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Insurers’ Solvency and Risk Management: The Effects on Loss Reserve Estimation Error

Elena Veprauskaite*, University of Bath, UK

Michael B. Adams, University of Bath, UK

Version: 24 February, 2014

ABSTRACT

We analyze the relation between loss reserving errors, solvency and risk management (reinsurance and derivatives hedging) in the United Kingdom’s (UK) property-casualty insurance industry using a dynamic panel data model. We test two alternative hypotheses. First, we test whether insurers under-reserve to reduce reported liabilities in order to improve their reported solvency position. This hypothesis implies a

positive relation between weak solvency and under-reserving. Second, we hypothesize that the insurance industry regulator is likely to require additional capital maintenance if an insurer’s loss reserves are understated. This implies a positive relation between weak solvency and over-reserving. Our results support the second hypothesis. We then examine whether risk management practices reduce the incentives for insurers to manage loss reserve accruals for solvency management. Our results suggest that insurers with high aggregate levels of reinsurance are less likely to manage their loss liabilities. However, we do not find that higher use of proportional reinsurance and derivatives affect loss reserving practices.

JEL Classification: G22, G32, L21

Keywords: Insurance; Solvency; Risk Management; Reserving; United Kingdom (UK).

Insurer Solvency, Risk Management & Reserve Errors

*Corresponding author: Ph: 00-44-(0)1225-384967 Fx: 00-44-(0)1225-386473 E: E.Veprauskaite@bath.ac.uk

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1. Introduction

In this paper we investigate the effects of United Kingdom (UK) property-casualty insurers’ solvency

risk and risk management practices on reported accounting earnings. A large body of research in the

accounting literature has examined whether, and if so, how managers use their discretion to manage

period earnings. For example, Healy and Wahlen [1999] note that earnings management occurs when

managers alter reported economic performance to mislead stakeholders and/or achieve certain self-

interest objectives such as the maximization of payoffs under bonus compensation plans. Firms can

manage reported earnings by either engaging in so-called ‘real’ earnings management or using

discretionary accounting accruals. Real earnings management includes changing investment strategies,

reducing/increasing research and development (R&D) expenditures, and/or modifying production

expenses (e.g., Lakdawalla and Zanjani [2012]). In contrast, accruals management involves adjusting

accounting numbers prepared under generally accepted accounting principles (GAAP) to affect reported

earnings (Healy [1985]). Here we examine earnings management decisions via the use of insurance loss

reserve accruals.

Prior research (e.g., Grace [1990], Petroni [1992]) highlights three main reasons for accrual analysis in

earnings and solvency management. First, as accruals are the main product of GAAP, it is more likely that

earnings management is exercised via accruals and not by the cash flow component of earnings. Second,

accruals analysis mitigates potential bias in measuring the effects of different accounting choices on

earnings. Third, given managerial judgment in setting accruals it is less likely that investors are able to

identify earnings management behavior from published accounting statements. However, the property-

casualty insurance industry is a potentially powerful setting for conducting accounting accruals research

as standardized statutory accounting data are publicly available that enables potential managerial bias in

loss reserving and solvency management decisions to be identified and analyzed (Petroni [1992]). This

attribute has spawned a large number of studies examining the impact of accruals management on

reported earnings, solvency reporting, and firm valuation – most notably in the United States (US)

property-casualty insurance industry (e.g., Browne, Ju, and Lei [2012], Eckles and Halek [2010], Gaver

and Paterson [2007], Petroni [1992], Weiss [1985]). However, regulatory and other institutional (e.g.,

accounting) differences between the US and other insurance markets such as the UK could influence

earnings management decisions in different ways (see section 2). For example, regulatory differences on

the use of reinsurance could affect the degree of discretion insurance managers have to make accrual

adjustments to loss reserves.

Our study has three main goals. First, we examine the relation between insurers’ solvency and the

management of loss reserve accruals. Insolvency risk management motives for reserve management

have political as well as economic importance for insurance firms as they are subject to ongoing

statutory solvency monitoring and prudential controls by industry-specific regulators (Serafeim [2011]).

Dechow, Ge, and Schrand [2010] observe that in the financial services sector there is often a direct link

between loss reserve accruals and capital requirements that heightens the regulatory significance of

research such as ours. Therefore, we test whether solvency of property-casualty insurance companies

affects the accuracy of loss reserves while controlling for firm-specific and institutional factors which

could affect the accuracy of loss reserving.

Second, we examine whether different risk management strategies influence the loss reserving

behavior of managers. Adiel [1996] argues that reinsurance can enhance accounting earnings and the

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regulatory capital position of insurance firms, and so creates opportunities for managers to meet

statutory solvency and other financial objectives. The relation between the levels of reinsurance and

discretionary loss reserving behavior has been analyzed recently for the US property-casualty insurance

industry (e.g., Grace and Leverty [2012], Plantin [2006]). However, the relation between the type of

reinsurance contract used (e.g., proportional and non-proportional) and reserving errors has not been

examined previously in the academic literature. The work of scholars, such as Eden and Kahane [1988],

however, implies that due to market information asymmetries the form of reinsurance contract (i.e.,

proportional versus non-proportional coverage) could affect the risk and capital management decisions

of insurance firms. That is, proportional and non-proportional reinsurance contracts can have variable

impacts on insurers’ reported period earnings as they affect differently the degree of reliance that

insurance managers place on the amount of capital and reserves needed to cover estimated future

losses. Therefore, our research fills a specific gap in the extant literature by examining whether different

reinsurance contracts affect the loss-reserving and earnings management practices of insurance firms. In

this sense, the study also contributes more broadly to the academic literature on costly contracting, risk

management, and their links with corporate accounting and financial reporting practices.

Insurance firms may not only use reinsurance to manage their solvency and other strategic (e.g.,

liquidity) risk positions but also use derivatives to hedge risks and uncertainties (Cummins, Phillips, and

Smith [2001], Harrington, Mann, and Niehaus [1995]). As derivative hedging can help insurance

companies to smooth period earnings and reduce the risks of financial distress and/or bankruptcy,

insurance companies that use derivatives could have less incentives to manage loss reserves for

purposes of earnings and solvency management than insurers that do not use derivatives. As such, our

third objective is to test whether risk management via derivative hedging reduces reserving errors.

We consider that our study makes three key contributions to the extant literature. First, our UK

results are in some ways different from prior US insurance research. For example, we find that UK

property-casualty insurers with higher solvency risk (measured by surplus-to-asset and net premium-to-

surplus ratios) tend to under-estimate their claim liabilities (increase shareholders’ capital and surplus).

This result suggests that insurance managers in the UK could be motivated to under-estimate claim

liabilities if they hold a sufficiently large amount of solvency capital; alternatively, the regulator could

require an additional capital to be held if the reserve levels are deemed to be under-estimated. This

result is contrary to prior US-based studies (e.g., see Gaver and Paterson [2004], Grace and Leverty

[2010]) that find that financially weak insurers usually understate loss reserves. Therefore, accounting

treatments (e.g., use of loss reserve accruals) and earnings management behavior could vary across

insurance markets as a result of different institutional (e.g., regulatory) and firm-specific (e.g., risk

management) practices. Second, our results suggest that the volume of reinsurance reduces the

incidence of reserve errors as it enables insurers to hedge non-core risks. In this regard, our findings are

consistent with prior US-based studies (e.g., see Adiel [1996]) suggesting similarities in the risk

management use of reinsurance between the UK and US. However, improved insurer monitoring due to

reduced information asymmetries under proportional reinsurance cover and reduced variability in future

firm’s value due to derivative hedging do not affect the accuracy of loss reserves. Third, our study

complements prior research by showing that the managers of insurance firms behave differently (e.g., in

terms of their risk management practices) depending on the direction of earnings management (i.e.,

earnings increasing or decreasing) and the regulatory regime under which they operate. This insight

could inform earnings management research in other industrial sectors (e.g., banking) and in this regard,

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our research could have wider appeal beyond the insurance industry. The reminder of our paper

proceeds as follows. In the next section we give an overview of the main reporting and regulatory

differences between UK and US property-casualty insurance markets. In section 3, we motivate and

formulate our research hypotheses. In section 4, we define the variables, describe the sources of data

used and sample selection. Section 5 specifies our modelling procedure and analyzes the empirical

results. Finally, section 6 concludes our study.

2. Regulatory and reporting in the UK and US property-casualty insurance markets

The systems of accounting and solvency monitoring in the UK and US property-casualty insurance

markets have evolved differently over the last two decades or so. For example, Gaver and Paterson

[1999] report that the US has had risk-based capital (RBC) solvency requirements since 1993/94 and that

the introduction of the RBC system has blunted managerial incentives to manage (understate) loss

reserves in order to improve solvency margins. This is because the new RBC rules incorporated a wider

assessment of insurance firm-specific risks (e.g., asset risk, credit risk, and so on) beyond statutory

minimum levels of capital adequacy. Such provisions gave US insurance industry regulators greater

powers of intervention in cases of non-compliance with RBC rules. Since 2005, the UK has had a less

formulaic and ‘lighter touch’ principles-based approach to solvency reporting than the US. For example,

UK solvency regulations allow insurers to build their own risk-based capital models that are then subject

to regulatory scrutiny ex-post. Conway and McCluskey [2008] note that this approach, which is currently

reflected in the European Union’s (EU) draft Solvency II capital requirements, derives from metrics that

are commonly used in the banking sector such as value-at-risk (VaR) models. In contrast, the US system

of solvency regulation has relied on factor-based methods adopted from rating agency formulae and

dynamic financial analysis (DFA). Moreover, accounting treatments and financial reporting practices in

the US are subject to potential enforcement actions by the omni-powerful Securities and Exchange

Commission (SEC) (McNichols [2000]). Therefore, different loss reserving methodologies could influence

the accounting (e.g., loss reserve accruals) decisions of UK insurance managers in different ways

compared with their counterparts in the US. For example, the UK’s less prescriptive principles-based

regulatory regime could give the managers of insurance firms relatively more discretion to manage loss

reserves and period earnings. As noted earlier, such institutional differences in regulation could help

explain observed differences in accruals (loss reserving) and earnings management behavior between UK

and US insurance firms.

The post-2005 solvency monitoring regime in the UK emerged at about the same time that the EU-

endorsed International Financial Reporting Standard (IFRS) 4 which established changes in the

accounting rules for UK and other European insurers from 1 January 2005. These changes differ from the

financial reporting for US property-casualty insurers covered by US GAAP. For example, IFRS 4

introduces, amongst other things, the recording of assets and liabilities at fair market value, which could

impact on loss reserving and solvency management. The increased volatility induced by fair market value

accounting and restrictions on earnings smoothing via the use of equalization reserves could encourage

the managers of UK property-casualty insurers to use discretionary loss reserve accruals to a greater

extent than previous. This is particularly likely given that IFRS 4 does not set out in detail the accounting

treatment and disclosure requirements for insurance transactions including movements on reserves

(Serafeim [2011]). Accordingly, variations in accounting rules could again potentially provide different

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managerial incentives for loss reserve management in the UK compared with the US. Additionally, over

the last three decades or so the US property-casualty insurance industry has been subject to legislative

developments, such as the Superfund (pollution) legislation. Such legal initiatives have created large

actual and potential numbers of environmental insurance liability (tort) claims that has put increased

pressure on US insurers to manage reserves and use other mechanisms (such as reinsurance) to manage

period earnings (e.g., see Hooker, Bulmer, Cooper, Green, and Hinton [1996]). In contrast, UK property-

casualty insurers have not been subject to such legislation, which could further influence the

discretionary loss reserving decisions of managers in ways that are different from their US counterparts.

Again, these jurisdictional attributes make the UK a particularly pertinent environment within which to

conduct the current study and compare our results with those of prior US studies.

Gaa and Krinsky [1988], Klein and Wang [2009], and others note that in the US each state is

responsible for regulating the market practices of insurers operating in its jurisdiction. Although the

states use the National Association of Insurance Commissioners (NAIC) standards to guide and

coordinate their regulatory activity, the adoption of NAIC standards is not compulsory leading to

regulatory and reporting differences among the states. In 1993 the NAIC added the Financial Analysis

and Surveillance Tracking (FAST) system that identifies those insurers that will be subject to regulatory

review, and if necessary, intervention (Grace and Leverty [2010]). Nelson [2000] reports that in the US,

insurance company managers subject to stringent premium rate regulation (e.g., as in New York state)

could be motivated to implicitly discount loss reserves from future to present values and report loss

reserves below the nominal level prescribed by accounting rules in order to increase period earnings1.

On the other hand, some US studies (e.g., Cummins and Harrington [1985]) provide evidence to the

contrary by suggesting that premium rate regulation could lead insurers to over-estimate reserves to

ensure that rates charged in the underwriting process are adequate. In contrast, the UK is, as mentioned

earlier, a unitary regulatory/fiscal regime, and so UK insurance firms are not subject to such potentially

confounding and conflicting regulation-induced effects in terms of their earnings management behavior.

As such, our UK-based study could provide potentially cleaner and more robust inferences on the risk

management behavior of insurance firms.

The Sarbanes-Oxley (SOX) Act was enacted in 2002 by the US Federal government to improve the

credibility of corporate financial reporting in listed companies. SOX is a rules-based corporate

governance Act and works on a ‘comply or be punished’ principle (Cummins and Trainar [2009]). A key

objective of SOX is to improve the reliability of financial statements reported to investors by reducing

earnings management and accounting fraud (Cowley and Cummins [2005]). Specifically, Section 302 of

Title III (Corporate Responsibility for Financial Reports) highlights the responsibility of the board to

ensure the ‘true and fair’ nature and transparency of financial reports. Finken and Laux [2009] in their

analysis of US nonfinancial firm data in the period of 1987-2005 find that accrual management increased

steadily before the implementation of SOX followed by a significant decline after the passage of SOX.

From their analysis of US listed company data Cowley and Cummins [2005] also find that SOX reduced

the scope for earnings management and improved the quality of financial statement information.

Following the passage of SOX in the US, the UK government passed the Companies Act [2006] which

came into force in 2008. The Companies Act [2006] contains revised measures on a wide range of issues, 1 Implicit discounting of property-casualty insurance company claims reserves is not generally accepted statutory

accounting practice in the US. However, some US researchers (e.g., Nelson [2000], Petroni [1992]) report that the implicit discounting of loss reserves is, nonetheless, common practice in the property-liability insurance industry.

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such as financial reporting and directors’ responsibilities. However, unlike SOX the Companies Act [2006]

is a ‘lighter touch’ statute that works on the ‘comply or explain’ principle (Cummins and Trainar [2009]).

Again, this implies that other things being equal, managers in UK property-casualty insurers are likely to

have relatively more discretion over the use of discretionary loss reserve accruals than their

counterparts in the US.

Cole and McCullough [2006] suggest that to minimize the risk of default on reinsurance contracts, US

regulations discriminate between domestic US reinsurers and foreign (‘alien’) reinsurance companies in

terms of prescribed differences in the amount of collateral that has to be maintained by US-based

primary insurance carriers. Failure to meet such collateralization rules penalizes the primary insurer by

requiring it to establish a liability provision in the balance sheet for ‘unauthorized reinsurance’.

Therefore, only primary US insurers purchasing reinsurance from authorized US reinsurers can reduce

their balance sheet liabilities (improve their capital strength) by reporting loss reserves net of

reinsurance. Collateralization rules can also distort the supply of reinsurance in the US insurance market.

For example, compared with foreign reinsurance companies, authorized US reinsurers are likely to be

better informed about the insolvency risk of insurers and so only reinsure financially strong entities.

Therefore, all else equal, financially weak primary insurance carriers reinsuring with unauthorized

reinsurance companies are expected to have a relatively high incidence of under-reserving error and

thus more likely to engage in earnings management (Petroni [1992]). In contrast, the UK’s insurance

regulations do not discriminate between domiciled and non-domiciled reinsurance suppliers. As such,

the present study avoids the potential biases that such discriminatory rules could have on primary

insurers’ use of loss contingent capital (reserves and reinsurance), reserving accounting practices, and

ultimately reported period earnings. This attribute is another potential advantage for focusing the

current research in the UK’s property-casualty insurance industry.

3. Hypotheses development

3.1 EFFECTS OF INSURERS’ SOLVENCY RISK ON LOSS RESERVING ERRORS

Sommer [1996] notes that insurers’ profitability is inversely related to insolvency risk, and that

increased financial distress can directly affect the market demand for insurance, particularly as

policyholders are likely to be concerned about the ability of insurance firms to meet their future fixed

claims under insurance contracts. Several US studies (e.g., Beaver, McNichols, and Nelson [2003], Gaver

and Paterson [1999], [2000], [2001], [2004], Petroni [1992]) report that insurance company managers

can understate loss reserves in order to reduce reported loss liabilities and avoid the costs of regulatory

scrutiny, financial distress, changes in the consumer demand for insurance products, and in extreme

cases, insolvency. Indeed, prior research (Abdul Kader, Adams, and Mouritidis [2010], Adiel [1996])

reports that solvency management goals often predominate over other financial management decisions,

particularly when leverage increases beyond target levels. Gaver and Paterson [2004] and Grace and

Leverty [2010] observe that discretionary accruals adjustments to loss reserves enables US property-

casualty insurers to meet statutory solvency performance measures known as Insurance Regulatory

Information Service (IRIS) ratios. As loss reserves represent the largest liability on insurers’ balance

sheets, under-reserving reduces reported liabilities, increases insurers’ surplus, and therefore enables

insurers to appear less risky than otherwise would be the case. Therefore, the first hypothesis is that:

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H1 A: Property-casualty insurers with higher solvency risk tend to report understated loss reserves.

Well-established solvency monitoring systems should identify insurance companies in weak or

deteriorating financial condition early enough to permit regulators to take corrective actions and

therefore minimize insolvency risk in insurance markets. In the UK, property-casualty insurers during the

period of our analysis were regulated by a sole regulator - the Financial Services Authority (FSA)2

(Financial Services and Markets Act [2000]). Following the failure (or financial distress) of an insurance

company, both market confidence falls and various stakeholders (e.g., investors and policyholders) suffer

economic losses (Cummins and Sommer [1996]). To maintain confidence in the UK’s financial markets,

the FSA monitors insurer solvency by conducting periodical audits and evaluating regulatory solvency

returns that have to be submitted on an annual basis by the insurance companies operating in the UK.

Furthermore, as both over-reserving and under-reserving can significantly affect insurers’ solvency

position, UK property-casualty insurers are required to disclose revisions to loss reserves in their

regulatory returns. Therefore, under statutory powers granted under section 138 of the Financial

Services and Markets Act [2000] the UK insurance industry regulator can insist on additional

regulatory capital to be held if an insurer’s loss reserve levels are deemed to be inadequate for the

purpose of statutory solvency maintenance. However, reporting loss inflating discretionary reserves

is less costly for a financially weak insurer than raising external finance (Myers and Majluf [1984]).

Inflating loss reserve estimates whilst keeping equity levels constant can enable financially weak UK

insurers to maintain a normal rate of return on equity and stabilize their cost of capital under

competitive market conditions3. Managerial discretion in structuring the balance sheet is also

permitted under the self-developed risk-based capital models used in the UK as long as the insurer’s

estimates of future claims experience and other risks (e.g., with regard to inflation) meet with

regulatory approval4. As a result, property-casualty insurers in the UK that are close to statutory

minimum levels of solvency are likely to have greater incentives to overstate than understate their

loss reserve estimates compared with their counterparts in the US. Therefore, an alternative

hypothesis is that:

H1 B: Property-casualty insurers with higher solvency risk tend to report overstated loss reserves.

An agency theory-based argument relevant to understanding the reserving-risk relation is provided by

Harrington and Danzon’s [1994] ‘moral hazard hypothesis’. This hypothesis holds that due to the ‘default

put option’ feature of corporate limited liability and the existence of market-wide policyholder

guarantee funds, the owners/managers of financially weak insurers could be motivated to increase

2 From 1 December 2001 FSA became the sole independent regulator of the UK insurance (and other financial

services) industry (Financial Services and Markets Act [2000]). The regulatory powers of insurance industry were held by the Department of Trade and Industry until 1997, and from 1997 by the Insurance Directorate of HM Treasury. From 1 April, 2013, a new regulatory regime for financial services came into effect. The FSA has been replaced by the Financial Conduct Authority (FCA) and the Prudential Regulation Authority (PRA) – two bodies that are part of the Bank of England’s UK financial services supervisory framework. The new regulatory regime is not relevant to our study as the current study covers the data from 1991 to 2005.

3 During the period of our analysis (1991 to 2005) the UK was a very price competitive international insurance

market (e.g., see Klumpes [2004]). 4 For example, Gamba and Triantis [2008] point out that highly levered firms can still retain high levels of liquidity

(e.g., in order to meet immediate debt obligations).

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underwriting risks (lower premiums) in order to increase rates of new business growth. This implies that

managers will under-reserve to mask increased underwriting risks resulting from growth in volumes of

new business premiums (e.g., given the possibility that assumed risks may be priced below actuarially

fair rates in order to meet new sales targets and possibly, managerial bonus plan targets). To increase

underwriting capacity and alleviate the risk of insolvency and potential agency problems, such as the

underinvestment incentive, the managers of insurance firms will reinsure some of the underwriting risk

assumed (Mayers and Smith [1990])5. Such use of reinsurance can strengthen the balance sheet and

improve the reported earnings position of insurers and so, again, have positive signaling benefits (Adiel

[1996]). As a consequence, the next hypothesis is:

H2: High premium growth and highly reinsured property-casualty insurers tend to report under-stated

loss reserves.

3.2. Effects of Risk Management on Loss Reserving Errors

Risk transfer via reinsurance can help to smooth company earnings and therefore reduce the need of

earnings management (Garven and Lamm-Tennant [2003]). Reinsurance enables primary insurers to

retain smaller risk exposures and reinsure larger ones thereby reducing their future claims liabilities.

The use of reinsurance to reduce risk and uncertainty enables insurers to reserve for future liabilities

more accurately, and thus reduce reserving errors. Reinsurance companies also play an important role

in alleviating information asymmetry problems (adverse selection and moral hazard) and controlling

agency incentive conflicts in the primary insurance carriers that they deal with (Browne, et al. [2012],

Doherty and Smetters [2005], Plantin [2006]). For example, reinsurance companies will adjust ex-post

reinsurance commissions and reinsurance premiums in the event of greater than anticipated loss

experience by the primary insurer. Reinsurance company managers also closely monitor and control

(audit) the primary insurers’ systems for underwriting, policy servicing, and claims settlement in order to

mitigate the risk of agency problems such as risk-shifting (asset substitution) behavior after reinsurance

arrangements have been agreed. Plantin’s [2006] notion of the ‘credible signaling’ benefit of reinsurance

further implies that insurers that purchase greater amounts of reinsurance are likely to be subject to a

greater degree of monitoring and control by reinsurance managers and thus have a lower incidence of

reserve estimation errors. Therefore:

H3: Highly reinsured property-casualty insurers tend to report more accurate loss reserves.

Eden and Kahane [1988] and Winton [1995] suggest that for information asymmetry reasons the form

of reinsurance contract used can also affect risk and capital management decisions in insurance firms.

Under proportional reinsurance (e.g., a quota-share cover) the insurer and reinsurer share premiums

and losses proportionally. Proportional reinsurance spreads the risk of loss and creates a ‘broad identity’

of financial interest between the insurer and reinsurer. As such, the reinsurer is able to acquire

5 The underinvestment incentive relates to the risk, particularly in highly leveraged states, that shareholders may

not reinstate collateral assets following a severe loss event as the gains from reinstatement accrue to debt-holders rather than themselves. In such a situation, shareholders may exercise their ‘default put option under limited liability rules and voluntarily liquidate the firm. However, Jia, Adams, and Buckle [2011] note that the underinvestment incentive can be mitigated by (re)insurance contracts in that the proceeds from (re)insurance claims can be used to reinstate assets after unexpectedly severe loss events and thus minimize the risks (costs) of financial distress and/or bankruptcy.

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information on the adequacy of the insurer’s capital, reserves and risk management systems, and

therefore act as an effective monitor of the insurer’s underwriting and other operations. In contrast,

under non-proportional reinsurance contract (e.g., excess-of-loss) the reinsurer does not participate in

every loss event. Therefore, if losses to the insurer are less than the retention specified in the

reinsurance contract then the reinsurer owes nothing. Accordingly, the insurer does not need to share as

much risk and other business information with its reinsurance partners under non-proportional

reinsurance compared with proportional reinsurance covers. As a result, because of increased

information asymmetries under non-proportional reinsurance the reinsurer becomes a relatively less

effective monitor of the insurer’s business operations. Thus:

H4: Property-casualty insurers that predominantly use proportional reinsurance cover tend to report

more accurate loss reserves.

Insurers can use both derivatives and reinsurance to hedge risk. Derivatives could either complement

or substitute for reinsurance. The use of derivatives can also help insurers to smooth period earnings,

manage tax liabilities, and avoid the costs of financial distress and/or bankruptcy. The concept of

reducing economic risk through the use of derivatives has been studied extensively in finance literature

(Cummins, et al. [2001], Harrington, et al. [1995], Smith and Stulz [1985]). Cummins, et al. [2001] note

that there is a penalty for insolvency risk in insurance markets and that hedging (and other risk

management activities) can help to maintain low insolvency probabilities. As derivatives hedging can

help insurance companies to smooth period earnings and reduce insolvency risk, insurers that engage in

derivative hedging are expected to have lower incentives to manage loss reserves for purposes of

earnings and solvency management than insurers that do not manage business risks using derivatives.

Therefore, our fifth hypothesis is:

H5: Property-casualty insurers that use derivatives tend to report more accurate loss reserves.

4. Sample selection, model, and variable definitions

4.1. SAMPLE SELECTION

All firms covered by Standards & Poor’s SynThesys Non-Life Insurance Companies Database were

initially selected to derive the final sample used in the current study. This database provides the details

on the annual solvency returns submitted to the UK regulatory authorities by UK-licensed insurance

companies for the period of 1985-2010. The data applies to domestic and overseas-owned insurance

companies that directly write insurance business in the UK. Regulatory returns are also reported

separately for each trading company within conglomerate insurance groups. Before 1996, UK property-

casualty insurers were only required to disclose their loss development history for the previous five

accident years. Both Weiss and KFS reserve-estimation techniques used in this study require a five to

nine-year resolution period to estimate Incurred/Developed Losses at t+5 (see section 4.3) thereby

reducing the reserve error sample period examined to 1991-2005. There were also some mergers and

acquisitions (particularly during the late 1990s) and intra-company restructurings in the UK’s property-

casualty insurance industry which could affect the reported financial data. Therefore, firm/years are

eliminated from the sample if the following criteria are not met:

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Missing values for any of the variables used in the models preclude an insurer from being

included in the sample.

Insurers must have positive reserves, incurred losses, total assets and gross premium written.

Insurers must have loss reserves that are subject to managerial discretion. Therefore, insurers

which cede all the premiums to other (re)insurers and/or write more than 25 percent of their

premiums for accident and health, surety and credit insurance or reinsurance contracts are

eliminated from the sample6.

Insurers should not have missing data and/or significant change in their loss reserves for the

same accident year. This was checked by comparing the figure for ‘claims outstanding (net) at

the end of the accident year’ t-1 (Form 23, Column 2, Row 12 in the FSA reports) in calendar year

t with the corresponding figure for the same accident year in the five calendar years t+1 to t+5

(e.g., Rows 13 to 17 respectively). Firm/years were rejected if any one of these five comparisons

differed by 5% or more of the original figure.

To conduct the dynamic panel analysis used in the present study, each insurance firm in our

sample had to have at least three consecutive years of data. Thus, insurers with less than three

years of consecutive data are eliminated from the sample.

Appendix A provides details of the initial and final sample over the period of our analysis (i.e., 1991 to

2005). Data limitations created by the five-year loss reserve error calculation methods and the

availability of at least three years consecutive data produce an unbalanced dataset of 1,386 firm/year

observations based on 151 UK property-casualty insurers ranging from 66 to 107 firm cases per annum.

4.2. MODEL

To test our hypotheses stated in section 3, the general form of regression equation is estimated as

follows:

( )

( )

(1)

where subscript i denotes ith insurer (i = 1, … , 151), subscript t denotes the tth year (t = 1991, … , 2005).

Errorit is our dependent variable – Weiss or KFS. Both the Weiss and KFS loss reserve error estimates are

scaled by total assets (e.g., see Beaver, et al. [2003], Eckles and Halek [2010], Grace and Leverty [2012]).

Over-Reserve and Under-Reserve are dummy variables indicating the direction of the error (e.g., Over-

Reserve is equal to 1 and Under-Reserve is equal to 0 if reserve-error is positive). and are

vectors with K representing the number of Incentives variables; while, and are vectors with L

representing the number of Controls variables. Subscripts O/U denotes coefficient estimates for

variables if reserve-errors are positive/negative. Incentivesit represents our (incentives-based)

6 Similar requirements are also imposed by Petroni [1992], and Gaver and Paterson [1999, 2000]. In addition,

Petroni [1992, p. 488] note that insurers that cede all their premiums to reinsurers do not have discretion over loss reserves. Insurers, that write the majority of their business for commercial financial loss (e.g., surety, credit), accident and health, have reduced discretion over loss reserves as reserves for these lines are largely determined using well-established actuarial tables.

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explanatory variables; and Controlsit includes relevant institutional and firm-specific variables described

in sections 4.4 – 4.6. The disturbance term is specified as a two-way error component model in the form:

(2)

where denotes an insurer-specific effects, λt denotes year-specific effects and denotes the

remainder disturbance.

In equation (1), if error term μi is correlated with the explanatory variable, the coefficient estimates

are biased. That is, the Within estimator produces upward biased results and Fixed-Effects downward

biased results. Accordingly, a lagged dependent variable (e.g., Errori,t-1) is included in the equation as an

explanatory variable that is correlated with μi. To solve a potential ‘bias problem’, Arellano and Bond

[1991] propose that firm-specific effects can be eliminated by taking the first difference of equation (1).

That is:

( )

( )

(3)

where

( ) ( ) ( )

(4)

Though fixed-effects (μi) are eliminated by first-differencing, Errori,t-1 is still potentially endogenous as

Errori,t-1 in is correlated with in .

However, this can be resolved using the lagged values of the explanatory variables in levels as

instruments in difference equation (Hsiao [2003]). For example, valid instruments for (

) are the lagged levels , as [ ( )] ,

as long as and are not serially correlated.

Two additional problems can nonetheless arise from estimating equation (1) by differencing. First, the

‘cross-insurer’ dimension of the data is lost because it does not vary with time. Second, if the dependent

variable in equation (1) is persistent over time, then the lagged value is a potentially weak instrument for

the differenced equation. Again, this can produce biased estimates (Baltagi [2005]). Blundell and Bond

[1998] demonstrate that the use of additional linear model conditions for the levels equations can

substantially improve estimates if the additional restriction of no serial correlation in is imposed. This

method employs lagged differences of variables as instruments for equations in levels, in addition to

lagged levels of variables as instruments for equations in first differences. This method, called System

GMM (GMM-SYS), has been proposed by Arellano and Bover [1995] and has been used in some of recent

studies reported in the finance literature (e.g., Florackis and Ozkan [2009]).

On the other hand, the asymptotic efficiency gain in GMM-SYS by including additional equations in

levels does not come without drawbacks. For example, the number of instruments increases

exponentially with the number of time periods which leads to finite sample bias which could render

12

specification tests, like the Hansen [1982] J-test, misleading (Baltagi [2005]). Roodman [2009] identifies

two main techniques to limit the number of instruments generated in GMM regression. The first is to

limit the lag number used for instruments. This technique still enables one to generate instruments for

each period, but the number of the instruments per period is capped. The second is the use of a

collapsed instrument matrix. Collapsing enables to lose a minimal amount of information and makes the

instrument count linear in Time. We both limit the lag number used for instruments and use a collapsed

form of instrument matrix in the present study.

In an unbalanced panel data design (as used in this study) first-differencing ‘enlarges gaps’ and may

possibly completely eliminate the data set in first-differences. Therefore, Arellano and Bover [1995]

propose a transformation called the “forward orthogonal deviation” or “orthogonal deviation”. This

method, instead of subtracting the previous observation from the contemporaneous, subtracts the

average of all future available observations. As a consequence, the orthogonal deviation is computable

for all observations, except the last for each insurer, no matter how many gaps exist in the sample. This

procedure thus helps to mitigate data loss.

4.3. LOSS RESERVE ERROR PROXIES

The difference between the quantum of loss reserves in any given period and the amounts actually

needed to settle a loss is known as the loss reserve estimation error (Nelson [2000]). Ideally, reserve

errors would be measured by taking the difference of the originally obtained reserve (i.e., outstanding

claims + incurred but not reported (IBNR) losses) and the fully developed reserve (i.e., the sum of all

claim payments associated with that reserve). However, this estimation is often impractical because of

the lack of complete and accurate loss development data. As noted earlier, prior insurance industry-

based accounting studies employ one of two main methods for calculating reserve errors. The Weiss

[1985] method is the difference between the estimated incurred value of losses (including IBNR)

reported in yeart and the cumulative actual amount of loss development settled in the future accounting

period yeart+n. That is:

(5)

The KFS approach is the variance of the estimated incurred value of losses (including IBNR) reported

in yeart and the re-estimate of these incurred losses given n years of loss development (e.g., in yeart+n)

(Kazenski, Feldhaus, and Schneider [1992]), namely:

. (6)

In estimating reserve errors, it is desirable for n to be as large as possible (Petroni [1992]). UK

regulatory filings require insurers to disclose, for the current and nine preceding (development) years,

the original reserve, the reserve as re-estimated in each following year, and the cumulative amount paid

against the reserve in each subsequent year. Thus, the largest possible n is nine years. Although ‘large’ n

results in more accurate loss reserve estimation error it can significantly reduce the size of the sample

dataset (e.g., for n=9, the sample is reduced by nine latest years). Therefore, the objective is to choose n

13

large enough to detect statistically significant reserve errors within a sample of insurers without unduly

limiting the sample size.

Figure 1 illustrates the average settlement periods for five main lines of UK property-casualty

insurance business, namely: motor (MOT), property (PROP), legal liability (LIAB), miscellaneous and

pecuniary loss (MIS&PEC), and aviation, marine and goods in transit (AMG). Figure 1 shows that there is

a substantial variation in average claims settlement across lines of insurance business. For example, over

90% of all PROP and MIS&PEC claims are settled within two years of occurrence, on average, compared

with only 40% of LIAB claims. The average settlement period recorded in Figure 1 further shows that the

optimal n for reserve error estimation differs across lines of insurance business. Managerial discretion

over loss reserves will thus tend to be significantly lower in relatively predictable lines of business (e.g.,

motor) where claims are settled relatively quickly relatively to more unpredictable segments of the

insurance market (e.g., legal liability) where the quantum and timing of losses can take many years to

determine – i.e., so-called long-tailed lines.

[INSERT FIGURE 1 HERE]

Kazenski, et al. [1992] examine the sufficiency of alternative loss development horizons in estimating

reserve errors and find that no single loss development horizon is adequate for all lines of property-

casualty insurance. However, Kazenski, et al. [1992] note that two to three years of loss development are

sufficient to detect statistically significant reserve errors within a sample of insurers. Figure 1 shows that

in the UK, only about 40% of legal liability claims (a typical long-tailed line) are settled inside three

development years. This can bias loss reserve error estimations for those companies that predominantly

write long-tailed lines of insurance business. Thus, as in prior studies (e.g., see Eckles and Halek [2010],

Gaver and Paterson [2004], Petroni [1992]), n=5 years is used here to examine the magnitude and

discretion of loss reserve error. Following Grace and Leverty [2012], we use the five most recent accident

years (e.g., t-4, …, t) to estimate the incurred losses (Incurred Lossesi,t) for both Weiss and KFS errors .

The five most recent accident years capture the greater part of calendar year reserves; loss reserves for

subsequent accident years (t-5 to t-9) generally form a small part of total reserves. In addition, the

following five year period (n=5) for unexpired risk ((t-4)+5, (t-3)+5 …, t+5 = t+1, t+2, …t+5) is used to

examine the magnitude and discretion of loss reserving error (Incurred Lossesi,t+5 and Developed Losses

Paidi,t+5).

4.4. SOLVENCY RISK

Solvency: To approximate insurer’s solvency risk we employ the following equations:

(7)

where Surplus is the sum of capital and shareholders fund ; Total Assets are tangible fixed and current

assets of an insurer that are used by UK insurance industry regulator to assess annual statutory minimum

levels of solvency . The smaller the ratio, the lower resource capability an insurer has to meet its financial

obligations to policyholders. If H1A is not rejected, we predict that financially ‘weak’ insurers (i.e., low

Solvency) will understate loss reserves so as to improve their reported financial condition and avoid

insolvency risk and the political costs associated with enhanced regulatory scrutiny (Beaver, et al. [2003],

14

Petroni [1992]). On the other hand, if H1B is not rejected, we predict that insurers with low Solvency

ratios will have positive reserve errors in order to improve statutory solvency requirements prescribed

by the regulator.

Leverage: For robustness we also employ an alternative measure of insurers’ solvency risk – Leverage,

which is estimated as a ratio of net premium written to surplus at year end (Eden and Kahane [1988],

Gaver and Paterson [1999]). Thus, Leverage measures the ability of insurer to absorb above-average

losses. The greater an insurer’s leverage, the higher the ratio. Therefore, insurers with higher ratios are

expected to be more risky (and financially weaker) than those insurers with lower Leverage measures. If

H1A is not rejected, we expect to find positive relation between Leverage and negative reserving errors.

Alternatively, if H1B is not rejected, we expect to find positive relation between Leverage and positive

reserving errors.

Rein x Growth: Harrington and Danzon [1994] suggest that managers of high premium growth

insurers can increase underwriting capacity and alleviate the risk of insolvency resulting from the growth

in volumes of new business premiums by reinsuring some of the underwriting risk assumed and under-

reserving their claim liabilities. Therefore, we predict that insurers with high rates of business growth

and high levels of reinsurance will have understated loss liabilities (H2).

Reinsurance: The level of reinsurance is measured employing the variable used commonly in previous

research analyzing the corporate demand for reinsurance (e.g., see Adiel [1996]), namely:

(8)

This measure represents the total volume of reinsurance purchased by an insurance company.

Growth: As in Grace and Leverty [2010], Growth is measured as the ratio of annual increase in net

premiums written. We use normalized Reinsurance and Growth variables to reduce potential

multicollinearity.

4.5. RISK MANAGEMENT

Reinsurance: Garven and Lamm-Tennant [2003] note that risk transfer via reinsurance can help to

smooth company earnings and therefore reduce the need of earnings management. Moreover, as a

highly reinsured insurer is likely to be a subject to tighter control and monitoring by its reinsurance

partner (Plantin [2006]), it is expected that Reinsurance will have a negative relation with respect to the

size of loss reserve errors (H3).

Proportional: To measure the level of proportional reinsurance ceded the following ratio is estimated:

(9)

Proportional reinsurance helps primary insurers minimize the effects information asymmetries at the

point of sale (e.g., adverse selection) by sharing with third party reinsurers a proportion of the expected

value of the loss distribution associated with the risks underwritten. Proportional reinsurance further

15

helps enhance the solvency position of primary insurers without changing the nature of the expected

distribution of future losses thereby enabling loss reserves to be more accurately determined ex-ante. In

contrast, non-proportional reinsurance helps reduces variance uncertainty only in the extreme tail of the

expected loss distribution (Eden and Kahane [1988]). This makes setting reserves for retained losses

difficult for insurance managers to establish with precision when non-proportional reinsurance

predominates – as it often does in long-tail lines of insurance such as legal liability. As a result, it is likely

that Proportional will have a negative relation with respect to the size of loss reserve estimation errors

(H4).

Derivatives: Smith and Stulz [1985] find that derivatives hedging reduces the variability of the future

value of the firm and so lowers the probability of insuring costs related to insolvency risk. Thus insurers

that use derivative hedging are expected to have lower incentives to manage their loss reserves for

purpose of earnings and solvency management. Following Colquitt and Hoyt [1997] and Shiu [2011], our

Derivatives variable is labeled 1 for a derivative user (i.e., an insurer has nonzero year-end derivative

position or if derivatives are open at the end of the previous year) and 0 for a nonuser.

Rein x Deriv: Insurers can use both reinsurance and derivatives to manage their business risks. It is

expected that the use of both reinsurance and derivative hedging reduces the volatility of insurers’

performance and so reduces the motives for insurers to manage their loss reserves to smooth their

reported performance. We thus create an interaction variable between Reinsurance and Derivatives. We

also use normalized Reinsurance and Derivatives variables to reduce multicollinearity.

4.6. CONTROL VARIABLES

We use various control variables that prior studies indicate to be associated with loss reserving

errors.

ROA: Petroni, Ryan, and Wahlen [2000] find that the return on assets (ROA) is associated with the

income smoothing hypothesis. That is, the greater (lower) past average ROA, the greater the

management incentives to under- (over-) reserve. ROA is measured as earnings before interest and tax

(EBIT) divided by the beginning of the year book value of total assets. Based on the extant literature (e.g.,

see Grace [1990]), the present study measures income smoothing as the average ROA over the past

three years. We anticipate that insurers with on average larger ROA over the past three years will have

underestimated their loss reserves.

Std_ROA: Higher risk insurers may have higher incentives to manage their loss reserve liabilities than

their lower risk counterparts. Furthermore, increased variability in insurer’s performance may lead to

higher incidence of reserve error. We therefore include a risk measure (Std_ROA) as a control variable

which is measured as the standard deviation of an insurer’s ROA over the past five years (e.g., see Berry-

Stölzle, Hoyt, and Wende [2013]).

Tax Shield: Adiel [1996] reports that the tax liabilities of property-casualty insurers are normally

calculated as a function of annual underwriting and investment income less incurred losses (which

include claims reserve estimates), and that over-reserving can reduce (or postpone) period taxes (by

reducing reported earnings), while under-reserving can have the opposite effect (by increasing reported

earnings). Petroni and Shackelford [1999] note that in the US insurers often shift premiums and losses

across state jurisdictions and accounting periods in order to reduce their overall corporate tax liabilities.

16

Prior research (e.g., Grace [1990]) measure the managerial incentives to reduce tax liabilities as a tax

shield benefit derived from:

( )

(10)

Equation (10) represents the level of taxable income before reserves as the ratio of total assets. Grace

[1990] contends that insurers tend to inflate reserves for future losses as their taxable income increases.

As a result we expect that Tax Shield will be positively related to over-reserving.

Long-Tail: Petroni and Beasley [1996] observe that insurers writing long-tail insurance (e.g., legal

liability) tend to have greater reserving errors than other insurers. This is due to the difficulty of

accurately estimating the probability, quantum and timing of potential insurance claims. Therefore, the

variable for insurer’s participation in long-tailed lines of business (Long-Tail) is included in the model. As

in Browne, et al. [2012] this variable is defined as the proportion of annual net (of reinsurance)

premiums written on legal liability insurance (e.g., employers liability, professional indemnity, public and

product liability) to total annual net premiums written.

Product Mix: Mayers and Smith (1990) suggest that all else equal, insurers with a more diversified

product mix are likely to be better able to diversify business risks and so less prone to reserve errors than

more specialist insurers. Accordingly, a product mix variable (Product Mix) is included in the model. As in

Mayers and Smith [1990], product mix is measured by a Herfindahl concentration index that is computed

using 12 major lines of products sold by UK property-casualty insurers7. The Herfindahl index is

computed for each company as:

∑(

)

(11)

where DPWl is the amount of direct premium written in the lth line of insurance and TPW is the amount

of total premium written across property and liability lines by an insurer i in year t (source: Form 20A of

the UK regulatory returns). The closer the Herfindahl index is to one, the more concentrated the

production function of insurance firms implying a positive relation with the size of loss reserve errors.

We identify organizational structure using two variables. The first variable (Group) is an indicator

variable that equals 1 if an insurer is affiliated to a conglomerate group and 0 otherwise. Prior research

(e.g., Grace and Leverty [2012]) suggests that group affiliation can affect reserving decisions. For

example, group insurers are expected to be able to draw on a ‘deep pool’ of actuarial and underwriting

expertise in order to reduce the incidence of reserving error. This implies an inverse relation between

group status and the size of loss reserve error. The second variable (Public) is an indicator variable equal

to 1 if an insurer is publically quoted, and 0 otherwise. Public and private firms potentially face different

demands for accounting information. External financing in public equity markets creates the demand for

good (high) disclosure of information which is used to evaluate company’s performance. Poor (low)

7 These classes of insurance business include personal accident and health, personal and commercial motor,

household and domestic all risks, personal and commercial financial loss, commercial property, commercial liability, aviation, marine, goods in transit, and miscellaneous and pecuniary insurance.

17

disclosure may discourage external investors to supply capital to firms. As a result being a public

corporate entity is likely to be associated with higher reporting quality (lower reserve estimation errors)

(Chiappori and Salanie [2000]). Approximately 95% of insurers in our UK sample are stock forms of

organization, which precludes us from testing the effect of organizational form on reserving behavior.

Age: The duration over which an insurer continuously operates in the market may affect the accuracy

of loss reserve estimates. England and Verrall [2002] argue that accurate data are needed to minimize

the incidence and scale of reserve errors. Insurers operating in the market for longer periods of time are

likely to have better data on loss experience and therefore produce more accurate loss reserve estimates

than relatively new entrants to the industry. We define firm age (Age) as a natural logarithm of the

number of years since establishment.

Firm Size: Firm size could be an important influence on reserving decisions – for example, relative to

large entities small insurance firms are likely to be inefficient at diversifying risk and more prone to

making reserving errors (e.g., because of lower business volumes and/or lack of in-house actuarial

experience). This implies an inverse relation between the accuracy of loss reserves and firm size. Beaver,

et al. [2003] find few firm size-effect differences in their analysis from the US property-casualty

insurance industry using the natural logarithm of total assets, policyholder’s surplus or earned premiums

as measures of firm size. In the present study, Firm Size is initially measured as the natural logarithm

total assets. We find that firm size is strongly and statistically significantly correlated with Product Mix

(i.e., Pearson correlation = -0.57). To separate the conjoint effect of product mix and firm size, and avoid

possible multicollinearity we use the residual firm size (Residual of Size) in our main analysis. Residual of

Size is measured by standardized residuals obtained by regressing Size with Product Mix. Appendix B

reports the Ordinary Least Square (OLS) regression estimation results and the correlation matrix.

5. Empirical results

5.1. UNIVARIATE ANALYSIS

Table 1 provides descriptive statistics for all the variables used in our study. The mean loss reserve is

over estimated by 1.4% of total assets according to the KFS error and 2% with Weiss error, indicating that

on average the insurers in our dataset tended to over-reserve between 1991 and 2005. The average

insurer has Solvency value equal to 0.3 indicating that average insurer’s surplus are equal to 30% of its

assets. The average Leverage ratio is 1.5, showing that average insurer net premiums written 1.5 times

exceed its capital and surplus. On average, sample insurers cede roughly a quarter of their annual gross

premiums to reinsurance companies (Reinsurance) and around 12% of our sample insurers engage in

derivatives hedging (Derivatives). More than 25% of sample observations have policies written in a single

line of insurance business (Product Mix = 1). Over 88% of our sample insurers are affiliated to a corporate

group and slightly less than 13% of the sample relate to publically listed companies. The average

(median) age of insurer in the sample is 43 years (34 years). The average company size in terms of total

assets held is £633 million. However, the median total assets size is significantly lower (i.e., £90.7

million), showing that the distribution of the sample is excessively skewed towards large firms.

[INSERT TABLE 1 HERE]

18

Table 2 gives the means and the standard deviations of reserve errors (Weiss and KFS scaled by total

assets) broken down by the levels of the hypothesized variables. It also reports the F-statistics of one

way analysis of variance (ANOVA) tests and Chi2-statistics of Kruskal Wallis (non-parametric version of

ANOVA)8. The null hypothesis for both tests is that the means of reserve errors do not differ among

different levels of distribution of hypothesized independent variables. We find only weak statistically

significant evidence that average loss reserving error differs across different quartiles of Solvency. We

find that insurer-year observations with the lowest Solvency value (surplus-to-asset ratio) (1st quartile)

have on average smallest loss reserve errors. However, the standard deviation of reserve errors in the

lowest quartile of Solvency is large indicating that some low-solvency insurers over-reserve and some

under-reserve their claim liabilities. Similarly, Table 2 does not indicate whether highly leveraged

insurers over- or under-reserve their claims liabilities. Chi2 statistics show that insurers with the highest

and the lowest Leverage (Q1 and Q4) have on average smallest reserving errors. As such, our univariate

analysis does not accept or reject our H1a and H1b. Therefore, to gain better insights on the relation

between insurers’ solvency risk and reserve errors regression analysis that distinguish observations with

positive and negative reserve errors are performed in the next section. Both F-statistics and Chi2

statistics indicate that the mean reserve errors significantly differ across quartiles of the Reinsurance

distribution. In line with H3, we find that observations with highest levels of reinsurance (Q4) have the

lowest average reserve errors. However, we do not find statistically significant evidence that average

reserve error differs in the groups that purchase (or do not purchase) Proportional reinsurance. Table 3

also shows that insurer-years that use derivatives on average have higher loss reserve errors. This finding

is in contrast to H5, which predicts that the use of derivatives reduces the incidence of reserving errors.

Finally, we also find statistically significant inferences that the average reserve error differs across

different quartile of the interaction between the Reinsurance and Growth. While the tests reported in

Table 3 indicate of possible linkage between the loss reserve errors and corresponding hypothesized

incentives for the management of loss reserves, they do not signify the direction of such relations.

[INSERT TABLE 2 HERE]

5.2. MULTIVARIATE REGRESSION ANALYSIS

This section presents the regression results for model (1). The five hypotheses, developed in section

3, are tested using a dynamic panel data design – GMM-SYS. The coefficient estimates for the magnitude

of the KFS reserve error, scaled by total assets, are shown in Table 4 and the corresponding results for

the Weiss error are presented in Table 5. To test the validity of the instrumental variables used, the

Hansen [1982] J-test is also conducted. In all regressions for both KFS and Weiss errors, the null

hypothesis is not rejected, supporting the validity of chosen instruments. In addition, a Hansen-

Difference test performed to examine the validity of the additional instruments utilized by the GMM-SYS

estimator. Again, in each case the null hypothesis is not rejected further supporting the use of additional

instruments. A diagnostic test for the presence of serial correlation was also conducted. If the errors are

correlated over time the GMM-SYS estimator in the dynamic model is likely to be inconsistent and

unreliable. Tables 4 and 5 thus report the Arellano-Bond test for first-order and second-order serial

correlation of the differenced residuals (AR(1) and AR(2) tests) (Arellano and Bond [1991]). In all

8 One-way ANOVA assumes that the variances of dependent variables (i.e., Weiss and KFS) are the same across the

groups. Bartlett’s Chi2 test for equal variances is rejected for all groups of independent variables. Therefore, we also

perform Kruskal Wallis Chi2

test which allows for different variances of dependent variables across the groups.

19

regressions, first-order, but not second-order correlation is present. This condition allows the null

hypothesis to be rejected in the first test (AR(1)) but not in the second test (AR(2)), and shows that loss

reserve errors are not correlated over time and that the GMM estimator is thus consistent and efficient.

[INSERT TABLES 3 & 4 HERE]

The coefficient estimates for the lagged dependent variable are positive and statistically significant (p

< 0.01, two-tailed) in all regressions, for both Weiss and KFS errors. This observation accords with Beaver

and McNichols [1998] and suggests that reserve errors are positively influenced by the previous year’s

reserving decisions. Therefore, exclusion of the lagged error from the regression analysis could lead to

misleading coefficient estimates of other explanatory variables incorporated in the regression model.

The coefficient estimate for Solvency is negatively linked with over-reserving and positively related to

under-reserving in both the Weiss and KFS regressions. This result suggests that UK property-casualty

insurers’ solvency position is inversely related to the sign of reserving error. In another words, the results

suggest that in view of the UK’s statutory solvency requirements, weak reserves are likely to require

larger amounts of regulatory capital. This situation could affect insurers’ reserving decisions in two main

ways. First, insurers could have incentives to under-estimate claim liabilities if they have sufficiently high

solvency capital. Second, the insurance industry regulator might insist on additional equity capital and/or

reserves to be held if an insurer’s financial condition is deemed to be inadequate for the purpose of

statutory solvency maintenance. This finding supports our hypothesis H1B, that insurers with higher

solvency risk (lower surplus-to-asset ratio) over-state their claim liabilities. To test the robustness of this

result we also employ an alternative measure of insurer’s insolvency risk – net premium-to-surplus ratio

(Leverage). When Solvency is substituted with Leverage measure in regression (5), a weak positive

relation (p < 0.10, two-tailed test) is found between positive reserving errors and Leverage in both Weiss

and KFS regression, again, showing that, all else being equal, financially weak insurers are more likely to

over-reserve supporting H1B.

The coefficient estimate for the interaction between Reinsurance and Growth (Re x Growth) is

positive and statistically significant with negative Weiss and KFS errors providing support for the moral

hazard hypothesis (H2) that highly reinsured and high premium growth insurers have incentives to

under-reserve in order to mask increased risk due to new business growth. This result supports the

agency theory-based argument of Harrington and Danzon [1994] that due to corporate limited liability

the managers of financial weak insurers may have incentives to increase their underwriting risk in order

to grow their business and increase product-market share. The managers of high-growth (risky) insurers

could also have incentives to under-reserve and reinsure part of their liabilities in order to mask and/or

reduce increased business risk.

The estimated coefficients for Reinsurance are negative and statistically significant with positive

errors in all Weiss and KFS regressions. These results support the hypothesis H3 that highly reinsured

insurers have a lower incidence of reserving errors than insurers that purchase less reinsurance. Prior

research (e.g., Grace and Leverty [2010], Plantin [2006]) holds that more accurate loss reserves result

from a reduction in information asymmetry problems (adverse selection and moral hazard) and control

of agency incentive conflicts. In mitigating such market imperfections, reinsurance companies play an

important role as effective monitors of primary insurers’ financial and risk management systems.

Furthermore, the use of reinsurance enables primary insurers to retain smaller risks and reinsure larger

20

ones thereby reducing the risk and uncertainty of future claims liabilities. Reduced risk and uncertainty

enables insurers to reserve for future liabilities more accurately, and thus, causes smaller loss reserve

estimation errors, other things being equal.

The estimations do not provide support for the hypothesis H5 that the insurers using derivative

hedging have lower incidence of reserving errors. All coefficient estimates for Derivatives are not

statistically significant in all are regression specifications. The coefficient estimates for the

interaction term between Reinsurance and Derivatives are not statistically significant in all

regression specification, showing that only reinsurance as a risk management tool is effective in

reducing the incidence of reserving errors. Therefore, derivatives hedging does not affect insurers’

loss reserving behavior. This result could indicate that insurance managers are cautious in their use

of derivatives – for example, as heavy reliance on derivatives could increase the risk and costs of

increased regulatory scrutiny.

In line with prior US-based research (Beaver and McNichols [1998], Grace [1990], Petroni [1992]),

ROA is positive and weakly statistically significant with negative reserve error and negative and weakly

significant with positive errors indicating that insurers with on average higher ROA over the past three

years tend to under-state their claim liabilities. The standard deviation of ROA over the past five years

(Std_ROA) is positively associated with over-reserving. This result is in line with our expectations that

increase risk due to variable performance leads to higher incidence of loss reserving errors. The

coefficient estimates for Tax Shield are negative and weakly statistically significant with negative Weiss

errors showing that UK property-casualty insurers with on average higher taxable income tend to have

lower incidence of under-reserving. This result is inconsistent with the prediction of that property-

casualty insurers use discretion over loss reserves to reduce/postpone period tax liabilities. US-based

insurance industry studies investigating the tax incentives to manage loss-reserves have also produced

mixed results. For example, Petroni [1992] does not find any statistically significant evidence that tax

incentives are associated with reserving errors. On the other hand, a number of more recent studies

(e.g., see Browne, et al. [2012], Gaver and Paterson [1999], Grace and Leverty [2010], [2012]) find that

insurers facing higher marginal tax rates in general over-reserve in order to reduce period taxable

income. Contrary to these results, some researchers (e.g., Gaver and Paterson [2000]) find that tax-

paying insurers tend to under-estimate rather than over-estimate loss reserve errors.

All five of our regression models also control for company type (group status and public-private

status), product mix, long-tail business, age, size, and time effects. We do not find that insurers

operating within a conglomerate group (Group) are associated with lower or higher incidence or

reserving errors compared with solo insurers. In line with our prediction, we find that public insurers

(Public) are associated with lower incidence of reserving error. This result is consistent with Chiappori

and Salanie [2000] that higher reporting quality is usually demanded from public corporate entities

leading to lower reserve estimation errors. In line with our prior expectations, we find that insurers

operating longer in the market (Age) also tend to have more accurate loss reserve estimates. This finding

could reflect the greater risk management experience and availability of more accurate claims data in

established insurers compared to later entrants to the market. However, contrary to expectations, the

results imply that lowly diversified insurers (Product Mix) tend to under-reserve less than insurers with a

less concentrated product range. This suggests that risk reduction via product diversification does not

reduce the overall incidence of reserving error in UK property-casualty insurers. Finally, our results show

21

that insurers writing longer-tail business (Long-Tail) have smaller positive errors than insurers that write

shorter tail business. This finding is inconsistent with our expectations and prior US findings (e.g., see

Browne, et al. [2012], Petroni and Beasley [1996]) that insurers with long-tail business (i.e., liability) have

larger loss reserve errors. This situation could reflect that the highly specialist risk knowledge and

experience of liability insurers accumulated across jurisdictions and over time is being reflected in

actuarially fair underwriting and more accurate reserving practices.

5.3. ADDITIONAL TESTS

Since some of the variables used in regression analysis contain extreme values (see Table 2),

Winsorization is employed in order to check whether these extreme values in the sample affect the

coefficient estimates in the regression analyses performed in section 5.2. We Winsorize our sample by

redefining the most extreme values in the tail(s) of distribution (covering the top 1 percent of the values

to the 99th percentile and the bottom 1 percent to the 1st percentile) to the next most extreme value

(e.g., Yale and Forsythe [1976]). Winsorized results from the regression analyses (not reported) are

found to lead to the same inferences as the non-Winsorized results.

To check the robustness of our results we also employed alternative scaling variable for reserving

errors. Specifically instead of calling loss reserve errors by total assets we scaled them by the developed

reserves (incurred value of losses (including IBNR) five years after year t). Our results from the regression

analyses (not reported) are found to be qualitatively the same as the main results reported in Tables 3

and 4. Prior studies (e.g., see Eckles and Halek [2010]) also find that the inferences of the results are not

affected by the scaling variable of reserving errors.

6. Conclusion

In this study we extend the earnings and risk management literature by analyzing whether UK

property-casualty insurers engage in earnings management activities (loss reserve accruals/errors) in

order to manage their reported solvency position. We also test whether risk management via

reinsurance and derivatives hedging affects discretionary loss reserving behavior of insurance managers.

Our UK study provides new and potentially important insights regarding discretionary loss reserve

management in the property-casualty insurance industry. We focus on the UK property-casualty

insurance sector – a major European market – whereas the vast majority of prior reserving management

studies have focused on the US property-casualty insurance industry. Given the institutional differences

between the US and the UK (and indeed, other major European insurance markets) a clear

understanding of earnings management behavior in the insurance sector warrants a transnational focus.

As the UK is a unitary regulatory/fiscal regime, we believe that interpretations of our results are not

unduly biased by state-based regulatory and reporting differences that can afflict US-based insurance

industry research.

We observe that over-reserving or under-reserving behavior usually persists from one year to

another. As such, we include lagged reserving errors in the regression analysis and employ a dynamic

panel data design (GMM-SYS) to control for serial correlation in error terms. We further show that

insurers that report income increasing reserves have different motives for earnings management than

insurers that report income decreasing reserves. We therefore differentiate between positive and

negative reserving errors in the regression analysis. This finding also raises the possibility that firms

22

operating in other industries (e.g., banking) that engage in accounting numbers-based or real earnings

management activities behave differently depending on the intention to reduce or increase period

reported earnings.

Our empirical findings suggest that UK property-casualty insurers with larger insolvency risk (as

measured by surplus-to-asset and net premium-to-surplus ratios) tend to under-estimate their claim

liabilities (increase shareholders’ capital and surplus). This result is in line with our alternative solvency

risk hypothesis, which predicts that property-casualty insurers could be motivated to under-estimate

claim liabilities if they hold sufficiently large amount of solvency capital; alternatively, the insurance

industry regulator can insist on additional capital to be held if the reserve levels are not adequate (e.g.,

under-estimated). This result is contrary to prior US-based studies (e.g., Gaver and Paterson [2004],

Grace and Leverty [2010]) that find that financially weak insurers tend to understate loss reserves. This

suggests that regulatory intervention on capital maintenance could be less proactive in some states of

the US than in a unitary regulatory authority such as the UK.

We also find some evidence that highly reinsured and high growth insurers tend to under-reserve

they loss liabilities. This result support Harrington and Danzon’s [1994] hypothesis that financially weak

(highly levered) insurers with high rates of new business growth tend to under-reserve and purchase

more reinsurance in order to alleviate underwriting risks. Therefore, a public policy implication

arising from our study is that insurance industry regulators may need to closely scrutinize the

solvency position of insurers that are growing market share by purchasing reinsurance and

understating their loss reserves.

The regression results also support our reinsurance hypothesis. We find that the level of reinsurance

is negatively associated with the magnitude of reserving errors which is consistent with prior US-based

studies (e.g., Adiel [1996]). The use of reinsurance enables primary insurers to retain smaller risks and

reinsure larger ones thereby reducing the risk and uncertainty of future claims liabilities. Reduced risk

and uncertainty enables insurers to reserve for future liabilities more accurately, and thus causes smaller

loss reserve estimation errors, other things being equal. We do not, however, find statistically significant

evidence to support Eden and Kahane’s [1988] hypothesis that due to reduced information asymmetries

between reinsurer and insurer in proportional reinsurance contracts insurers that predominantly use

proportional reinsurance report more accurate reserving errors. Further, we do not find that derivatives

hedging reduces managerial incentives to manage loss reserves. In summary, our results suggest that the

volume of reinsurance can reduce the incidence of reserve errors as it enables insurers to hedge non-

core and tail risks. Improved insurer monitoring due to reduced information asymmetries under

proportional reinsurance cover and reduced variability in future firm’s value due to derivative hedging

do not have an effect on the practices of loss reserving.

Finally, we believe that our research contributes new and potentially important insights on the relation

between reserving errors, solvency risk and risk in international insurance markets that have a different

regulatory infrastructure. We consider that our research results provide insights on motives for

managerial discretion over loss reserves in the property-casualty insurance industry that could be of

direct interest to investors, policyholders, insurance industry regulators, and other parties such as credit

rating agencies and accounting standard-setters. For example, by contributing new insights on the inter-

relation between risk management decisions (reinsurance), discretionary accruals, and earnings

23

management the present study could help scholars, accounting standard-setters, and others (e.g., credit

rating agencies) conduct more informed financial analyses that could be applicable in more generalized

as well as international business contexts. This is particularly likely to be the case in important global

industrial sectors such as banking, mining and oil and gas production where managers have considerable

discretion in making material accruals choices with regard to setting reserves and provisions, and taking

decisions to retain and/or transfer risks (e.g., using insurance).

24

FIG. 1. Average Cumulative Ratios of Claims Paid by Development Year This figure shows the average ratio of claims paid to total insurance losses. The cumulative ratio of claims paid in any

development year (e.g., 0 to 9) is estimated as the ratio of total losses paid to total incurred claims in a particular accident year. The sample consists of all UK property-casualty insurer/year observations for the period 1991 to 2001 obtained from the Standard & Poor’s UK Non-Life Insurance Companies Database (SynThesys). The time period is the only period in the database with nine years of claims development available. Observations are ‘pulled across’ calendar year and aligned in event time, with year 0 indicating the year in which the claims were incurred. The lines of insurance are defined as follows: MOT – motor, e.g., commercial and personal motor insurance; PROP – property, e.g., household and domestic all risk and commercial lines property insurance; LIAB – liability, e.g., employers’ liability, professional indemnity, public and product liability, and mixed commercial package insurance; MIS&PEC – miscellaneous and pecuniary loss, e.g., personal and commercial financial loss insurance; AMG – aviation, marine and goods in transit.

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7 8 9 10

MOT

PROP

LIAB

MIS&PEC

AMG

Years Since Claim Occurence

Cu

mu

lati

ve R

atio

of

Cla

ims

Pai

d

25

TABLE 1 Descriptive Statistics, UK Property-Casualty Insurers, 1991-2005

Variable Mean Median Std. Dev. 1st Quart. 3rd Quart. Obs.

KFS 0.014 0.009 0.085 -0.004 0.047 1386 KFS (O) 0.044 0.027 0.047 0.008 0.067 959 KFS (U) -0.056 -0.023 0.107 -0.061 -0.006 427 Weiss 0.020 0.012 0.082 -0.001 0.052 1386 Weiss (O) 0.047 0.028 0.052 0.008 0.072 1017 Weiss (U) -0.059 -0.023 0.111 -0.060 -0.007 369 Solvency 0.297 0.252 0.175 0.171 0.395 1386 Leverage 1.535 1.378 1.123 0.623 2.201 1386 Reinsurance 0.259 0.176 0.249 0.059 0.404 1386 Proportional 0.011 0.000 0.054 0.000 0.000 1386 Derivatives 0.120 0.000 0.326 0.000 0.000 1386 Growth 0.174 0.055 1.022 -0.072 0.224 1386 ROA 0.057 0.038 0.126 0.003 0.093 1386 Std_ROA 0.108 0.043 0.760 0.025 0.078 1386 Tax Shield 0.344 0.222 0.978 0.118 0.339 1386 Long-Tail 0.107 0.008 0.203 0.000 0.111 1386 Product Mix 0.651 0.606 0.286 0.384 1.000 1386 Group 0.881 1.000 0.324 1.000 1.000 1386

Public 0.128 0.000 0.335 0.000 0.000 1386 Age 43.404 34.000 34.580 13.000 68.000 1386 Total Assets (mln. £) 633.323 90.676 1,665.047 230.030 439.705 1386 This table reports the summary statistics for the years 1991 to 2005. KFS error is defined as the difference between the

incurred losses in the current period and a revised estimate five years in the future. Weiss error is the difference between the incurred losses in the current period and the developed losses paid five years in the future. Both errors are scaled by total assets. Positive (O) reserve errors indicate that the insurer initially over-reserved, while negative reserve errors (U) indicate under-reserving. Solvency is a surplus-to-asset ratio; Leverage is a net premium-to-surplus ratio; Reinsurance is the ratio of gross premium written ceded to reinsurer; Proportional – proportion of gross premium ceded under proportional reinsurance cover; Derivatives = 1 for a derivative user (i.e., an insurer has nonzero year-end derivative position or if derivatives are open at the end of the previous year) and 0 for a nonuser; Growth is the ratio one-year increase in net premium written; Long-Tail is the ratio of losses incurred in long-tail lines of insurance; ROA is measured as average returns on assets over the period of past three years; Std_ROA is measured as standard deviation of ROA over the period of past five years; Tax Shield is the sum of net income and estimated reserves divided by the total admitted assets; Product Mix is the line of business Herfindahl index, which measures an insurer’s product diversification; Long-Tail defined as the share of annual net premiums written on liability insurance to total annual premiums written; Group is an indicator variable for insurers that are associated with a group; Public is dummy variable equal to 1 if an insurer is publically quoted and 0 otherwise; Age is dummy variable equal to 1 if an insurer is affiliated to a group and 0 otherwise.

26

TABLE 2 Comparison of KFS and Weiss Reserve Errors by the Levels of Hypothesized Variables, UK Property-

Casualty Insurers, 1991-2005

Group Variable Obs. KFS Weiss

Mean Std. Dev. F-test Ch2-test Mean Std. Dev. F-test Ch2-test

Solvency: Q1 347 0.0048 0.1233

2.35

4.39

0.0151 0.1129

1.66

6.9

Solvency: Q2 346 0.0218 0.0746 0.0281 0.0759 Solvency: Q3 347 0.0134 0.0665 0.0178 0.0639 Solvency: Q4 346 0.0142 0.0595 * 0.0190 0.0656 *

Leverage: Q1 346 0.0080 0.0727

1.11

18.3

0.0156 0.0729

1.00

17.1

Leverage: Q2 347 0.0172 0.0752 0.0228 0.0748 Leverage: Q3 346 0.0179 0.1041 0.0247 0.0969 Leverage: Q4 347 0.0110 0.0839 *** 0.0169 0.0815 ***

Reinsurance: Q1 346 0.0233 0.0670

5.97

13.26

0.0267 0.0723

5.40

15.6

Reinsurance: Q2 347 0.0205 0.0870 0.0284 0.0878 Reinsurance: Q3 346 0.0117 0.0887 0.0190 0.0833 Reinsurance: Q4 347 -0.001 0.0927 *** *** 0.0060 0.0825 *** ***

Proportional: > 0 344 0.0105 0.0763

0.57

0.64

0.0175 0.0762

0.43

0.00

Proportional: = 0 1042 0.0145 0.0876 0.0208 0.0839

Derivatives: = 1 167 0.0244 0.0536

3.13

10.2

0.0308 0.0568

3.28

12.59

Derivatives: = 0 1219 0.0120 0.0882 * *** 0.0185 0.0849 * ***

Rein x Growth: Q1 346 0.0021 0.0940

3.53

11.8

0.0107 0.0912

2.75

10.7

Rein x Growth: Q2 347 0.0207 0.0709 0.0257 0.0698

Rein x Growth: Q3 346 0.0194 0.0899 0.0259 0.0839

Rein x Growth: Q4 347 0.0118 0.0821 ** *** 0.0177 0.0813 ** ** This table reports the means and standard deviations of KFS and Weiss errors (scaled by total assets) broken down by the

levels of the hypothesized independent variables. Solvency is surplus-to-asset ratio; Leverage is a net premium-to-surplus ratio; Reinsurance is the ratio of gross premium written ceded to reinsurer; Proportional – proportion of gross premium ceded under proportional reinsurance cover; Derivatives = 1 for a derivative user (i.e., an insurer has nonzero year-end derivative position or if derivatives are open at the end of the previous year) and 0 for a nonuser; Rein x Growth is the interaction term between Reinsurance and Growth; Growth is the ratio one-year increase in net premium written. Q1-Q4 represents 1st - 4th quartiles of the distribution. F-statistics of one-way analysis of variance (ANOVA) and Chi2-statistics of Kruskal Wallis (non-parametric version of ANOVA) tests whether mean of loss reserve errors differs significantly among the different levels.

27

TABLE 3 Regression Test of Discretionary Reserving Behavior in UK Property-Casualty Insurance Market 1991 to

2005: Magnitude of KFS Reserve Errors (1) (2) (3) (4) (5)

Variable Coef. Std Err. Coef. Std Err. Coef. Std Err. Coef. Std Err. Coef. Std Err.

Intercept 0.065 *** 0.024 0.071 *** 0.024

0.073 *** 0.026

0.057 ** 0.024 0.050 * 0.026

lagWeiss 0.759 *** 0.168 0.756 *** 0.170

0.748 *** 0.172

0.763 *** 0.171 0.761 *** 0.175

Over-Reserving

Solvency -0.068 ** 0.036 -0.065 ** 0.031 -0.062 ** 0.028 -0.059 * 0.032

Leverage 0.014 * 0.008

Reinsurance -0.039 ** 0.020 -0.051 ** 0.021

-0.038 ** 0.016

-0.044 ** 0.022 -0.040 * 0.027

Proportional

0.213 0.156

Derivatives -0.001 0.011 -0.004 0.011 -0.004 0.011 -0.006 0.009 -0.004 0.014

Rein x Growth -0.019 0.024

Rein x Deriv

0.003 0.005

Growth -0.005 0.006 -0.007 0.008

-0.005 0.007

-0.005 0.007 -0.009 0.009

ROA -0.050 * 0.032 -0.063 * 0.040

-0.051 * 0.031

-0.049 * 0.028 -0.060 * 0.040

Std_ROA 0.012 * 0.008 0.014 * 0.008

0.011 * 0.005

0.011 * 0.005 0.013 * 0.009

Tax Shield -0.009 0.006 -0.009 0.006

-0.008 0.006

-0.008 0.006 -0.009 0.007

Long-Tail -0.038 * 0.021 -0.036 * 0.020

-0.045 * 0.026

-0.038 * 0.022 -0.037 * 0.022

Product Mix -0.005 0.011 -0.001 0.010

-0.001 0.013

-0.002 0.009 -0.014 0.012

Group -0.005 0.007 -0.005 0.008

-0.007 0.008

-0.008 0.008 -0.013 0.009

Public -0.011 * 0.006 -0.010 * 0.005

-0.012 * 0.006

-0.011 * 0.006 -0.007 0.007

Age 0.001 0.002 0.001 0.002

0.001 0.002

0.001 0.002 -0.003 0.003

Resid_Size 0.001 0.006 0.001 0.006

0.002 0.006

0.003 0.005 0.004 0.005

Under-Reserving

Solvency 0.191 ** 0.100 0.188 ** 0.097 0.160 * 0.098 0.192 ** 0.100 -0.018 * 0.011

Leverage

Reinsurance -0.018 0.043 -0.010 0.045 -0.018 0.044 -0.031 0.040 -0.054 0.060

Proportional

0.101 0.156

Derivatives -0.015 0.031 -0.015 0.031

-0.031 0.032

-0.006 0.032 -0.012 0.030

Rein x Growth 0.168 ** 0.076

Rein x Deriv

-0.019 0.018

Growth 0.004 0.020 -0.004 0.025

0.003 0.019

0.003 0.019 0.014 0.020

ROA 0.097 * 0.058 0.080 * 0.051

0.094 * 0.058

0.084 * 0.051 0.126 * 0.067

Std_ROA -0.002 0.003 -0.001 0.003

-0.002 0.003

-0.002 0.003 -0.001 0.003

Tax Shield -0.012 0.018 -0.014 0.017

-0.011 0.018

-0.009 0.017 -0.003 0.016

Long-Tail -0.052 0.044 -0.065 0.044

-0.050 0.047

-0.054 0.042 -0.078 * 0.046

Product Mix -0.081 ** 0.038 -0.082 ** 0.037

-0.078 ** 0.037

-0.076 ** 0.036 -0.041 * 0.022

Group 0.018 0.017 0.019 0.018

0.023 0.018

0.017 0.018 0.058 * 0.031

Public -0.002 0.019 -0.001 0.020

-0.008 0.021

-0.005 0.019 -0.006 0.018

Age -0.016 *** 0.006 -0.017 *** 0.006

-0.016 ** 0.006

-0.017 *** 0.006 -0.014 ** 0.007

Resid_Size 0.008 0.008 0.008 0.007

0.008 0.007

0.007 0.007 0.003 0.007

Time Effects Yes Yes Yes Yes Yes Hansen 0.661 0.685 0.662 0.828 0.716 Diff-Hansen 0.286 0.199 0.580 0.366 0.414 AR(1) 0.006 0.006 0.006 0.005 0.005 AR(2) 0.521 0.521 0.422 0.518 0.388 No. of observations 1226 1226 1226 1226 1226 No. of groups 151 151 151 151 151 No. of instruments 136 148 148 148 136

This table reports the results of GMM-SYS regressions. The dependent variable is the absolute value of KFS reserve error scaled by total assets. All remaining variables are defined in Appendix C. Asymptotically robust standard errors are reported. Lagged levels (dated t-2,…, t-6) in the first-difference equations, combined with lagged first-differences (dated t-1) in the level equations are used as instruments. The values reported for the Hansen test are the p-values for the null hypothesis of the validity of the instruments. The Difference-Hansen test gives the p-values for the validity of the additional moment restrictions required by the GMM-SYS estimator. AR(1) and AR(2) report the p-values for first-order and second-order autocorrelated disturbances in the first-difference equations. ***, **, and * indicate significance at the 0.01, 0.05, and 0.10 levels, respectively.

28

TABLE 4 Regression Test of Discretionary Reserving Behavior in UK Property-Casualty Insurance Market 1991 to

2005: Magnitude of Weiss Reserve Errors (1) (2) (3) (4) (5)

Variable Coef. Std Err. Coef. Std Err. Coef. Std Err. Coef. Std Err. Coef. Std Err.

Intercept 0.086 *** 0.024 0.086 *** 0.028

0.096 *** 0.030

0.086 *** 0.027 0.069 ** 0.027

lagWeiss 0.646 *** 0.172 0.658 *** 0.139

0.626 *** 0.142

0.643 *** 0.139 0.624 *** 0.150

Over-Reserving

Solvency -0.084 ** 0.041 -0.076 ** 0.040 -0.087 ** 0.042 -0.074 ** 0.039

Leverage 0.012 * 0.007

Reinsurance -0.047 ** 0.023 -0.048 ** 0.021

-0.049 ** 0.024

-0.047 ** 0.023 -0.030 * 0.014

Proportional

0.039 0.113

Derivatives -0.007 0.011 -0.007 0.011 -0.009 0.012 -0.008 0.009 -0.010 0.012

Rein x Growth 0.011 0.018

Rein x Deriv

0.009 0.006

Growth -0.015 * 0.008 -0.012 * 0.007

-0.016 * 0.008

-0.015 * 0.009 -0.020 * 0.010

ROA -0.094 * 0.052 -0.100 ** 0.050

-0.085 * 0.048

-0.095 * 0.051 -0.083 * 0.051

Std_ROA 0.024 ** 0.010 0.020 ** 0.010

0.025 ** 0.010

0.024 ** 0.010 0.026 ** 0.011

Tax Shield -0.005 0.004 -0.004 0.004

-0.004 0.004

-0.004 0.004 -0.004 0.005

Long-Tail -0.050 * 0.030 -0.054 * 0.032

-0.061 * 0.035

-0.054 * 0.032 -0.049 0.032

Product Mix 0.002 0.011 -0.001 0.011

-0.007 0.012

-0.001 0.011 -0.021 0.013

Group -0.005 0.008 -0.006 0.008

-0.008 0.008

-0.006 0.008 -0.011 0.009

Public -0.012 * 0.007 -0.011 * 0.007

-0.014 * 0.008

-0.013 * 0.007 -0.008 0.007

Age 0.001 0.003 0.001 0.003

0.001 0.003

0.001 0.003 -0.002 0.003

Resid_Size 0.001 0.005 0.001 0.006

0.001 0.005

0.002 0.004 0.003 0.005

Under-Reserving

Solvency 0.261 ** 0.131 0.224 ** 0.122 0.240 ** 0.124 0.261 ** 0.129 -0.017 * 0.010

Leverage

Reinsurance -0.018 0.048 -0.029 0.053 -0.022 0.045 -0.021 0.045 -0.052 0.052

Proportional

0.113 0.141

Derivatives -0.028 0.036 -0.027 0.037

-0.034 0.037

-0.022 0.038 0.002 0.032

Rein x Growth 0.195 ** 0.096

Rein x Deriv

-0.014 0.019

Growth 0.007 0.024 0.012 0.029

0.013 0.024

0.006 0.024 0.018 0.025

ROA 0.092 * 0.061 0.073 * 0.045

0.086 0.069

0.088 * 0.048 0.131 * 0.080

Std_ROA -0.003 0.003 -0.002 0.003

-0.002 0.003

-0.002 0.003 -0.001 0.002

Tax Shield -0.083 ** 0.046 -0.091 ** 0.047

-0.079 * 0.046

-0.073 * 0.044 -0.047 0.037

Long-Tail -0.013 0.060 -0.011 0.056

-0.022 0.064

-0.020 0.060 -0.044 0.059

Product Mix -0.098 ** 0.042 -0.092 ** 0.044

-0.097 ** 0.045

-0.097 ** 0.042 -0.096 ** 0.045

Group 0.023 0.021 0.037 * 0.022

0.026 0.020

0.021 0.021 0.056 ** 0.027

Public 0.007 0.030 0.013 0.032

0.001 0.032

0.007 0.029 -0.006 0.019

Age -0.020 *** 0.008 -0.018 *** 0.007

-0.020 *** 0.008

-0.021 *** 0.007 0.016 ** 0.006

Resid_Size 0.016 ** 0.007 0.013 * 0.007

0.015 ** 0.008

0.016 ** 0.007 0.013 * 0.007

Time Effects Yes Yes Yes Yes Yes

Hansen 0.473 0.553 0.617 0.467 0.425

Diff-Hansen 0.308 0.781 0.318 0.498 0.394

AR(1) 0.001 0.001 0.001 0.001 0.002

AR(2) 0.458 0.451 0.438 0.420 0.172

No. of observations 1226 1226 1226 1226 1226

No. of groups 151 151 151 151 151

No. of instruments 136 148 148 148 136

This table reports the results of GMM-SYS regressions. The dependent variable is the absolute value of Weiss reserve error scaled by total assets. All remaining variables are defined in Appendix C. Asymptotically robust standard errors are reported. Lagged levels (dated t-2, …, t-6) in the first-difference equations, combined with lagged first-differences (dated t-1) in the level equations are used as instruments. The values reported for the Hansen test are the p-values for the null hypothesis of the validity of the instruments. The Difference-Hansen test gives the p-values for the validity of the additional moment restrictions required by the GMM-SYS estimator. AR(1) and AR(2) report the p-values for first-order and second-order autocorrelated disturbances in the first-difference equations. ***, **, and * indicate significance at the 0.01, 0.05, and 0.10 levels, respectively.

29

APPENDIX A.

Sample Characteristics

Panel A: Construction of Sample

Observations Number of Companies

Initial Sample 1985-2010 12,168 468

Sample 1991-2005 7,020 468

Sample after deleting the missing data 2,488 255

Sample after eliminating observations with negative reserves, incurred losses, total assets, and/or grow premiums written

2,423 255

Sample after eliminating observations with all gross premiums ceded to reinsurers

2,305 252

Sample after eliminating observations with >25% of gross premiums written to accident and health insurance

1,974 227

Sample after eliminating observations with >25% of gross premiums written to surety and health insurance

1,968 226

Sample after eliminating observations with >25% of gross premiums written to reinsurance

1,628 190

Sample after eliminating observations with extreme errors and/or missing data in their loss reserves

1,502 182

Sample after eliminating companies with <3 years of consecutive data

1,386 151

This table provides the information on study sample construction. The sample of property-casualty insurers is obtained from Standard & Poor’s Non-Life Insurance Companies (SynThesis) Database.

30

Panel B: Initial and Study Sample

Year Initial Sample Study Sample

1991 273 83

1992 276 89

1993 287 96 1994 291 104

1995 292 105

1996 302 105

1997 307 107

1998 303 106

1999 301 100

2000 296 99

2001 293 89

2002 291 86

2003 297 78

2004 297 73

2005 296 66

Total No. of Companies 465 151 This table provides yearly distribution the sample of property-casualty insurers reported in Standard & Poor’s Non-Life

Insurance Companies (SynThesis) Database (12,168 insurer-year observations) and the sample of insurers used in current study from 1991 to 2005 (1,386 insurer-year observations).

31

APPENDIX B.

Residual of Size Estimation

Panel A: OLS estimation

Variable Coefficient Std. Error t-statistics

Intercept 14.150 0.112 *** 125.990

Product Mix -4.066 0.158 *** -25.760

No. of observations 1386

Adjusted R2 0.324

Panel B: Pearson Correlation Matrix

Size Product Mix

Size -

Product Mix -0.569 *** -

Residual of Size 0.822 *** -0.000 *** Penel A reports the coefficient estimates of firm size OLS regression. The dependent variable is natural logarithm of total

assets. Product Mix, measured by Herfindahl index, is used as explanatory variable. Estimated standardized residuals (Residual of Size) are used as the proxy for firm size in the regression analysis. Panel B reports Pearson correlation matrix between Size, Product Mix, and firm size estimate Residual of Size. *** represents a 1% significance level, two tailed.

32

APPENDIX C.

Variable description

* These lines include Personal Accident and Health, Personal and Commercial Motor, Household and Domestic All Risks, Personal and Commercial Financial Loss, Commercial Property, Commercial Liability, Aviation, Marine, Goods in Transit, and Miscellaneous.

Variable Definition Reference/source

Error

Both errors are scaled by total assets.

Weiss [1985]; Kazenski, et al. [1992] Standard and Poor’s S&P’s SynThesys

Over-Reserve Takes 1 if Error >0 and 0 otherwise.

Under-Reserve Takes 1 if Error <0 and 0 otherwise.

Solvency Defined as the ratio of surplus (‘net admissible assets’) and total assets (‘total admissible assets’).

S&P’s SynThesys

Leverage Defined as the ratio of net premiums written and surplus. S&P’s SynThesys

Reinsurance Measured by the ratio of annual gross premiums written ceded to reinsurers.

Adiel [1996] S&P’s SynThesys

Proportional Defined as the proportion of reinsurance premium ceded under proportional reinsurance cover relative to total reinsurance premium ceded.

S&P’s SynThesys

Derivatives Dummy variable equal to 1 for a derivative user (i.e., an insurer has nonzero year-end derivative position or if derivatives are open at the end of the previous year) and 0 for a nonuser.

(Colquitt and Hoyt [1997]) S&P’s SynThesys

Growth Measured as the ratio of annual increase in net premiums written. Grace and Leverty [2010] S&P’s SynThesys

ROA Defined as an average ROA over the period of the past three years. ROA is measured as net income divided by the beginning of the year total assets.

Grace [1990] S&P’s SynThesys

Std_ROA

Measured as standard deviation of ROA over the period of past five years. (Berry-Stölzle, et al. [2013]) S&P’s SynThesys

Tax Shield Defined as the sum of net income and estimated reserves divided by total assets.

Grace [1990] S&P’s SynThesys

Long-Tail Defined as the share of annual net (of reinsurance) premiums written on liability insurance to total annual premiums written.

(Browne, et al. [2012]) S&P’s SynThesys

Product Mix ∑(

)

where DPWl is the amount of direct premium written in the lth

line* of insurance and TPW is the amount of total premium written across property and liability lines.

Mayers and Smith [1990] S&P’s SynThesys

Group Dummy variable equal to 1 if an insurer is affiliated to a group, and 0 otherwise.

S&P’s SynThesys

Public Dummy variable equal to 1 if an insurer is publically quoted, and 0 otherwise.

Fame

Age Defined as a natural logarithm of the number of years since establishment.

Fame

Residual of Size Measured by standardized residuals obtained by regressing ln(Total Assets) with Product Mix.

S&P’s SynThesys

Time Effects

Dummy variables for each year are employed to proxy for changes in unspecified macroeconomic factors, which are cross-sectional constant (such as change in underwriting cycles, prices, inflation and interest rates).

33

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