adverse selection in reinsurance markets - james r....

Adverse Selection in Reinsurance MarketsJames R. Garvena, James I. Hilliardb and Martin F. GracecaDepartment of Finance, Insurance and Real Estate, Baylor University, One Bear Place #98004, Waco, TX76798-8004, U.S.A.E-mail: [email protected]. Franke College of Business, Northern Arizona University, 20 W. McConnell Dr., Flagstaff, AZ86011, U.S.A.E-mail: [email protected] Risk Management and Insurance at the Robinson School of Business, Georgia State University,P.O. Box 4036, Atlanta, GA 30302-4036, U.S.A.E-mail: [email protected]

This paper looks for evidence of adverse selection in the relationship between primaryinsurers and reinsurers. We test the implications of a model in which informationalasymmetry—and therefore, its negative consequences—decline over time. Our testsinvolve a data panel consisting of U.S. property-liability insurance firms that reported tothe National Association of Insurance Commissioners during the period 1993–2012. Wefind that the amount of reinsurance, insurer profitability, and insurer credit quality allincrease with the tenure of the insurer–reinsurer relationship.The Geneva Risk and Insurance Review (2014) 39, 222–253. doi:10.1057/grir.2014.13

Keywords: reinsurance; adverse selection; asymmetric information

Article submitted 25 October 2013; accepted 23 June 2014; published onlineSeptember 2014

Introduction

This paper empirically explores some implications of adverse selection for thedemand for reinsurance. Typically, the primary insurer ceding the risk (the “cedant”)will have better information about the underlying risk than the reinsurer. The extentto which information is asymmetric depends upon the nature of the underlying risk.For example, we would expect less information asymmetry concerning highfrequency, low severity risk such as automobile physical damage than low frequency,high severity risk such as commercial liability. The greater the informationasymmetry, the greater is the cost of adverse selection to the ceding insurer.However, adverse selection costs may be mitigated through long-standing relation-ships, joint risk sharing, or improved information flows. Therefore, we may expectdifferences in insurer risk policy and strategy depending on the nature of theunderlying risk written by the ceding insurer.

The Geneva Risk and Insurance Review, 2014, 39, (222–253)© 2014 The International Association for the Study of Insurance Economics 1554-964X/14www.palgrave-journals.com/grir/

http://dx.doi.org/10.1057/grir.2014.13

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Jean-Baptiste and Santomero1 provide a formal theoretical analysis of howinformation problems affect the efficiency of the allocation of risk between cedantsand their reinsurers. Their theory shows that long-term implicit contracts2 allow theinclusion of new information in the pricing of both future and past reinsurancecoverage. Because of these features, Jean-Baptiste and Santomero show that long-termrelationships between the ceding insurer and its reinsurer enable the ceding insurer topurchase a more efficient quantity of reinsurance at a more favourable price.3 Thecomparative statics of their model suggest the following set of testable hypotheses:

Hypothesis 1: Other things equal, cedants demand more reinsurance as the lengthof the cedant–reinsurer relationship increases.

Hypothesis 2: Other things equal, cedants become more profitable as the length ofthe cedant–reinsurer relationship increases.

Hypothesis 3: Other things equal, insurer bankruptcy risk declines as the length ofthe cedant–reinsurer relationship increases.

Conceptually, the Jean-Baptiste and Santomero model not only shows howlong-term cedant–reinsurer relationships mitigate adverse selection; it also clarifieswhy broader and more efficient risk sharing, higher insurer profitability, and highersolvency levels are important consequences.4 Instead of focusing attention on the basiccoverage-risk prediction of adverse selection theory, that is the notion that cedantswho buy more reinsurance coverage are likely to be riskier, the Jean-Baptiste andSantomero model is forensic in nature, in that it calls for empirically examining thefinancial consequences of mitigation via long-term cedant–reinsurer relationships.5

1 Jean-Baptiste and Santomero (2000).2 Reinsurance contracts are typically written for either a fixed term or on a “continuous until cancelled”basis. Consequently, long-term implicit contracts result either from repeated contracting (wherean expiring fixed contract is effectively renewed by rolling over into another contract) or asa result of non-cancellation of a continuous contract (see the definition for “Expiration” from theGuy Carpenter glossary located at http://bit.ly/guycarpenter).

3 Industry executives generally believe that long-term reinsurance relationships are important. Jean-Baptiste and Santomero provide theoretical grounding for this belief, showing that long-termrelationships play an important role in mitigating adverse selection.

4 An anonymous reviewer suggested an alternative view of these hypotheses. Specifically, changes incontract length could be caused by reinsurance experience, relationships, and increased profitability,rather than the other way around. Furthermore, there could be an omitted variable correlated with bothdemand and profit that causes them to appear to be correlated with sustainability and reinsurer focus.We recognize the possibility of such biases; we may not be able to firmly say that the causality runs inthe favoured direction, except to say that it is based on the rigorous theoretical framework provided byJean-Baptiste and Santomero.

5 Rothschild and Stiglitz (1976) demonstrate that adverse selection may be mitigated through contractdesign, in which insureds self-select based upon price and coverage. Jean-Baptiste and Santomero’s theoryseeks a better solution, since, as they note, the Rothschild and Stiglitz result is not first-best. Therefore,

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A key feature of the Jean-Baptiste and Santomero model is that informationalasymmetry—and therefore, its negative consequences—decline over time because oflong-term cedant–reinsurer relationships. This particular feature is not unique toJean-Baptiste and Santomero; indeed, there exists a substantial literature on learningand asymmetric information in insurance markets,6 which theoretically and empiri-cally examines the implications of informational asymmetries falling over time asa result of repeated contracts.7

Repeated contracting may also be motivated by moral hazard. For example,Rubinstein and Yaari8 show that by offering repeated insurance contracts featuringdiscounts to insureds with favourable claims histories, such discounts enable bothinsurer and insured to counteract the inefficiency that arises from moral hazard.Doherty and Smetters9 provide a dynamic model of the reinsurance market and show(empirically as well as theoretically) that reinsurers use loss-sensitive premiums as astrategy for mitigating moral hazard, a result that is not inconsistent with Rubinsteinand Yaari’s theory. Consequently, even in the absence of adverse selection, onecould reasonably expect an empirical confirmation of Jean-Baptiste and Santomero’sfirst hypothesis; that is that cedants demand more reinsurance as the length of thecedant–reinsurer relationship increases. However, without a formal theory that alsolinks moral hazard with cedant profitability and bankruptcy risk, it is not clear thatless moral hazard would necessarily imply higher profitability and lower bankruptcyrisk for cedants.10

Jean-Baptiste and Santomero take the cedant–reinsurer relationship as given and rely instead uponrelationship sustainability as the mechanism that separates risk types in the long run. Moreover, theiranalysis suggests that contingent pricing schemes (loss-sensitive contracts and large deductibles) decreasein importance as the length of the cedant/reinsurer relationship increases (as is implied by our empiricalresults). A researcher with access to a reinsurer’s proprietary book of business, including pricing andcontract design information, could potentially test the sensitivity of our results to the relationshipassumption and estimate the combined effect of contract design a priori and sustainability ex post.

6 For example see Kunreuther and Pauly (1985), D’Arcy and Doherty (1990), Hendel and Lizzeri(2003), de Garidel-Thoron (2005), and Cohen (2012).

7 When considering the learning and asymmetric information literature, the study closest to ours is by Cohen(2012). Cohen uses a unique panel data set of an Israeli auto insurer’s transactions with repeat customers.She finds that (1) repeat customers with good (bad) claims histories are more likely to stay with (flee from)the same insurer, and (2) the insurer and customers with good claims histories both benefit; the insurerearns higher profit whereas the customers enjoy lower premiums. Although we (unlike Cohen) lackdata on earned premiums for cedants, the notion that cedants enjoy lower reinsurance premiums isimplicit in Hypothesis 1; the reason why cedants demand more reinsurance as the expected lengthof the relationship increases is because reinsurance becomes less expensive as the costs of adverseselection are mitigated.

8 Rubinstein and Yaari (1983).9 Doherty and Smetters (2005).

10 See Cohen and Siegelman (2010) for an excellent survey of the empirical literature on thedisentangling of moral hazard and adverse selection.

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Factors other than informational asymmetries per se could also possibly contributetowards insurers increasing their demand for reinsurance as well as becoming moreprofitable and solvent over time. An important example is financial innovation, withthe emergence of risk-linked securities such as catastrophe bonds, risk swaps,industry loss warranties, and sidecars.11 Cummins notes that risk-linked securitiescomplement the reinsurance market by providing additional risk-bearing capacity forthe financing of catastrophic risk. However, such instruments may also act assubstitutes for catastrophe reinsurance; for example see Bouriaux and MacMinn.12

As these markets evolve over time and improve their efficiency, the use of risk-linkedsecurities would also likely affect insurer profitability and solvency in addition to theextent to which insurers rely upon traditional reinsurance products for managing risk.Furthermore, technological innovation13 substantially mitigates information pro-blems encountered by the ceding insurer and reinsurer alike. For example, reinsurerscan readily observe Global Positioning System coordinates and use cat risk modelsto accurately assess the frequency and severity of catastrophe-related claims for realproperty that is part of a ceding insurer’s book of business. To the extent that insurersrely upon reinsurers to help them select and manage risk more effectively,technological innovation in and of itself could positively influence reinsurancedemand as well as insurer profitability and solvency in the ways described by Jean-Baptiste and Santomero.

Nothwithstanding the various caveats raised above, we focus our efforts on testingthe Jean-Baptiste and Santomero hypotheses after controlling for various factors thatare known from previous studies to influence reinsurance contracting behaviour. Weanalyse panel data consisting of U.S. property-liability insurance firms that reportedto the National Association of Insurance Commissioners (NAIC) during the period1993–2012. By implementing empirical tests of the Jean-Baptiste and Santomerohypotheses, our paper provides an important contribution to the empirical literatureconcerning the impact of adverse selection on the operation and industrial organiza-tion of insurance firms and markets.

The paper is organized as follows. In the next section of the paper, we present ourdata and methodology. In the third section of the paper, we present our empiricalresults and a series of robustness tests. Concluding remarks are provided in the fourthsection of the paper.

11 For example see Cummins (2008).12 Bouriaux and MacMinn (2009).13 For example in the forms of so-called “big data” and data analytics; see McAfee and Brynjolfsson

(2012).


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Data and methodology

Measuring the demand for reinsurance

In this study, the unit of analysis is the individual ceding insurer, or cedant. Oursample consists of insurers that are either affiliated with insurance groups or exist asstandalone, unaffiliated single companies.14 Thus, we do not study the reinsurancecontracting behaviour of insurance groups per se.

Following the lead of previous empirical studies of the demand for reinsu-rance,15 we use the following definition for ceded reinsurance (referred to here as

Table 1 Summary statistics

Variable Obs Mean Std. dev Min Max

CededReinsurance 33,557 0.458 0.326 0.002 1AgencyDummy 34,111 0.626 0.489 0 1AMBestRating 34,111 5.321 4.343 1 15DirectDummy 34,111 0.191 0.393 0 1GeographicHerfindahl 34,111 0.406 0.140 0.054 1GroupDummy 34,111 0.725 0.447 0 1Liquidity 34,111 0.120 0.160 −0.988 1.864PercentLongtail 34,111 0.806 0.248 0 1PercentAuthorized 33,352 0.896 0.219 <0.001 1ProductHerfindahl 34,111 0.688 0.282 0 1PremiumSurplusRatio 34,111 2.419 2.801 0.010 18.817ReinsuranceHerfindahl 34,111 0.640 0.347 0.022 1ReciprocalDummy 34,111 0.027 0.162 0 1ReturnOnAssets 34,111 0.023 0.051 −0.162 0.165ReturnOnEquity 34,111 0.049 0.138 −0.505 0.385CashFlowVolatility 34,111 0.164 0.058 0.001 0.940CedantSize 34,111 18.203 1.902 11.969 25.570StockDummy 34,111 0.729 0.444 0 1PctChangeSurplus 34,105 0.081 0.220 −0.484 0.985Sustainability5 30,342 1.716 1.394 0.618 5Sustainability3 34,111 1.527 0.800 0.732 3CedantTaxRate 34,061 0.209 0.318 −0.879 1.262

Note: Financial and organizational form data are from the InfoPro Database (NAIC, 1993–2012). A.M.Best Ratings and distribution method are from Best’s Insurance Reports (A.M. Best, 1995–2012).

14 In our unbalanced panel consisting of 34,111 firm-years, 72 percent of these observations involvegroup affiliates, whereas the remaining observations involve unaffiliated single companies (seeTable 1).

15 For example Mayers and Smith (1990), Garven and Lamm-Tennant (2003), Cole and McCullough(2006).


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CededReinsurance):

CededReinsurance¼ internal & external ceded reinsurancedirect premiumswritten + internal & external assumed reinsurance

(1)

Thus, CededReinsurance measures the proportion of total business premiumswritten by the cedant that it cedes to its reinsurers in a given year.16 By construction,CededReinsurance is bounded from below at 0 and from above at 1, where0 indicates that no reinsurance is ceded and 1 indicates the ceding insurer reinsures100 per cent of its total business premiums.

Our source of data for the ceded reinsurance variable is Schedule F, Part 3 of theannual statement. There, reinsurance transactions between cedants and reinsurers aredocumented according to the NAIC company codes for these companies. However,since a majority of reinsurers listed in this schedule do not have NAIC company codes,we identify them according to their Federal Employer Identification numbers.Furthermore, Schedule F, Part 3 provides 14 different codes that categorize thenature of each reinsurance transaction; for example, whether the reinsurer is authorizedor unauthorized,17 whether it is a domestic or foreign group affiliate or unaffiliatedcompany, etc. Two of these 14 categories document authorized and unauthorizedpooling arrangements in which participation is compulsory; all other reinsurancecategories involve discretionary transactions, which is what is being modelled here.Since the theory upon which this paper is based involves reinsurance decision-makingwhere participation is discretionary, we omit compulsory reinsurance from our sample.

Modelling reinsurance contracting behaviour

Although theory does not imply a specific method for determining whether a cedant–reinsurer relationship is long or short term in nature, we capture this effect by creatinga “reinsurance sustainability index” called Sustainability. The first step in calculatingSustainability involves creating 16 separate 5-year rolling windows: 1993–1997,1994–1998, … , 2008–2012. From Part 3 of Schedule F, we count how many years

16 Total ceded reinsurance is defined in the numerator of Eq. (1) as the sum of reinsurance ceded internally(to group affiliates) and externally (to unaffiliated reinsurers). In the denominator, total businesspremiums written is defined as direct premiums written plus the sum of reinsurance assumed internally(from group affiliates) and externally (from unaffiliated companies).

17 Unlike authorized reinsurers, unauthorized reinsurers typically do not post letters of credit. Thus, AMBest and regulators provide insurers with less “surplus relief” in their solvency ratings becauseunauthorized reinsurers are believed to have higher counterparty credit risk than authorized reinsurers,other things equal. However, since unauthorized reinsurers are legitimate risk transfer agents from thecedant’s perspective, we include both authorized and unauthorized reinsurers in our sample, and use avariable called PercentAuthorized (which measures the percentage of reinsurance premiums ceded toauthorized reinsurers) as a control variable in our reinsurance demand equation.


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within each 5-year window that a given cedant cedes reinsurance to each of itsreinsurers, and then compute the mean and standard deviation for each cedant’sreinsurer count distribution. Thus,

Sustainability ¼ mean of the reinsurer count distributionstandard deviation of the reinsurer count distribution + 1

: (2)

The reinsurance sustainability index given by the ratio shown in Eq. (2) isessentially the inverse of a coefficient of variation. The highest possible value for thenumerator of this ratio is 5. This occurs when the cedant cedes reinsurance to thesame group of reinsurers throughout the course of a given 5-year window. We referto the average of the reinsurer count distribution as persistency. The lowest possiblevalue for the denominator of this ratio is 1. This also occurs when the insurer cedesreinsurance to the same group of reinsurers throughout the course of a given 5-yearwindow.18 The higher (lower) the standard deviation, the lower (higher) is theconsistency of the cedant’s relationship with a given reinsurer. Thus, cedants thattypically have long-term relationships with the same set of reinsurers receive highreinsurance sustainability index scores by virtue of having high levels of persistencyand consistency. On the other hand, cedants that frequently change their reinsuranceprogrammes receive low reinsurance sustainability index scores (since persistencyand consistency are typically low in such cases).19

The Appendix numerically illustrates how differences in reinsurance contractingbehaviour give rise to different reinsurance sustainability index values for cedants.In the first example, an insurer cedes reinsurance to the same set of three reinsurerswithin a 5-year window of time. Thus the mean of the reinsurer count distribution(μcount1) is 5, the standard deviation (σcount1) is 0, and the reinsurance sustainabilityindex is μcount1/(σcount1+1)= 5/(0+1)= 5. However, in the second example, anothercedant is constantly changing its reinsurance programme with three different reinsurers;in the first 2 years, it only deals with reinsurer A, then switches to reinsurer B in thethird year, and subsequently deals only with reinsurer C in the fourth and fifth years.In this example, the mean of the reinsurer count distribution (μcount2) is 1.67, thestandard deviation (σcount2) is 0.47, and the reinsurance sustainability index is μcount2/(σcount2+1)= 1.67/(0.47+1)= 1.13.

18 Since the standard deviation of the reinsurer count distribution will be zero if the cedant always cedesreinsurance to the same group of reinsurers, we add 1 to the standard deviation so as to ensure thatthere never is division by zero.

19 As a robustness check, we also calculate a reinsurance sustainability index (called Sustainability3) for18 3-year rolling windows: 1993–1995, 1994–1996, … , 2010–2012. Since the reinsurer countdistribution used for Sustainability3 is calculated over 3-year rather than 5-year rolling windows, thisimplies that Sustainability3 is defined over the closed interval [0,3], whereas the 5-year version ofSustainability (subsequently referred to as Sustainability5) is defined over the closed interval [0,5].


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While the reinsurance sustainability index indicates whether the cedant isengaging in short vs long-term reinsurance contracting, an important related questionconcerns the degree to which the cedant tends to have focused vs diffuse contractualrelationships with its reinsurers. In order to capture the effect of reinsurance concen-tration, we construct a Herfindahl index (called ReinsuranceHerfindahl) for eachcedant year in our sample. This variable enables us to determine how focusedor diffuse the cedant’s relationship is with a given set of reinsurers. In cases wherethe ceding insurer contracts with a small (large) number of reinsurers, then thereinsurance Herfindahl index approaches 1 (0).20

Asymmetric information in reinsurance contracts

As shown by Rothschild and Stiglitz,21 full insurance contracts induce adverseselection and other information asymmetry problems, including moral hazard. Theyshow that contract design (including partial as well as full insurance coverage) canpartially correct for these concerns, but will still not be first best as some insureds willobtain less coverage than they desired. In our model, one potential correction forthis problem is that learning over time will induce the insured to invest in safety ina way that partial coverage will not. Therefore, we conduct a set of standard tests todetermine whether reinsurance intensity is correlated with actual claim experience.We do so by employing the time-series test for joint autocorrelation in the reinsurancedemand and loss ratio models. These tests are similar to those suggested byChiappori and Salanie,22 but in a time-series context.

Our specific tests involve estimating both the reinsurance demand model (which isdescribed more fully in the section “Reinsurance demand equation (for testingHypothesis 1)”) and the loss realization model (using the 3-year ceded reinsuranceunderwriting ratio as the dependent variable with the same explanatory variables usedin the reinsurance demand model). Residuals from these models were captured andmultiplied for each observation. Intuitively, if prediction errors for both the demandmodel and the underwriting performance move consistently in the same direction, thereis reason to believe that insurance demand and risk-taking are jointly determined (thatis, information asymmetry problems are not mitigated by any of the explanatoryvariables). However, if the prediction errors diverge frequently, then there is evidencethat reinsurers may be learning over time and adjusting premiums and reinsurancecapacity appropriately. By multiplying the residuals from each observation in both thereinsurance demand model and the loss realization model, we can determine whether

20 Since our data are time-series in nature, autocorrelation is a potential problem. While we reportheteroscedasticity and autocorrelation robust standard errors, unreported standard errors pooled bycedant were not materially different.

21 Rothschild and Stiglitz (1976).22 Chiappori and Salanie (2000).


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prediction errors move in the same direction, as the product will be positive when theresiduals are simultaneously either positive or negative. If the prediction errors move inthe opposite direction, then reinsurance demand and loss realization are not jointlydetermined, and information asymmetry problems are not present.

The first test uses a t-test to determine whether the product of residuals issignificantly different from zero. Formally, the null hypothesis is that informationasymmetry will generate prediction errors in the same direction, so the averageproduct of residuals is positive. The alternative hypothesis is that informationasymmetry has been mitigated and the average product of residuals is non-positive.

In Table 2, Panel A, we report t-test results for the product of the residualsfor the models using both Sustainability3 and Sustainability5. The t-test resultsindicate a negative and significant result, suggesting that the residuals for eachmodel have opposite signs more frequently than similar signs. This provides supportfor the alternative hypothesis that information asymmetry has been mitigated.Indeed, the negative and significant result suggests that information asymmetry isfalling.

Table 2 Correlation tests for asymmetric information

Panel A: t-tests

Model N Mean Std. dev t-stat

Sustainability3 32,709 −3.41 349.52 −1.762(0.961)

Sustainability5 28,945 −3.27 321.699 −1.729(0.958)

Panel B: Regression tests

Variable Sustainability3 Sustainability5

Sustainability 2.571 2.557 0.726 0.699(2.429) (2.436) (1.374) (1.376)

Year 0.030 0.158(0.394) (0.436)

Constant −7.300 −66.545 −4.497 −321.091(4.155)* (788.81) (2.995) (873.507)

Observations 32.709 32.709 28.945 28.945R2 0.000 0.000 0.000 0.000

Robust standard errors in parentheses.One-tail test significance: ***P<0.01, **P<0.05, *P<0.1.Notes: Means test to evaluate the products of residuals from reinsurance demand and underwritingperformance models. P-values in parentheses beneath t-statistic. Null hypothesis: Mean>0.Dependent variable is the product of the regressions of the reinsurance demand and underwriting ratioequations. Sustainability 5 and Sustainability 3 refer to the sustainability definitions used in the underlyingmodels, respectively.


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In the second test, we use the product of residuals as the dependent variable and thesustainability measure as the explanatory variable. In another specification, we includea time trend as an explanatory variable. The null hypothesis (information asymmetryeffects are correlated with sustainability) would be supported by a positive coefficient onsustainability. The alternative hypothesis (information asymmetry effects are mitigatedby sustained contracts) would be supported by a negative coefficient on sustainability.

In Table 2, Panel B, we report the results of regressions in which the dependentvariable is the product of the residuals and the explanatory variables are Sustain-ability3 and Sustainability5, respectively. The results are similar in models thatinclude a time trend. In each specification, the coefficient on our sustainability mea-sures are not significantly different from zero, providing support for the alternativehypothesis that information asymmetry problems have been mitigated. These resultsprovide a basis for exploring the specific hypotheses proposed by Jean-Baptiste andSantomero, which we explore in the balance of this section.23

Reinsurance demand equation (for testing Hypothesis 1)

Since we wish to study the effects that reinsurance sustainability and concentrationhave upon the demand for reinsurance, we are particularly interested in thecoefficients and standard errors associated with these variables. However, we mustalso control for other determinants of the demand for reinsurance that have beendocumented by previous empirical studies.15 Thus, our regression also includes thefollowing set of right-hand side control variables in addition to reinsurancesustainability and concentration:

● ProductHerfindahl= product Herfindahl index—measures the extent to which thecedant’s lines of business are focused or diffuse.

● GeographicHerfindahl= geographic Herfindahl index—measures the extent towhich the cedant’s business operations are geographically concentrated or dispersed.

● CedantSize= natural logarithm of the cedant’s total assets.● PremiumSurplusRatio= premium to surplus ratio definitionpremium to surplus

ratio, calculated as the ratio of the sum of direct premiums written plus reinsuranceassumed, divided by the cedant’s surplus.

● CashFlowVolatility= cash flow volatility, calculated as the standard deviation ofthe cedant’s assets and liabilities.24

● Liquidity= percentage of cedant’s assets that are liquid, calculated as the ratio ofcash plus short-term investments divided by total admitted assets.

23 We analysed numerous unreported specifications of this model and found no evidence of positivecorrelation in any of the models, further supporting our contention that information asymmetries arenot growing over time.

24 Here, we follow the cash flow volatility calculation method given by Cummins and Sommer (1996).


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● PercentLongtail= proportion of the cedant’s premiums written in long tail lines.25

● PercentAuthorized= percentage of reinsurance premiums ceded to authorizedreinsurers.

● StockDummy= stock indicator variable, which equals 1 if the cedant is a stockinsurer, 0 otherwise.

● ReciprocalDummy= reciprocal indicator variable, which equals 1 if the cedant is areciprocal insurer, 0 otherwise.

● GroupDummy= group indicator variable, which equals 1 if the cedant is a memberof an insurance group, 0 otherwise.

● CedantTaxRate= cedant’s tax rate= 1—NetIncomet/BeforeTaxNetIncomet, whereNetIncomet= period t after-tax net income and BeforeTaxNetIncomet= period tbefore-tax net income.

We also interact cedant size (CedantSize) with the reinsurance sustainability(Sustainability) and reinsurance Herfindahl (ReinsuranceHerfindahl) variables,26 thereinsurance Herfindahl variable (ReinsuranceHerfindahl) with the group indicator(GroupDummy),27 and control for non-linearities by squaring the firm size (Cedant-Size),28 tax rate (CedantTaxRate),29 and cash flow volatility (CashFlowVolatility)variables.30 Finally, we use a 1-year lagged (rather than contemporaneous) value forboth the 5-year and 3-year reinsurance sustainability indices; thus we model thecedant insurer as basing its decision to purchase reinsurance in period t upon theextent to which it has previously (as of period t−1) engaged in long-term implicitcontracting with its reinsurers.

25 We define long tail lines in the same manner as Phillips et al. (1998); that is long tail lines includeFarmowners Multiple Peril, Homeowners Multiple Peril, Commercial Multiple Peril, Ocean Marine,Medical Malpractice, International, Reinsurance, Workers’ Compensation, Other Liability, ProductsLiability, Aircraft, Boiler and Machinery, and Automobile Liability.

26 This interaction effect enables us to calibrate whether relationship sustainability and focus havedifferent reinsurance demand implications for large vs small firms; we find that other things equal,reinsurance demand is positively influenced by relationship sustainability and focus, although theeffect is smaller for large compared with small firms.

27 By interacting ReinsuranceHerfindahl with GroupDummy, this allows us to differentiate somewhatbetween reinsurance contracts that take place within groups with reinsurance contracts that take placeoutside of groups.

28 The basic intuition for squaring firm size is to determine whether there may be scale economies in riskbearing that make reinsurance marginally less attractive for large firms compared with small firms.

29 This approach (i.e. including CedantTaxRate and CedantTaxRate2 as right-hand side variables) isconsistent with approaches followed in a number of studies that have empirically investigated theimplications of tax convexity for reinsurance demand; for example see Adiel (1996), Adams et al.(2008), and Kader et al. (2010).

30 This enables us to calibrate whether the marginal effect of volatility is different at high compared withlow levels of volatility; we find that other things equal, reinsurance demand is higher (lower) at higher(lower) levels of volatility.


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Profitability equations (for testing Hypothesis 2)

We measure cedant profitability by calculating ReturnOnAssets (after-tax returnon (admitted) assets) and ReturnOnEquity (after-tax return on equity (surplus)) and usethese measures as left-hand side variables for our profitability equations. Although weare primarily interested in studying how reinsurance sustainability (Sustainability) andfocus (ReinsuranceHerfindahl ) affect cedant profitability, we also control for variousother variables that are known to be important determinants of insurer profitability.31

For example, Lamm-Tennant et al.32 show that net underwriting profit is significantlyrelated to ownership structure, with stock insurers being more profitable (and riskier) onaverage than mutual insurers. Therefore we include the stock (StockDummy), reciprocal(ReciprocalDummy), and group (GroupDummy) indicator variables, as these variablescapture important differences in ownership structure.

Furthermore, Berger et al.33 find that independent agency firms are less cost-efficient than direct writers, although this does not result in profit inefficiencies.Thus we include indicator variables for the type of distribution system employed bythe cedant insurers in our sample. Specifically, we include an indicator variablecalled AgencyDummy that equals 1 if the cedant insurer employs an independentagent marketing system and 0 otherwise, along with another indicator variable calledDirectDummy that equals 1 if the cedant insurer employs a direct writer marketingsystem and 0 otherwise.34 Firm size is included because of the possibility thateconomies or diseconomies of scale could affect profitability. Since the financialpricing model literature35 shows that differences in average claim delays acrosslines of business create a trade-off between investment income and underwritingprofitability, we control for this trade-off by including the PercentLongtail variablethat measures percentage of premiums written in long tail lines of business. Wealso interact firm size with the stock indicator variable (StockDummy), thereinsurance Herfindahl index (ReinsuranceHerfindahl), and reinsurance sustainabi-lity index (Sustainability), and test for non-linearities by including squared values ofthe premium to surplus ratio (PremiumSurplusRatio), firm size (CedantSize), andcash flow volatility (CashFlowVolatility).

31 In the profitability and bankruptcy risk equations, we utilize the contemporaneous rather than 1-yearlagged values for our Sustainability and Sustainability3 variables. This is appropriate since profit-ability and insurer rating outcomes depend upon the current status of the cedant firm’s reinsuranceprogram.

32 Lamm-Tennant et al. (1996).33 Berger et al. (1997).34 Thus, the reference variable for type of distribution system is the broker marketing system (see

Hilliard et al. (2013)).35 See Bauer et al. (2013).


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Bankruptcy risk equation (for testing Hypothesis 3)

In order to measure the bankruptcy risk of the insurer, we rely upon A. M. Best’sRatings. A. M. Best assigns financial strength ratings to companies using a discretealphabetic scale; specifically, by applying letter ratings A++, A+, A, A−, B++, etc., andthey record the letter rating for each firm i in each year t. For the purposes of thisstudy, we assign the various A. M. Best financial strength ratings to a variable calledAMBestRating that has numerical scores ranging from 1 to 15. The following listprovides the numbering scheme for the various rating categories:

● If the insurer falls within the various A rating categories; that is A++, A+, A, andA−, then it is assigned scores of 1, 2, 3, and 4, respectively.

● If the insurer falls within the various B rating categories; that is B++, B+, B, and B−,then it is assigned scores of 5, 6, 7, and 8, respectively.

● If the insurer falls within the various C rating categories; that is C++, C+, C, and C−,then it is assigned scores of 9, 10, 11, and 12, respectively.

● If the insurer falls within the D, E, or F rating categories, then it is assigned a scoreof 13.

● If the insurer is not assigned a rating, then it is assigned a score of 15.

We estimate the bankruptcy risk equation using an ordered probit model. Theordered probit model is appropriate because there are only 14 possible discrete valuesthat can be assumed by the left-hand side variable, ranging from 1 (high) to 15 (low).Consequently, ordinary least squares (OLS) should not be used since it would produceinefficient coefficient estimates. Furthermore, a fixed or random effects model isinappropriate here since the firm identifiers are collinear with the A. M. Best rating.

We follow the lead of Lamm-Tennant et al.32 in our selection of the right-handside control variables for the bankruptcy risk equation. Lamm-Tennant et al showthat liquidity and capital adequacy are important determinants of insurer bank-ruptcies, as are the asset-liability management strategies employed by such firms.Thus our bankruptcy risk regression equation employs the (Liquidity) variablereferenced in the section “Reinsurance demand equation (for testing Hypothesis 1)”,in order to control for differences in liquidity among the cedant companiesrepresented in our data set. We empirically control for capital adequacy by includingthe premium to surplus ratio (PremiumSurplusRatio) as well as the percentagechange in surplus from the prior year variable (PctChgSurplus).36 Finally, cash flowvolatility (CashFlowVolatility) is included since it is the standard deviation ofcedant’s portfolio of assets and liabilities and therefore provides a summary statistic

36 By using both PremiumSurplusRatio and PctChgSurplus we are able to provide a more dynamic viewof bankruptcy risk; that is, PremiumSurplusRatio indicates whether the cedant is currently adequatelycapitalized, whereas PctChgSurplus indicates where capital adequacy is either improving ordeteriorating from its current level.


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of the overall risk effects of the cedant insurer’s asset-liability managementstrategies. Other right-hand side variables besides reinsurance sustainability (Sustain-ability) and reinsurance concentration (ReinsuranceHerfindahl) include firm size(CedantSize), ownership structure (StockDummy, ReciprocalDummy, and Group-Dummy), type of distribution system (DirectDummy and AgencyDummy), cedantprofitability as indicated by ReturnOnEquity, and PercentLongtail (which measuresthe percentage of premiums written in long tail lines).

Empirical results

Summary statistics

The summary statistics for our sample are provided in Table 1. Regressions involvingthe reinsurance sustainability index based upon 5-year rolling windows (Sustainability5)as a right-hand side variable are based upon an unbalanced panel for the period 1998–2012 that consists of 30,342 firm-year observations, for an average of 2,022.8 firms peryear. For regressions involving the reinsurance sustainability index based upon 3-yearrolling windows (Sustainability3) as a right-hand side variable, there are 34,111 firm-year observations from the period 1996–2012, for an average of 2006.5 firms per year.Seventy-three per cent of these observations involve group affiliates, whereas theremaining observations involve unaffiliated single companies.

Our sample consists of 21 unique variables, including five ownership structure(StockDummy, ReciprocalDummy, and GroupDummy) and distribution system (Direct-Dummy and AgencyDummy) indicator variables (which may only assume values ofeither 0 or 1), and six continuous variables (CededReinsurance, GeographicHerfindahl,PercentLongtail, PercentAuthorized, ProductHerfindahl, and ReinsuranceHerfindahl)defined over the [0,1] closed interval.37 Six variables, specifically, CededReinsurance,PremiumSurplusRatio, ReturnOnAssets, return on equity ReturnOnEquity, percentagechange in surplus from the prior year PctChangeSurplus, and the cedant’s effectivetax rate CedantTaxRate, were winsorized at the 2nd and 98th percentiles in order toreduce the impact of outliers and data errors.38

37 As noted earlier, the reinsurance sustainability index based upon 5-year rolling windows (Sustain-ability) is a continuous variable defined over the [0,5] closed interval, whereas the reinsurancesustainability index based upon 3-year rolling windows (Sustainability3) is a continuous variabledefined over the [0,3] closed interval.

38 See Barnett and Lewis (1994) for a discussion of winsorizing and for references to the relevantstatistical literature.


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Table 3 Reinsurance equation—dependent variable is CededReinsurance

Panel A: Cedant fixed effects model

Variables Sustainability5 Sustainability3

Sustainability(Lag) 0.035* 0.106**(0.027) (0.049)

ReinsuranceHerfindahl 0.470*** 0.564***(0.148) (0.130)

ProductHerfindahl −0.036 −0.034(0.034) (0.034)

GeographicHerfindahl −0.317*** −0.311***(0.056) (0.062)

StockDummy 0.205 0.034(0.350) (0.320)

ReciprocalDummy 0.078 0.069(0.072) (0.067)

GroupDummy 0.021 0.014(0.025) (0.024)

CedantSize −0.164* −0.119(0.112) (0.099)

PremiumSurplusRatio 0.019*** 0.021***(0.003) (0.003)

CashFlowVolatility −1.098*** −0.906**(0.401) (0.410)

Liquidity 0.062* 0.081**(0.047) (0.048)

PercentLongtail 0.012 −0.001(0.027) (0.027)

PercentAuthorized 0.027 0.029(0.022) (0.022)

CedantTaxRate −0.003 −0.005(0.007) (0.007)

CedantSize2 0.002 0.001(0.003) (0.027)

Sustainability(Lag)*CedantSize −0.002* −0.005**(0.001) (0.002)

StockDummy*CedantSize −0.006 0.003(0.016) (0.015)

ReinsuranceHerfindahl*CedantSize −0.024*** −0.029***(0.007) (0.007)

ReinsuranceHerfindahl*GroupDummy 0.159*** 0.176***(0.040) (0.039)

CedantTaxRate2 −0.002 −0.000(0.007) (0.007)

CashFlowVolatility2 2.374*** 2.103**(0.868) (0.890)


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Reinsurance equation

Table 3 presents our regression results for our reinsurance equation describedabove. We estimated a firm fixed effects model using CededReinsurance (as defined

Table 3: (Continued )

Panel A: Cedant fixed effects model


Constant 2.857*** 2.348**(1.051) (0.936)

Observations 28,945 32,715R2 0.176 0.186Number of cedants 2,729 2,824

Panel B: Marginal effects measured at means

Sustainability5 Sustainability3

Sustainability −0.004 −0.014(0.00) (0.009)

ReinsuranceHerfindahl 0.083*** 0.080***(0.026) (0.023)

CedantSize −0.086*** −0.088***(0.025) (0.021)


CashFlowVolatility −0.376** −0.262(0.179) (0.177)

StockDummy0 0.241*** 0.226***

(0.039) (0.034)1 0.314*** 0.318***

(0.018) (0.016)GroupDummy0 0.199*** 0.195***

(0.020) (0.021)1 0.296*** 0.293***

(0.001) (0.001)

Robust standard errors in parentheses.One-tail test significance: *** P<0.01, ** P<0.05, * P<0.1.Notes: Coefficients for cedant and year indicator variables are omitted for clarity of presentation. Themodel labelled Sustainability5 uses the lagged 5-year sustainability index and the model labelledSustainability3 uses the lagged 3-year sustainability index.Marginal effects are measured at the means for continuous variables and levels for indicator variables toillustrate the sensitivity of terms used in interactions. The model labelled Sustainability5 uses the lagged5-year sustainability index and the model labelled Sustainability3 uses the lagged 3-year sustainabilityindex.


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in Eq. (1)) as our dependent variable. As we noted earlier, the model shown in Table3 tests for the relationship between reinsurance demand (as measured by CededRein-surance) and reinsurance sustainability (as measured by the 5-year and 3-yearversions of Sustainability; labelled in Table 3 as Sustainability5 and Sustainability3,respectively) as well as the relationship between reinsurance demand and reinsurancefocus (as measured by ReinsuranceHerfindahl), after controlling for various firm-specific factors. These factors include line of business and geographic characteristics(PercentLongtail, ProductHerfindahl, and GeographicHerfindahl), ownership struc-ture (StockDummy, ReciprocalDummy, and GroupDummy), firm size (CedantSize),leverage (PremiumSurplusRatio), reinsurer credit quality (AMBestRating), risk of thecedant (CashFlowVolatility and Liquidity), and the cedant’s effective tax rate(CedantTaxRate), with additional interaction terms based upon size, sustainability,ownership structure, risk, and taxes.

The regression results reported in Table 3 confirm Hypothesis 1. Other thingsequal, the higher Sustainability and ReinsuranceHerfindahl are, the higher Ceded-Reinsurance is; that is long-term and focused contracting relationships withreinsurers are associated with higher levels of reinsurance coverage, consistent withexpectations regarding the positive effects of repeated interactions for reducingadverse selection. The somewhat weaker relationship in the 5-year sustainabilityspecification suggests that the benefits of sustained relationships are mitigated overtime by other factors. Other control variables that emerge as significant includeGeographicHerfindahl (negative and significant in both specifications, indicatingthat reinsurance demand decreases in geographic focus) and PremiumSurplusRatio,suggesting that firms with higher business risk also demand more reinsurance. Thelinear relationship between CashFlowVolatility and reinsurance demand is also signi-ficant and negative, suggesting the firms with more volatile balance sheets demandless reinsurance. However, the quadratic relationship between reinsurance demandand cash flow volatility is positive and significant, indicating that at higher levels ofbalance sheet volatility, the relationship between reinsurance demand and balancesheet volatility is positive, in line with most prior literature about insurance demand.

When examining interaction effects, we find that the joint effect of sustainabilityand firm size (CedantSize) is negative and significant, suggesting that larger firmsbenefit less from repeated contracts. Similarly, the joint effect of reinsurer concentra-tion (ReinsuranceHerfindahl) and firm size is negative, suggesting that reinsurancedemand is lower for large firms that rely on a concentrated group of reinsurers.However, group members’ demand for reinsurance increases in reinsurer concentra-tion, as measured by the interaction between ReinsuranceHerfindahl and the groupmember indicator.

Examining the marginal effects provided in Table 3, Panel B, we see that the meanmarginal impact of sustainability is not significant. This suggests that the slope onsustainability is constant at the mean. However, the marginal effects on Reinsur-anceHerfindahl and PremiumSurplusRatio are positive at the means, suggesting that


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sustainability is more important for more firms that focus their reinsurance businesswith a small number of reinsurers, and is more important for firms that take on moreunderwriting risk, as measured by PremiumSurplusRatio. The negative marginaleffects associated with CedantSize provide further evidence that sustainability is lessimportant for larger firms.

Both the model testing the 5-year version of Sustainability (i.e. Sustainability5)as well as the robustness test examining the 3-year version of Sustainability(i.e. Sustainability3) have reasonably strong R2 values, suggesting that between17 and 19 per cent of the variation in reinsurance demand is explained by theseregressions.

Profitability equations

Table 4 presents the results of our firm fixed effects estimations of the profitabilityequations. We estimate two different models; one uses ReturnOnAssets as thedependent variable, whereas the other uses ReturnOnEquity.

Recall our second hypothesis: other things equal, insurers become more profitableas the length of the cedant–reinsurer relationship increases. The regression resultsreported in Table 4 confirm Hypothesis 2. Other things equal, longer-term (as well asmore focused) contracting relationships with reinsurers are associated with higherlevels profitability. Panel B of Table 4 indicates that for the average firm in oursample, there is little relationship between profitability (as indicated by Return-OnAssets and ReturnOnEquity alike) and our Sustainability5, Sustainability3, andReinsuranceHerfindahl variables. While the signs on each sustainability variable arepositive, only the 5-year sustainability variable is significant at the 10 per cent level.There appears to be no definitive relationship between profitability and reinsurerfocus. Thus, while we are not able to assert a definitive positive relationship betweensustainability and profitability, neither do we find evidence of an inverse relationship.

We also tested the impact of other variables believed to influence firm profitabilityyielded similarly anticipated results, after controlling for reinsurance sustainabilityand focus. In particular, PremiumSurplusRatio illustrates a negative effect on profit(linear for profit measured by ROA and quadratic for profit measured by ROE).Cedants that primarily distribute through agents have lower ROA profitability,consistent with earlier literature.

Marginal effects shown in Table 4, Panel B, demonstrate that the marginaleffect of size on profitability is indeed positive, though not significant. As shownabove, firm underwriting risk measured by PremiumSurplusRatio indicates anegative linear relationship between risk and profit measured by ROA, but thesquared term reveals a non-linear relationship for profit measured by ROE. Themarginal effects reported in Panel B show that the negative relationship persistsfor the average firm.


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Table 4 Profitability equations—dependent variables are ReturnOnAssets and ReturnOnEquity

Panel A: Cedant Fixed Effects Model

ROA ROE

Sustainability5 Sustainability3 Sustainability5 Sustainability3

Sustainability 0.0136 0.0051 0.0456* 0.0174(0.0111) (0.0166) (0.029) (0.0502)

CedantSize −0.0005 −0.002 0.0156 0.0155(0.02) (0.0139) (0.0646) (0.0489)

CashFlowVolatility 0.0092 −0.0365 −0.0751 −0.1336(0.1009) (0.0809) (0.3011) (0.2765)

ReinsuranceHerfindahl −0.005 0.0015 −0.101 −0.077(0.0347) (0.0346) (0.0999) (0.0846)

PremiumSurplusRatio −0.0224*** −0.0185*** 0.0014 0.0072(0.0064) (0.0057) (0.0224) (0.0201)

PremiumSurplusRatio2 0.0025 0.0017 −0.0116* −0.0108*(0.0022) (0.002) (0.0079) (0.007)

GroupDummy −0.0012 −0.0014 −0.0054 −0.0057(0.0035) (0.0034) (0.0095) (0.0086)

StockDummy 0.011 0.0341 0.0215 0.1751(0.0791) (0.0652) (0.2833) (0.2511)

ReciprocalDummy −0.0281 0.0679 0.0453 0.2665(0.1677) (0.1251) (0.4401) (0.3465)

AgencyDummy −0.0112** −0.0097** −0.0211 −0.0156(0.0054) (0.0051) (0.0214) (0.0216)

DirectDummy −0.0023 −0.0008 −0.0064 −0.0034(0.0031) (0.0026) (0.0102) (0.0101)

PercentLongtail −0.0062* −0.006* −0.0095 −0.0095(0.0047) (0.0045) (0.0146) (0.0144)

CashFlowVolatility2 −0.2669 −0.0955 −0.6406 −0.2482(0.2458) (0.1767) (0.7012) (0.5769)

CedantSize2 0.0002 0.0002 0.0001 0.0001(0.0005) (0.0004) (0.0018) (0.0015)

CedantSize*ReinsuranceHerfindahl 0.0002 −0.0001 0.0048 0.0037(0.0017) (0.0017) (0.0048) (0.0041)

StockDummy*CedantSize −0.0009 −0.0017 −0.0021 −0.0084(0.004) (0.0033) (0.0137) (0.0121)

ReciprocalDummy*CedantSize 0.0003 −0.0044 −0.0053 −0.0155(0.0089) (0.0068) (0.023) (0.0183)

CedantSize*Sustainability −0.0006 −0.0001 −0.002 −0.0005(0.0006) (0.0009) (0.0015) (0.0026)

Constant 0.0172 0.0224 −0.1619 −0.2355(0.1992) (0.1397) (0.5787) (0.4172)

Observations 30,185 33,814 30,185 33,814R2 (per cent) 20.08 18.51 16.76 15.58Number of cedants 2716 2800 2716 2800


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Bankruptcy risk equation

Table 5 shows the ordered probit estimates for the bankruptcy risk equation. In thismodel we analyse the effect of Sustainability (and Sustainability3) on A. M. Bestratings. Our third hypothesis was that firms with longer reinsurance sustainabilitywould have a lower risk of bankruptcy. In this case, we use the A. M. Best creditrating as a proxy for bankruptcy risk. We compress the various ratings into a 15-pointordinal scale as discussed earlier with “1” being the highest and “15” being thelowest.


Panel B: Marginal effects measured at means

ROA ROE

Sustainability5 Sustainability3 Sustainability5 Sustainability3

Sustainability 0.0010 0.0018 0.0013 0.0062(0.0016) (0.0027) (0.0042) (0.0086)

CedantSize 0.0059 0.0051 0.0163 0.0158(0.004) (0.0033) (0.0155) (0.0136)

CashFlowVolatility −0.0717* −0.0658* −0.2693** −0.2098(0.0427) (0.0367) (0.1368) (0.13)

ReinsuranceHerfindahl −0.0007 −0.0003 0.0064 0.0051(0.0048) (0.0043) (0.0144) (0.0126)

PremiumSurplusRatio −0.0170*** −0.0147*** −0.0237*** −0.0165**(0.0028) (0.0025) (0.0086) (0.0083)

GroupDummy0 0.0289*** 0.0296*** 0.0774*** 0.0805***

(0.0034) (0.0032) (0.0092) (0.0083)1 0.0277*** 0.0282*** 0.0720*** 0.0748***

(0.0001) (0.0001) (0.0004) (0.0003)StockDummy0 0.0334*** 0.0307*** 0.0900*** 0.0814***

(0.0108) (0.0079) (0.0313) (0.0231)1 0.0251*** 0.0268*** 0.0639*** 0.0702***

(0.0054) (0.0041) (0.0155) (0.0118)

Robust standard errors in parentheses.One-tailed test results indicated by: *** P<0.01, **P<0.05, *P<0.1.Notes: Coefficients for cedant and year indicator variables are omitted for clarity of presentation. Themodel labelled Sustainability5 uses the contemporaneous 5-year sustainability index and the modellabelled Sustainability3 uses the contemporaneous 3-year sustainability index.Marginal effects are measured at the means for continuous variables and levels for indicator variables toillustrate the sensitivity of terms used in interactions. The model labelled Sustainability5 uses thecontemporaneous 5-year sustainability index and the model labelled Sustainability3 uses the contempora-neous 3-year sustainability index.


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Again, our hypothesis is a one-tailed test (that sustainability will have a positiveeffect on credit rating) and under this test, the result is significant at the .05 level. Inaddition, our measure of focus is highly significant and negative, which suggests apenalty for lack of reinsurance monitoring, other things equal.

The ordered probit model reveals largely anticipated relationships between bank-ruptcy risk and the other predicted independent variables. For example, reinsurer

Table 5 Bankruptcy risk equation—dependent variable is AMBestRating


Sustainability −0.068*** −0.161***(0.007) (0.011)

ReinsuranceHerfindahl −0.437*** −0.409***(0.021) (0.020)


PctChangeSurplus −0.322*** −0.280***(0.037) (0.035)

CedantSize −0.354*** −0.333***(0.004) (0.004)

ReturnOnEquity −0.705*** −0.743***(0.056) (0.053)

Liquidity −0.651*** −0.313***(0.085) (0.082)

PercentLongtail 0.311*** 0.330***(0.031) (0.030)

CashFlowVolatility 3.889*** 4.225***(0.160) (0.149)

GroupDummy −0.537*** −0.522***(0.034) (0.032)

StockDummy 0.131*** 0.121***(0.016) (0.015)

ReciprocalDummy 0.094*** 0.116***(0.029) (0.027)

DirectDummy −0.005 0.076***(0.018) (0.017)

AgencyDummy −0.012 0.031*(0.017) (0.016)

Observations 30,697 34,105Pseudo R2 (per cent) 14.42 13.76

Robust standard errors in parentheses.***P<0.01, **P<0.05, *P<0.1.Note: The dependent variable (AMBestRating) is defined over the closed interval, Doherty and Smetters(2005), Adams et al. (2008). A level of 1 indicates high credit quality, whereas a level of 15 represents lowcredit quality. The model labelled Sustainability5 uses the lagged 5-year sustainability index and the modellabelled Sustainability3 uses the lagged 3-year sustainability index. The model is estimated using anOrdered Probit model.


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concentration is negatively related to cedant credit quality. Indeed, relying more on asmall number of reinsurers increases counterparty risk for the cedant that impacts theirown presumed bankruptcy risk. Increased risk related to capitalization (measured byPremiumSurplusRatio) shows that bankruptcy risk increases in leverage. Firms that aregrowing their surplus, as anticipated, decrease their bankruptcy risk and large firms aredeemed less likely to fail than small firms. Firm operating risk, represented byLiquidity, PercentLongtail, and CashFlowVolatility, all further confirm that predictionthat firms engaging in risky behaviour are deemed more likely to face financial distress.

Since the relatively small amount of firm-level variation in ratings over timeprevent controlling for unobserved firm-level variables, we implement a robustnesstest that provides additional support for our findings. Specifically, we use InsuranceRegulatory Information System (IRIS) solvency ratios and insurer failure data toestimate the probability of failure over time. IRIS ratios provide early warningsignals to insurance regulators and have been used in prior studies, including Graceand Leverty.39 We collected insurance firm failures from 1995 to 2012 and collectedor calculated IRIS ratios from the SNL database. We also added firm size(CedantSize) and an indicator for mutual companies. Using these variables, wecalculate the probability of failure using a discrete-time hazard model, where thedependent variable is equal to 1 if the insurer is insolvent in either year t+1 or t+2,following Shumway.40 We identify 237 firm failures within our useful data set of17,227 firm-years and 3,106 individual firms. The average predicted failure for theentire data set is 1.38 per cent with a standard deviation of 2.60 per cent. The meanprobability of failure for firms that did not ultimately fail was 1.34 per cent (2.39 percent) and the mean probability of failure for firms that ultimately did fail was 4.28 percent (8.50 per cent).41 Results for the hazard model and summary statistics aboutpredicted probability of insolvency are presented in Table 6.

After estimating the probability of failure for each firm, we use that predictedprobability as the dependent variable in an OLS regression employing the sameexplanatory variables as the ordered probit model. Because the predicted values arepoint estimates only, we bootstrap the regression (10,000 iterations) and includecedant and year fixed effects. The predictions for the effect of contract sustainabilityare presented in Table 7 and are similar in sign to those of the ordered probit model,although the model lacks significance for the sustainability measure. Due to thelimited sample size for the robustness test and the potential errors in variables bias, itis not surprising that significance is lacking, but these results do not invalidate thoseof the A.M. Best ratings models.

39 Grace and Leverty (2010).40 Shumway (2001).41 Due to the lack of data to calculate meaningful IRIS ratios for some smaller firms, the sample for this

analysis was notably smaller than the sample size for the ordered probit analysis.


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Robustness tests

To determine whether our results are driven by model specification, we conduct aseries of robustness tests. Essentially, these tests involve estimating a series ofregressions that omit variables that may drive the results we observe. For both thereinsurance demand and profit hypotheses, we estimate models that omit non-linearterms, dummy variable terms, and then one of the variables of interest (in this case,Sustainability5 and ReinsuranceHerfindahl).42 If the coefficient estimates differ

Table 6 Estimation of probability of insurer insolvency—Discrete-time hazard model

Panel A: Hazard model results

Variable Coeff. Std. err. Chi sq. stat.

NPW/Surplus 0.0041 0.0002 322.0582***ΔNPW −0.0001 0.0001 0.5171Surplus Aid/Surplus 0.0009 0.0004 5.5351**2yrOpRatio 0.0000 0.0000 0.0049InvestmentYld −0.0027 0.0131 0.0427ΔGrossSurplus −0.0023 0.0003 68.7557***ΔAdjSurplus −0.0027 0.0008 12.0943***AdjLiabilities/LiquidAssets 0.0019 0.0002 62.2313***GrossAgentsBalances/Surplus 0.0024 0.0009 7.4172***1yrReserveDev/Surplus −0.0009 0.0007 1.70812yrReserveDev/Surplus 0.0000 0.0000 0.0001ReserveDeficiency/Surplus −0.0001 0.0000 3.8005*StockDummy 0.7120 0.1639 18.8826***ReciprocalDummy 0.1432 0.4400 0.1060GroupDummy 0.6180 0.1418 19.0045***CedantSize −0.3354 0.0095 1250.1429***

Observations 17,227Pseudo R2 (per cent) 84.33%Log likelihood function value −17,098.56

Panel B: Predicted probability of insolvency

Firm type Obs Mean (%) Median (%) Std. dev. (%) 1st pct.(%) 99th pct. (%)

Solvent 16,990 1.34 0.96 2.39 0.15 6.78Insolvent 237 4.28 2.04 8.50 0.29 48.09

Standard errors in parentheses.***P<0.01, **P<0.05, *P<0.1.

42 Since the robustness test results for Sustainability3 were not materially different from the robustnesstest results for Sustainability5, we only report the Sustainability5 results. Robustness test results forSustainability3 are available from the authors upon request.


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significantly from those in the previously reported model, we look to the F-test tocompare the unrestricted, original model with the restricted model. The nullhypothesis is that the omitted variables in the restricted models add no explanatorypower to unrestricted model.

Table 7 Bankruptcy risk equation—dependent variable is Predicted Insolvency


Sustainability −0.0001 −0.0003(0.0002) (0.0003)

ReinsuranceHerfindahl 0.0001 −0.0004(0.0008) (0.001)


PctChangeSurplus −0.0002 −0.0002(0.0022) (0.0045)

CedantSize −0.0043*** −0.0048***(0.0006) (0.0009)

ReturnOnEquity −0.0174*** −0.0195***(0.0037) (0.0046)

Liquidity −0.0015 0.0026(0.0016) (0.0025)

PercentLongtail −0.0007 −0.0019(0.0012) (0.0016)

CashFlowVolatility −0.0060* −0.0083(0.0043) (0.007)

GroupDummy 0.0088*** 0.0088***(0.0017) (0.0017)

StockDummy 0.0116*** 0.0117***(0.0018) (0.0018)

ReciprocalDummy 0.0043** 0.0059***(0.0019) (0.0022)

DirectDummy −0.0002 −0.0016(0.0009) (0.0015)

AgencyDummy −0.0008 0.0005(0.0017) (0.0018)

Constant 0.0684*** 0.0055(0.0083) (0.0025)***

Observations 9,209 11,762R2 (per cent) 16.25 14.14Number of cedants 1,336 2,317

Standard errors in parentheses.One-tailed test results indicated by: ***P<0.01, **P<0.05, *P<0.1.Note: Coefficients for cedant and year indicator variables are omitted for clarity of presentation. The modellabelled Sustainability5 uses the contemporaneous 5-year sustainability index and the model labelledSustainability3 uses the contemporaneous 3-year sustainability index. To correct for errors-in-variablesbias, each model was estimated using bootstrapped standard errors (10,000 iterations.)


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For the reinsurance demand equation, robustness tests are reported in Table 8. Inthis table, only the first restricted model generates markedly different results from theunrestricted model. Both of these restricted models remove the non-linear (quadraticand interaction) terms. The rationale for including these non-linear terms is explainedmore fully in a prior section. Indeed, the model is weaker when the non-linear termsare omitted, as suggested by the significant F-statistic in each of these tables. Theother restricted models reported in these tables also show similar evidence that theomitted variables add explanatory power to the models, but the coefficients on thevariables of interest in these restricted models do not differ materially from that of theunrestricted model.

In Tables 9 and 10, we report results for alternative model specifications for theprofitability models in a similar manner to those reported for the reinsurance demand

Table 8 Reinsurance demand robustness tests—Sustainability5

Unrestricted Restricted(1)

Restricted(2)

Restricted(3)

Restricted(4)

Sustainability5(Lag) 0.035* −0.002 0.048** 0.039*(0.027) (0.003) (0.027) (0.028)

ReinsuranceHerfindahl 0.470*** 0.079*** 0.518*** 0.532***(0.148) (0.028) (0.158) (0.155)

ProductHerfindahl −0.036 −0.036 −0.037 −0.030 −0.033(0.034) (0.035) (0.036) (0.034) (0.034)

GeographicHerfindahl −0.317*** −0.303*** −0.304*** −0.322*** −0.323***(0.056) (0.055) (0.056) (0.055) (0.055)

StockDummy 0.205 0.071 0.236(0.350) (0.060) (0.354)

ReciprocalDummy 0.078 0.035 0.063(0.072) (0.074) (0.074)

GroupDummy 0.021 0.091*** 0.094***(0.025) (0.023) (0.023)

CedantSize −0.164* −0.104*** −0.229** −0.170* −0.173*(0.112) (0.013) (0.113) (0.125) (0.126)

PremiumSurplusRatio 0.019*** 0.019*** 0.019*** 0.019*** 0.019***(0.003) (0.003) (0.003) (0.003) (0.003)

CashFlowVolatility −1.098*** −0.123 −0.994*** −1.093*** −1.081***(0.401) (0.154) (0.415) (0.396) (0.397)

Liquidity 0.062* 0.063* 0.068* 0.056 0.058(0.047) (0.047) (0.044) (0.047) (0.046)

PercentLongtail 0.012 0.016 0.006 0.010 0.010(0.027) (0.028) (0.029) (0.028) (0.028)

PercentAuthorized 0.027 0.024 0.049** 0.025 0.025(0.022) (0.022) (0.023) (0.024) (0.024)

CedantTaxRate −0.003 −0.002 −0.003 −0.002 −0.002(0.007) (0.006) (0.007) (0.007) (0.007)


246



Restricted(2)

Restricted(3)

Restricted(4)

CedantSize2 0.002 0.003 0.002 0.002(0.003) (0.003) (0.003) (0.003)

Sustainability5(Lag) −0.002* −0.002** −0.002*(0.001) (0.001) (0.001)

StockDummy*CedantSize −0.006 −0.007(0.016) (0.017)

ReinsuranceHerfindahl*CedantSize −0.024*** −0.019*** −0.020***(0.007) (0.007) (0.007)

GroupDummy*ReinsuranceHerfindahl 0.159***(0.040)

CedantTaxRate2 −0.002 −0.005 −0.004 −0.004(0.007) (0.007) (0.006) (0.006)

CashFlowVolatility2 2.374*** 2.329*** 2.411*** 2.392***(0.868) (0.874) (0.837) (0.839)

Constant 2.857*** 2.437*** 3.676*** 3.068*** 3.126***(1.052) (0.303) (1.070) (1.159) (1.177)

Observations 28,945 28,945 28,945 28,945 28,945R2 0.176 0.164 0.154 0.166 0.166F-statistic (Restricted vs Unrestricted) — 4.70 8.95 7.43 5.60P-value — 0.00 0.00 0.00 0.00

Robust standard errors in parentheses.One-tail test significance: ***P<0.01, **P<0.05, *P<0.1.Note: Coefficients for cedant and year indicator variables are omitted for clarity of presentation. The F-testcompares the restricted model with the unrestricted model and is compared against a critical value with knumerator degrees of freedom and n−k denominator degrees of freedom where k is the number of droppedvariables in the restricted model and n is the number of cedants.

Table 9 Profitability robustness tests—ROA and Sustainability5


Restricted(2)

Restricted(3)

Restricted(4)

Sustainability5 0.014 0.002** 0.013 0.013(0.011) (0.001) (0.011) (0.011)

CedantSize −0.001 0.004* 0.001 0.000 −0.001(0.020) (0.003) (0.022) (0.020) (0.020)

CashFlowVolatility 0.009 −0.093*** 0.003 0.009 0.010(0.101) (0.039) (0.108) (0.099) (0.103)

ReinsuranceHerfindahl −0.005 −0.000 0.000 0.002(0.035) (0.005) (0.035) (0.035)


247



Restricted(2)

Restricted(3)

Restricted(4)

PremiumSurplusRatio −0.022*** −0.015*** −0.022*** −0.022*** −0.022***(0.006) (0.003) (0.006) (0.006) (0.006)

PremiumSurplusRatio2 0.002 0.002 0.002 0.002(0.002) (0.002) (0.002) (0.002)

GroupDummy −0.001 −0.002 −0.001 −0.001(0.004) (0.003) (0.004) (0.004)

StockDummy 0.011 −0.008 0.011 0.009(0.079) (0.017) (0.079) (0.080)

ReciprocalDummy −0.028 −0.020* −0.026 −0.024(0.168) (0.014) (0.168) (0.171)

AgencyDummy −0.011** −0.011** −0.011** −0.011**(0.005) (0.005) (0.005) (0.005)

DirectDummy −0.002 −0.002 −0.002 −0.002(0.003) (0.003) (0.003) (0.003)

PercentLongtail −0.006* −0.007* −0.006 −0.006* −0.006*(0.005) (0.005) (0.005) (0.005) (0.005)


CedantSize2 0.000 0.000 0.000 0.000(0.001) (0.001) (0.001) (0.001)

CedantSize*ReinsuranceHerfindahl 0.000 −0.000 −0.000(0.002) (0.002) (0.002)

StockDummy*CedantSize −0.001 −0.001 −0.001(0.004) (0.004) (0.004)

ReciprocalDummy*CedantSize 0.000 0.000 0.000(0.009) (0.009) (0.009)

Sustainability5*CedantSize −0.001 −0.001 −0.001(0.001) (0.001) (0.001)

Constant 0.017 0.001 −0.006 0.009 0.032(0.199) (0.060) (0.216) (0.200) (0.200)

Observations 30,185 30,185 30,185 30,185 30,185R2 0.201 0.199 0.198 0.201 0.200F-statistic (Restricted vsUnrestricted)

— 0.400 0.760 0.040 5.00

P-value — 0.906 0.622 0.9628 0.0068



248

Table 10 Profitability robustness tests—ROE and Sustainability5


Restricted(2)

Restricted(3)

Restricted(4)

Sustainability5 0.046* 0.004** 0.044* 0.040*(0.029) (0.003) (0.029) (0.026)

CedantSize 0.016 0.019** 0.018 0.021 0.014(0.065) (0.009) (0.071) (0.066) (0.065)

CashFlowVolatility -0.075 −0.312*** −0.096 −0.038 −0.069(0.301) (0.119) (0.322) (0.312) (0.305)

ReinsuranceHerfindahl −0.101 0.005 −0.090 −0.078(0.100) (0.016) (0.099) (0.097)

PremiumSurplusRatio 0.001 −0.032*** 0.002 0.001 0.001(0.022) (0.008) (0.022) (0.022) (0.022)

PremiumSurplusRatio2 −0.012* −0.012* −0.011* −0.012*(0.008) (0.008) (0.008) (0.008)

GroupDummy −0.005 −0.006 −0.006 −0.005(0.010) (0.009) (0.010) (0.010)

StockDummy 0.021 −0.025 0.024 0.019(0.283) (0.049) (0.281) (0.285)

ReciprocalDummy 0.045 −0.049 0.039 0.058(0.440) (0.041) (0.441) (0.452)

AgencyDummy −0.021 −0.021 −0.020 −0.021(0.021) (0.021) (0.021) (0.021)

DirectDummy −0.006 −0.007 −0.005 −0.006(0.010) (0.010) (0.010) (0.010)

PercentLongtail −0.010 −0.010 −0.009 −0.009 −0.010(0.015) (0.015) (0.015) (0.015) (0.015)


CedantSize 0.000 −0.000 0.000 0.000(0.002) (0.002) (0.002) (0.002)

CedantSize*ReinsuranceHerfindahl 0.005 0.004 0.004(0.005) (0.005) (0.005)

StockDummy*CedantSize −0.002 −0.002 −0.002(0.014) (0.014) (0.014)

ReciprocalDummy*CedantSize −0.005 −0.005 −0.006(0.023) (0.023) (0.024)

Sustainability5*CedantSize −0.002* −0.002* −0.002*(0.001) (0.001) (0.001)

Constant −0.162 −0.169 −0.198 −0.255 −0.112(0.579) (0.202) (0.671) (0.596) (0.579)

Observations 30,185 30,185 30,185 30,185 30,185R2 0.168 0.165 0.166 0.167 0.167F-statistic (Restricted vsUnrestricted)

— 0.310 0.680 0.000 1.51

P-value — 0.952 0.693 0.998 0.221



249

models. None of these restricted models differ materially from the unrestrictedmodel, and the F-tests suggest that in most cases, the models are not improved byadding these additional variables that are inspired by theory. Interestingly, the fourthrestricted model in each of these tables drops the sustainability measure. In both theROA and ROE tests, the sustainability variable actually does improve the models,providing further support for our inclusion of this newly identified measure ofreinsurer relationship intensity.

Conclusion

In this paper, we examined three hypotheses inspired by Jean-Baptiste and Santomeroconcerning how long-term repeated contracting between cedants and reinsurers influ-ence the demand for reinsurance, insurer profitability, and solvency. We also empiri-cally examined a related issue; specifically, how the degree to which the ceding insurertends to have “focused” vs diffuse contractual relationships with its reinsurers impactsthe demand for reinsurance, insurer profitability, and solvency. Subject to the potentialfor reverse causality and omitted variable bias, we find that long-term repeatedcontracting with reinsurers (as measured by our Sustainability variables), along with“focused” reinsurer relationships are associated with higher levels of reinsurancecoverage, higher insurer profitability, and lower risk of bankruptcy, other things equal.We also note that, following Jean-Baptiste and Santomero, we take the presence of theinsurance contracts as given, and analyse the impact of contract sustainability inimproving the contract terms for both parties. Analysis of ex-ante contract design isbeyond the scope of this study. In conclusion, our paper provides an importantcontribution to the empirical adverse selection literature by empirically examining thefinancial consequences of mitigating adverse selection via long-term and focusedcedant–reinsurer relationships.

Acknowledgements

The authors acknowledge valuable feedback and contributions from Muhammed Altuntas, Mark Browne,David Cummins, Joan Lamm-Tennant, Andrew Petersen, Alex Muermann (the guest editor), and twoanonymous reviewers. Of course, we are solely responsible for any remaining errors.

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Appendix

Numerical example of the reinsurance sustainability indexExample #1:

Year 1 Year 2 Year 3 Year 4 Year 5 Count

A A A A A 5B B B B B 5C C C C C 5

In this first numerical example, since

● μcount 1 ¼13

X3i¼1

Counti;1 ¼ 13

5 + 5 + 5ð Þ ¼ 5;

and

● σcount1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13

X3i¼1

Counti;1 - μcount1� �2

vuut ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13

0 + 0 + 0ð Þ2r

¼ 0;

it follows that SUSTAIN1= μcount1/(σcount1+1)= 5/1= 5.

Example #2:

Year 1 Year 2 Year 3 Year 4 Year 5 Count

A A 2B 1

C C 2

In this second numerical example, since

● μcount2 ¼13

X3i¼1

Counti;2 ¼ 13

2 + 1 + 2ð Þ ¼ 1:67


252

and

● σcount2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13

X3i¼1

Counti;2 - μcount2� �2

vuut

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13

2 - 1:67ð Þ2 + 13

1 - 1:67ð Þ2 + 13

2 - 1:67ð Þ2r

¼ 0:47;

it follows that SUSTAIN2= μcount2/(σcount2+1)= 1.67/1.47= 1.13.

About the Authors

James R. Garven is the Frank S. Groner Memorial Chair in Finance at theHankamer School of Business, Department of Finance, Insurance and Real Estate,Baylor University.

James I. Hilliard is Assistant Professor of Finance at the W.A. Franke College ofBusiness, Northern Arizona University.

Martin F. Grace is the James S. Kemper Professor of Risk Management andInsurance at the Robinson School of Business, Georgia State University.


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adverse selection in reinsurance markets - james r....

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