INTRODUCTION

The unexpected demise of Big 5 accounting firm Arthur Andersen is an important event in the history of the accounting profession. Considerable legislative changes were enacted as a consequence, resulting in the passage of the Sarbanes–Oxley Act of 2002. While advocates of a legislative cure point to the Enron fiasco and related failures at WorldCom, the Baptist Foundation of Arizona, and several others, as symptomatic of an audit firm that allowed clients to push the envelope too far, others argue that these were relatively isolated events and that the US Government went too far in forcing the closure of Arthur Andersen. This study asks whether Andersen tolerated more earnings management by its clients relative to other Big 5 auditors, particularly in the Houston office that served Enron. In seeking an answer, we examine several methodologies to assess earnings management and earnings quality of audit clients of both Andersen and other Big 5 auditors.

There is limited empirical evidence on the characteristics of the accounting information produced by Arthur Andersen clients. Krishnan¹ finds that asymmetric timeliness — recognition of bad news than good news — is weaker for Andersen's Houston-based clients compared to Houston-based clients of other Big 5 auditors or Andersen's clients served by other offices. Subsequently, Krishnan² finds that in 2001, earnings of Andersen's clients were less conservative relative to earnings of non-Andersen clients and, following the switch to non-Andersen audit firms in 2002, conservatism increased for Andersen's former clients. Using the frequency of financial statement restatements as a measure of performance, however, Eisenberg and Macey³ conclude that Andersen's performance does not significantly differ from the performance of other large auditors.^{3, 4, 5 and 6}

This study provides evidence on additional attributes of Arthur Andersen client earnings to better understand the extent to which the financial reporting quality of Andersen clients differed from that of other Big 5 audit firm clients. The attributes we examine are:

• the aggregate earnings management score developed by Leuz et al.⁷ that combines four different measures of earnings management;
• earnings persistence, an important indicator of earnings quality; and^{8, 9}
• the probability of earnings manipulation developed by Beneish.¹⁰

This use of multiple measures of earnings management frequently seen in other empirical research should mitigate measurement error associated with assessing the presence and extent of earnings management.

Our sample period covers 1996–2000, primarily because these years immediately precede Andersen's demise and could reveal the relevant characteristics of Andersen's client portfolio in its final years. Moreover, our results can be compared with those of Krishnan,¹ who also studied the 1996–2000 period. Even though this sample period represents a small portion of Andersen's long history, that period should reflect the audit environment that helped bring Andersen down. This study seeks to capture that environment by comparing Andersen's clients' financial reporting with that of the other Big 5 firms, both nationally and in their Houston offices. The importance of examining Houston separately follows from Krishnan.^{1, 2}

Summary of key findings

The key findings suggest a general inferiority of the financial reporting quality of Andersen's clients audited statements compared to other Big 5 audit firms.

• Considering all clients, Deloitte Touche Tohmatsu's clients rank the highest in earnings management among all Big 5 auditors based on the aggregate earnings management score. Andersen clients rank second here but first (highest) when we consider only Houston-based clients of Big 5 auditors.
• The earnings persistence of Andersen clients, overall and Houston-based, is lower than the earnings persistence of other Big 5 firm clients.
• Results for the Beneish¹⁰ measure of earnings manipulation indicate that the Houston-office clients of Andersen had a higher probability of earnings manipulation than clients of other Big 5 auditors, while the difference in the overall client base was similar between Andersen and other Big 5 auditors.

These findings augment the results reported by Krishnan¹ and reinforce the notion that Andersen and its Houston office, in particular, was likely more tolerant of earnings manipulation than other Big 5 auditors in the years immediately preceding its collapse.

METHODOLOGY

To address whether Arthur Andersen (hereafter 'AA') clients differ from clients of other Big 5 auditors, we use several measures of earnings management and quality. Multiple measures provide assurance that the results are not sensitive to the shortcomings of a particular measure. Our primary measures incorporate the procedures developed in Leuz et al.,^{7, 11, 12, 13, 14 and 15} Jones et al.,15 leading to four different measures of earnings management that capture various ways of exercising discretion in managing earnings. Two of these measures seek to capture smoothing of earnings and two others to capture discretion in reported earnings. After constructing the four measures separately, an aggregate score is constructed based on the four measures.

The four earnings management measures from Leuz et al.⁷

1. The first measure, EM1, uses accruals to assess the extent of smoothing of earnings, in which managers take actions to reduce the variability of earnings.

EM1=the median ratio of firm-level standard deviation of earnings divided by the firm-level standard deviation of cash flow from operations, a measure of unsmoothed earnings.

Low values of EM1 indicate smoother earnings and imply earnings management because the presence of accruals in earnings causes earnings to vary relative to operating cash flow. Therefore, low variation in earnings relative to operating cash flows is consistent with greater earnings management.

2. The second measure, EM2, also captures managers' tendencies to smooth earnings.

EM2=the contemporaneous correlation between changes in accruals and changes in operating cash flow.

Because accrual accounting implies a negative correlation between changes in accruals and changes in cash flows,¹⁶ a high positive correlation may be due to managers' smoothing actions taken to conceal economic shocks to cash flows. Thus high negative correlations imply more smoothing.

3. The third measure, EM3, reflects the amount of discretion available to manage earnings.

EM3=the absolute value of accruals scaled by the absolute value of operating cash flow.

As our purpose is to capture the magni-tude of discretion, not the direction, we use absolute values. Larger values of EM3 indicate more discretion.

4. The final measure of earnings management, EM4, also measures discretion in reported earnings by focusing on managers' tendencies to avoid reporting small losses as documented in Burgstahler and Dichev.¹⁷

EM4=the ratio of small losses to small profits, using after-tax earnings (losses) scaled by total assets.

High values of the EM4 ratio imply greater discretion in reporting by avoiding small losses.

We compute these four measures for each Big 5 auditor, and rank the auditors by the (absolute) size of each of the four earnings management measures. For example, lower values of EM1 imply more smoothing, and the auditor with the lowest value receives the highest rank of 5, and the auditor with the highest EM1 receives the lowest rank of 1. For EM2, we rank the auditor with the highest negative correlation the highest, and the auditor with the lowest negative correlation the lowest. With higher values of EM3 and EM4 indicating more discretion in reported earnings, the auditor with the highest value receives the highest rank and the auditor with the lowest value is ranked the lowest. Finally, we compute an aggregate earnings management score for each auditor by averaging the ranks across the four measures — a high aggregate earnings management score suggests that the auditor's clients engage in earnings management more than the clients of other auditors.

The measure of earnings persistence

Our second attempt to capture earnings management is by examining the earnings persistence of Big 5 firm audit clients. Collins and Kothari¹⁸ report a positive association between earnings persistence and earnings response coefficients. Higher earnings persistence is also commonly perceived to indicate higher earnings quality.^{8, 9} We measure earnings persistence as the slope coefficient obtained by regressing future earnings on current earnings.

SAMPLE

Our initial sample includes all firms available on Compustat for all the years 1996–2000, following Krishnan.¹ We then exclude firms audited by non-Big 5 auditors and firms that changed auditors during this period in order to generate a homogeneous sample that facilitates comparison among the Big 5 audit firms. To remain in the sample, client firms must have all the data needed to compute our earnings management measures EM1 to EM4. Finally, to avoid the potential undue influence of outliers we exclude firms with absolute values of earnings or operating cash flows deflated by beginning assets greater than 2. These procedures result in a sample size of 6,027 firm-years for AA, 4,464 firm-years for DTT, 6,089 firm-years for E&Y, 4,725 firm years for KPMG, and 4,735 firm-years for PWC.

DISCUSSION OF RESULTS

The Leuz et al.,⁷ earnings management measures: All Big 5 firm audit clients

We first report results using all Big 5 firm audit clients. Panel A of Figure 1 presents the values of the four earnings management measures graphically for each Big 5 audit firm. The values for each earnings management measure, by auditor, are tabulated below.

Figure 1.

Earnings management scores for clients of Big 5 auditors for the years 1996–2000 (a) By auditor. (b) Andersen vs other Big 5 auditors Total number of client observations for AA, DTT, E&Y, KPMG, and PWC are 6,027, 4,464, 6,089, 4,725, and 4,735 respectively. EM1 is computed as the median ratio of firm-level standard deviation of earnings divided by the firm-level standard deviation of cash flow from operations. EM2 is the contemporaneous correlation between changes in accruals and changes in operating cash flows for all firms audited by an audit firm. EM3 is the absolute value of accruals scaled by absolute value of cash flow from operations for all firms audited by an audit firm. EM4 is the ratio of firms that report small losses to firms that report small profits among all firms audited by an audit firm. Both profits and losses were computed by using after-tax earnings scaled by total assets. For EM1 and EM2, lower values indicate more earnings management and for EM3 and EM4 higher values indicate higher earnings management. The aggregate earnings management score is computed by first ranking each firm for each of the four earnings management measures and then by averaging the ranks across the four measures for each auditor. Auditors are ranked based on the aggregate earnings management score. The higher the aggregate score, the greater the earnings management.

Full figure and legend (103K)

DTT ranks the highest in both earnings smoothing measures, as the bar for DTT is the shortest for EM1 and the longest below 0 for EM2, meaning that DTT clients exhibit the highest amount of earnings smoothing tendencies among all the Big 5 audit clients. AA ranks the second highest in both earnings smoothing measures and E&Y ranks the lowest in earnings smoothing measures. KPMG ranks the highest in earnings discretion measures, as the bars for KPMG are the tallest, indicating that KPMG clients exercise more discretion over reported earnings than clients of other Big 5 auditors. In contrast, PWC clients rank the lowest in both earnings discretion measures. AA ranks in the middle on EM3 and ranks the second highest on EM4. Overall, while AA does not rank the highest or the lowest on any of the individual earnings management measures, in three of the four measures it ranks the second highest and in one measure it ranks in the middle.

The last part of panel A presents the aggregate earnings management score that is equal to the average of the ranks obtained on each of the four earnings management measures. As discussed previously, ranks are ordered such that rank 5 represents the highest earnings management while rank 1 represents the least earnings management. Thus, AA has a rank of 4 for EM1, EM2, and EM4 as it has the second highest rank in those measures and a rank of 3 for EM3. The average of the four ranks [(4+4+4+3)/4] equals 3.75, which is the aggregate earnings management score for AA. KPMG clients report this same 3.75 score. On this aggregate earnings management score, DTT ranks first (most earnings management), PWC ranks last (least earnings management), and AA (and KPMG) has the second highest aggregate score. Thus, AA clients engaged in greater earnings management than clients of competitors E&Y and PWC and are much closer to top-ranked DTT than to lowest-ranked E&Y and PWC.

Panel B of Figure 1 reports the values of EM1–EM4 for AA clients (from panel A) and as computed for the other Big 5 audit firm clients as a group. With higher values of EM3-EM4 and lower values of EM1–EM2 being bad signals, these results indicate that AA ranks worse than the rest of the Big 5 on all four measures, such that AA clients engaged in relatively more aggressive earnings management than clients of other Big 5 auditors.

The earnings persistence measure: All Big 5 firm audit clients

Table 1 reports the results for our measure of earnings persistence reported by Big 5 firm audit clients. Column 4 reports the persistence coefficient, ₀, and the last column reports the model's explanatory power measured by the adjusted R². ₀ is the lowest for AA at 0.537 among all Big 5 auditors as is the adjusted R² of 0.363. Because persistence is considered a measure of earnings quality, the lowest ₀ exhibited by AA's clients suggests that AA's clients had the lowest earnings quality among all Big 5 audit firm clients.

Table 1 - Earnings persistence coefficients for clients of Big 5 auditors for the years 1996–2000.

Full table

We also estimate a variation of the persistence model to test whether the persistence coefficient is lower for Andersen clients relative to the clients of all other Big 5 auditors as a group. A dummy variable, ANDER, is set equal to 1 for Andersen clients and 0 for non-Andersen clients. Untabulated results showing the coefficient of the interaction variable, ANDER Õ Earnings_t-1, to be -0.054 and significant at the 0.0001 level, corroborate the Table 1 results — AA's clients had lower earnings quality than clients of other Big 5 auditors.

Comparison of AA's Houston-based clients with those of other Big 5 audit firms

We now repeat the above analysis, focusing on Houston-office clients only. AA's Houston office was of particular interest because it managed the Enron audit. When Enron filed for bankruptcy, events associated therewith led to AA's downfall. Recall Krishnan's¹ finding that AA's Houston-office clients were more likely to delay reporting bad news about future cash flows than clients audited by other Big 5 auditors. This finding motivates us to examine whether the results reported in Figure 1 and Table 1 for AA as a whole apply to Houston-office clients.

To pursue the Houston connection, we first follow procedures described in Figure 1 and compute earnings management measures for the Houston-based clients of each Big 5 auditor. Figure 2 presents these results graphically. The values for each earnings management measure, by auditor, are tabulated below.

Figure 2.

Earnings management scores for Houston-based clients of Big 5 auditors for the years 1996–2000 (a) By auditor. (b) Andersen vs other Big 5 auditors EM1–4 and the aggregate earnings management score are as defined in Figure 1.

Full figure and legend (103K)

Panel A presents the four earnings management measures for each auditor and the aggregate earnings management score. AA's Houston-office clients rank in the middle in the two earnings smoothing measures, second highest in the two earnings discretion measures, and compile the highest aggregate earnings management score. Panel B groups all non-AA Big 5 auditors together and presents the four earnings management measures for this group. Then we compare AA's Houston-office clients'EM1–4 measures with the measures for all other Big 5 firms' Houston-office audit clients. In measures EM2 and EM3, AA ranks higher in earnings management characteristics and in measures EM1 and EM4 AA ranks lower than other Big 5 auditors as a group.¹⁹ In sum, the results in Figure 2 are consistent with Krishnan¹ and indicate that clients of AA's Houston office were more aggressive in managing earnings in comparison to clients of other Big 5 auditors.

Note that Figure 1 panel A results show that AA has the second highest aggregate earnings management score while for Houston clients the results in Figure 2 panel A show that AA has the highest aggregate score. This indicates that Andersen's Houston office was more tolerant of earnings management than AA as a whole. In contrast, the results in panel B of Figures 1 and 2 paint a mixed picture. AA appears worse than other Big 5 in all measures in panel B of Figure 1 while it is worse only in two of the four measures in panel B of Figure 2 for the Houston office. This difference in results is driven by the methodology used in panel A vs panel B. The grouping procedure in panel B appears to offset the magnitude of ranking in panel A of Figure 2. The results in Figures 1 and 2 collectively are consistent with the interpretation that AA was one of the more tolerant of the Big 5 auditors and in particular the Houston office of AA was as tolerant or more tolerant than AA as a whole.

Table 2 provides the results for our second measure of interest, the earnings persistence reported by the Houston clients of AA and other Big 5 auditors. Column 4 reports the persistence coefficient, ₀, and the last column reports the explanatory power of the model measured by the adjusted R². ₀ is 0.365 for AA, 0.508 for other Big 5 auditors, and AA's adjusted R² of 0.208 is lower than 0.279 for other Big 5 Houston clients. These results indicate that Houston clients of AA had lower earnings persistence than Houston clients of other Big 5 auditors. Also it can be noted from Table 2 that earnings persistence is lower for AA's Houston-based clients relative to all AA clients. To check for the statistical significance of this difference in persistence between AA and other Big 5 auditors, we re-estimate the Table 2 model, adding ANDER, a dummy variable equal to 1 for Andersen clients and 0 for non-Andersen clients. As in our discussion of Table 1, we interact ANDER with Earnings_t-1. The untabulated results show that ANDER Õ Earnings_t-1 is -0.143 and significant at the 0.05 level.

Table 2 - Earnings persistence coefficients for Houston-based clients of Big 5 auditors for the years 1996–2000: Andersen vs other Big 5.

Full table

Additional analysis: The Beneish¹⁰ earnings manipulation model

In addition to the earnings management and earnings quality measures already examined, we estimate the Beneish¹⁰ model of earnings manipulation for our sample. To do so, we apply Beneish's procedures for estimating the probability of earnings manipulation to the clients of Big 5 auditors. Beneish¹⁰ proposes a model for discriminating manipulators from a control group of non-manipulators based on financial statement variables. His unweighted probit model that we use is as follows:

Beneish's variables are as follows:

MI is the manipulation index that is converted to a probability of earnings manipulation using a standard normal distribution table; DSRI is days' sales receivable index ([AR/REV]/[AR_t-1/REV_t-1]), where AR is accounts receivable and REV is the sales revenue; GMI is the gross margin index [(REV_t-1-Cost of goods sold_t-1)/REV_t-1]/[(REV_t-cost of goods sold_t/REV_t]; AQI is the asset quality index [1-(Current assets_t+PPE_t)/AT_t]/[1-(Current assets_t-1+PPEt-1)/AT_t-1], where PPE is property, plant, and equipment and AT is total assets; SGI is the sales growth index (REV_t/REV_t-1); DEPI is the depreciation index [Depreciation_t-1/(Depreciation_t-1+PPE_t-1)]/[(Depreciation_t/(Depreciation_t+PPE_t)]; SGAI is the sales, general, and administrative (SGA) expense index (SGA expense_t/REV_t)/(SGA expense_t-1/REV_t-1); TATA is total accruals to total assets [(Current assets_t-Cash_t)-(Current liabilities_t-Current maturities of long-term debt_t-Income tax payable_t)-Depreciation and amortisation_t]/AT_t; LVGI is the leverage index [(Long-term debt_t+Current liabilities_t)/AT_t]/[(Long-term debt_t-1+Current liabilities_t-1)/AT_t-1].

Beniesh reports that the probability of earnings manipulation for non-manipulators in his estimation sample is 0.011 compared to 0.099 for the manipulators. Therefore, we classify a client with an estimated probability of earnings manipulation greater than 0.011 as an aggressive accruer and a client with probability less than or equal to 0.011 as a non-aggressive accruer. Note that since accruals are often used to manage earnings, the likelihood of earnings management increases with accruals.

Table 3 reports the results for Big 5 audit clients based on estimation of probability of earnings manipulation. The total number of observations available to estimate the probability for AA and other Big 5 auditors were, respectively, 4,080 and 14,911. Panel A reports the results for all clients of AA and other Big 5. Some 38.36 per cent of all AA clients are deemed aggressive accruers compared with 37.52 per cent of all other Big 5 audit firm clients. The difference in the two proportions is not statistically significant (not reported). Similarly, we estimate the mean probability of earnings manipulation to be 0.106 for all clients of AA and 0.108 for all clients of other Big 5 auditors. These results indicate that the overall client profile of AA does not differ significantly in the probability of earnings manipulation from other Big 5 client profiles.

Table 3 - Probability of earnings manipulation and proportion of aggressive accruers for clients of Big 5 auditors and for Houston-based clients for the years 1996–2000: Andersen vs other Big 5 (a) For all clients; (b) For Houston-based clients.

Full table

The results in panel B replicate the results in panel A for Houston clients of AA and other Big 5, with 172 observations for AA and 236 for other Big 5 audit clients. Compared with the overall client base, Houston-based clients exhibit notable differences. AA has a higher proportion of aggressive accruers (49.42 vs 39.83 per cent) and a higher mean probability of earnings manipulation (0.149 vs 0.09). The difference in mean probability of earnings manipulation is statistically significant at the 0.05 level (not reported) and the difference in the proportion of aggressive accruers is near significant at the 0.10 level. These results provide evidence that AA's Houston-office clients were more aggressive in managing their earnings compared to clients of other Big 5 auditors. The results also corroborate the Figure 2 and Table 2 results based on other metrics and are consistent with the findings in Krishnan.¹

CONCLUSION

The collapse of Enron Corporation and the subsequent demise of Andersen are signal events for the accounting profession. Significant new legislation aimed at the accounting profession occurred in response to these events, especially the Sarbanes–Oxley Act (2002). Given this setting, it is important to understand whether events that preceded Andersen's demise are the result of an isolated aberration committed by an otherwise good auditor or symptomatic of AA's broader willingness to tolerate more aggressive client behaviour than other Big 5 auditors. In seeking answers, this study compares the financial statement data of Andersen clients with clients of other Big 5 auditors both at the national level and at the Houston office level. The study uses a variety of earnings manage-ment/quality measures developed in the literature to examine whether the differences in the attributes of earnings by Andersen's clients and those of other Big 5 auditors are systematic.

The results using four different earnings management measures separately and in aggregate, and a measure of earnings persistence indicate that Andersen clients were more aggressive in their earnings management at the national and Houston office levels in comparison to other Big 5 auditors. Although Andersen clients do not appear to be the worst in any one individual measure of earnings management, when compared with other Big 5 auditors as a group, Andersen clients were more aggressive at the national level and at the Houston office level. Moreover, procedures using Beneish's¹⁰ earnings manipulation model indicate that Andersen clients included a relatively greater proportion of aggressive accruers that demonstrated a relatively higher probability of earnings manipulation at the Houston office level but not at the national level.

These results have some important implications.

• The results augment the results in Krishnan¹ and further our understanding of whether Andersen was more (or less) tolerant in the clients' manipulation of earnings compared to other Big 5 auditors.
• Second, the differences documented in this study mean that researchers using data from the 1995 to 2000 period may need to control for whether a firm in their sample is audited by Andersen or by another auditor.
• Finally, the results for Houston office indicate that studies that focus on auditor differences at the national level may overlook significant differences at the regional or the local level.

References

1. Krishnan, G. (2005) 'Did Houston clients of Arthur Andersen recognize publicly available bad news in a timely fashion', Contemporary Accounting Research, 22 (Spring), 165–193. | Article |
2. Krishnan, G. (2006) 'Did earnings conservatism increase for former Andersen clients?', Journal of Accounting, Auditing & Finance (forthcoming).
3. Eisenberg, T. and Macey, J. (2004) 'Was Arthur Andersen different? An empirical examination of major accounting firm audits of large clients', Journal of Empirical Legal Studies, 1 (July), 263–300. | Article |
4. Eisenberg and Macey examine large clients, firms with sales in excess of $1bn. The rate of errors, restatements, or internal control weaknesses may be higher for smaller firms relative to larger firms.^5,6
5. Kreutzfeldt, R. W. and Wallace, W. A. (1986) 'Error characteristics in audit populations: Their profile and relationship to environmental factors', Auditing: A Journal of Practice & Theory (Fall), 20–43.
6. Glass Lewis & Co. (2006) 'Trend alert', Getting It Wrong the First Time (March).
7. Leuz, C., Nanda, D. and Wysocki, P. D. (2003) 'Earnings management and investor protection: An international comparison', Journal of Financial Economics (69), 505–527. | Article |
8. Penman, S. (2001). Financial Statement Analysis and Security Valuation, New York, NY: McGraw-Hill, Irwin.
9. Dechow, P. and Dichev, I. D. (2002) 'The quality of accruals and earnings: The role of accrual estimation errors', The Accounting Review, 77 (Supplement), 35–59.
10. Beneish, M. D. (1999) 'The detection of earnings manipulation', Financial Analysts Journal, 55 (5), 24–36. | Article |
11. We do not use measures of abnormal or discretionary accruals because they are subject to serious measurement error.^12–14 Further, Jones et al., find that the commonly used discretionary accrual measures do not capture many instances of extreme earnings management (fraudulent earnings and restatement of financial statements).
12. Guay, W. R., Kothari, S. P. and Watts, R. L. (1996) 'A market-based evaluation of discretionary accrual models', Journal of Accounting Research, 34, 83–105. | Article |
13. McNichols, M. F. (2000) 'Research design issues in earnings management studies', Journal of Accounting and Public Policy, 19 (4–5), 313–345. | Article |
14. McNichols, M. F. (2002) 'Discussion of the quality of accruals and earnings: The role of accrual estimation errors', The Accounting Review, 77 (Supplement), 61–69.
15. Jones, K. L., Krishnan, G. V. and Melendrez, K. (2006) 'Do discretionary accruals models detect actual cases of fraudulent and restated earnings? An empirical evaluation', Working paper, George Mason University and Louisiana State University.
16. Dechow, P. (1994) 'Accounting earnings and cash flows as measures of firm performance: The role of accounting accruals 18, 3–42.
17. Burgstahler, D. and Dichev, I. (1997) 'Earnings management to avoid earnings decreases and losses', Journal of Accounting and Economics, 24, 99–129. | Article |
18. Collins, D. and Kothari, S. P. (1989) 'An analysis of intertemporal and cross-sectional deter-minants of earnings response coefficients', Journal of Accounting and Economics (July), 143–181. | Article |
19. The percentage of clients reporting small profits, however, is much higher for Andersen's Houston-based clients relative to the other Big 5 auditors (4.76 vs 2.46 per cent). Similarly, the percentage of clients reporting small losses is also higher for Andersen (4.29 vs 2.15 per cent). Further, it appears that Andersen's Houston clients are more likely to report small profits than Andersen's other clients. For all clients of Andersen's (all clients of other Big 5 auditors), the percentage of clients reporting small profits and small losses are, respectively, 4.30 and 1.99 per cent (4.14 and 2.00 per cent).

Acknowledgements

We thank Jim Largay and Linda Parsons for valuable comments.