the BHAR of each restating firm is defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Where [R.sub.jt] and [R.sub.ct] are the returns of sample firm j and its control firm, respectively, in month t; T denotes the number of month and is equal to 6 or 12 depending on the length of the holding period. The average BHAR is defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Where n is the number of firms in the buy-and-hold portfolio. The t-statistic is computed as the AHAR divided by the estimated standard error of AHAR.

We modify the methods used by Lyon, et al (1999) and Desai et al. (2002) to identify a size-, BM ratio-, and momentum- matched control firm for each sample firm. The control firms are required to be selling above one dollar and remain listed within the (0, 20) event date window. For each restating firm, we identify all the non-restating firms with market value and BM ratio between 70 percent and 130 percent of those of the restating firm at the end of the month when restatement is announced. We do not match the value at the beginning of the event month since the market is more likely to accept the price after the restatement as reference than the price before. From this set of firms, the non-restating firm that has past one-year returns closest to that of the restating firm is selected as the control firm.

BHR's of the restating firms, those of the control firms, and the difference between the two are presented in Table 6. Average BHAR, the excess of BHR's of restating firms over those of the matching non-restating firms, are not significant in any single month and holding period following the announcement of earnings restatements. This indicates that restating firms do not significantly under-perform their size-, BM ratio-, and momentum- matched control firms in either the six-month period or one-year holding period. In other words, there are no abnormal stock returns of restating firms after controlling for the firm characteristics over the post announcement holding period, consistent with the efficient market hypothesis. This may also imply that the results presented in Table 5 may be contaminated by the firm characteristics.

Putting together, the results from Table 5 and Table 6 suggest that although restating firms underperform the market, the underperformance may be due to their firm characteristics, such as the size, BM ratio, and momentum, rather than earnings restatement. After controlling for these firm specific characteristics, there are no significant abnormal returns of restating firms, which supports the efficient market hypothesis.

Calendar-Time Portfolio Approach

We use the calendar-time portfolio approach advocated by Desai et al. (2002). To measure abnormal returns over the one year holding period after earnings restatements, at the beginning of each month from June 1997 through December 2002, a portfolio of firms that announced restatement during the past 1 year is formed. The portfolios in June 1997 and December 2002 include 14 and 84 stocks, respectively, compared with the median (mean) of 61 (59) for the whole period. The portfolio return is then regressed on the Fama and French's (1993) three factors and the momentum factor suggested by Carhart (1997). To allow for heteroskedasticity, the regression is run with the Weighted Least Square (WLS) technique using the number of stocks in the portfolio as the weight. The model can be expressed as follow,

[PRET.sub.t] = [alpha] + [[beta].sub.1][MRET.sub.t] + [[beta].sub.2][SMB.sub.t] + [[beta].sub.3][HML.sub.t] + [[beta].sub.4][MOMT.sub.t] + [[epsilon].sub.t] (2)

where [PRET.sub.t] is the monthly portfolio return of restating firms in excess of the one-month risk-free rate (proxied by one-month Treasury bill rate); [MRET.sub.t] is the excess return on a broad market portfolio; [SMB.sub.t] is the return differential between a portfolio of small stocks and a portfolio of large stocks; [HML.sub.t] is the return differential between a portfolio of high BM ratio stocks and a portfolio of low BM ratio stocks; [MOMT.sub.t], a measure of momentum, is the return differential between a portfolio with high returns in the past one year and a portfolio of stocks with low returns in the past one year. The breakpoint for size portfolios is the median of NYSE market equity. The breakpoints for BM ratio and momentum portfolios are the 30th and 70th percentiles of NYSE stocks.

To measure the abnormal return over the six months following earnings restatement, the portfolio is formed in a slightly different way. That is, at the beginning of each month firms that announced earnings restatement during the past six months are selected to form the portfolio. To reduce the problem caused by small number of stocks in the portfolios at the beginning and the end of the sample period, the portfolio is formed from April 1997 through September 2002.

Since the calendar-time portfolio approach equally weighs each month, if the stock price performance in periods of high activity is different from that in periods of low activity, the regression method will average out the differences, making the approach less likely to detect abnormal performance (Loughran and Ritter, 2000). We perform two types of robust checks. First, the post-announcement performance in a period when the market is going up might be different from that in a period of market collapse. We rerun the regressions in two subsample periods divided at March 2000, an inflection point where the S&P 500 index turns from gaining to losing. The second robust check is on whether the performance varies in heavy- and low- earnings restatement periods. The reason for the performance differential is that high frequency of earnings restatement might be driven by problems widely existing in the industry, causing the stock prices to drop more in the period following heavy restatement announcements. Two dummy variables, LOW and HIG, are used to measure the frequency of earnings restatements. The frequency of earnings restatement is calculated by dividing the number of restating firms in the calendar-time portfolio each month by the total number of firms having return data in the CRSP in that month. HIG is equal to 1 if the frequency in that month lies above the 70th percentile in all the monthly activities and zero otherwise; while LOW is equal to 1 if the frequency is below 30th percentile of all monthly activities and zero otherwise. Since the small number of stocks included in the portfolio at the beginning and the end of the sample period is driven mainly by the short period of restatement records, we set LOW to be equal to 0 for the 1-year holding portfolios in the June 1997 - December 1997 and August 2002--December 2002 periods. For the 6-month holding portfolios, LOW is equal to 0 in the April 1997--June 1997 and August 2002--September 2002 periods. A regression model incorporating HIG and LOW can be described as follow,

[PRET.sub.t] = [alpha] + [[beta].sub.1][MRET.sub.t] + [[beta].sub.2][SMB.sub.t] + [[beta].sub.3][HML.sub.t] + [[beta].sub.4][MOMT.sub.t] + [[beta].sub.5][HIG.sub.t] + [[beta].sub.6][LOW.sub.t] [[epsilon].sub.t] (3)

Results from the time calendar portfolio approach are shown in Table 7. Panel A and Panel B present the stock price performance of restating firms over the one year and the six months holding periods following earnings restatement, respectively. The intercepts from regression models (2) and (3), measures of abnormal stock returns, are 0.881 and 0.191, respectively over the one year holding period, while those from regression models (2) and (3) are 1.120 and 1.985, respectively over six month holding period. None of these intercept values are significant, suggesting that restating firms do not have abnormal return after controlling for market excess returns, size, BM ratio, the momentum, and/or the frequency of earnings restatements. Moreover, regression coefficients of the two dummy variables, HIG and LOW, are not significant in any regression, suggesting that the frequency of earnings restatement does not have material impact on the post-announcement stock price performance of restating firms and the failure to detect abnormal returns is not due to averaging between months with more restatements and months with fewer restatements.

Results from the regression tests on two sub periods (i.e., before April 1, 2000 (bull market) and after April 1, 2000 (bear market)) are presented in Panels C and D of Table 7. Test results on the one year holding period are reported in Panel C, while those on the six month holding period are in panel D. The results show no material difference in the stock price performance between the two periods and the intercept terms for the both sub periods and holdings periods remain insignificant, suggesting that the previous regression results are not influenced by variation in the market conditions and restating firms do not have abnormal return after controlling for market, excess returns, size, BM ratio, the momentum, and/or the frequency of earnings restatements.

The adjusted R2 of the eight regressions in Table 7 varies from 0.67 to 0.83, suggesting that the four return generating factors, especially the market excess return, the size, and momentum factors, explain a large portion of the variance of the stock returns of the restating firms. Market excess return is a significant explanatory variable in all the regressions. The market [beta] is smaller than one in five of the eight regressions, suggesting that stock price of the restating firms is no more volatile than the market. The size factor is significantly and positively correlated with the excess returns of the restating firms in all the regressions, suggesting that restating firms perform well when small stocks perform well. The coefficient of the BM ratio factor is significant in only 2 of the 8 regressions. This result is in line with the finding that restating firms do not significantly differ from the other firms in BM ratio. The coefficient of the momentum factor is negative in all the regressions and is significant in 6 of the 8 regressions. This result is consistent with the fact that restating firms experience negative price drift before earnings restatement and suggests that part of the underperformance following earnings restatement is due to momentum.

CONCLUSIONS

We investigate the long-term stock performance of restating firms after the announcement of earnings restatements using three major approaches such as CAR, BHAR, and calendar time portfolio approaches in this study. All three approaches to measure long-term stock performance of restating firms show that there are no significant abnormal returns over the six month and the one year post announcement holding periods, supporting the efficient market hypothesis but not the under reaction hypothesis. The results are robust across different testing periods, investment holding periods, and methodologies. Our results are not consistent with those of the previous studies on this issue which exclusively used CAR approach to measure the long-term stock performance. As addressed before, the conventional CAR approach does not provide a precise picture of long-term stock performance due to its embedded structural problem of simple summation of periodic abnormal returns rather than compounding of them and its cross-sectional dependence problem. These inconsistent results may be because we use different methodologies that mitigate or resolve misspecification problems in the previous studies.

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Tan Xu, Old Dominion University

John Jongdae Jin, California State University, San Bernardino

Diane Li, University of Maryland-Eastern Shore

ENDNOTES

(1) This study adopts the definition of accounting irregularity made by General Accounting Office (2002), i.e., it is "an instance in which a company restates its financial statements because they were not fairly presented in accordance with generally accepted accounting principles (GAAP). This would include material errors and fraud."

(2) Jegadeesh and Titman (1993) document that, on average, stocks that have high returns in the past three to twelve months continue to outperform stocks that have low returns in that period. This stock price continuation in the intermediate horizon is referred as momentum effect.

(3) Since results from the bootstrapped approach are very similar to those from the conventional method, results from the bootstrapped approach only are presented in Table 5.

Table 1: Descriptive Statistics of Restating Firms and All COMPUSTAT
Firms

Year N1 Restating firms N2 All firms

Panel A Book-to-market ratio

1997 61 0.572 33032 0.648
1998 70 0.502 32633 0.772
1999 122 0.694 31348 1.009
2000 155 0.854 31629 0.983
2001 173 1.514 30032 1.837
2002 91 1.382 27145 1.774
Total 672 1.004 185819 1.145

Year Diff z-stat Industry t-stat
 adjusted

Panel A Book-to-market ratio

1997 -0.076 -0.71 0.153 1.95
1998 -0.27 -1.79 0.023 0.54
1999 -0.315 -1.78 0.153 2.43 *
2000 -0.129 1.15 0.271 4.05 **
2001 -0.323 -1.64 0.371 1.75
2002 -0.392 -0.15 0.353 2.06 *
Total -0.141 -0.35 0.249 3.89 **

Year N1 Restating firms N2 All firms

Panel B Market value (Million dollars)

1997 64 550.80 36827 1034.13
1998 70 2450.27 36857 1292.68
1999 128 2234.65 36404 1566.89
2000 166 1935.09 37222 1902.6
2001 183 2796.24 35970 1580.11
2002 92 2695.20 33886 1496.68
Total 703 2230.89 217166 1484.35

Year Diff z-stat Industry t-stat
 adjusted

Panel B Market value (Million dollars)

1997 -483.33 -0.94 379.02 1.81
1998 1157.59 0.70 2366.71 2.26 *
1999 667.76 2.99 ** 1737.54 2.06 *
2000 32.43 2.15 * 1815.02 2.07 *
2001 1216.13 7.98 ** 2601.81 4.09 **
2002 1198.52 5.74 ** 1716.04 2.16 *
Total 746.54 8.44 ** 1921.11 5.66 **

Year N1 Restating firms N2 All firms

Panel C Total debt / Total asset

1997 64 0.330 40002 0.513
1998 71 0.234 39410 0.386
1999 132 0.309 40310 0.486
2000 167 0.281 40616 0.601
2001 192 0.269 37973 0.900
2002 96 0.132 34591 0.281
Total 722 0.283 232902 0.685

Year Diff z-stat Industry t-stat
 adjusted

Panel C Total debt / Total asset

1997 -0.184 3.11 ** 0.107 4.10 **
1998 -0.152 -0.18 0.661 3.17 **
1999 -0.177 0.47 0.116 3.66 **
2000 -0.320 0.46 0.947 4.11 **
2001 -0.630 0.65 0.520 3.52 **
2002 -0.149 0.84 0.342 1.55
Total -0.402 2.10 * 0.779 7.87 **

N1 = the number of restating firms with non-negative value,

N2= the number of all COMPUSTAT firms with non-negative value,

Diff = the difference between the median (mean) of the restating
firms and those of all the COMPUSTAT firms.

*, and ** = statistical significance at the 5% and 1% levels,
respectively, using a 2-tail test.

Table 2: Abnormal Returns of Earnings Restatement Announcement

Day Obs. Mean Abnormal Median Abnormal
 Return (%) Return (%)

-7 517 -0.61 -0.28
-6 517 0.06 -0.08
-5 517 -0.43 -0.36
-4 517 -0.17 -0.47
-3 517 -0.94 -0.49
-2 516 -0.21 -0.14
-1 515 -0.24 -0.16
0 510 -2.89 -1.01
1 505 -4.39 -1.41
2 507 0.04 -0.29
3 507 0.12 -0.17
4 506 -0.09 -0.24
5 507 0.00 -0.19
6 508 -0.02 -0.1
7 508 -0.25 -0.25

 CAR

(-1,+1) 515 -7.40 -3.62
(-5,+5) 517 -9.05 -4.1

Day Positive: Standardized General
 Negative z-stat Sign z-stat

-7 231:286 -2.754 ** -1.012
-6 252:265 0.266 0.839
-5 225:292 -1.711 -1.54
-4 222:295 -0.811 -1.805
-3 209:308 -2.994 ** -2.950 **
-2 246:270 -1.413 0.352

-1 241:274 -0.461 -0.048
0 204:306 -6.141 ** -3.123 **
1 187:318 -7.321 ** -4.445 **
2 235:272 0.388 -0.248
3 240:267 -0.218 0.197
4 230:276 -0.357 -0.652
5 239:268 -0.591 0.108
6 242:266 -0.175 0.333
7 237:271 -0.896 -0.112

 CAR

(-1,+1) 165:350 -9.227 ** -6.759 **
(-5,+5) 184:333 -8.630 ** -5.154 **

The abnormal returns = the difference between the actual return and
the predicted returns calculated by the market model.

Obs. = the number of sample firms.

*, and ** = statistical significance at the 5% and 1% level,
respectively, using a 2-tail test.

Table 3: GARCH-Adjusted Abnormal Returns of Earnings Restatement
Announcement

Day Obs. Mean Median
 Abnormal Abnormal
 Return (%) Return (%)

-7 517 -0.58 -0.25
-6 517 0.09 -0.12
-5 517 -0.42 -0.36
-4 517 -0.16 -0.41
-3 517 -0.93 -0.46
-2 516 -0.20 -0.12
-1 515 -0.25 -0.19
0 510 -2.90 -0.94
1 505 -4.38 -1.48
2 507 0.07 -0.18
3 507 0.15 -0.13
4 506 -0.08 -0.33
5 507 0.01 -0.17
6 508 0.04 -0.09
7 508 -0.24 -0.22

 CAR
(-1, +1) 515 -7.42 -3.54
(-5, +5) 517 -8.96 -3.99

Day Positive:Negative t-stat Generalized
 Sign Z

-7 230:287 -2.640 ** -1.207
-6 246:271 0.388 0.203
-5 224:293 -1.878 -1.735
-4 221:296 -0.715 -2.000 *
-3 204:313 -4.187 *** -3.497 ***
-2 241:275 -0.913 -0.196
-1 239:276 -1.118 -0.331
0 204:306 -13.128 *** -3.229 **
1 187:318 -19.798 *** -4.550 ***
2 239:268 0.294 0.002
3 241:266 0.665 0.18
4 233:273 -0.366 -0.491
5 240:267 0.032 0.091
6 243:265 0.16 0.315
7 239:269 -1.065 -0.04

 CAR
(-1, +1) 167:348 -9.750*** -6.687 ***
(-5, +5) 190:327 -8.723*** -4.731 ***

The abnormal returns = the difference between the actual return and
the predicted returns calculated by the GARCHadjusted market model.

Obs = the number of sample firms.

* and ** = statistical significance at 5% & 1%, respectively using
a 2-tail test

Table 4: Post-Announcement CARs of Restating Firms

Event Obs. Conventional Precision
Day CAR (%) Weighted
 CAR (%)

(2,22) 510 -2.22 -1.80
(23,43) 509 0.11 0.03
(44,64) 495 0.27 0.14
(65,85) 488 1 0.19
(86,106) 481 -1.19 -1.14
(107,128) 471 1.7 1.05
(129,149) 467 0.42 -0.27
(150,170) 450 1.01 1.11
(171,191) 423 1 0.22
(192,212) 409 0.65 0.85
(213,233) 392 -0.66 -0.47
(234,255) 367 -0.38 0.09
(2,128) 515 -0.22 -1.53
(2,255) 515 1.48 0.01

Event Positive: SCS test Generalized
Day Negative z-stat Sign test
 z-stat

(2,22) 229:281 -2.420 * -0.905
(23,43) 241:268 0.058 0.202
(44,64) 228:267 -0.111 -0.375
(65,85) 251:237 0.146 2.007 *
(86,106) 210:271 -1.448 -1.425
(107,128) 244:227 1.345 2.133 *
(129,149) 227:240 -0.284 0.739
(150,170) 238:212 1.246 2.545 *
(171,191) 209:214 -0.002 1.034
(192,212) 190:219 0.82 -0.181
(213,233) 187:205 -0.524 0.319
(234,255) 183:184 0.112 1.137
(2,128) 258:257 -0.792 1.454
(2,255) 262:253 -0.169 1.807

CAR = the sum of abnormal returns in a period.
Obs = the number of sample firms.
Positive = the number of sample firms with positive CAR.
Negative = the number of sample firms with negative CAR.
* = statistical significance at 5% using a 2-tail test.

Table 5: Buy-and-Hold Abnormal Returns of Restating Firms
Panel A. BHAR calculated by compounding monthly returns

Holding N Mean Median
Period BHAR (%) BHAR (%)

6-month 517 -9.97 -14.62

1-year 517 -16.93 -24.58

Panel B. BHAR calculated by compounding daily returns

Holding N Mean Median
Period BHAR (%) BHAR (%)

(2,22) 511 -3.16 -2.53
(23,43) 510 -1.37 -1.88
(44,64) 496 -0.62 -1.58
(65,85) 489 -0.18 -0.90
(86,106) 482 -2.07 -4.17
(107,128) 472 0.38 -0.48
(129,149) 467 0.27 -2.10
(150,170) 450 0.26 -0.44
(171,191) 423 -1.19 -1.68
(192,212) 409 -0.49 -2.28
(213,233) 392 -1.49 -2.54
(234,255) 367 -1.13 -1.65
(2,128) 516 -16.39 -12.4
(2,255) 516 -64.03 -21.51

Holding Positive:Negative t-stat
Period

6-month 208:309 -4.86 **

1-year 206:311 -4.32 **

Panel B. BHAR calculated by compounding daily returns

Holding Positive:Negative Generalized Skewness
Period Sign z-stat adj. t-stat

(2,22) 203:308 -3.259 ** -3.137 **
(23,43) 218:292 -1.889 -1.206
(44,64) 216:280 -1.505 -0.563
(65,85) 233:256 0.323 -0.188
(86,106) 190:292 -3.300 ** -1.913
(107,128) 229:243 0.695 0.337
(129,149) 206:261 -1.216 0.245
(150,170) 219:231 0.742 0.228
(171,191) 185:238 -1.313 -1.034
(192,212) 173:236 -1.873 -0.435
(213,233) 172:220 -1.207 -1.186
(234,255) 171:196 -0.125 -0.869
(2,128) 190:326 -4.597 ** -6.046 **
(2,255) 192:324 -4.420 ** -6.673 **

BHAR = the buy-and-hold return differential between the restating
firm and the equally weighted CRSP market index.

*, ** = statistical significance at 5% & 1%, respectively using
a 2-tail test.

Table 6.: Buy-and-Hold Returns of the Restating Firms and
Control Firms

 Sample Firms
Holding
Period N Mean Median t-stat
 BHR (%) BHR (%)

1st month 459 -1.98 -1.53 -1.75
2nd month 456 -0.25 -0.78 -0.2
3rd month 447 2.09 0.07 1.69
4th month 443 -0.20 -0.95 -0.19
5th month 438 -0.17 -1.69 -0.14
6th month 432 1.42 0.00 1.15
7th month 429 -1.08 -2.03 -0.96
8th month 413 0.93 0.00 0.76
9th month 386 0.67 0.00 0.58
10th month 373 1.45 -0.02 1.25
11th month 359 0.76 -0.63 0.56
12th month 337 0.10 -0.89 0.07
6-month 459 -1.09 -3.98 -0.41
1-year 459 4.51 -6.38 1.07

 Control Firms
Holding
Period Mean Median t-stat AHAR t-stat
 BHR (%) BHR (%)

1st month -1.74 -1.50 -1.97 -0.40 -0.97
2nd month 0.46 -0.42 0.45 -0.45 -0.17
3rd month 0.43 0.00 0.49 0.73 -0.74
4th month 1.92 -1.11 1.26 -1.08 0.16
5th month -0.34 0.16 -0.36 -0.34 -0.34
6th month 0.18 -0.48 0.2 1.78 1.14
7th month -0.51 -0.48 -0.56 -0.83 -1.31
8th month 2.75 0.23 2.28 -1.15 -0.42
9th month 1.25 0.00 1.14 -0.15 0.00
10th month 3.10 0.75 2.56 * -1.44 -0.68
11th month 1.16 -0.05 0.82 0.79 0.00
12th month 2.81 0.50 2.05 -1.65 -1.79
6-month 0.13 -3.15 0.04 0.00 0.00
1-year 16.4 0.89 2.99 * -7.11 -1.03

BHR = the buy and hold returns.
AHAR is the average BHAR of the sample firms.
BHAR = the buy-and-hold return differential between the restating
 firm and its control firm.
* = statistical significance at 5% using a 2-tail test.

Table 7: Equal Weighted Calendar Time Portfolio Abnormal Returns

[PRET.sub.t] [alpha] + [[beta].sub.1][MRET.sub.t] + [[beta].sub.2]
[SMB.sub.t] + [[beta].sub.3][HML.sub.t] + [[beta].sub.4][MOMT.sub.t]
+ [[member of].sub.t] (2)

[PRET.sub.t] = [alpha] + [[beta].sub.1][MRET.sub.t] + [[beta].sub.2]
[SMB.sub.t] + [[beta].sub.3][HML.sub.t] + [[beta].sub.4][MOMT.sub.t]
+ [[beta].sub.5][HIG.sub.t] + [[beta].sub.6][LOW.sub.t] + [[member
of].sub.t] (3)

Panel A. 1-year post-announcement performance

 Intercept MKRET SMB HML

(2) 0.881 0.989 0.825 0.087
 (1.57) (7.67 **) (6.67 **) (0.54)

(3) 0.191 1.018 0.787 0.062
 (0.24) (7.86 **) (5.97 **) (0.37)

 MOMT HIG LOW Adj. [R.sup.2]

(2) -0.425 0.765
 (-5.24)

(3) -0.417 2.060 0.265 0.768
 (-5.16 **) (1.65) (0.18)

Panel B. 6-month post-announcement performance

 Intercept MKRET SMB HML

(2) 1.120 0.878 0.756 -0.127
 (1.63) (5.55 **) (5.09* *) (-0.65)

(3) 1.985 0.898 0.716 -0.154
 (1.95) (5.62 **) (4.69 **) (-0.78)

 MOMT HIG LOW Adj. [R.sup.2]

(2) -0.514 0.692
 (-5.04 **)

(3) -0.507 -0.743 -2.407 0.693
 (-4.96 **) (-0.48) (-1.46)

Table 7: Equal Weighted Calendar Time Portfolio Abnormal Returns

[PRET.sub.t] = [alpha] + [[beta].sub.1][MRET.sub.t] + [[beta].sub.[2]
SMB.sub.t] + [[beta].sub.3][HML.sub.t] + [[beta].sub.4][MOMT.sub.t]+
[[member].sub.t] (2)

[PRET.sub.t] = [alpha] + [[beta].sub.1][MRET.sub.t] + [[beta].sub.2]
[SMB.sub.t] + [[beta].sub.3][HML.sub.t] + [[beta].sub.4][MOMT.sub.t]+
[[beta].sub.5][HIG.sub.t] + [[beta].sub.6][LOW.sub.t] + [[member of]
.sub.t] (3)

Panel C. 1-year post-announcement performance

Period Intercept MKRET SMB

06/1997-03/2000 0.469 0.680 0.795
 (0.56) (3.64 **) (4.49 **)

04/2000-12/2002 1.323 1.186 0.716
 (1.69) (6.99 **) (4.39 **)

Period HML MOMT Adj. [R.sub.2]

06/1997-03/2000 -0.821 -0.798 0.729
 (-2.30 *) (-3.86 **)

04/2000-12/2002 0.236 -0.376 0.830
 (1.23) (-3.97 **)

Panel D. 6-month post-announcement performance

Period Intercept MKRET SMB

04/1997-03/2000 1.217 0.475 0.733
 (1.34) (2.28 *) (3.79 **)

04/2000-08/2002 0.761 1.204 0.701
 (0.73) (5.45 **) (3.30 **)

Period HML MOMT Adj. [R.sub.2]

04/1997-03/2000 -0.985 -0.876 0.670
 (-2.53 *) (-4.17 **)

04/2000-08/2002 0.182 -0.452 0.767
 (0.73) (-3.63)

PRET = the monthly portfolio return for restating firms in excess of
the one-month risk-free rate (onemonth Treasury bill rate).

MRET = the excess return on a broad market portfolio.

SMB = the return differential between a portfolio of small stocks and
a portfolio of large stocks.

HML = the return differential between portfolio of high book-to-market
ratio stocks and a portfolio of low book-to-market ratio stocks.

MOMT = the return differential between a portfolio with high returns
in the past one year and a portfolio with low returns in the past one
year.

HIG = a dummy variable for the frequency of earnings restatement.
HIG is equal to 1 if the number earnings restatement in that month
lies above the seventieth percentile in all the monthly activities
and zero otherwise.

LOW = a dummy variable for the frequency of earnings restatement. LOW
is equal to 1 if the number earnings restatement is below thirtieth
percentile of all monthly activities and zero otherwise.

(.) = t-value.

*, ** = statistical significance at 5% and 1%, respectively.