empirical investigation of the effect of growth on loss ... empirical investigation of the effect of...

An Empirical Investigation of the Effect of Growth on Loss Reserve Errors

Michael M. Barth1 and David L. Eckles2

Abstract: This study analyzes the relationship between the excess growth risk factorin the National Association of Insurance Commissioners’ (NAIC) risk‐based capitalformula and subsequent reserve development error. The inclusion of the excessivegrowth risk charge for reserves was predicated on the assumption that excessivegrowth creates reserve error bias. We measure the impact on different lines of businessand find no relationship between subsequent reserve errors and the excessive growthrisk factor included in the NAIC risk‐based capital formula. We do find a relationship,however, between reserve estimation error and an alternative measure of growth risk,based on claim counts reported in Schedule P Part 5. [Key words: risk‐based capital,growth risk, insurance regulation, insurance reserve errors.] JEL Classification:G22, G28

INTRODUCTION

he purpose of this research is to test the impact of aggregate premiumgrowth on loss reserve estimation errors. We test two alternate mea‐

sures of growth while controlling for other factors associated with reserveerror bias, including taxes, income smoothing, and product variations. Wespecifically test the growth risk charge for reserve development that isincluded in the National Association of Insurance Commissioners (NAIC)Risk‐Based Capital (RBC) formula against an alternative by‐line growthmeasure, claim counts. The NAIC RBC growth risk factor is computed onaggregate premiums and applied to aggregate reserves, but insurers can

1Associate Professor, The Citadel. Office: (843) 953‐0835, Email: [email protected],School of Business Administration, 171 Moultrie Street, Charleston, SC 294092Associate Professor, University of Georgia. Office: (706) 542‐3578, Email: [email protected],296 Brooks Hall, University of Georgia, Athens, GA 30602

T

96Journal of Insurance Issues, 2015, 38 (1): 96–123.Copyright © 2015 by the Western Risk and Insurance Association.All rights reserved.

EFFECT OF GROWTH ON LOSS RESERVE ERRORS 97

have excess growth in some lines and shrinkage in others. We test whetherthe aggregate growth risk factor is predictive of by‐line reserve error bias.We also test whether by‐line measures of growth are predictive of by‐linereserve error bias.

The impact of the growth risk charge in the NAIC formula is typicallyminor for the industry as a whole, but the impact on individual insurerscan be material. This is particularly important when one considers thatpremium growth attributable to price strengthening may actually be ben‐eficial. However, there is little empirical research into the specific effects ofgrowth. As an example, during litigation with the California InsuranceDepartment, the State Compensation Insurance Fund (SCIF), California’scompetitive state workers’ compensation insurance fund, made the argu‐ment that the excessive growth it experienced during a hard market in thelate 1990s and early 2000s resulted in a more financially sound position.However, SCIF actually triggered regulatory action under California’s RBCstatute because its growth rate triggered excessive growth rate charges forboth its written premiums and its reserves under the NAIC’s RBC formula.Disruptions in the California workers’ compensation market had increasedSCIF’s share of the California workers’ compensation market to over 50percent, though those same market disruptions allowed SCIF to raise itspremiums simultaneously. SCIF argued that the increase in policy countswas coupled with significant price increases, and therefore the excessivepremium growth was actually making the facility sounder, despite theresults of the RBC formula.

Over the years, a number of studies have cited excessive growth as oneof the leading causes of financial impairment (e.g., American Academy ofActuaries 2010, A.M. Best, 2010a, 2006, 2001; Government AccountabilityOffice, 1989). Excessive growth can cause an insurer to book a large amountof unprofitable business, resulting in an immediate effect on surplus.However, excessive growth can also make it more difficult to estimate theultimate obligations and can lead to underestimated loss reserves. There‐fore, the effect of excessive growth on an insurer’s reserving errors is animportant question, and even if the effect is “on average” benign. That is,if the loss reserve estimates become more variable, then financial impair‐ment risk is increased.

The NAIC includes premium growth ratios in both of its primary earlywarning systems—the Insurance Regulatory Information System (IRIS)and the Financial Analysis and Solvency Tracking system (FAST). Addi‐tionally, both the NAIC RBC formula and the A.M. Best Company’s BestCapital Adequacy Ratio (BCAR) include specific capital charges for exces‐sive growth. Unlike the NAIC’s RBC formula, Best’s BCAR formula usesexposure data to measure growth risk:

98 BARTH AND ECKLES

Growth Charge: The reserve growth charge reflects the additionalrisk that typically comes from growth and is based on the growth ina company’s exposures. The growth charge applied to the loss reserveaggregate required capital reflects the substantial risk a companyfaces in the claims and reserving areas during a time of significantgrowth (A.M. Best, 2010b, p. 12).

The inclusion of the growth charge is based, in part, on past researchshowing that insolvent insurers often experience high periods of growthjust prior to insolvency. However, other studies have shown that highperiods of growth are common in financially solvent insurers as well. Barth(2002) reports that one‐quarter of all insurers failed IRIS Ratio 5—Changein Net Written Premiums, during the period 1992–1996.3 Historical insol‐vency rates for insurers hover around one percent, however, which is muchlower than the twenty‐five percent of insurers that routinely trigger theabnormal growth measures each year.

The Impact of Growth on Reserve Estimation Errors

Premium growth can be the result of an influx of new customers, butcan also arise from price increases on the existing customer base. Eithertype of growth can affect reserve errors. Price changes alter the mix ofcustomers and may result in estimation errors because the past incurredloss development history may not accurately predict the future incurredloss development. An influx of new customers would produce the sametype of estimation errors, but the influx may also be the result of under‐pricing. The under‐pricing may be deliberate or inadvertent. Deliberateunder‐pricing, also known as cash flow underwriting, may result in adeliberate understatement of reserves to avoid regulatory scrutiny. Inad‐vertent under‐pricing may lead to reserve errors because the business turnsout to have higher expected loss costs than anticipated in the pricingstructure.

Current regulatory solvency models do not distinguish between thesetwo distinct sources of risk (price‐related and exposure‐related). A.M. Best,on the other hand, uses exposure data to calculate excessive growth in itsBest’s Capital Adequacy Ratio (BCAR) model. Policy counts from the A.M.Best Supplemental Rating Questionnaire or other exposure count informa‐tion from the insurer is used to calculate one‐year and three‐year growthrates, and growth in excess of the industry average generates capital

3Although not specifically included in this research, the authors’ calculations show that asignificant number of insurers continue to trigger IRIS Ratio 5, as well as the excess growthrate charge in the NAIC’s RBC formula.


charges. If exposure counts are not available, then growth in unaffiliatedgross premiums is used (A. M. Best, 2014).

Notably, the BCAR calculation is based on growth in excess of anindustry average, while the NAIC’s model is based on growth in excess ofa fixed 10 percent.

Setting aside for a moment its effect on reserving, price growth canactually enhance financial solvency and reduce an insurer’s insolvencyrisk. Theoretically, if an insurer doubled its prices across the board whilemaintaining the same set of loss exposures, or even increasing its lossexposures, the higher rates paid by both the new customers and the existingcustomers would increase the insurer’s financial health. Surplus wouldincrease because the insurer collects more premium dollars to pay for thesame set of claims.

If an insurer were to double the number of loss exposures whilemaintaining the same prices, the effect on the insurer’s financial healthwould depend on the degree to which the business was fairly priced. If thebusiness were underpriced, adding twice the number of exposures woulddrain surplus twice as fast. However, there would be a salutary effectregardless of the pricing because of the effect on predictability of ultimateclaims costs. The law of large numbers suggests that doubling the numberof exposures would reduce the statistical variance of the estimated valueof the portfolio of claims, even if it were underpriced.

In competitive insurance markets, an insurer should not be able todouble prices while at the same time maintaining the same set of custom‐ers.4 Changes in price would cause some of the existing exposures to moveto other insurance carriers while also affecting the influx of new exposures.Depending on the price elasticity of the product, increases in prices couldlead to reductions in overall premiums, just as reductions in price couldlead to increases in overall premium volume. The insurer’s financial riskchanges because the makeup of the book of business changes, which inturn makes it harder to forecast the future loss experience. Since thepremiums for a given block of policies must be established in the presentat an adequate level to pay all future losses associated with that block ofpolicies, anything that makes that forecasting process more difficultincreases the insurer’s financial impairment risk.

Additionally, changes in the makeup of the insurer’s basic book ofbusiness makes it more difficult to forecast the insurer’s ultimate lossexperience, which would tend to increase the variability of reserve estima‐tion errors. Additionally, the “aging phenomenon” (where new business

4California’s State Compensation Insurance Fund is one of the exceptions to this generalrule.

100 BARTH AND ECKLES

has a tendency towards poorer profitability than aged business), wouldtend to exacerbate the variability of reserve estimates.5 Therefore, whileprice increases, by themselves, may actually reduce an insurer’s insolvencyrisk, the changes to the insurer’s book of business resulting from priceincreases may make it harder to estimate reserves accurately since theseprice changes affect the customer mix in the book of business. Similarly, anincrease in the number of loss exposures in the book of business may ormay not directly alter historical loss reserve development patterns, but maysimply cause more instability.

In addition to greater instability in forecasting errors, insurers mayalso deliberately manipulate loss reserve estimates for a variety of otherreasons, such as to garner tax benefits, to disguise financial impairment, orto smooth earnings over time. While this research does make an effort toidentify and control for deliberate manipulations of reserves using similartechniques that have been used in other reserve error studies, our primaryinterest is in non‐deliberate forecasting errors that arise from statisticalvariance. Therefore, we are most interested in changes in the price andquantity of insurance sold that generate forecasting errors in the currentlevel of reserves.

The NAIC RBC Growth Risk Charge

Given that loss reserves are one of the largest components of insurers’balance sheets, it should be no surprise that reserve risk is one of the majorcomponents of the NAIC’s RBC formula. Reserve risk RBC develops acapital requirement for the risk that the insurer is under‐reserving, andthus overstating its policyholders’ surplus. To compute the reserve riskcharge, line‐specific risk factors are applied to the firm’s outstandingreserves for each of the major lines of business. Each line‐specific risk factoris adjusted for the company’s own recent loss development experience,based on the average development over the prior ten years. The RBCrequirements for the individual lines of business are then aggregated andadjusted for covariance between lines to arrive at the reserve risk RBC.

Additional reserve risk RBC is required if the company has experi‐enced excessive premium growth in the prior three‐year period. Excessivegrowth is defined by a formula that measures the three‐year average rateof change in direct written premiums plus written premiums assumedfrom non‐affiliates less written premiums ceded to non‐affiliates. If the

5There are several theories as to why the “aging phenomenon” occurs, but there has been noconclusive proof offered in the academic literature to identify the source of the risk. SeeD’Arcy and Gorvett (2004) for a more complete discussion.


average growth rate is above 10 percent, then a growth risk penalty of upto 13.5 percent of aggregate reserves is levied.

Interestingly, while the basic RBC requirement for reserve risk iscalculated on a by‐line basis, the risk charge for excessive premium growthis calculated on the aggregate book of business and applied to aggregatereserves. Thus, a company could have extremely high growth in one lineof business such as workers compensation while it is simultaneouslyreducing its commercial general liability business. The result would be thatthere would be no excess growth risk recognized because the growth inone line was offset by shrinkage in the other. Similarly, a firm with a stablebook of workers compensation insurance in runoff could trigger significantRBC charges from growth in its fire insurance business. If the firm hasexcess premium growth, the RBC charge is applied to all reserves and notjust the reserves resulting from the rapidly growing line of business.

Part of the original rationale in using aggregate premiums was thatthere might be spillover to other lines of business. That is, if there wasexcessive growth on a company‐wide basis, the strain on the claims depart‐ment could lead to increased errors even in those lines that were notdirectly experiencing excessive growth. Ultimately, this is an empiricalquestion that this research hopes to address. Feldblum (1996) also cites theconcern that managers of an insurance group could disguise financialweakness by shifting blocks of business among the member companies.The excess growth charge is therefore calculated on a group basis ratherthan a company‐specific basis. Given the proliferation of intercompanypooling arrangements, this seems to be a valid concern, and one that is alsosubject to empirical testing.

PAST RESEARCH ON RESERVE ERRORS

Extending back more than four decades, there is a wealth of researchon loss reserve estimation error. Early research was focused on the impactof reserving error on industry aggregate estimates and, to a limited extent,on insurer solvency. Subsequent research, particularly in the accountingliterature, has attempted to measure the degree to which insurers manip‐ulate reserves to manage earnings. A body of literature has also evolvedwhich measures the solvency risk associated with loss reserve develop‐ment. Over the years, several different measures of reserve error haveappeared in the literature.

In some of the earliest work, Anderson (1971) suggested two potentialmethods of measuring loss reserve development error: the loss reservedifference and the loss reserve adjustment. Anderson defined the loss reserve


difference as the initial reserve for a specific calendar‐accident year less thedeveloped reserve for the same calendar‐accident year measured fouryears later (e.g., incurred losses for accident year 1960 as of 12/31/1960minus incurred losses for accident year 1960 as of 12/31/1964). The lossreserve adjustment was defined as the one‐year development in an insurer’saggregate unpaid losses (e.g., incurred losses for accident years 1955–1959as of 12/31/1959 minus incurred losses for accident years 1955–1959 as of12/31/1960). The loss reserve difference approach essentially tracks reserveerrors for individual accident years, while the loss reserve adjustmentapproach tracks aggregate reserve errors for a bundle of accident years.Figure 1 illustrates the two approaches using a modern version of ScheduleP Part 2.

Although Anderson (1971) wrote about changes in incurred losses, theloss reserve difference and the loss reserve adjustment actually measurechanges in reserves. Total incurred losses can be classified by their settle‐ment status, as shown in Figure 2. Paid losses on closed claims and/or onclaims that are still in the process of being settled are known with certainty.Although some closed claims will be reopened, the amount that hasalready been paid is known.6 Uncertainty creeps into the loss estimates forclaims that are still being investigated or negotiated. When reported, theseclaim amounts are estimates of the ultimate incurred losses. For someclaims, the estimates are relatively simple and there is little variation. Forothers, particularly those that are the subject of litigation or involve long‐term medical issues, the estimates are subject to significant variation. Thefinal category of incurred losses is the unreported claims, commonlyreferred to by the acronym “IBNR” (Incurred But Not Reported) losses. Bydefinition, loss reserves set aside for these claims are strictly estimates.Insurers arrive at the estimates for these claims using historical claimsemergence patterns, forecasts of cost inflation, and actuarial judgment.

If an insurer were a perfect forecaster, each claim dollar for eachparticular accident year would make an orderly transition through each ofthese stages of incurred losses: from unreported to reported to settled topaid. That is, as claims are reported and a specific (case) reserve is estab‐lished for that claim, the IBNR reserve would decline by the same amount.As the claim is paid, the case reserve should drop by exactly the sameamount as the loss payment. Any difference in the incurred loss estimatestems from the unpaid portion. However, insurers are not perfect forecast‐ers, and systematic errors have been noted by a number of researchers.

6Some claims that have been settled for a known amount have not yet been paid because ofinherent delays in the transfer of funds from insurer to claimant, but those amounts areknown as well.


Fig. 1. Sched

ule P Part 2 incurred loss development data.

Line

number

Accident

year

Incurred losses and LAE rep

orted at year end

Development

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

One‐

year

Two‐

year

1Prior

12

34

56

78

910

100

200

21998

1112

1314

1516

1718

1920

101

201

31999

XXXX

2122

2324

2526

2728

29102

202

42000

XXXX

XXXX

3031

3233

3435

3637

103

203

52001

XXXX

XXXX

XXXX

3839

4041

4243

44104

204

62002

XXXX

XXXX

XXXX

XXXX

4546

4748

4950

105

205

72003

XXXX

XXXX

XXXX

XXXX

XXXX

5152

5354

55106

206

82004

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

5657

5859

107

207

92005

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

6061

62108

208

102006

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

6364

109

XXXX

112007

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

65XXXX

XXXX

12Totals

110

209

The four‐year loss reserve difference for accident year 2003 as of 12/31/2007 is 51–55.

The four‐year loss reserve ad

justment from 12/31/2003 to 12/31/2007 is the sum of (6 + 16 + 25 + 33 + 40 + 46 + 51) minus the sum of (10 + 20 +

29 + 37 + 44 + 50 + 55).

Line 12 of the sched

ule rep

orts the one‐year loss reserve ad

justment an

d the tw

o‐year loss reserve ad

justment, w

hich are shown as 110 an

d

209, respectively.


Most of the prior research into reserve estimation error has studied

systematic industry‐wide misstatements, income manipulation explana‐tions for reserving practices, and/or solvency‐related reserving issues.Early research (e.g., Forbes, 1970 and Anderson, 1971) found systematicreserve errors in samples of insurers in the 1940s, 1950s, and 1960s. Ander‐son (1971) also put forth the idea of deliberate manipulations by insurersto smooth earnings. Subsequent research by Smith (1980), Weiss (1985), andGrace (1990) looked for evidence of deliberate manipulations meant tosmooth earnings, to disguise financial instability, or to manipulate taxobligations.7

Petroni (1992) shows evidence of reserving practices being used tosmooth earnings to avoid regulatory scrutiny. However, recently publishedresearch (Grace and Leverty 2012) suggests that reserve errors are morelikely a function of reserves being inherently difficult to set as an alternativeinterpretation of some of these early findings. Petroni and Shackelford(1999) found manipulation of premiums and losses across states in an effortfor insurers to minimize their tax burden. Grace (1990) and Cummins andGrace (1994) further show insurers may be manipulating reserves to reduce

7These early papers were hampered by the relatively rudimentary reporting in the NAICannual statement blank. In 1989, loss reserve reporting in Schedule P was expanded to tenfull years and additional of lines of business were reported. This trend in enhanced report‐ing continued into the 1990s as the NAIC added more lines of business and sought toenhance the reporting to conform to the risk‐based capital program that was under develop‐ment at the time.

Fig. 2. Breakdown of incurred losses by settlement status.


their tax liability. More recently, Eckles and Halek (2010) and Eckles et al.(2011) show a relationship between reserve error and managerial compen‐sation. Hoyt and McCullough (2010) found evidence that insurers withrelatively low risk‐based capital ratios manipulate earnings throughreserve estimations.

From a regulatory perspective, Grace and Leverty (2009) found evi‐dence that insurers in stringently regulated states tended to manipulatereserves so as to justify price increases. However, Grace and Leverty (2012)ultimately conclude that the bulk of reserve errors were the result ofestimation error rather than deliberate manipulation. They also found thatIBNR reserves had relatively little impact and were not the primary sourceof reserve manipulation, contrary to Aiuppa and Trieschmann (1987), whoconcluded that the IBNR reserves were the most susceptible to deliberatemanipulation. Kerdpholngarm (2007) proposes that actuarial methods andpractices can generate systematic reserve errors as well.

While there is ample evidence that systematic errors exist, the specificimpact of growth on those errors has not been fully developed. Mostreserve error research focuses on aggregate reserves, and there is very littleresearch into the effect of these factors on individual lines of business. Thisresearch extends the literature by measuring the impact of these variousfactors on the individual lines of business within each firm. We furtherextend the literature by tracking the effect on individual accident years, sothat the same block of policies that were added to the business mix in thewake of the excessive premium growth period are evaluated.

RESEARCH DESIGN

The data for this research comes from the NAIC financial statementdatabase. We employ data from statement years 1998 through 2007. Wemeasure the by‐line reserve error bias for these major lines of business:

NAIC Line Line Description

A Homeowners/Farmowners Multi Peril

B Private Passenger Auto Liability

C Commercial Auto Liability

D Workers Compensation

E Commercial Multi Peril

FA Medical Malpractice—Occurrence

FB Medical Malpractice—Claims Made


The restriction on the lines of business arises from data limitations inthe NAIC annual statement blank. One of the key research questions iswhether claims counts serve as a better proxy for reserve risk than premi‐ums. Those claims counts are available in Schedule P Part 5, but only forthe lines of business shown here. The initial claim count data from that partof Schedule P is our proxy for exposures since true exposure counts are notavailable through the publicly reported data.8

It is important to distinguish reserve development from incurred lossdevelopment. As an example, consider two insurers, A and B, that bothreport $10 million of incurred losses for Accident Year 2014. Insurer A’sestimate includes $2 million of paid losses during 2014 and $8 million ofunpaid loss reserves, while Insurer B’s estimate includes $8 million of paidlosses during 2014 and $2 million of unpaid loss reserves. One year later,both insurers revise their estimate of their 2014 accident year incurredlosses to $11 million. While both made a $1 million error, the reserve baseson which the error was made are substantially different. The reserveestimation error and its effect on surplus, which the NAIC’s RBC formulaand A.M. Best’s BCAR formula are meant to address, is much greater on apercentage basis for Insurer B than for Insurer A.

We calculate reserve error growth as the natural log of the ratio of thedeveloped estimate of the original accident year reserve divided by theinitial estimate of the accident year reserve by major line of business usingthe following statistic:

Reserve Error Growthx, y =

ln[(Incurredx, y, t = 3 – Paidx, y, t = 0)/(Incurredx, y, t = 0 – Paidx, y, t = 0)]

HA General Liability—Occurrence

HB General Liability—Claims Made

RA Products Liability—Occurrence

RB Products Liability—Claims Made

8Interestingly, A.M. Best is able to collect exposure data from insurers and incorporates thatinformation in their BCAR formula. Presumably, that data would be available to regulatorsas well, but it is not included in the publicly available data reported in the annual statement.Developed claim counts are available by accident year in Schedule P Part 1, but not the orig‐inal estimate, which we use to measure accident year to accident year growth.


where x is the line of business, y is the accident year, and t is the develop‐ment year. This is the loss reserve difference statistic, originally proposed byAnderson (1971). It measures the change in the original estimate of theaccident year unpaid reserve over a three‐year time horizon. For example,the 2004 accident year incurred losses as of 12/31/2004 minus the accidentyear paid losses for the same accident year at the same point in timeprovides the original estimate of the unpaid portion of incurred losses.Subsequent re‐estimates of that original reserve constitute reserve error. Inour example, the reserve error growth for accident year 2004 would be thedeveloped original estimate as of 12/31/2007 divided by the original esti‐mate as of 12/31/2004.

Much of the literature on reserve smoothing has used the loss reserveadjustment statistic, although usually for periods of four or five yearsrather than the single year proposed by Anderson (1971). We use the lossreserve difference approach to better isolate the effect of growth on aparticular block of business, assuming that the excessive growth has amuch greater impact on the new business coming into the firm than on theexisting business. Assuming that there is no systematic estimation error,this statistic should have a mean of zero. If an insurer records a negative(positive) value, then the original accident year reserve was over‐stated(under‐stated).

We use three years as the duration for reserve development as atradeoff between accuracy and degrees of freedom. For most lines ofbusiness, three years is a relatively short duration for estimating theultimate value of the accident year (AY) incurred losses. Many of the earlystudies on reserve development used either four years (e.g., Forbes, 1970;Anderson, 1971; Weiss, 1985; Grace, 1990) or five years (e.g., Smith, 1980;Petroni, 1992; Harrington and Danzon 1994) as the development horizon.These early studies of loss reserving errors were restricted by data avail‐ability because prior to 1989, the NAIC annual statement only showed fiveyears of development data. Kazenski et al. (1992) showed that as little astwo years were sufficient to measure systematic errors for the industry, butalso found that the number of years required for accurate forecasts ofultimate incurred losses for individual insurers was substantially longer.

Given that there is no theoretical justification for using five years asthe development horizon, we took steps to evaluate alternative develop‐ment horizons. We computed the proportion of insurers in our sample thatreported at least 75 percent of total incurred losses as paid losses bydevelopment year. The paid losses are not subject to any material develop‐ment, so the higher the proportion of total incurred losses that have beenfixed, the less the potential for adverse development.


We also computed the mean absolute percentage error (MAPE) ofreserve development by line of business. The percentage error is definedas the developed initial reserve divided by the original initial reserve minus1. We winsorized the data to alleviate outlier issues and then computed themean of the absolute value of the result. The incremental change in theMAPE for each progressive development year shows that the initial devel‐opment year captures the bulk of the reserve development error. Forexample, Line A shows 18.5% MAPE at the AYt+4 development point, whichis the fourth development after the initial accident year where the losseswere recorded. Of that total MAPE, 15.1% comes from the first develop‐ment year, 2.3% in the second development year, 0.8% in the third devel‐opment year, and 0.3% in the fourth development year. Although there aredifferences between the lines of business, the bulk of the variability comesin the first three development years beyond the initial accident year.

Our goal is not to estimate the ultimate liability, but rather to identifyfactors that predict systematic errors. Therefore, a shorter time horizon isacceptable if it picks up the bulk of the errors. Our use of a three‐year lossreserve development horizon for the individual accident years providessome measure of the magnitude of errors, as the bulk of errors related togrowth should show up fairly quickly. The three‐year horizon by no meanscaptures the full impact of reserving errors for each line, but then neither

Table 1. Percentage of Observations Where Paid/Incurred Is Greater Than or Equal To 75% by Development Year

Line AYt AY t+1 AY t+2 AY t+3 AY t+4 AY t+5 AY t+6 AY t+7 AY t+8 AY t+9

A 24% 96% 99% 100% 100% 100% 100% 100% 100% 100%

B 1% 31% 87% 98% 99% 100% 100% 100% 100% 100%

C 0% 4% 28% 84% 97% 99% 99% 100% 100% 100%

D 1% 4% 22% 50% 68% 78% 83% 90% 95% 95%

E 2% 22% 46% 77% 94% 97% 99% 99% 99% 99%

FA 0% 1% 2% 11% 31% 62% 81% 89% 93% 93%

FB 1% 1% 9% 42% 73% 90% 94% 98% 99% 99%

HA 4% 8% 13% 25% 48% 70% 81% 90% 94% 95%

HB 1% 3% 13% 36% 57% 77% 90% 95% 98% 98%

RA 0% 1% 3% 7% 24% 40% 58% 75% 86% 85%

RB 1% 5% 14% 33% 52% 69% 82% 92% 96% 92%


Table 2. Panel A: Mean Absolute Percentage Error of Initial Reserve Development

Line AY t+1 AY t+2 AY t+3 AY t+4 AY t+5 AY t+6 AY t+7 AY t+8 AY t+9

A 15.1% 17.3% 18.2% 18.5% 18.5% 18.4% 18.2% 18.0% 18.1%

B 10.2% 13.2% 14.7% 15.5% 15.8% 15.9% 16.1% 16.1% 16.2%

C 12.7% 17.2% 20.2% 21.5% 22.3% 22.6% 22.6% 22.3% 21.7%

D 11.8% 16.5% 19.9% 21.5% 22.8% 24.0% 24.7% 24.0% 22.8%

E 14.7% 18.6% 20.8% 22.3% 23.5% 24.4% 24.7% 25.0% 24.6%

FA 21.5% 34.2% 43.6% 50.4% 54.1% 55.6% 56.0% 55.8% 52.7%

FB 15.0% 23.1% 28.7% 32.5% 34.7% 36.1% 37.7% 35.4% 32.9%

HA 14.8% 20.2% 24.7% 27.7% 29.6% 31.0% 31.0% 30.7% 30.3%

HB 17.6% 25.3% 32.4% 37.7% 40.1% 41.0% 40.5% 39.5% 38.2%

RA 20.1% 27.9% 34.5% 39.8% 45.4% 49.6% 50.8% 49.6% 46.6%

RB 21.6% 35.8% 43.8% 46.1% 46.7% 49.9% 42.8% 41.6% 43.1%

Panel B: Marginal Change in Mean Absolute Percentage Error of Initial Reserve Development

Line AY t+1 AY t+2 AY t+3 AY t+4 AY t+5 AY t+6 AY t+7 AY t+8 AY t+9

A 15.1% 2.3% 0.8% 0.3% –0.1% 0.0% –0.3% –0.2% 0.1%

B 10.2% 3.0% 1.5% 0.8% 0.3% 0.1% 0.2% –0.1% 0.1%

C 12.7% 4.5% 3.0% 1.3% 0.9% 0.3% 0.0% –0.3% –0.5%

D 11.8% 4.6% 3.4% 1.6% 1.3% 1.2% 0.6% –0.7% –1.2%

E 14.7% 3.9% 2.2% 1.5% 1.3% 0.8% 0.3% 0.3% –0.4%

FA 21.5% 12.7% 9.4% 6.8% 3.7% 1.5% 0.4% –0.2% –3.1%

FB 15.0% 8.1% 5.6% 3.8% 2.2% 1.3% 1.6% –2.3% –2.5%

HA 14.8% 5.3% 4.5% 3.0% 2.0% 1.4% 0.0% –0.2% –0.4%

HB 17.6% 7.7% 7.1% 5.3% 2.4% 1.0% –0.5% –1.1% –1.3%

RA 20.1% 7.9% 6.6% 5.3% 5.6% 4.2% 1.3% –1.3% –3.0%

RB 21.6% 14.3% 7.9% 2.3% 0.7% 3.2% –7.1% –1.2% 1.4%


does the five‐year development horizon. We assume that random errorswill for the most part emerge fairly quickly following a rapid influx of newpolicyholders, which supports the use of a shorter development horizon.9

To avoid the impact of outlier values, we limit our sample to insurerswith assets or surplus equal to or greater than $2,000,000. We also omittedany observations where the initial accident year unpaid loss estimate wasless than $500,000. Additionally, since many insurers participate in inter‐company pooling arrangements where member insurers are assigned afixed percentage of pooled reserve, pool participants that held less thanseventy five percent of the pooled business were also omitted.

While we are primarily interested in the effect of growth on reserveerrors, we also used control variables to test for regulatory effects, incomesmoothing, and other factors that might be affecting reserve errors. Ourfixed effects regression model employed is:

where δt and νi are time and company fixed effects, εi,t is the error term, andthe independent variables are as described below. Prior research has exam‐ined company demographic factors to explain systematic reserve errordifferences. For example, it has been argued that mutual insurers wouldhave less incentive to manipulate results than stock insurers. The fixedeffects model precludes testing for demographics of individual insurersthat do not change from period to period. Similarly, we use time dummiesto pick up differences in the average industry experience for each year. Theexplanatory variables in our model include the following:

9We also analyzed the sample using five‐year development rather than three‐year develop‐ment, and the results were unchanged. There were a handful of instances where the p‐valueof a particular parameter estimate shrank or increased, but the basic results wereunchanged. Of course, that result does not necessarily confirm that three‐year developmentis an adequate time horizon. It simply means that three‐year development is not materiallydifferent than five‐year development when measuring these effects.

ReserveErrorGrowthi t, 0 1AGRi t, 2CLMGRi t,3REGULATORY 4AVGDEVi t, 5IBNRPROPi t,

6SMOOTH 7LSRi t, t vi i t,

+ ++ + +

+ + + + +

=


AGR The average premium growth rate used in the NAIC RBC formula, calculated by the authors based on the formula described in the NAIC RBC’s formula instructions (NAIC, 2009). If excessive growth leads to adverse reserve development, or leads to greater variability in the loss reserve estimates, then this variable should show a positive relationship. If we find a positive relationship between the premium growth and reserve error growth, this would lend credence to the RBC’s growth risk charge. The average growth factor is calculated on the aggregate book of business. For a multi-line insurer, the use of the aggregate growth rate may not be appropriate if the growth is not across-the-boards. That is, if some lines are growing and some are shrinking, the average growth may pick up excessive risk in some lines but not in others.

CLMGR The natural log of the growth in the initial estimate of direct plus assumed claims from accident year t-1 to accident year t, as reported in Schedule P Part 5. Claim counts serve as a proxy, albeit an imperfect one, for exposure growth. If the assumption that growth leads to under-reserving is correct, the sign on this variable should be positive. Note that this measure is specific to the particular line of business, unlike the AGR risk measure.

REGULATORY The Company Action Level RBC reported by each insurer divided by total admitted assets for each accident year. This variable is meant to capture the incentive for insurers to avoid regulatory scrutiny. Other proxies for regulatory scrutiny used in the past include IRIS ratio results and surplus to assets. The RBC results are a better measure of regulatory scrutiny because the formula results define the point at which regulators begin taking action. The higher the RBC requirement per dollar of assets, the more likely regulatory scrutiny would be triggered. This would be the case regardless of whether the RBC formula is accurate or not. An insurer could quickly improve its surplus position by under-reserving and thus avoid triggering the RBC formula regulatory actions. Therefore, the higher the value of REGULATORY the greater the incentive to under-reserve. This incentive suggests a positive coefficient on this variable if insurers with positive reserve development (those that have been under-reserved) also have relatively higher RBC requirements.


AVGDEV The natural log of the company development value as computed in the NAIC’s RBC formula (NAIC, 2009, p. PR016.2), by line of business. This value is a measure of the company’s average over- or under-estimation of incurred losses in the past ten years and is used to adjust the company’s reserve risk risk-based capital (R4) to recognize company-specific risk. The computation takes the sum of the developed incurred losses and defense and cost containment expenses for the past nine accident years and divides by the sum of the initial estimates for those same incurred losses and defense and cost containment expenses. If the initial incurred losses for any accident year is negative, the sum of the initial incurred losses is zero, or the current estimated incurred losses for any accident year is zero or less, the company development is set equal to the industry average. This calculation results in a ratio that, if greater than (less than) 1.0, indicates that the insurer has, on average, underestimated (overestimated) the initial reserves during the past nine years. A priori, it is assumed that an insurer that has traditionally underestimated its reserves in the past will underestimate this year’s reserves, so the expected sign for this variable is positive.

IBNRPROP The proportion of IBNR reserves included in the initial estimate of incurred losses. As discussed in Grace and Leverty (2012), IBNR reserves are the easiest reserves to manipulate. A negative parameter estimate would suggest that the higher the proportion of IBNR reserves in the mix, the more likely the insurer is over-reserving rather than under-reserving, consistent with the income smoothing hypothesis. Low proportions of IBNR may suggest that the insurer is under-estimating the reserves, which could lead to positive reserve development. We would expect to see a negative parameter estimate with this predictor variable.

SMOOTH This variable serves as a proxy to capture the tax incentive for insurers to overstate this year’s incurred losses and is similar to a measure found in Grace (1990). The numerator is a measure of the taxable income for the accident year and is the sum of underwriting gain plus net investment gain plus twenty percent of the change in the unearned premium reserve. This result is then scaled by total assets. We modify the statistic used by Grace because beginning in 1987, tax laws were changed to require insurers to discount loss reserves when computing taxable income, which would create an incentive to over-estimate this year’s reserves in order to save on taxes. Insurers are also required to deduct twenty percent of the change in the net unearned premium reserve from their expenses when calculating taxable income. The higher the taxable income per dollar of assets, the higher the incentive to over-state reserves. Therefore, a negative value for the parameter estimate would support the tax manipulation hypothesis, implying that insurers with high amounts of taxable income would have over-estimated reserves, not under-estimated reserves.


RESULTS

Summary statistics for the dependent and independent variables areshown in Panels A and B of Table 3. Regression results are shown in PanelsA and B of Table 4. Although not reported further, the fixed effects forindividual companies and accident years were statistically significant.

One of our key research questions was whether the premium growthmeasure used in the NAIC RBC formula (AGR) is a consistent predictor ofreserve error. Specifically, a positive and significant coefficient on AGRwould suggest a positive relationship between the premium growth ratecurrently being used to assess capital standards for insurers and theobserved reserve error problems that the RBC formula is meant to assuage.We find a positive and significant result for only the two auto liability lines(line B (private passenger) and line C (commercial)).10 That is, only thesetwo lines show support for the existing NAIC growth risk charge in theRBC formula. In no other lines is the coefficient significant. Further, thesigns are not consistent from line to line.

The current RBC formula considers the growth rate of total premiums.As discussed above, a multi‐line insurer could expand one line of business,contract another, and have no net growth. However, this apparent zerogrowth could mask tremendous growth in a particular line. Our results onAGR highlight this potential problem. Finding a significant coefficient ona couple of lines and finding no significance on all other lines suggests thatthe current measure of premium growth does a poor job at predicting theeffect of growth on reserve risk.

However, the alternative measure of growth risk, claim counts(CLMGR), was consistently positive and was statistically significant in themajority of the lines of business.11 We use claim counts to serve as a proxy

LSR The percentage of loss sensitive reserves to the total reserves, which is reported in Schedule P Part 7. Loss sensitive business transfers underwriting risk from the insurer back to the insured. Having a higher percentage of loss sensitive business should therefore reduce reserving errors. Loss sensitive reserves are more common in commercial lines of business. A priori, we would expect a negative coefficient on the variable, meaning that insurers with large amounts of loss sensitive business tend to have lower reserve errors.

10When using a five year development, we again find a positive relationship between line C,but not B. Also, using five years, line RA (Products liability occurrence‐based forms) wassignificant. Again, we note a general inconsistency in the results, suggesting AGR to be apoor indicator of reserve risk.


Table 3. P

anel A: Summary Statistics for Dep

endent an

d Indep

endent Variables by Line of Business, A–E

A. H

omeowners/Farmowners Multi Peril

B. Private Passenger Auto Liability

Description

Mean

StdDev

Min.

Max.

Description

Mean

StdDev

Min.

Max.

Reserve Error Growth

–0.123

0.390

–2.943

3.000


–0.052

0.304

–2.905

3.000

Premium Growth Rate

0.040

0.076

0.000

0.300

Premium Growth Rate

0.054

0.089

0.000

0.300

Claim Count Growth Rate

0.011

0.514

–2.927

3.000


0.060

0.515

–2.685

3.000

RBC as % of Admitted Assets

0.030

0.052

–0.193

0.191


0.029

0.057

–0.198

0.195

Compan

y R4 Experience Adjustment

–0.016

0.075

–0.679

0.551

Compan


–0.017

0.088

–1.057

0.716

IBNR as % of Initial Incurred

0.148

0.141

0.000

1.000


0.249

0.153

0.000

1.000

Net Income as % of Admitted Assets

0.231

0.272

0.000

1.988


0.227

0.264

0.000

1.988

Percent Loss Sensitive Reserves

0.012

0.095

0.000

1.000


0.007

0.066

0.000

1.000

C. C

ommercial Auto Liability

D. W

orkers Compensation

Description

Mean

StdDev

Min.

Max.

Description

Mean

StdDev

Min.

Max.


–0.011

0.418

–2.963

3.000


–0.070

0.404

–2.944

2.463

Premium Growth Rate

0.049

0.083

0.000

0.300

Premium Growth Rate

0.056

0.091

0.000

0.300


0.026

0.491

–2.930

3.000


0.010

0.524

–2.996

3.000


0.033

0.049

–0.192

0.199


0.034

0.048

–0.197

0.198

Compan


–0.013

0.150

–1.366

1.376

Compan


–0.017

0.143

–0.923

1.398


0.390

0.200

0.000

1.000


0.447

0.199

0.000

1.000


0.219

0.253

0.000

1.649


0.210

0.250

0.000

1.810


0.011

0.080

0.000

1.000


0.023

0.102

0.000

1.000

E. Commercial M

ulti Peril

Description

Mean

StdDev

Min.

Max.


–0.055

0.441

–2.828

2.596

Premium Growth Rate

0.046

0.079

0.000

0.300


0.010

0.513

–2.879

3.000


0.031

0.049

–0.193

0.195

Compan


–0.004

0.152

–1.900

1.383


0.337

0.192

0.000

1.000


0.226

0.257

0.000

1.649


0.007

0.062

0.000

1.000


Table 3. P

anel B: Summary Statistics for Dep

endent an

d Indep

endent Variables by Line of Business, Lines FA‐RB

FA. M

edical M

alpractice—

Occurrence

FB. M

edical M

alpractice—

Claim M

ade

Description

Mean

StdDev

Min.

Max.

Description

Mean

StdDev

Min.

Max.


–0.004

0.737

–2.989

3.000


–0.051

0.473

–2.089

2.954

Premium Growth Rate

0.053

0.082

0.000

0.300

Premium Growth Rate

0.070

0.098

0.000

0.300


–0.065

0.658

–2.890

2.944


0.028

0.521

–2.858

3.000


0.028

0.048

–0.188

0.182


0.030

0.049

–0.188

0.183

Compan


–0.047

0.403

–1.997

1.387

Comparry R4 Experience Adjustment

–0.071

0.200

–1.437

1.248


0.831

0.193

0.000

1.000


0.481

0.290

0.000

1.000


0.217

0.198

0.000

1.497


0.252

0.292

0.000

1.650


0.013

0.096

0.000

1.000


0.004

0.033

0.000

0.381

HA. General Liability—Occurrence

HB. General Liability—Claim

s Mad

e

Description

Mean

StdDev

Min.

Max.

Description

Mean

StdDev

Min.

Max.


–0.116

0.550

–2.952

3.000


–0.162

0.592

–2.956

2.376

Premium Growth Rate

0.051

0.084

0.000

0.300

Premium Growth Rate

0.063

0.094

0.000

0.300


0.007

0.602

–2.884

3.000


0.036

0.649

–2.878

3.000


0.035

0.050

–0.197

0.199


0.039

0.052

–0.188

0.200

Compan


–0.047

0.250

–1.601

1.418

Compan


–0.078

0.273

–2.083

1.386


0.653

0.235

0.000

1.000


0.647

0.264

0.000

1.000


0.239

0.276

0.000

1.858


0.266

0.298

0.000

1.791


0.011

0.077

0.000

1.000


0.006

0.045

0.000

0.854

RA. P

roducts Liability—Occurrence

RB. P

roducts Liability—Claim

s Made

Description

Mean

StdDev

Min.

Max.

Description

Mean

StdDev

Min.

Max.


–0.118

0.670

–2.874

2.738


–0.272

0.783

–2.906

2.073

Premium Growth Rate

0.046

0.078

0.000

0.300

Premium Growth Rate

0.062

0.092

0.000

0.300


–0.011

0.638

–2.639

3.000


0.072

0.830

–2.358

3.000


0.032

0.049

–0.181

0.199


0.037

0.046

–0.181

0.181

Compan


–0.037

0.358

–1.530

1.379

Compan


–0.105

0.311

–0.993

1.377


0.817

0.191

0.000

1.000


0.757

0.255

0.000

1.000


0.239

0.240

0.000

1.603


0.230

0.224

0.000

1.449


0.020

0.113

0.000

1.000


0.010

0.101

0.000

1.000


Table 4. P

anel A: Fixed Effects Results (Lines A through E)

Dep

end

ent V

aria

ble:

Res

erve

Err

or G

row

thA

BC

DE

Prem

ium

Gro

wth

Rat

e 0.

0005

***

0.15

06**

*0.

3193

***

0.09

62**

*–0

.038

2***

(AG

R)

(0.1

053)

**

(0.0

617)

**

(0.0

978)

**

(0.0

951)

**

(0.1

105)

**

Cla

im C

ount

Gro

wth

Rat

e 0.

0284

***

0.07

36**

*0.

0466

***

0.05

78**

*0.

0455

***

(CLM

GR

)(0

.012

5) *

*(0

.008

5) *

*(0

.013

4) *

*(0

.013

0) *

*(0

.013

5) *

*

RB

C a

s %

of A

dm

itte

d A

sset

s –0

.153

6***

0.04

11**

*–0

.051

4***

0.32

72**

*0.

0941

***

(Reg

ulat

ory)

(0.0

526)

**

(0.0

363)

**

(0.0

553)

**

(0.0

569)

**

(0.0

641)

**

Com

pany

R4

Expe

rien

ce A

djus

tmen

t –0

.482

0***

–0.4

276*

**–0

.497

4***

–0.2

595*

**–0

.393

5***

(AV

GD

EV)

(0.1

296)

**

(0.0

747)

**

(0.0

629)

**

(0.0

606)

**

(0.0

780)

**

IBN

R a

s %

of I

niti

al In

curr

ed–1

.530

2***

–0.8

907*

**–1

.050

5***

–0.7

415*

**–1

.099

4***

(IN

BRPR

OP)

(0.0

669)

**

(0.0

435)

**

(0.0

501)

**

(0.0

508)

**

(0.0

533)

**

Net

Inco

me

as %

of A

dmit

ted

Ass

ets

–0.2

016*

**0.

3285

***

–0.0

890*

**–0

.093

1***

0.11

39**

*

(SM

OO

TH)

(0.1

342)

**

(0.0

874)

**

(0.1

576)

**

(0.1

574)

**

(0.1

613)

**

Perc

ent L

oss

Sens

itiv

e R

eser

ves

0.10

98**

*–0

.184

4***

0.05

27**

*0.

1898

***

0.15

29**

*

(LSR

)(0

.079

0) *

*(0

.072

6) *

*(0

.094

2) *

*(0

.083

5) *

*(0

.121

4) *

*

Con

stan

t0.

1716

***

0.06

95**

*0.

3527

***

–0.0

785*

**0.

1998

***

(0.0

453)

**

(0.0

328)

**

(0.0

503)

**

(0.0

502)

**

(0.0

555)

**

Num

ber

of O

bser

vati

ons

3584

4920

3677

3383

3542

Num

ber

of C

ompa

nies

571

769

592

561

573

R-s

quar

ed0.

1998

0.16

370.

1858

0.19

280.

1861

***,

**,

* r

epre

sent

sig

nifi

canc

e at

the

1%, 5

%, a

nd 1

0% le

vels

, res

pect

ivel

y.


Table 4. P

anel B: Fixed Effects Results (Lines FA through RB)

Dep

end

ent V

aria

ble:

Res

erve

Err

or G

row

thFA

FBH

AH

BR

AR

B

Prem

ium

Gro

wth

Rat

e –0

.460

2***

0.00

99**

*0.

1648

***

0.08

98**

*0.

4929

***

–0.8

902*

**

(AG

R)

(0.3

824)

**

(0.1

842)

**

(0.1

232)

**

(0.1

810)

**

(0.3

463)

**

(1.1

318)

**

Cla

im C

ount

Gro

wth

Rat

e0.

0583

***

0.08

86**

*0.

0510

***

0.02

38**

*0.

0575

***

0.08

57**

*

(CLM

GR

)(0

.035

3) *

*(0

.025

4) *

*(0

.013

6) *

*(0

.019

2) *

*(0

.030

3) *

*(0

.086

8) *

*

RB

C a

s %

of A

dm

itte

d A

sset

s0.

2111

***

0.21

35**

*0.

0284

***

0.21

79**

*0.

3565

***

1.01

86**

*

(Reg

ulat

ory)

(0.2

825)

**

(0.0

918)

**

(0.0

656)

**

(0.0

837)

**

(0.2

180)

**

(0.5

956)

**

Com

pany

R4

Expe

rien

ce A

djus

tmen

t –0

.203

4***

–0.3

965*

**–0

.267

2***

–0.1

463*

**–0

.374

1***

–0.6

939*

**

(AV

GD

EV)

(0.0

934)

**

(0.0

842)

**

(0.0

486)

**

(0.0

703)

**

(0.0

863)

**

(0.3

053)

**

IBN

R a

s %

of I

niti

al In

curr

ed–0

.815

8***

–0.6

516*

**–0

.706

9***

–0.8

622*

**–1

.169

6***

–0.8

332*

**

(IN

BRP

RO

P)

(0.1

653)

**

(0.0

799)

**

(0.0

578)

**

(0.0

851)

**

(0.1

505)

**

(0.2

895)

**

Net

Inco

me

as %

of A

dmit

ted

Ass

ets

–0.5

688*

**0.

1819

***

0.04

59**

*0.

0655

***

0.73

56**

*–1

.355

5***

(SM

OO

TH)

(0.6

383)

**

(0.3

207)

**

(0.1

951)

**

(0.3

142)

**

(0.4

981)

**

(1.8

539)

**

Perc

ent L

oss

Sens

itiv

e R

eser

ves

–0.6

549*

**0.

6747

***

–0.0

350*

**–0

.045

7***

–0.0

635*

**0.

4389

***

(LSR

)(0

.494

3) *

*(0

.533

7) *

*(0

.131

0) *

*(0

.371

2) *

*(0

.293

6) *

*(0

.726

6) *

*

Con

stan

t0.

6125

***

–0.0

216*

**0.

2034

***

0.15

08**

*0.

4889

***

–0.1

745*

**

(0.2

089)

**

(0.0

785)

**

(0.0

661)

**

(0.0

953)

**

(0.1

949)

**

(0.4

814)

**

Num

ber

of O

bser

vati

ons

783

1099

3961

1670

959

195

Num

ber

of C

ompa

nies

129

214

645

292

181

47

R-s

quar

ed0.

0887

0.18

740.

0812

0.10

830.

1431

0.20

01

***,

**,

* r

epre

sent

sig

nifi

canc

e at

the

1%, 5

%, a

nd 1

0% le

vels

, res

pect

ivel

y.


for exposures as an alternative to premium growth as a measure of growthrisk.12 These results are consistent with those reported in Barth and Eckles(2009), which found that claim counts were a better measure of the under‐writing risk inherent in short‐term changes in loss ratios.13

The measure of systematic over‐ and under‐reserving, AVGDEV (thecompany R4 company experience adjustment), is statistically significantand negative for each line of business, contrary to the expected relationshipwith reserving error. We hypothesized that companies that consistentlyunder‐reserved in the past would continue to under‐reserve into the future,which would suggest that the parameter estimate have a positive sign.Upon closer examination of the results, we noted anomalies in the lengthof the development period measured in the R4 experience adjustmentfactor and the pattern of systematic errors in industry‐wide results. If thereis a reserving cycle that differs in periodicity from the reserve developmentperiod used in the NAIC RBC formula, then we might expect to see similarpatterns. This potential mismatch between loss reserve cycles and thedevelopment factor used in the NAIC RBC formula is an area for futureresearch.

The measure of regulatory scrutiny, RBC as a percentage of totaladmitted assets, provided mixed results for support of the regulatoryscrutiny hypothesis that reserve estimation errors are driven by insurers’desires to avoid regulatory attention by under‐stating reserves. In a fewlong‐tailed liability lines, we do find a positive and significant coefficient.In homeowners’, however, we find a negative and significant coefficient.

Our results do not support the tax smoothing hypothesis that suggeststhat insurers manipulate their reserves in order to minimize taxes. Theparameter estimate for our measure of the tax incentive was generally notstatistically significant except for one line of business, private passengerauto liability. Individual insurers undoubtedly make business decisionsbased on the tax consequences, but it is arguable whether that is an over‐arching concern for the average insurer. There are a host of other consid‐erations that go into the estimation of reserves, and while taxes may wellbe a consideration, the complexity of the actual tax system makes it very

11Using five‐year development, the results are again effectively the same.12Again, we recognize that claims counts are not necessarily a perfect measure of exposurecount because of their natural statistical variability, because of their ability to be manipu‐lated, because they are subject to catastrophe risk, and because they are not determined in aconsistent manner across insurers (Barth and Eckles, 2009). 13We emphasize, though, that “better” does not mean “best.” Some form of exposure count,even a policy count, would be an improvement over the current system.


difficult to come up with an adequate proxy that measures individualinsurers’ tax incentives.

The percentage of IBNR in the initial estimate of the incurred losseswas consistently statistically significant and negative, which indicates thatthe greater the proportion of IBNR in the initial reported reserves, the morelikely the insurer will report favorable loss development of existingreserves. This finding is consistent with the results reported in Grace andLeverty (2012), who found that the level of IBNR in total reported reservesdid impact reserve errors, although they reported that the effect wasrelatively small. Hoyt and McCullough (2010) also found evidence thatinsurers under regulatory scrutiny had greater incentives to manipulateIBNR reserves to mask problems. Our results suggest that while themagnitude of the IBNR effect may be relatively small, the percentage ofIBNR included in the reserve estimate is nonetheless one of the strongestpredictor variables that we tested, based on the partial sum of squarescriteria. Since IBNR reserves are often based on historical developmentpatterns, past errors would tend to reinforce current errors. Therefore, ourresults are also consistent with the results reported by Kerdpholngarm(2007), who found that the actuarial practice of using past loss history toforecast future results could exacerbate cyclical reserving errors.

The proportion of loss sensitive business was not a statistically signif‐icant predictor of reserve errors. There are relative few companies report‐ing material amounts of loss sensitive business, which may help to explainthe lack of statistical significance.

CONCLUSIONS AND RECOMMENDATIONS

From a public policy perspective, growth risk has long been a concernof insurance industry stakeholders. Regulators, particularly, are concernedthat insurers which grow too fast may be taking on excessive risk, increas‐ing the probability of insolvency. The NAIC RBC formula has two growthrisk components, one for short‐term underwriting risk (R5 risk) and theother for long‐term reserving risk (R4 risk). Both of these growth riskcomponents use premium growth to measure growth risk and assesscapital charges when average premium growth over the past three yearsexceeds 10 percent. Barth and Eckles (2009) previously showed that pre‐mium growth is a poor measure of short‐term underwriting risk. Weextend that study and show similar results for long‐term reserving risk.Specifically, we show that the aggregate premium growth measureincluded in the NAIC RBC formula seems to be a poor predictor of reserveestimation risk. We find the growth rate of claim counts reported in


Schedule P Part 5 to be a better predictor of reserve risk, although we donot suggest that it is the optimal predictor. What is needed, rather, is anappropriate and consistent measure of exposures.

Our results suggest that there is a problem with the NAIC RBC formulawith respect to measuring growth risk. Specifically, we find that the currentmeasure (premium growth) of long‐term growth risk is not appropriateand may actually serve to exacerbate cyclical over‐ and under‐reservingswings in the industry. This effect was predicted by critics during thedevelopment of the RBC formula in the early 1990s. Studies over the yearshave found that excessive growth is a risk factor in insolvencies, especiallywhen it occurs during a soft market (A.M. Best, 2010a). Our results suggestthat exposure growth (CLMGR), rather than premium growth (AGR), is thetrue underlying cause of financial impairment.

Simplistic measures of premium growth tend to over‐identify thepotential solvency risk. Table 5 shows the percentage of insurance compa‐nies and insurance groups that generated an excessive premium growthcharge as defined in the NAIC RBC formula between 1993 and 2007.14 Incertain years, more than sixty percent of the insurers generate an excessivegrowth risk charge in their RBC results.15 Although the aggregate growthrisk charges are not very large, the impact on individual insurers can be.Therefore, the accuracy of the growth risk charge goes beyond a simpleacademic exercise. California’s largest workers’ compensation insurancecarrier triggered regulatory intervention in the early 2000s, largely basedon the excess growth charge that may or may not have been warranted.

Excessive growth may indeed be a precursor to financial impairment.However, regulatory monitoring systems that routinely assign a highproportion of the regulated population to the “at risk” category producethe wrong set of incentives and incorrect signals to the market. In the wakeof the recent global financial turmoil, there should be additional scrutinyplaced on regulatory monitoring systems to avoid a repeat performance.Our results suggest that premium growth, in and of itself, is not necessarilya source of reserve estimation risk.

14This table is generated by the authors, not the NAIC.15Although the NAIC’s RBC formula is applied only to individual companies and not to theinsurer groups, the formula requires member companies within a group to use group pre‐miums rather than individual company premiums when calculating the excessive growthcharge. The percentage of groups reporting a positive value for the excessive growth ratecharge is higher than the percentage of individual companies in most years, which meansthat the proportion of insurers that actually trigger the excessive growth charge would besomewhat higher than the proportion reported in the table.


REFERENCES

A. M. Best (2001) Best’s Insolvency Study: Property/Casualty Insurers, 1969–1990, A. M.Best Company.

A. M. Best (2006) P/C Financial Impairments: Update for Year‐End 2005, A. M. BestCompany.

A. M. Best (2010a) Best’s Special Report: 1969–2009 Impairment Review, A. M. BestCompany.

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Table 5. Insurer Groups and Companies That Would Incur an Excessive Premium Growth Charge in the NAIC RBC Formula, 1993–2007*

YearNumber of groups

Number with excessive premium growth factor above

zero

% of

total

Number of

companies

Number with excessive

premium growth factor above zero

% of

total

1993 266 114 43% 2,461 1,044 42%

1994 323 169 52% 2,463 1,062 43%

1995 333 167 50% 2,481 1,040 42%

1996 326 147 45% 2,508 981 39%

1997 310 120 39% 2,512 930 37%

1998 314 119 38% 2,517 908 36%

1999 284 105 37% 2,487 871 35%

2000 285 119 42% 2,484 919 37%

2001 290 161 56% 2,473 1,095 44%

2002 295 203 69% 2,449 1,350 55%

2003 288 206 72% 2,439 1,408 58%

2004 298 188 63% 2,486 1,373 55%

2005 293 128 44% 2,502 1,150 46%

2006 306 95 31% 2,513 948 38%

2007 299 77 26% 2,543 847 33%

*Results are based on authors’ calculations using the formula published by the NAIC.


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