Full Information Reserve Errors and Their Relation to Auditor and Actuary Quality

Transcription

1 Full Information Reserve Errors and Their Relation to Auditor and Actuary Quality Martin F. Grace + and J. Tyler Leverty ++ July 18, 2011 Abstract Using a new measure of reserve error based on stochastic loss reserving models we examine the role of auditor and actuary reputation on the quality of P/L insurer reserve estimates. We find high reputation actuaries are associated with more accurate reserves. They reduce over-estimation errors by 53 to 59 percent and underestimation errors by 23 to 36 percent. We find little evidence that high reputation auditors are related to the accuracy of reserve estimates. We also find confirmation for some of the prior hypotheses investigated in the literature: rate regulation, taxes, and earnings smoothing. We, however, find no evidence that weak firms underreserve to a greater extent than strong firms. JEL classification: M41, G22 Keywords: Discretionary Accruals; Insurance; Reputation; Audit Firm Fixed Effects, Actuarial Firm Fixed Effects + Corresponding Author: James S. Kemper Professor, Department of Risk Management & Insurance, Georgia State University, PO Box 4035, Atlanta, Georgia ; mgrace@gsu.edu ++ Assistant Professor, TRISTAR Risk Management Fellow, Department of Finance, Henry B. Tippie College of Business, University of Iowa, Iowa City, Iowa ; Phone: ; ty-leverty@uiowa.edu

2 Full Information Reserve Errors and Their Relation to Auditor and Actuary Quality External oversight of firm performance is important. This is especially true after the recent financial crisis. The extant literature recognizes that all providers of external oversight (e.g., auditors, rating agencies, and actuaries) may not be of equal quality due to differences in the technical abilities or the scope of the particular profession. We study the role of data assurance professionals and specifically consider the role of auditor and actuary reputation in the property-liability (P/L) insurance industry. We use the P/L insurance industry because it provides two important advantages in the study of managerial discretion. It provides a homogeneous sample of firms which allows for easier decomposition of discretionary and nondiscretionary components (McNichols, 2000). Even more advantageous is the fact that P/L insurers are required to disclose revisions to a material accrual, the reserve for policy claim losses. These revisions offer a direct measure of the estimation error in a loss reserve. We investigate the extent to which the magnitude of reserve error is associated with auditor and actuary reputation, while controlling for nondiscretionary components of the estimation error (e.g., lines of business, firm size, etc.). We also control for previously tested hypotheses. Prior research examines whether firms manage earnings with their reserve estimates (e.g., Weiss, 1985; Grace, 1990; Beaver, et al., 2003). In addition, loss reserves, which are pretax deductions from earnings, provide managers an opportunity to shelter earnings from taxation (Grace, 1990). Prior studies also hypothesize that weak insurers under-reserve to a greater extent than healthy firms (Petroni, 1992; Harrington and Danzon, 1994; Petroni and Beasley, 1996; Penalva, 1998; Petroni, Ryan, and Wahlen, 2000; Gaver and Paterson, 2004). Insurers may also manage their reserves for rate regulation purposes (e.g., Nelson, 2000; Grace and Leverty, 2010). 1

3 In the extant literature, P/L loss reserve error is measured in two ways: (1) comparing the originally reported loss reserve to a future revised estimate (typically five years in the future) (e.g., Kazenski, Feldhaus, and Schneider, 1992; Petroni, 1992; Beaver et al., 2003); and (2) comparing the originally reported loss reserve to future claims paid (again, typically five years in the future)(e.g., Weiss, 1985, Grace, 1990). The first error we refer to as the KFS error and the second as the Weiss error. These error definitions are essentially point estimates of reserve error. In this paper, we take a different approach and estimate what we call full information reserve errors. The procedure uses all the information in Schedule P to estimate a reserve error based on stochastic loss reserving models, such as those proposed by Taylor (2000), Wuthrich & Mertz (2008), and Kaas, Goovaerts, Dhaene, & Denuit (2008). Our method is superior to the Weiss and KFS errors for two main reasons. The first is a practical concern about the data. Using the KFS or Weiss error is not possible for our sample as we only have information on auditors and actuaries for 2005 to The KFS and Weiss errors require five years of data to calculate (a 2004 reserve error is calculated using 2009 data). The full information reserve error requires only two years of data, years t-1 and t (e.g., a 2005 full information reserve error is calculated using 2004 and 2005 data). Thus, with a stochastic loss reserve model we can use all five years of the actuary and auditor data, while with the KFS and Weiss errors we would have to wait until the release of the 2014 data. The second reason to promote our method is the loss reserve models we use to estimate the full information reserve error are related to how insurers model and assess the adequacy of their reserves. Our method is related to the chain-ladder approach to estimate reserves which has been used for decades. It is a stochastic reserve model promoted in the actuarial literature and is used by practicing actuaries. The KFS and Weiss errors are essentially point estimates of reserve adequacy that are not available to managers in real time. In contrast, the stochastic model we employ is 2

4 available in real time, it has a forecast error to provide information about the relative uncertainty in the reserve estimate, and managers can and do make decisions using models like the one we use. By way of preview, we find high reputation actuaries are associated with more accurate reserves. High reputation actuaries reduce over-estimation errors by 53 to 59 percent and under-estimation errors by 23 to 36 percent. We find little evidence that high reputation auditors are related to the accuracy of reserve estimates. We also examine whether there are systematic differences in the estimation of reserves by individual independent actuarial and audit firms. The annual statements of P/L insurers report the identity of the certifying actuary and auditor and the firm they are employed by for each insurer from 2005 to We use this information to construct actuarial firm-insurer and auditor-insurer matched panel data sets, which allow us to track actuarial and audit firms across different insurers in a given year and over time, enabling us to determine the extent reserve errors are linked to actuarial and audit firms above and beyond firm, group, and year effects. 1 This is important as we will be able to assess the relative importance of individual actuarial firms and auditors. Our results show the actuarial firm fixed effects are an empirically and economically important determinant of reserve estimates. The inclusion of actuarial firm fixed effects increases the adjusted R-squared. Moreover, the proportion of actuarial firm fixed effects that are statistically related to insurer reserve error is greater than the proportion of firm and group fixed effects. These findings provide evidence that actuaries play an economically and statistically important role in influencing insurer reserve estimates. We do not find this to be true for audit firms. We also find confirmation for some of the prior hypotheses investigated in the literature. Consistent with Grace and Leverty (2010) we see that the managers of insurers subject to stringent rate regulation bias their reserves upward to a greater extent than other insurers. Similar to prior 1 This approach is similar to the one used by Leverty and Grace (2011) to identify the extent firm efficiency is linked to individual CEOs. 3

5 studies we see evidence of a tax incentive to over-reserve (Grace, 1990; Penalva, 1998; Gaver and Paterson, 1999, 2000; Nelson, 2000; Beaver, et al., 2003). Our results also show evidence of managerial discretion over earnings (Beaver, et al., 2003). Our results, however, depart from the prior literature for the most commonly tested hypothesis that weak insurers under-reserve to a greater extent than stronger firms (see e.g., Petroni, 1992; Petroni and Beasley, 1996, Penalva, 1998, Petroni, et al., 2000, Gaver and Paterson, 2000, 2004). We find no evidence that weak insurers under-reserve more than strong insurers. This suggests that the finding of under-reserving with the traditional reserve error measures (which requires a five year data lag to calculate) may not be related to managerial manipulation to avoid regulatory scrutiny, but rather that weak firms have less to devote to reserves, i.e. they are weak firms. This is an important point because it has implications for causality. AM Best, for example, believes low reserves are one of the major causes of insurer failure. Our evidence suggests under-reserving is a symptom of weakness and not necessarily the cause of failure (A.M. Best, 2004). Our paper contributes to the literature on managerial discretion in the property-liability (P/L) insurance industry by investigating the extent to which auditor and actuary reputation influence reserve accuracy. Petroni and Beasley (1996) study the role of audit quality on the accuracy of property-liability (P/L) insurer reserves and find no systematic differences in claim loss reserve estimation accuracy between high reputation auditors and other audit firms. Kelly, Kleffner and Li (2010) examine whether in-house or consultant actuaries provide more accurate reserves for Canadian insurers. They find no evidence of systematic differences in loss reserve accuracy between in-house and consultant actuaries. Our study improves upon these studies in a number of ways. First, we are the first to investigate the role of actuary reputation. Second, we jointly examine the influence of actuaries and auditors. Third, we investigate the role of auditor and actuary reputation, while controlling for all of the hypothesized rationales for why insurers might manage loss reserves. 4

6 This is important as the exclusion of alternative or additional motivations may influence econometric inferences, as prior findings could be the result of an omitted incentive (Grace and Leverty, 2011). Finally, we are the first to investigate whether there are systematic differences in the estimation of reserves by individual actuarial and audit firms. 2 The remainder of the paper proceeds as follows. Section II provides background information on reserve estimation, including a discussion of the traditional definitions of reserve error and the full information reserve error. Section III describes our data. Section IV discusses our empirical strategy and describes the results. Section V concludes. II. LOSS RESERVES Loss reserves are the largest liability on a P/L insurer s balance sheet. The establishment of loss reserves ordinarily begins with the collection of information about an insurer s loss experience as well as information about the industry s loss experience (through entities like Insurance Services Organization). Once this information has been compiled, an insurer s actuaries generate predictions about future loss payments and expenses. Actuaries usually recommend a range and then management chooses the actual loss reserve levels to be reported. Estimation of claims is difficult as not all claims for current period losses are filed by the balance sheet date. Moreover, even when claims are filed in the current period, the ultimate settlement date is often delayed several years. Estimates based solely on past claims may not yield accurate predictions of future claims, and thus reserves are likely to be revised as new information about claims arises over time. Given the uncertainties involved in estimating loss reserves it is conceivable that reserve errors result from a failure to account for all the available information. Developments in litigation as well as costs can 2 We also extend the literature by accounting for the possibility that insurers and actuaries (auditors) may not match randomly. Actuaries (auditors) may choose (self-select) to work for higher quality insurers out of reputation concerns. Moreover, insurers may choose to work with high quality actuaries (auditors) out of reputation concerns. Thus, there is potential endogeneity in the matching of insurers and actuaries (auditors). We, however, find no evidence of endogeneity. 5

7 change significantly and give the perception that managers are cooking the books when, in fact, different expectations of future loss development result from new information. It is also possible that reserve errors result from managers exercising discretion. Under statutory accounting principles (SAP) the loss reserve is the firm s estimated liability for unpaid claims on all losses that occurred prior to the balance sheet date. The unique aspect of the insurer loss reserve is that firms must disclose the gradual settlement of claims over time and record all revisions of the loss reserve estimate. Revisions, known as development, provide an indication of whether the previously reported amount was under- or over-stated. Schedule P of the National Association of Insurance Commissioner s Annual Statement records the insurer s description of their accident year loss development over a ten-year period. All U.S. P/L insurers must compile Schedule P part of their regulatory annual filings. Table 1 shows an insurer s Schedule P - Parts 2 and 3 for year The data in the table are excerpted from the Statutory Annual Statement of State Farm Mutual Automobile Insurance Company (henceforth State Farm). Schedule P Part 2 reports losses estimated in the year incurred as well as subsequent adjustments in the estimate as claims are settled. It documents how insurers provide extensive disclosures about the incremental settlement of claims over time. In particular, it shows incurred losses by the year in which the losses were incurred, the accident year (rows 1 thru 11), and the evaluation date, the calendar year (columns 1 thru 11). For instance, in calendar year 2002, State Farm estimated that $23,515 million (M) of losses occurred during the accident year 2002 (row 6, column 6, in bold and italics). This estimate of 2002 accident year losses was revised downward to $22,275 M by calendar year 2007 (row 6, column 11, in bold and italics). [Insert Table 1 Here] Schedule P Part 3 reports cumulative losses paid at the end of a year. It shows cumulative losses paid by the accident year (rows 1 thru 11) and the evaluation date, the calendar year (columns 6

8 1 thru 11). For example, in calendar year 2002, State Farm paid $14,826 M for losses associated with accidents that occurred in 2002 (row 6, column 6, in bold and italics). Of the estimated $23,515 M in losses that occurred during the accident year 2002, percent are paid in The cumulative amount of losses paid for accident year 2002 increased to $21,950 M in calendar year 2007 (row 6, column 11, in bold and italics). As a result, given the 2007 revised estimate of $22,275 M in losses that occurred during the accident year 2002, 98.5 percent of estimated losses are paid by In the literature on managerial discretion in the P/L insurance industry there are two methods for calculating reserve error. The first reserve error, which we call the Weiss (1985) or W error, is the difference between total incurred loss for firm i as of a given calendar year t and cumulative developed losses paid in a future calendar year t+j. Wit, = Incurred Lossesit, Developed Losses Paid it, + j (1) Incurred losses are losses that are known to the insurer plus those that are estimated to have occurred. Developed losses paid are those losses actually paid. The subscript t denotes the end of the year valuation of the loss and the subscript j denotes some future year s accumulated loss payment. The W error is positive (negative) if the originally reported reserve is overestimated (underestimated) relative to what is eventually paid on these losses. This definition of reserve error is also used in other studies (see e.g. Grace, 1990; Diacon et al., 2004; Browne et al., 2008). The second reserve error, which we call the KFS error (Kazenski, Feldhaus, and Schneider (1992)), is the difference between total incurred losses for firm i as of a given calendar year t and a revised estimate of incurred losses in calendar year t+j: KFSit, = Incurred Lossesit, Incurred Losses it, + j (2) The KFS error is positive if the originally reported reserve is overestimated. This error measure has also been used in other studies (see e.g., Petroni, 1992; Beaver et al., 2003; Eckles and Halek, 2010). 7

9 We further describe these two reserve errors using the data in Table 1. A majority of the extant literature (e.g., Petroni 1992; Beaver et al. 2003; Gaver and Paterson 2004, Grace and Leverty 2011), examine reserve error five years prior to resolution, so j is five. The KFS error is the difference between total losses incurred in a given calendar year and a revised estimate of total losses incurred five calendar years in the future (Beaver et al., 2003; Gaver and Paterson, 2004). It relies upon information reported in Schedule P Part 2. The estimate of total incurred losses for a given calendar year is the sum of the losses in the column of that year. For State Farm, at the end of 2002, estimated losses for all years up to and including 2002 totaled $105,560 M (the sum of the italicized values in Part 2, column ). By the end of 2007, the estimate for the same accident years had been reduced to $103,820 M (the sum of the italicized values in Part 2, column ). To capture the revised estimate five years in the future, annual statement data from 2007 is used. Initial over- (under) reserving yields a positive (negative) reserve error since the revised estimate of total losses incurred five years in the future is greater (less) than the initial estimate. Accordingly, the KFS reserve error for State Farm in 2002 is $1,740 M ($105,560 M minus $103,820 M), indicating that State Farm over-estimated their reserves by $1,740 M. The strength of the KFS error is that it is not dependent on the development of losses, i.e., when losses are eventually paid. The weakness of the KFS error is it is affected by possible reserve manipulation in the initial estimate (in year t) and in the revised estimate (in year t+5). Nevertheless, the potential for error in the revised estimate is considerable less than in the initial estimate. Insurers cannot manipulate paid claims and more claims are paid each year. The Weiss error is the difference between total losses incurred in a given calendar year and total cumulative losses paid five calendar years in the future (Weiss, 1992). It relies upon information reported in Parts 2 and 3 of Schedule P. The estimate of total incurred losses for a given calendar year is the same as in the KFS error. For State Farm, at the end of 2002, estimated losses for all 8

10 years up to and including 2002 totaled $105,560 M (the sum of the italicized values in Part 2, column ). Total cumulative losses paid five calendar years in the future is the sum of cumulative losses paid in the column of that year. By the end of 2007, total losses paid by State Farm are $102,618 M (the sum of the italicized values in Part 3, column ). Accordingly, State Farm s W error for 2002 is $2,942 M ($105,560 M minus $102,618 M), indicating that State Farm overestimated their reserves by $2,942 M. The strength of the W error is that it uses losses paid to determine the error. Error is determined by comparing the initial estimate of reserves with claims paid. The weakness of the W error is that these claims paid are not ultimate claims paid (where 100% of claims are paid), but rather claims paid 5-years later. It is important to note that few lines of business have 100% of losses paid within 5 years. Nelson (2000) reports the average time to claims development exhaustion (i.e., when all outstanding claims are paid) is 7-years for homeowners insurance and 20-years for medical malpractice insurance. If the time between when a claim is declared and the payment is long (i.e., greater than five years), then the W error will overstate the reserve error. A weakness of both the KFS error and the W error is that there is a great deal of loss development information that is not used. Another weakness is that they require 5-years of data to estimate reserve error. We propose a full information definition of reserve error that accounts for all the available information in the loss reserve schedule (Schedule P Part 2) to make a rationale forecast about the ultimate reserve using stochastic reserving estimation techniques. It requires only two years of data. The assumption behind the full information reserve error is that firms are using best practices to develop their estimates of loss reserves. The extent to which they deviate from best practices is measured as reserve error. We now describe the details behind estimating the full information reserve error. First, we transform the information in Schedule P Part 2 into a loss development triangle. A loss 9

11 development triangle reports estimated losses by the year they were incurred (i.e., the accident year), as well as subsequent adjustments in these estimates over time (development years). It documents how insurers update information about losses over time. Second, we use this information to estimate a stochastic loss reserve model. In particular, we estimate the following model for each firm and year: (3) x ( ft) = α + λr+ δ C+ ε ij i j ij i= 2 j= 2 where x ij (ft) are the cells from the loss development triangle for a given firm (f) in a given year (t); i indexes the rows in the loss development triangle; j indexes the columns; α is an intercept term, λi andδ are the coefficients on the indices for the rows (R) and columns (C), respectively. We estimate j (3) for each firm and year for 1989 to Third, we use the fitted values from (3) to forecast next year s loss development, ˆx ij(ct)for year t+1. We then compare ˆx ij (ct)for year t+1 to true x(ct)in ij year t+1: Δ i = ˆx ij (t+ 1) x(t ij + 1). Finally, we sum the Δ i to obtain the full information reserve error, Θ (ct) = Δ 10 i (ct). i= 2 We further describe the full information reserve error using the data in Table 2, which shows the 2001 Schedule P Part 2 for State Farm. To calculate the 2002 reserve error using the KFS or W reserve error annual statement data from 2007 is used. In contrast, to calculate the 2002 reserve error using the full information reserve error, the 2001 annual statement is used. [Insert Table 2 Here] We transform the information in the Schedule P Part 2 (shown in Table 2) into a loss development triangle, which is shown in Table 3. Each cell in Table 2 corresponds to an x ij, where i indexes the columns (the loss development) and j indexes the rows (the accident year). Using these values, we estimate equation (3) for State Farm in The results are reported in Table 4. We use 10

12 these parameter estimates to forecast next year s loss development. The predicted values, ˆx ij (ct), are highlighted in yellow in Panel A of Table 5. Panel B shows State Farm s actual loss development in 2002, highlighted in green. The full information reserve error, Θ, is $467 M ($161,596 M (the sum of the green cells) minus $161,129 M (the sum of the yellow cells)), indicating that State Farm overestimated their reserves in 2002 by $467 M. [Insert Table 3, 4, 5, & 6 Here] Table 6 shows the descriptive statistics of the full information reserve error scaled by total assets for 1990 to It also shows the descriptive statistics of the explanatory power (i.e. the R-squared) of the stochastic loss reserving model (equation 3). In contrast to prior studies that use the W and KFS reserve errors, we find the average insurer slightly under-estimates reserves. The mean scaled full information reserve error is The average firm in this sample has $604 million in total assets. Thus, the average firm under-estimates reserves by approximately $624,000. The lowest average full information reserve error is in 1993 (the year following Hurricane Andrew) where the average firm under-estimated reserves by roughly $61 million, while the greatest is in 2003 (two years after 9/11) with the average firm over-estimating reserves by approximately $172 million. The explanatory power of the stochastic loss reserving model is high with the average R 2 over 95 percent. III. DATA We use data from the NAIC annual statement database, which are prepared using Statutory Accounting Principles (SAP). 3 Our reported findings are based on affiliated and unaffiliated single insurers. We also examine a sample of group and unaffiliated single insurers. The results for this sample are qualitatively similar to the reported results. Data for Schedule P of the NAIC Annual 3 A majority of the prior research on P/L insurer reserve estimates relies on statutory accounting data (e.g., Weiss, 1985; Grace, 1990; Petroni, 1992; Penalva, 1998; Gaver and Paterson, 1999; Nelson, 2000; Beaver, et al., 2003; and Gaver and Paterson, 2004). 11

13 Statement is collected for the years 1989 to We estimate the stochastic loss reserve model using this sample, which gives us the full information reserve for the years 1990 to Our main objective is to investigate the role of auditor and actuary reputation on the quality of P/L insurer reserve estimates to determine whether there are systematic differences in reserve accuracy between high and low reputation firms. The NAIC annual statements report the identity of the certifying actuary and auditor and the firm they are employed by for each insurer from 2005 to We use this information to calculate actuarial and audit firm market share and to construct actuary-insurer and auditor-insurer matched panel data sets, which allows us to track actuaries and auditors across different insurers over time. Thus, even though we estimate the full information reserve error for 1990 to 2009, our main analysis is for the 2005 to 2009 period. In all of our tests we control for the other hypotheses for why insurers manage reserves that are investigated in the literature (Grace and Leverty, 2011). These hypotheses include: financial weakness (e.g., Petroni, 1992; Harrington and Danzon, 1994; Gaver and Paterson, 2004), tax (e.g, Grace, 1990), income smoothing (e.g., Weiss, 1985; Beaver, et al., 2003), and rate regulation incentives (e.g., Nelson, 2000; Grace and Leverty, 2010). Studies hypothesize that weak insurers under-reserve to a greater extent than stronger firms (see e.g., Petroni, 1992; Harrington and Danzon, 1994; Petroni and Beasley, 1996, Penalva, 1998, Petroni, et al., 2000, Gaver and Paterson, 2000, 2004). We measure financial weakness similar to Grace and Leverty (2011) and estimate each firm s probability of failure. In particular, we follow the P/L insurer insolvency literature (e.g., Cummins et al. [1999]) and estimate the following model: I = α + β X + δ X + ε (4) rst fc it it it it 12

14 where for insurer i and data year t: Iit is the unobserved propensity to fail, α is an intercept term, rst X it is a vector of time-varying regulatory solvency tools, fc X it is a vector of time-varying firm characteristics, andε it is an error term. We estimate equation (4) using a discrete-time hazard model (Shumway, 2001). The dependent variable is equal to one if the insurer is insolvent in either year t+1 or t+2. 4 The firm characteristics are the natural logarithm of total assets and a mutual indicator. The regulatory solvency tools are fourteen balance sheet and income statement ratios in the FAST system. 5 We use all insurers for which we have data to calculate the fourteen FAST ratios. The only insurers we omit are those who do not have data available in at least one of the two years prior to their year of insolvency. In an effort to include as many insolvent observations in the analysis, we include insurers who report data two years prior to their insolvency if they do not report in the year prior to their insolvency. We identify 191 P/L insurers that fail between 1990 and The results are shown in Panel A of Appendix A. The explanatory power of the model is reasonable. For parsimony we do not discuss the hazard model results in detail. We do note, however, that our results are consistent with those reported by other studies (e.g., Doherty et al., 2008; Grace and Leverty, 2010). Panel B of Appendix A reports the estimated one-year probabilities of failure for healthy and insolvent insurers. The mean (median) probability of insolvency for the solvent firms is 0.47 (0.12) percent, while the mean (median) is (3.92) percent for insolvent insurers in the year before they fail. The average (median) estimated one-year probability of failure 4 We define the year of insolvency as the year of the first formal regulatory action taken against a troubled insurer (Grace et al., 1998). In prior studies (e.g., Grace and Leverty, 2011), insurers are classified as subject to formal regulatory proceedings for conservation of assets, rehabilitation, receivership, or liquidation. In contrast, we classify insurers as subject to formal regulatory proceedings for liquidations only. Our definition, therefore, is more conservative as we focus only on insolvencies rather than just troubled companies and as a result our sample includes a smaller number of insolvencies than found in previous studies. The source for this information is the NAIC s Global Receivership Information Database. 5 Grace et al. (1998) list 25 FAST ratios. There is no guarantee the NAIC still uses these same ratios. Using the full set of FAST ratios considerably reduces the number of observations without significantly improving the fit. 13

15 for firms that fail in the next year is over 24 (33) times larger than the average (median) probability for solvent firms. Overall, the model appears to adequately distinguish weak insurers from healthy insurers. The hypothesis for taxes is that over-estimating reserves provides an opportunity for a firm to shelter earnings, ceteris paribus (see e.g., Grace, 1990). By overestimating future losses attributable to current premiums, the insurer increases its reserves and incurred losses and reduces its current tax liability. The insurer does not eliminate any taxes with reserve errors, but it does postpone the tax payments until future periods when ultimate claim costs are realized. Similar to a majority of the prior literature (e.g., Petroni, 1992; Penalva, 1998; Nelson, 2000), we measure the tax incentive using an indicator variable. The tax indicator takes the value of one if the insurer has a high tax rate, and zero otherwise. This proxy is based on the tax-paying status of the firm (Scholes et al., 1990). Firms are assumed to have a low tax rate if they have an NOL carryforward, which is identified by the insurer not currently paying any taxes or receiving a refund of prior-year taxes. All other insurers are assumed not to have a NOL carryforward. According to the income smoothing hypothesis, a firm may manage earnings to avoid reporting accounting losses (Weiss, 1985; Grace, 1990; Beaver, et al., 2003). Beaver, et al. (2003) find that insurers manage reserves across the distribution of earnings. In particular, they document that firms with small positive earnings report the most income-increasing reserve levels, while firms with the highest earnings report the most income-decreasing reserves. We also investigate the incentive to smooth earnings along the earnings distribution. Similar to Beaver et al. (2003), we create indicator variables that identify the position of an insurer in the earnings distribution (small profit, profit, small loss, and loss) in each year of our sample. Small Profit identifies insurers with reported earnings in the first 10 percent of the distribution to the right of zero. Small Loss classifies insurers with earnings in the first 10 percent of the distribution to the left of zero, i.e., the top 10 percent of 14

16 the negative earnings distribution. Profit and Loss identify insurers with earnings in the top 90 percent of the positive and negative earnings distribution, respectively. Nelson (2000) hypothesizes that insurers operating in strict rate regulatory environments will under-state reserves to convince regulators they can charge lower rates. Since the evidence on rate regulation in the insurance industry suggests regulation has often held rates below the economic cost of writing business since the mid-1970s (e.g., Cummins and Harrington, 1987; Grabowski, et al., 1989; Harrington, 2002; Cummins, et al., 2001; Grace and Phillips, 2008; Weiss, Tennyson, and Regan, 2010), Grace and Leverty (2010) hypothesize the opposite. If regulation suppresses rates below the economic cost of writing business, then stringent rate regulation will create an incentive for managers to bias reserve estimates upward in an attempt to reduce the effect of rate suppression. To examine these two hypotheses we need a measure of rate regulation. Because rate regulation varies by state and by line of business and few insurers operate only in states and lines with strict rate regulation, we create a rate regulation index variable (% Reg) that weights the stringency of rate regulation. Using the description of the lines of business subject to rate regulation in the NAIC s Compendium of State Laws on Insurance Topics (National Association of Insurance Commissioners, various years), we calculate for each firm the percent of total premiums written subject to these regulations. The rate regulation variable for firm i, in year t, in line of business l, operating in states indexed by s is given by: % Reg = istl,,, Premiums Written istl,,, istl * Stringent Reg Law ( PremiumsWritten ) istl stl (5) where Stringent Reg Law is an indicator variable set equal to one if state s has a stringent rate regulation law that applies to line l in year t, and zero otherwise. 15

17 Similar to Harrington (2002) a state is classified as having a stringent rate regulation law if it had either state-made rates, a prior approval law, or a file-and-use law that required prior approval of deviations from rates filed by a rate advisory organization. A state is classified as not having a stringent rate regulation law if it permitted file-and-use, use-and-file, filing only, or had flex rating with a large flex band. Since states maintain their rate regulation laws for extended periods of time, there is little concern that reserve decisions arise endogenously with state rate regulation. Our main objective is to examine the role of auditor and actuary reputation on the quality of P/L insurer reserve estimates to determine whether there are systematic differences in reserve accuracy between high and low reputation firms. We measure the reputation of actuarial and audit firms using each firm s market share in the P/L insurance industry by year (Actuary M.S. and Auditor M.S.). Intuitively, market share captures the brand name and goodwill of a firm. As Klein and Leffler (1981) point out, if a firm engages in quality cutting, this information disseminates more rapidly if the firm has a large market share. Table 7 shows the top ten auditing and actuarial firms by market share for the period 2005 to PricewaterhouseCoopers has the greatest auditor and actuarial market share at 21 and 8 percent, respectively. After the top four firms, the market share of auditing firms drops precipitously. Accordingly, we also use a dichotomous measure of whether or not the firm is a member of one of the top four actuarial or audit firms by market share (Top Four Actuary and Top Four Auditor). DeAngelo (1981) provides the theoretical foundation for the use of a dichotomous reputation measure based on the relationship between firm size and costs related to loss of reputation. Francis and Wilson (1988) motivate the use of a dichotomous reputation measure based on brand name reputation protection. [Insert Table 7 Here] 16

18 To be included in the sample, firms must have positive reserves, losses incurred, and direct premiums written. To allow comparability with other studies (e.g., Petroni, 1992; Beaver, et al., 2003), we implement a similar firm screen. 6 We only include in the regressions the observations that have non-missing values for all the independent variables. All regressions are performed using the full and the screened samples. The results of the two samples are qualitatively identical. For ease of exposition, we tabulate and discuss the results of only the screened sample. Table 8 shows the descriptive statistics of our main sample for the years 2005 to The mean loss reserve is under-estimated by 1.3 percent of total assets. The average actuarial firm has 1.5 percent of the market and the average audit firm 8.6 percent. Twenty-six percent of the sample uses a top four actuarial firm and 60.6 percent use a top four audit firm. Turning to the other hypothesized incentives, 47.6 percent of the sample is identified as having a high tax rate (Tax Indicator). Profit and Loss firms comprise 77 and 15 percent of the sample, respectively. Roughly 7 percent of firms report earnings in the first 10 percent of the earnings distribution to the right of zero (Small Profit), while 1.4 percent report earnings in the first 10 percent to the left of zero (Small Loss). The average firm has a probability of failure (PrFail) of 0.1 percent and 18.3 percent of business subject to stringent rate regulation (% Reg). The research design for our multivariate analyses includes measures for both discretion and nondiscretion. This methodology mitigates biased coefficients and the mis-estimation of the reserve components in the case that the determinants of non-discretion and discretion are interrelated (Petroni, et al., 2000). The set of non-discretionary variables reflects the firm s economic condition, organizational structure, and strategic choices. These economic factors may also impact the incentives and ability of management to exercise discretion over reserves. Studies indicate that 6 Firms that have extreme errors in their loss reserves (observations with an original loss reserve estimate that differs from the revised estimated by greater than 50 percent in absolute value) are eliminated from the full sample. In addition, firms which cede all premiums to reinsurers and/or write greater than twenty-five percent of their premiums in workers compensation, accident and health, surety, credit, and/or reinsurance are also excluded. 17

19 reserve mis-estimation results from managerial mistakes related to the difficulty of determining an insurer s liabilities (e.g., Weiss, 1985; Grace, 1990). The difficultly is related to the type(s) of business written, the incentives inherent in different ownership structures (e.g., Lamm-Tennant and Starks, 1993; Mayers and Smith, 2001) and distribution systems (e.g, Berger, et al., 1997; Regan and Tennyson, 2001), and product and geographical diversification (e.g, Comment and Jarrell, 1995; Berger and Ofek, 1995; Berger, et al., 2000). Failure to include these variables in our econometric models may result in omitted variables bias. We identify organizational structure using three variables. The first two variables are indicators of whether the firm is a mutual or stock insurer (He and Sommer, 2010; Mayers and Smith, 2010). We categorize firms according to the ownership structure of their ultimate owner (Mayers and Smith, 1994). Mutual insurers make up a quarter of our sample; the other three-quarters are stock. The third variable is an indicator of whether the firm is part of a group of insurers under common ownership (see e.g., Powell, Sommer, and Eckles, 2008). Roughly seventy-four percent of the firms are associated with a group. Prior research finds insurers underwriting long-tailed lines of business have more discretion over their reserves (e.g., Petroni and Beasley, 1996; Beaver et al., 2003). Accordingly, we account for the percent of losses incurred in long-tail lines of insurance (as defined by Phillips et al., 1998). The average firm has 68.4 percent of its losses in long-tail lines and 33.4 percent in short-tail lines. We also account for differences in product and geographical diversification. Product diversification is measured using the product line Herfindahl Index, which is calculated as the sum of the squared percentage of premiums earned in each of the 26 lines of P/L insurance. The average firm has a product line Herfindahl of 0.418, which is equivalent to approximately 2 lines of business. Geographical diversification is gauged using the geographical Herfindahl Index, the sum of the 18

20 squared percentage of business written in each of the 50 states and the District of Columbia. The mean geographical Herfindahl is 0.546, indicating the average firm operates in roughly two states. We also use other control variables. Harrington and Danzon (1994) find that firms with weak safety (solvency) incentives under-report reserves to increase firm growth. They also discover that these firms attempt to hide their under-reserving with reinsurance. We account for growth using the one-year percent increase in net premiums written and reinsurance usage with the percent of gross premiums written ceded to reinsurers. The mean firm has a growth rate of 2.9 percent and cedes 30 percent of its business to reinsurers. We also account for firm size (total assets). The mean firm has approximately $ million in total assets. Finally, we control for whether the firm directly sells its products. Roughly nine percent of the firms distribute their products directly. IV. EMPIRICAL STRATEGY AND RESULTS A. Magnitude of Full Information Reserve Error To investigate the magnitude of reserve error and determine how it relates to the role of auditor and actuary reputation while controlling for other hypothesized incentives and non-discretionary components, we estimate the following model: y = α + δ + βx + λz + e (6) it t i it it it where i indexes firms, t indexes time periods, yit is the full information reserve error scaled by total assets, α t is year fixed effects; δ i is firm fixed effects; variables, and Z it is the hypothesized incentives. X it is the institutional and firm characteristic A potential concern for our analysis is the endogeneity of actuarial (audit) firm reputation. In particular, actuaries (auditors) may choose (self-select) to work for higher quality insurers out of reputation concerns. Moreover, insurers may choose to work with high quality actuaries (auditors) 19

21 out of reputation concerns. Thus, there is potential endogeneity in the matching of insurers and actuaries (auditors). Accordingly, we undertake a Hausman test of endogeneity. We instrument the choice of top four actuary and top four accountant with the insurer s A.M. Best rating, as this is a common measure of a firm s quality, and return on assets. The Hausman test does not reject the null hypothesis that top four actuary and top four accountant are exogenous (χ 2 =2.36, p=0.30). In our multivariate analysis of the magnitude of reserve error, we examine three samples: (1) the full sample of firms; (2) the subsample of over-reserving firms; and (3) the subsample of underreserving firms. We split the sample into over- and under-reserving firms to determine whether high quality audit and actuarial firms provide advice that leads to more accurate reserves, i.e., less overreserving and less under-reserving. To allow the regression results to be interpreted in this way, the dependent variable in the under-reserving firms subsample is the absolute value of the full information reserve error scaled by total assets. A positive coefficient would indicate greater underreserving and a negative coefficient would indicate less under-reserving. For each sample, we estimate two specifications. The first includes the continuous measures of auditor and actuary reputation market share in the P/L insurance industry. The second includes the top four audit and actuarial firm indicator variables. Our estimation results are shown in Table 9. In the full sample, there is no observed relationship between actuary reputation and reserve error. The over- and under-reserving subsamples, however, show that high reputation actuaries are associated with more accurate reserves. In the over-reserving sample, high reputation actuaries are significantly related to less over-reserving, i.e., more precise reserve estimates. The coefficient on Actuary M.S. is (p<0.01) (regression (3)). In the regression sample, the standard deviation of actuary market share is and the mean of reserve error is Thus, a one standard deviation increase in actuary market share corresponds to 58.6 percentage reduction in over-reserving ((0.025*-1.50)/0.064)). The coefficient on Top Four Actuary is 20

22 (p<0.05) (regression (4)). A high reputation actuary is associated with a 53.1 percent reduction in over-reserving (-0.034/0.064). In monetary terms, a high-reputation actuary reduces over-reserving by $3.9 M to $4.3 M for the average over-reserving firm. In the under-reserving sample, high reputation actuaries are significantly related to less underreserving. The coefficient on Actuary M.S. is (p<0.01) (regression (5)). The standard deviation of actuary market share in the regression sample is and the mean reserve error is A one standard deviation increase in actuary market share corresponds to 22.6 percent reduction in underreserving ((0.024*-0.442)/abs(-0.047)). The coefficient on Top Four Actuary is (p<0.01) (regression (6)), indicating that a high reputation actuary reduces the magnitude of under-reserving by 36.2 percent (-0.017/abs(-0.047)). In monetary terms, a high-reputation actuary reduces underreserving by $1.9 to $3.0 M for the mean firm. In sum, high-reputation actuaries provide more accurate reserve estimates. In untabulated regressions we examine whether switching to or from a top four actuary is associated with reserve accuracy. We find that firms that switch to a top four actuary report less under-reserving error and less over-reserving error. Thus, the switch to a high reputation actuary from a lower reputation actuary results in more accurate reserve estimates. Similar to Petroni and Beasley (1996), we find little difference in claim loss reserve estimation accuracy between high reputation auditors and other audit firms. Only one auditor reputation variable is statistically significant. In the under-reserving subsample, the coefficient on Auditor M.S. is and it is statistically significant at the 5 percent level (regression (5)). This suggests that high reputation auditors are associated with greater under-reserving. The standard deviation of auditor market share in this regression is A one standard deviation increase in auditor market share corresponds to 20.2 percentage increase in under-reserving ((0.078*0.122)/abs(-0.047)). 21

23 We now turn to the other hypothesized rationales for why insurers may use discretion over their loss reserves. Consistent with Grace and Leverty (2010) we see that the managers of insurers subject to stringent rate regulation bias their reserves upward to a greater extent than other insurers. In the full sample, the mean effect of a one standard deviation increase in the percent of insurance subject to rate regulation is a loss reserve estimate inflated by roughly $3.5 million. Similar to Grace and Leverty (2010), we find that a majority of the response occurs from under-reserving firms underreserving less because of stringent rate regulation. We find no support for Nelson s (2000) hypothesis that rate regulation influences insurers to under-state reserves. Similar to prior studies we see evidence of a tax incentive to over-reserve (Grace, 1990; Penalva, 1998; Gaver and Paterson, 1999, 2000; Nelson, 2000; Beaver, et al., 2003). The coefficient on Tax Indicator is positive and significantly related to the magnitude of over-reserving (regressions (3) and (4)), indicating that firms with high tax rates over-state reserves compared to insurers with low tax rates. The difference is roughly 42 percent. In monetary terms, high tax firms over-reserve by approximately $3.0 million. Our results also show evidence of managerial discretion over earnings. Insurers reporting a small profit (earnings in the bottom 10% of the positive earning distribution) significantly under-state reserves (i.e., report income-increasing reserves) to a greater extent than insurers reporting losses (Loss firms are the base effect). The effect is significant only amongst over-reserving firms (p<0.01). Insurers with earnings in the top 90% of the positive earnings distribution (Profit) report statistically significant income-increasing reserves in the full sample and in the sample of over-reserving firms (p<0.01). In the over-reserving sample, the magnitude of over-reserving by small profit firms is significantly greater than it is for profit firms (in regression (3) the difference is (p-value=0.06); in regression (4) it is -027 (p-value=0.04)). 22

24 The most commonly confirmed hypothesis in the literature on managerial discretion in the P/L insurance industry is that weak insurers under-reserve to a greater extent than stronger firms (see e.g., Petroni, 1992; Petroni and Beasley, 1996, Penalva, 1998, Petroni, et al., 2000, Gaver and Paterson, 2000, 2004). Financial weakness is typically measured using IRIS ratios (e.g., Petroni, 1992; Nelson, 2000; Beaver et al., 2003; Gaver and Paterson, 2004). We investigate whether weak firms under-estimate reserves using each firm s probability of failure. The coefficient on the probability of failure (PrFail) is never statistically significant at the 10 percent level of confidence. Thus, using a more sophisticated measure of weakness and a more sophisticated measure of reserve error, we find no evidence that weak insurers under-reserve more than strong insurers. This suggests that the finding of under-reserving with the traditional reserve error measures (which require a five year data lag to calculate) may be unrelated to managerial manipulation to avoid regulatory scrutiny. B. Actuary and Auditor Effects on Full Information Reserve Error To further investigate the extent to which auditors and actuaries influence firm reserve errors above and beyond firm effects, we determine whether there are systematic differences in the reserve errors of individual actuarial and accounting firms, controlling for observable firm- and group-level characteristics. Since there may be lasting differences in practices across firms and groups due to some unobservable factors (which may be correlated with the actuary and accountant fixed effects), we separate actuary and accountant fixed effects from firm and group fixed effects. Specifically, we construct an actuary-firm (accountant-firm) matched panel data set that allows us to track the same actuarial firms (auditors) across different firms from 2005 to While many individual insurers belong to a group, we examine actuaries (accountants) at the individual insurer level. 7 This provides more heterogeneity in our actuary-firm and accountant-firm subsamples. We confine our analysis to 7 Each group of affiliated insurers utilizes a different organizational structure. In some groups, the chief actuary of the group is also the acting actuary of each individual affiliated insurer. In other groups, separate actuaries are appointed at the individual insurer level. 23