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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: [email protected]
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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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