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Efficiency in the Greek insurance industry
European Journal of Operational Research 205 (2010) 431–436
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Innovative applications of O.R.
Efficiency in the Greek insurance industry Carlos Pestana Barros a,*, Milton Nektarios b, A. Assaf c a
Instituto Superior de Economia e Gestão, Technical University of Lisbon, Rua Miguel Lupi, 20, 1249-078 Lisbon, Portugal Dept. of Statistics and Insurance, University of Piraeus, Greece c Isenberg School of Management, University of Massachusetts, Amherst, USA b
a r t i c l e
i n f o
Article history: Received 24 July 2007 Accepted 7 January 2010 Available online 13 January 2010 Keywords: Insurance Greece Productivity change Bootstrapped DEA
a b s t r a c t This paper employs the two-stage procedure of Simar and Wilson (2007) to analyse the effects of deregulation on the efficiency of the Greek insurance industry. The efficiency is estimated by means of data envelopment analysis (DEA). The companies are ranked according to their CRS efficiency score for the period 1994–2003. The first stage results indicate a decline in efficiency over the sample period, while the second stage results confirm that the competition for market shares is a major driver of efficiency in the Greek insurance industry. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The implementation of the Third Generation Insurance Directive (1994) aimed to deregulate the EU insurance markets, with the objective of improving market efficiency and enhancing consumer choice through increased competition. Exits from the insurance market may take place either through voluntary or involuntary withdrawals (run-off or insolvency),or through mergers and acquisitions (M&As). With the current contradiction in the literature regarding the impact deregulation and consolidation on the efficiency of insurance companies (Mahlberg and Url, 2003), this study aims to provide additional evidences on the effects of deregulation and consolidation on the Greek insurance market. Following the deregulation, the Greek insurance market witnessed on the one hand, a significant decline in the number of companies, and on the other hand, a significant increase in firm size. Other accompanying trends included the abolition of the premium tariff system (for Motor TPL and Fire Branches). A criticism of the consolidation process was however the lack of direct supervision in the Greek insurance market, which has left several weak players from the market. To provide further evidence whether the local Greek insurance companies have been able to improve their efficiency as a result of the deregulation and consolidation process, we aim in this paper to analyse the efficiency of the Greek insurance market using the
* Corresponding author. E-mail addresses: [email protected] (C.P. Barros), [email protected] (M. Nektarios), [email protected] (A. Assaf). 0377-2217/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2010.01.011
innovative two-stage procedure proposed by Simar and Wilson (2007). We use data from 1994 to 2003, which cover the implementation of the Third Directive. To the authors’ knowledge, this the first article to examine the relative efficiency of all Greek insurance companies for such an extensive period of time. From an academic perspective, the particular contribution of this paper lies in its presentation of a broader literature review and in the adoption of the new two-stage procedure proposed by Simar and Wilson (2007). The paper is organized as follows: in Section 2, we describe the contextual setting; Section 3, surveys the existing literature on the topic; Section 4, explains the theoretical framework supporting the model used; Section 5, presents the data and results; Section 6, employs a bootstrapped regression model to determine the drivers of efficiency; and finally Section 7 presents the concluding remarks. 2. Overview of the Greek insurance market The Greek insurance market is often described as under-developed in comparison to other insurance markets in the EU-15 countries, despite a significant increase in total premium between 1994 and 2003. The most growing sector in the Greek insurance market has been the Non-Life sector, mainly due to the fact that Greece has not completed yet the reform of its pensions system. Over the period 1994–2003, the Greek insurance market has also experienced a significant decrease in the number of companies, mainly due financial difficulties or mergers and acquisition (M&A) activities. Indirectly, this also helped to increase the average firm size. Historically, the market concentration has been very high
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in the Life sector, while concentration in the Non-Life sector is comparable to EU standards. In terms of economic contribution, the Greek insurance industry is however still behind other related industries, and is often described as lacking efficiency. For more detail on the Greek insurance marker, refer to Nektarios and Barros (Forthcoming).
we mainly rely on the CRS assumption, given that it has several desirable mathematical properties (for details see Russell, 1990, 1997). However, we also validate the results actors the VRS and NIRS assumption. CRS is relatively easy to compute, straightforward in interpretation and, thus, it seems to be the most popular in the insurance literature.
3. Literature survey
4.1.2. The bootstrap The DEA model is relatively simple to estimate, but has long been criticised for being a non-statistical or deterministic technique. A solution to this problem has been recently proposed by Simar and Wilson (1998, 1999, 2000) who showed that it is possible to obtain statistical properties for DEA via the use of the ‘‘bootstrap” approach. The basic idea of bootstrapping is to approximate the distribution of the estimator via re-sampling and recalculation of the parameter of interest, which in our case is the DEA efficiency score. The bootstrap procedure was also later extended by Simar and Wilson (2007) to account for the impact of environmental variables2 on efficiency. For example, if we take the following model:
Recent studies on the efficiency analysis of insurance companies have mainly relied on the use of frontier methodologies, with the two most common are the econometric frontier analysis and the data envelopment analysis (DEA). Both have their advantages and drawbacks. Unlike the econometric stochastic frontier approach, the DEA permits the use of multiple inputs and outputs and does not impose any functional form on the data, neither does it make distributional assumptions on the inefficiency term. Both methods assume that the production function of the fully efficient decision unit is known. In practice, this is not the case and the efficient isoquant must be estimated from the sample data. In these conditions, the frontier is relative to the sample considered in the analysis. Table 1 provides a detailed description of previous research. As it is clear from the above table, studies currently exist on several international insurance markets. However, several weaknesses can be noticed from the existing literature. Frist, there are too many papers replicating previous research with a scant improvement in methodology. Second, we have not yet seen papers applying innovative techniques, such as Fourier frontiers (Altunbas et al., 2001) and output distance functions (Coelli and Perelman, 1999, 2000) in estimating the efficiency of insurance industries. More importantly, none of the applications has used the Simar and Wilson (2007) method, despite its several advantages over the traditional DEA method. 4. Theoretical framework 4.1. Estimation of efficiency scores 4.1.1. Data envelopment analysis Measure DEA is a well established method in the literature and aims to technical efficiency by defining a frontier envelopment surface for all sample observations. Firms are considered as fully efficient if they lie on the frontier, while inefficient otherwise. The output oriented DEA efficiency estimator ^ di can be simply derived by solving the following linear programming:
) n n X X ^di ¼ max d > 0^di y 6 yi k; xi P xi k; k P 0 ; ^d ;k i i i¼1 i¼1 (
¼ 1; . . . ; n firms
i ð1Þ
where yi is vector of outputs, xi is s vector of inputs, k is a I 1 vector of constants. The value of ^ di obtained is the technical efficiency score for the ith firm. A measure of ^ di ¼ 1 indicates that the firm is technically efficient, and inefficient if ^ di > 1. This linear programming problem must be solved n times, once for each firm in the sample. Note that the DEA model described above is a constant returns to scale (CRS) model. It is also possible to impose a variable returns to scale (VRS)1 assumption on the above model by introducing the Pn returns to scale (NIRS) constraint i¼1 k ¼ 1, or a non-increasing P assumption by introducing the constraint ni¼1 k 6 1. In this paper 1 A production function is said to exhibit constant return to scale (CRS) if a proportionate increase in inputs results in the same proportionate increase in outputs. The variable return to scale (VRS), on the other hand, does not assume full proportionality between the inputs and outputs.
^di ¼ zi b þ ei
ð2Þ
where zi is a vector of management related variables which is expected to affect the efficiency of firms under consideration and b refers to a vector of parameters with some statistical noise ei . A popular procedure in the literature is to use the Ordinarily Least Square (OLS) regression to estimate this relationship. However, as described in Simar and Wilson (2007), this might lead to two main problems. First, efficiency scores estimated by DEA are expected to be correlated with each other, as the calculation of efficiency of one firm incorporates observation of all other firms in the same data set. Therefore, direct regression analysis is invalid because of the dependency of the efficiency scores. Similarly, in small samples, a strong correlation is expected between the input/output variables and environmental variables, therefore, violating the regression assumption that ei are independent of zi . To overcome the above problem, Simar and Wilson (2007) proposed the double bootstrapping procedure, in which the bootstrap estimators are substituted from the estimators in the regression stage to calculate the standard error of the estimates. In this way, it is possible to solve the dependency problem and produce valid estimates for the parameters in the second stage regression. More details on the bootstrap procedure used in this stage refer to Simar and Wilson (2007). ^i for i. Calculate the DEA output-orientated efficiency score d each firm, using the linear programming problem in (1). ii. Use the maximum likelihood method to estimate the trun^ of b cated regression of ^ di on zi , to provide and estimate b ^ e of re . and an estimate r iii. For each insurance company i ¼ 1; . . . ; n, repeat the next four steps (1–4) B times oto yield a set of bootstrap n estimates ^ di;b ; b ¼ 1; . . . ; B . ^ 2e Þ distribution with left trunca1. Draw ei from the Nð0; r ^ i Þ. tion at ð1 bz ^ i þ ei . 2. Compute di ¼ bz 3. Construct a pseudo data set ðxi ; yi Þ, where xi ¼ xi and di =di . yi ¼ yi ^ 4. Compute a new DEA estimate di on the set of pseudo data ðxi ; yi Þ, i.e. iv. For each insurance company, compute the bias corrected ^ ^si , where bia ^s is the bootstrap estimadi bia estimate ^ di ¼ ^ Pi di;b ^ di . tor of bias obtained as: b^iasi ¼ 1B Bb¼1 ^ 2 These are variables that are neither inputs nor outputs but are used to mainly explain the variation in the efficiency scores.
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Table 1 Summary of previous research. Papers
Method
Units
Inputs
Outputs
Barros and Barroso (2005) Ennsfellner et al. (2004)
DEA-Malmquist
27 Portuguese insurance companies
Wages, capital, total investment income and premiums issued
Claims paid and profits
Bayesian stochastic frontier
Health, life and non-life: net operating expenses, equity capital and technical provisions net of reinsurance
Cummins et al. (2004)
DEA input distance function
Austrian health, life and non-life insurance companies, 1994–1999 Spanish stock and mutual insurance companies, 1989– 1997
Health and life: incurred benefits net of reinsurance, changes in reserves net of reinsurance, total invested assets. Non-life: claims incurred net of reinsurance, total invested assets Total output, non-life output, life output
Mahlberg and Url (2003)
DEA-Malmquist index
Austrian insurance companies, 1992– 1999
Diacon et al. (2002)
DEA–CRS and DEA–VRS
Noulas et al. (2001)
DEA–CRS model
Total operating expenses net of reinsurance commissions, total capital, total technical reserves, total borrowings Direct cost (claims) and indirect costs (salaries and other expenditures)
Cummins et al. (1999)
DEA input oriented distance function, DEAMalmquist index Deterministic cost frontier, DEA– CRS, DEA–VRS and DEA–NIRS DEA-Malmquist index
Standard & Poor’s Eurothesys data base, 1996–1999 11 Greek insurance companies, 1991– 1996 USA insurers 1981– 1990
Labour costs, materials, policy holders supplied debt capital and equity capital and real invested assets
Short tail personal lines, short tail commercial lines, long tail personal tail, long tail commercial tail, return on assets
USA insurance companies, 1988– 1992
Labour, financial capital and materials
Incurred benefits desegregated into ordinary life insurance, group life insurance and individual annuities, addition to reserves
25 Japanese life insurance companies, 1988–1993 17 Italian life, 58 non-life and 19 mixed insurance companies, 1985– 1993 84 life and 243 nonlife French insurance companies, 1984– 1989 From 38 to 134 USA insurance companies, 1980–1988
Asset value, number of workers and tied agents or sales representatives
Insurance reserves, loans
Wages, administrative wages, fixed capital, equity capital and other ratios
Life insurance benefits and changes in reserves, non-life incurred losses in auto property, in auto liability, in other property and in other liability, and invested assets
Wages, other outlays, distribution ratio, reinsurance ratio and claims ratio
Gross premiums, desegregated by sectors and the sum of dividends, coupons and rents
Labour, capital and intermediate expenditures
561 USA life insurance companies, 1985–1990
Labour, physical capital and miscellaneous items
Discounted long tail incurred losses for unregulated and regulated states; discounted long tail incurred losses for unregulated and regulated states, the sum of loss reserves, loss adjustment expense reserve and unearned premium reserve and the sum of loss adjustment expenses Ordinary life insurance premiums, group life insurance premiums, ordinary annuity, group annuity, group accident and health premiums
Cummins and Zi (1998)
Fukuyama (1997) Cummins et al. (1996)
DEA input distance function and DEAMalmquist index
Fecher et al. (1993)
DEA–BCC and stochastic Cobb– Douglas frontier
Cummins and Weiss (1993)
Translog stochastic frontier
Gardner and Grace (1993)
Deterministic Cobb–Douglas frontier
Price of non-life output, price of life output, labour input, materials, equity capital, debt capital, price of labour, price of materials, price of equity capital, price of debt capital, total costs, total assets, non-life premiums, life premiums, net income, reserves/total assets, net income/equity income, debt capital/total capital, equity capital/ total assets, net income/total assets Administration and distribution costs and costs of capital investments
v. Use the maximum likelihood method to estimate the trun^ ^ ^ ^ r ^ Þ of cated regression of ^ di on zi , providing estimates ðb; ðb; re Þ. vi. Repeat the next three steps (1–3) B2 times to obtain a set of n o ^ ^ ; b ¼ 1; . . . ; B ^ ; r ^ . bootstrap estimates b 2 b b ^ ^ with left trun1. For i ¼ 1; . . . ; n; ei is drawn from N 0; r ^ ^ i . cation at 1 bz ^ ^ i þ ei . 2. For i ¼ 1; . . . ; n, compute d ¼ bz i
3. The maximum likelihood method is again used to estimate the truncated regression of d i on zi , providing esti^ ^ ^ ; r ^ Þ. mates ðb vii. Use the bootstrap results to construct confidence intervals, Zelenyuk and Zheka (2006).
Aggregate value of: expenditure on claims incurred, net change in technical provisions and the amount of returned premiums desegregated on Health insurance, Life insurance, property– liability insurance General insurance net earned premiums, long term insurance net earned premium, total investment income Premium income and revenue from investments
5. Data and results To estimate the production frontier, we used panel data for the years 1994–2003, obtained from the Association of Insurance Companies of Greece, on 71 insurance companies, (10 years 71 companies = 710 observations).The sample consists of 17 life insurers, 41 non-life insurers, and 10 mixed insurance companies. The insurance companies that are considered in this analysis represent almost 90% of the market, thus being abundantly representative of the Greek insurance market. We respected the DEA convention that the minimum number of DMUs is greater than three times the number of inputs plus output (Vassiloglou and Giokas, 1990; Dyson et al., 2001). Determination of inputs and outputs was based on the literature review section. Therefore we measured output by: (i) invested
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Table 2 Average CRS relative efficiency observed in Greek insurance companies: 1994–2003. Name of insurance company
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Average efficient scores
INTERAMERICAN INT. LIFE SCOPLIFE EXPRESS SERVICE NON-LIFE ELLINOBRETANIKI LIFE HELVETIA/POSEIDON LIFE PROODOS NON-LIFE INTERAMERICAN ROAD ASSISTANCE NON-LIFE INTERSALONICA LIFE METROLIFE LIFE IMPERIO LIFE EVROPAIKI PISTI NON-LIFE ELLINOBRETANIKI NON-LIFE COMMERCIAL UNION LIFE DAS NON-LIFE GENIKI EPAGELMATIKI NON-LIFE OLYMPIAKI/VICTORIA LIFE INTERNATIONAL LIFE INTERAMERICAN ASSISTANCE AMYNA NON-LIFE AKMI NON-LIFE AKMI/EFG LIFE NORDSTERN LIFE AEGAION NON-LIFE UNIVERSAL LIFE INTERAMERICAN LIFE HELVETIA NON-LIFE EGNATIA NON-LIFE SKOURTIS NON-LIFE PHOENIX MIXED IMPERIAL NON-LIFE EVROPAIKI PRONOIA NON-LIFE INTERNATIONAL NON-LIFE INTERAMERICAN NON-LIFE GENERALI LIFE EUROSTAR NON-LIFE ASPIS PRONOIA MIXED ALPHA NON-LIFE AGROTIKI NON-LIFE AGROTIKI LIFE YDROGEIOS NON-LIFE POSEIDON NON-LIFE PIGASOS NON-LIFE NORDSTERN NON-LIFE METROLIFE NON-LIFE MAGDEMBOURGER NON-LIFE INTERSALONICA NON-LIFE INTERLIFE NON-LIFE GENIKI PISTI NON-LIFE EVROPAIKI PISTI MIXED EVROPAIKI ENOSIS MIXED ESTIA MIXED DYNAMIS NON-LIFE ASPIS PRONOIA NON-LIFE ARGONAYTIKI NON-LIFE SYNETAIRISTIKI MIXED OIKONOMIKI NON-LIFE GOTAER MIXED GENERALI NON-LIFE GALAXIAS NON-LIFE EVROPI NON-LIFE ETHNIKI MIXED DIETHNIS ENOSIS NON-LIFE ALLIANZ LIFE PERSONAL NON-LIFE ORIZON MIXED OLYMPIAKI/VICTORIA NON-LIFE GENERAL UNION NON-LIFE ELLAS NON-LIFE SIDERIS NON-LIFE ALLIANZ NON-LIFE ATLANTIKI ENOSIS MIXED
0.9 1 1 0.92 0.94 1 1 0.98 0.98 1 0.99 0.92 1 0.96 0.97 0.99 1 1 1 1 1 0.9 0.97 0.99 0.89 0.92 1 0.97 0.91 1 1 0.93 0.9 0.9 0.92 0.95 0.98 0.92 0.92 0.96 0.91 0.91 0.93 0.94 0.89 0.91 0.96 1 0.94 0.93 0.94 0.95 0.99 0.99 0.95 0.9 0.91 0.95 0.9 0.97 0.89 0.87 0.92 0.9 0.99 0.94 0.93 0.86 0.9 0.93 0.88
1 0.96 1 0.84 0.89 1 1 0.89 0.93 1 0.89 0.87 0.98 0.91 0.89 0.9 0.93 0.95 0.92 0.92 0.97 0.87 1 0.87 0.85 0.88 0.96 0.91 0.9 0.9 1 0.89 0.86 0.87 0.88 0.88 0.91 0.91 0.87 0.88 0.89 0.83 0.88 0.88 0.83 0.87 0.89 0.89 0.87 0.91 0.85 0.89 0.94 0.9 0.89 0.86 0.88 0.9 0.84 0.89 0.83 0.87 0.87 0.87 0.87 0.87 0.87 0.86 0.86 0.88 0.85
1 1 1 1 0.95 1 1 0.93 0.97 1 0.94 0.91 1 0.94 0.92 0.92 0.94 1 0.94 0.97 0.97 0.94 1 0.93 0.92 0.91 1 0.95 0.94 0.93 1 0.93 0.91 0.92 0.93 0.95 0.95 0.94 0.92 0.94 0.91 0.87 0.92 0.91 0.86 0.93 0.92 0.93 0.91 0.94 0.95 0.93 0.93 0.94 0.9 0.91 0.92 0.93 0.9 0.91 0.96 0.93 0.9 0.92 0.9 0.91 0.93 0.94 0.9 0.9 0.9
1 1 1 1 0.99 1 1 0.98 1 1 1 0.92 1 0.97 0.97 0.99 0.97 1 0.96 0.96 0.94 0.92 0.96 1 1 0.91 0.94 0.97 0.97 0.97 0.97 0.95 0.93 0.97 0.93 0.98 0.94 0.97 0.97 0.99 0.93 0.89 0.9 0.93 0.89 0.96 0.94 0.93 0.96 0.96 0.99 0.94 0.95 0.93 0.92 0.92 0.92 0.97 0.94 0.92 1 0.94 0.93 0.95 0.9 0.93 0.92 0.91 0.89 0.92 0.92
1 1 1 1 0.9 1 1 0.92 0.9 0.93 1 0.85 0.99 0.93 0.9 0.86 0.86 0.91 0.88 0.89 0.89 0.84 0.85 0.86 0.96 0.85 1 0.86 0.86 0.87 0.84 0.88 0.86 0.89 0.88 0.88 0.93 0.9 0.88 0.85 0.85 0.75 0.85 0.89 0.84 0.88 0.82 0.87 0.88 0.87 0.86 0.87 0.85 0.86 0.87 0.88 0.89 0.9 0.81 0.85 0.91 0.89 0.84 0.84 0.85 0.86 0.87 0.88 0.82 0.83 0.86
1 0.9 1 1 1 1 0.78 0.96 0.88 1 1 1 0.9 0.86 0.91 0.9 0.83 0.81 0.9 0.88 1 0.81 0.82 0.83 0.86 0.8 1 0.78 1 0.89 0.81 0.8 1 0.76 0.8 0.78 0.82 0.83 0.86 0.78 0.81 0.78 0.77 0.78 0.79 0.78 0.82 0.8 0.79 0.84 0.8 0.79 0.8 0.8 0.79 0.77 0.77 0.81 0.76 0.81 0.81 0.8 0.79 0.68 0.82 0.78 0.79 0.79 0.82 0.77 0.82
1 0.92 0.88 1 1 1 0.83 1 0.94 1 0.83 1 0.95 1 0.93 0.89 0.95 1 0.95 0.96 0.95 0.75 0.87 0.91 0.87 1 0.89 0.85 1 0.83 0.86 1 0.85 0.89 0.89 0.85 0.84 0.87 0.9 0.81 0.89 0.87 0.8 0.92 0.83 0.98 0.84 0.83 0.83 0.85 0.85 0.83 0.83 1 0.91 0.81 0.82 0.95 0.82 0.83 0.84 0.86 0.82 0.84 0.78 0.81 0.82 1 0.8 0.75
1 0.97 1 1 1 0.97 1 1 0.88 0.88 0.99 1 0.88 0.84 0.91 0.9 0.89 0.86 0.78 0.83 0.85 0.85 0.84 0.83 0.89 0.88 0.81 0.82 0.82 1 0.81 0.79 0.82 0.85 0.83 0.82 0.79 0.81 0.85 0.82 1 1 0.77 0.8 0.89 0.83 0.8 0.8 0.82 0.8 0.78 0.81 0.79 0.8 0.8 0.78 0.82 0.78 0.77 0.78 0.74 0.8 0.8 0.87 0.78 0.79 0.77 0.79 0.8 0.75 0.77
1 1 0.99 1 1 1 1 1 1 0.68 1 1 0.87 1 0.77 0.89 0.89 0.81 0.96 0.86 0.76 1 0.83 0.82 0.8 1 0.94 0.81 0.78 0.77 0.76 0.74 0.73 0.83 0.79 0.75 0.74 0.77 0.74 0.76 0.76 0.81 0.79 0.72 0.82 0.79 0.7 0.74 0.76 0.74 0.71 0.76 0.73 0.73 0.75 0.73 0.73 0.72 1 0.77 0.7 0.74 0.76 0.75 0.7 0.73 0.71 0.76 0.74 0.7 0.73
1 1 1 1 1 0.91 1 0.74 0.82 0.81 0.76 0.89 0.74 1 1 0.71 0.71 0.73 0.74 0.71 0.64 1 0.74 0.73 0.73 0.69 0.72 0.72 0.74 0.69 0.7 0.69 0.73 0.69 0.71 0.74 0.7 0.71 0.68 0.69 0.7 0.76 1 1 0.77 0.74 0.66 0.7 0.71 0.7 0.74 0.73 0.68 0.71 0.7 0.7 0.73 0.68 0.71 0.68 0.72 0.71 0.68 0.72 0.67 0.71 0.68 0.72 0.69 0.68 0.68
0.99 0.98 0.98 0.98 0.97 0.96 0.95 0.94 0.93 0.93 0.93 0.93 0.93 0.92 0.91 0.9 0.9 0.9 0.9 0.9 0.9 0.89 0.89 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.87 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.83 0.83 0.83 0.83 0.83 0.82 0.82 0.81
Average efficiency (over firms) Median St. dev.
0.95 0.94 0.04
0.90 0.89 0.05
0.94 0.93 0.03
0.95 0.96 0.03
0.89 0.88 0.05
0.85 0.81 0.08
0.89 0.87 0.07
0.85 0.82 0.08
0.82 0.77 0.11
0.76 0.72 0.11
0.88 0.86 0.04
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assets; (ii) losses incurred; (iii) reinsurance reserves and (iv) own reserves; and measured inputs by (v) labour cost, (vi) non labour cost and (vii) equity capital. We may note that for the life insurance companies the term ‘‘losses incurred” is the sum of ‘‘life benefits” plus ‘‘change in reserves”. All variables have been deflated, using the GDP deflator (1994 = 100) obtained from the Annual Report of the Central Bank of Greece.
Table 3 Truncated bootstrapped second stage regression. Model 1 Const Life Non-Life M_A Foreign Big Quoted Log(MktShare) Log(CastNew) Variance
5.1. Results Table 3 presents the CRS efficiency scores for the sample insurance companies in a ranking order. Certain conclusions may be derived from Table 3. First, the analysis is based on a period by period; the overall inefficiency gap for the Greek insurance industry is 0.12. It should be noted, however, that this gap was only 0.05 in 1994, started decline after 1997 and reached a value of 0.24 in 2003. This finding implies that some units moved rapidly ahead following deregulation, leaving others behind in relative term. Second, fifteen insurance companies (7 life and 8 non-life) managed to maintain their competitive positions during the sample period, having on average efficiency scores above 0.90. It seems that life insurers (7 out of 17) and a smaller proportion of non-life companies (8 out of 44) were able to withstand the pressures of deregulation, whereas all mixed insurers proved to be less prepared for the difficulties of the period. Note, that in further analysis we have also checked the robustness of the results, by estimating the VRS and NIRS models. We verified that the ranks are preserved by the three methods adopted, signifying that the results are robust to alternative methods of estimation (see Table 2). 6. Determinants of efficiency In order to examine the hypothesis that insurance efficiency is determined by different contextual variables, we followed the two-step approach, as suggested by Coelli et al. (1998), estimating the regression shown below. It is recognised in the DEA literature that the efficiency scores obtained in the first stage are correlated with the explanatory variables used in the second term, and that the second stage estimates will then be inconsistent and biased (Efron, 1979). A bootstrap procedure is needed to overcome this problem (Efron and Tibshirani, 1993). Therefore, we set:
^dit ¼ b þ b Life þ b Non Life þ b M&Ait þ b Foreign 1 2 3 4 5 it it it þ b6 Big it þ b7 Quotedit þ b8 logðMKShareÞit þ b9 LogðCastNewÞit þ eit
ð3Þ
where ^ d represents the CRS efficiency score. Life is a dummy variable, which is one for life insurance companies. Non-life is a dummy variable which is one for non-life insurance companies. M&A is a dummy variable which is one for enterprises linked to mergers and acquisitions, aiming to capture the effect of mergers and acquisitions in the efficient score. Foreign is a dummy variable, which is equal to one for foreign insurance companies in the sample. The inclusion of this variable is based on the assumption that foreign companies may exhibit higher efficiency due to advanced knowhow. Big is a dummy variable which is one for big companies measured by the total value of assets. Quoted is a dummy variable which is one for companies quoted in the stock market, aiming to capture the effect of transparency due to the stock market governance requirements. Log(MkShare) is the logarithm of the market share of the insurance companies analysed. Log(CastNew) is the logarithm of the ratio equity/invested assets, aiming to capture the effect of capital structure. Following Simar and Wilson (2007) we employ a MATLAB program developed by Valentin Zelenyuk to bootstrap the
** ***
***
1.16 0.11*** 0.03 0.03 0.03 0.16*** 0.01 0.06*** 0.02** 0.03
Model 2 ***
1.10 0.09** 0.07** 0.00 0.00 0.13*** – 0.07*** 0.04*** 0.03
Model 3 ***
1.16 0.19*** 0.07 – 0.04 0.15*** – 0.06*** 0.04*** 0.04
Model 4 ***
1.09 0.19*** 0.01 – 0.09*** – 0.05*** 0.07*** 0.03
Model 5 1.14*** 0.14*** – – – 0.15*** – 0.07*** 0.05*** 0.03
Statistically significant parameters at the 5% level. Statistically significant parameters at the 1% level.
confidence intervals, with 2000 replications. The results are presented in Table 3. Several models are estimated for comparative purpose. The results are quite robust since the variables that were significant in the starting model 1, remained significant after dropping the insignificant variables. A first conclusion is that ‘‘life” companies contribute negatively to efficiency, signifying that this type of companies face different constraints in the Greek insurance market. Second, the variable ‘‘big”(determined on the basis of invested assets) has, also, a negative influence on efficiency; a result associated with the inefficiency of the big(mainly ‘‘mixed”) insurers in the local market. Third, the variable log(market share) has a positive impact on efficiency, implying that consolidation and scale are desirable characteristics of the local market. Finally, the variable log(equity/invested assets) shows that the specific capital structure of Greek insurance companies exercises a negative influence on efficiency. 7. Concluding remarks In this paper, we have analysed technical efficiency in a representative sample of Greek insurance companies between 1994 and 2003, a period of intense volatility due to the deregulation of the market. The analysis is based on a two-stage procedure proposed by Simar and Wilson (2007). Benchmarks are provided for improving the operations of poorly performing insurance companies. It is important to note that a major finding of this study was that competition for market share is the main driver of efficiency in the Greek insurance market. However, the degree of consolidation has not been adequate enough to improve the efficiency of the market. After 1997, the majority of insurance companies operated on declining efficiency, obviously due to inadequacies in management, scale, and technology. What should the managers of inefficient Greek insurance companies do to improve efficiency? First, they should adopt a benchmark management procedure in order to evaluate their relative position and to adopt appropriate managerial procedures for catching up with the frontier of ‘‘best practices”. Second, they should upgrade the quality of their management practices, responding to the results of the present research. Third, they should adopt human resources policies that limit the principal-agent relationship, as well as eliminating collective action problems. Finally, they should pursue market-oriented strategies which increase outputs and decrease inputs. Moreover, the regulatory authority has an important role to play in improving the efficiency of insurance companies by (1) abandoning complacency in enforcing its regulatory duties, (2) publishing information on individual companies in order to introduce greater transparency into the market, and (3) enforcing ‘best practices’ adopted by other regulatory authorities in protecting consumer rights.
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Acknowledgements The authors thanks two anonymous referees for their comments, which contributed to improving the paper. Any remaining errors are our own. References Altunbas, Y., Gardener, E.P.M., Molyneux, P., Moore, B., 2001. Efficiency in European banking. European Economic Review 45, 1931–1955. Barros, C.P., Barroso, N., 2005. Evaluating the efficiency and productivity of insurance companies with a Malmquist index: A case study for Portugal. Geneva Papers on Insurance: Issues and Practice 30 (2), 244–267. Coelli, T.J., Perelman, S., 1999. A comparison of parametric and nonparametric distance functions: with application to European railways. European Journal of Operations Research 117 (2), 326–339. Coelli, T.J., Perelman, S., 2000. Technical efficiency of European railways: A distance function approach. Applied Mathematics 32 (15), 1967–1976. Coelli, T.J., Rao, P., Battese, G.E., 1998. An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Press. Cummins, J.D., Weiss, M.A., 1993. Measuring cost efficiency in the property–liability insurance industry. Journal of Banking and Finance 17, 463–481. Cummins, J.D., Zi, H., 1998. Comparison of frontier efficient methods: An application to the US life insurance industry. Journal of Productivity Analysis 10 (2), 131– 152. Cummins, J.D., Turchetti, G., Weiss, M.A., 1996. Productivity and Technical Efficiency in the Italian Insurance Industry. Working Paper 96-10, Wharton School. Cummins, J.D., Weiss, M.A., Zi, H., 1999. Organizational form and efficiency: The coexistence of stock and mutual property–liability insurers. Management Science 45 (9), 1254–1269. Cummins, J.D., Rubio-Misas, M., Zi, H., 2004. The effects of organisational structure on efficiency: evidence from Spanish insurance industry. Journal of Banking and Finance 28, 3113–3150. Diacon, S.R., Starkey, K., O’Brien, C.O., 2002. Size and efficiency in European longterm insurance companies: An international comparison. Geneva Papers on Risk and Insurance 27, 444–466. Dyson, R.G., Allen, R., Camanho, A.S., Podimovski, V.V., Sarrico, C., Shale, S., 2001. Pitfalls and protocols in DEA. European Journal of Operational Research 132 (2), 245–259.
Efron, B., 1979. Bootstrap methods: another look at the Jackknife. Annals of Statistics 7, 1–26. Efron, B., Tibshirani, R.J., 1993. An Introduction to Bootstrap. Chapman and Hall, London. Ennsfellner, Karl C., Lewis, D., Anderson, Randy I., 2004. Production efficiency in the Australian insurance. The Journal of Risk and Insurance 71 (1), 135–159. Fecher, F., Kessler, D., Perelman, S., Pestieu, P., 1993. Productive performance of the French industry. Journal of Productivity Analysis 4, 77–93. Fukuyama, H., 1997. Investigating productive efficiency and productive changes of Japanese life insurance companies. Pacific-Basin Finance Journal 5 (4), 481–509. Gardner, L.A., Grace, M.F., 1993. X-efficiency in the US life insurance industry. Journal of Banking and Finance 17, 410–497. Mahlberg, B., Url, T., 2003. The effects of the single market on the Austrian insurance industry. Empirical Economics 28, 813–838. Nektarios, M., Barros, C.P., Forthcoming. A Malmquist index for the Greek insurance industry. Geneva Papers on Insurance: Theory and Practice. Noulas, A.G., Hatzigayios, T., Lazaridis, J., Lyroudi, K., 2001. Non-parametric production frontier approach to the study of efficiency of non-life insurance companies in Greece. Journal of Financial Management and Analysis 14 (1), 19– 26. Russell, R.R., 1990. Continuity of measures of technical efficiency. Journal of Economic Theory 51, 255–267. Russell, R.R., 1997. Distance functions in consumer and producer theory. In: Index Number Theory: Essays in Honor of Sten Malmquist. Kluwer Academic Publishers, Boston, pp. 7–90. Simar, L., Wilson, P., 1998. Sensitivity analysis of efficiency scores: how to bootstrap in non-parametric frontier models. Management Science 44 (1), 49–61. Simar, L., Wilson, P.W., 1999. Estimating and bootstrapping Malmquist indices. European Journal of Operational Research 115, 459–471. Simar, L., Wilson, P.W., 2000. Statistical inference in nonparametric frontier models: The state of the art. Journal of Productivity Analysis 13, 49–78. Simar, L., Wilson, P.W., 2007. Estimation and inference in two-stage, semiparametric models of production processes. Journal of Econometrics 136, 31– 64. Vassiloglou, M., Giokas, D., 1990. A study of the relative efficiency of banks branches: An application of data envelopment analysis. The Journal of Operational Research Society 41 (7), 591–597. Zelenyuk, V., Zheka, V., 2006. Corporate governance and firm’s efficiency: The case of a transitional country, Ukraine. Journal of Productivity Analysis 25, 143–168.
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European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor
Innovative applications of O.R.
Efficiency in the Greek insurance industry Carlos Pestana Barros a,*, Milton Nektarios b, A. Assaf c a
Instituto Superior de Economia e Gestão, Technical University of Lisbon, Rua Miguel Lupi, 20, 1249-078 Lisbon, Portugal Dept. of Statistics and Insurance, University of Piraeus, Greece c Isenberg School of Management, University of Massachusetts, Amherst, USA b
a r t i c l e
i n f o
Article history: Received 24 July 2007 Accepted 7 January 2010 Available online 13 January 2010 Keywords: Insurance Greece Productivity change Bootstrapped DEA
a b s t r a c t This paper employs the two-stage procedure of Simar and Wilson (2007) to analyse the effects of deregulation on the efficiency of the Greek insurance industry. The efficiency is estimated by means of data envelopment analysis (DEA). The companies are ranked according to their CRS efficiency score for the period 1994–2003. The first stage results indicate a decline in efficiency over the sample period, while the second stage results confirm that the competition for market shares is a major driver of efficiency in the Greek insurance industry. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The implementation of the Third Generation Insurance Directive (1994) aimed to deregulate the EU insurance markets, with the objective of improving market efficiency and enhancing consumer choice through increased competition. Exits from the insurance market may take place either through voluntary or involuntary withdrawals (run-off or insolvency),or through mergers and acquisitions (M&As). With the current contradiction in the literature regarding the impact deregulation and consolidation on the efficiency of insurance companies (Mahlberg and Url, 2003), this study aims to provide additional evidences on the effects of deregulation and consolidation on the Greek insurance market. Following the deregulation, the Greek insurance market witnessed on the one hand, a significant decline in the number of companies, and on the other hand, a significant increase in firm size. Other accompanying trends included the abolition of the premium tariff system (for Motor TPL and Fire Branches). A criticism of the consolidation process was however the lack of direct supervision in the Greek insurance market, which has left several weak players from the market. To provide further evidence whether the local Greek insurance companies have been able to improve their efficiency as a result of the deregulation and consolidation process, we aim in this paper to analyse the efficiency of the Greek insurance market using the
* Corresponding author. E-mail addresses: [email protected] (C.P. Barros), [email protected] (M. Nektarios), [email protected] (A. Assaf). 0377-2217/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2010.01.011
innovative two-stage procedure proposed by Simar and Wilson (2007). We use data from 1994 to 2003, which cover the implementation of the Third Directive. To the authors’ knowledge, this the first article to examine the relative efficiency of all Greek insurance companies for such an extensive period of time. From an academic perspective, the particular contribution of this paper lies in its presentation of a broader literature review and in the adoption of the new two-stage procedure proposed by Simar and Wilson (2007). The paper is organized as follows: in Section 2, we describe the contextual setting; Section 3, surveys the existing literature on the topic; Section 4, explains the theoretical framework supporting the model used; Section 5, presents the data and results; Section 6, employs a bootstrapped regression model to determine the drivers of efficiency; and finally Section 7 presents the concluding remarks. 2. Overview of the Greek insurance market The Greek insurance market is often described as under-developed in comparison to other insurance markets in the EU-15 countries, despite a significant increase in total premium between 1994 and 2003. The most growing sector in the Greek insurance market has been the Non-Life sector, mainly due to the fact that Greece has not completed yet the reform of its pensions system. Over the period 1994–2003, the Greek insurance market has also experienced a significant decrease in the number of companies, mainly due financial difficulties or mergers and acquisition (M&A) activities. Indirectly, this also helped to increase the average firm size. Historically, the market concentration has been very high
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in the Life sector, while concentration in the Non-Life sector is comparable to EU standards. In terms of economic contribution, the Greek insurance industry is however still behind other related industries, and is often described as lacking efficiency. For more detail on the Greek insurance marker, refer to Nektarios and Barros (Forthcoming).
we mainly rely on the CRS assumption, given that it has several desirable mathematical properties (for details see Russell, 1990, 1997). However, we also validate the results actors the VRS and NIRS assumption. CRS is relatively easy to compute, straightforward in interpretation and, thus, it seems to be the most popular in the insurance literature.
3. Literature survey
4.1.2. The bootstrap The DEA model is relatively simple to estimate, but has long been criticised for being a non-statistical or deterministic technique. A solution to this problem has been recently proposed by Simar and Wilson (1998, 1999, 2000) who showed that it is possible to obtain statistical properties for DEA via the use of the ‘‘bootstrap” approach. The basic idea of bootstrapping is to approximate the distribution of the estimator via re-sampling and recalculation of the parameter of interest, which in our case is the DEA efficiency score. The bootstrap procedure was also later extended by Simar and Wilson (2007) to account for the impact of environmental variables2 on efficiency. For example, if we take the following model:
Recent studies on the efficiency analysis of insurance companies have mainly relied on the use of frontier methodologies, with the two most common are the econometric frontier analysis and the data envelopment analysis (DEA). Both have their advantages and drawbacks. Unlike the econometric stochastic frontier approach, the DEA permits the use of multiple inputs and outputs and does not impose any functional form on the data, neither does it make distributional assumptions on the inefficiency term. Both methods assume that the production function of the fully efficient decision unit is known. In practice, this is not the case and the efficient isoquant must be estimated from the sample data. In these conditions, the frontier is relative to the sample considered in the analysis. Table 1 provides a detailed description of previous research. As it is clear from the above table, studies currently exist on several international insurance markets. However, several weaknesses can be noticed from the existing literature. Frist, there are too many papers replicating previous research with a scant improvement in methodology. Second, we have not yet seen papers applying innovative techniques, such as Fourier frontiers (Altunbas et al., 2001) and output distance functions (Coelli and Perelman, 1999, 2000) in estimating the efficiency of insurance industries. More importantly, none of the applications has used the Simar and Wilson (2007) method, despite its several advantages over the traditional DEA method. 4. Theoretical framework 4.1. Estimation of efficiency scores 4.1.1. Data envelopment analysis Measure DEA is a well established method in the literature and aims to technical efficiency by defining a frontier envelopment surface for all sample observations. Firms are considered as fully efficient if they lie on the frontier, while inefficient otherwise. The output oriented DEA efficiency estimator ^ di can be simply derived by solving the following linear programming:
) n n X X ^di ¼ max d > 0^di y 6 yi k; xi P xi k; k P 0 ; ^d ;k i i i¼1 i¼1 (
¼ 1; . . . ; n firms
i ð1Þ
where yi is vector of outputs, xi is s vector of inputs, k is a I 1 vector of constants. The value of ^ di obtained is the technical efficiency score for the ith firm. A measure of ^ di ¼ 1 indicates that the firm is technically efficient, and inefficient if ^ di > 1. This linear programming problem must be solved n times, once for each firm in the sample. Note that the DEA model described above is a constant returns to scale (CRS) model. It is also possible to impose a variable returns to scale (VRS)1 assumption on the above model by introducing the Pn returns to scale (NIRS) constraint i¼1 k ¼ 1, or a non-increasing P assumption by introducing the constraint ni¼1 k 6 1. In this paper 1 A production function is said to exhibit constant return to scale (CRS) if a proportionate increase in inputs results in the same proportionate increase in outputs. The variable return to scale (VRS), on the other hand, does not assume full proportionality between the inputs and outputs.
^di ¼ zi b þ ei
ð2Þ
where zi is a vector of management related variables which is expected to affect the efficiency of firms under consideration and b refers to a vector of parameters with some statistical noise ei . A popular procedure in the literature is to use the Ordinarily Least Square (OLS) regression to estimate this relationship. However, as described in Simar and Wilson (2007), this might lead to two main problems. First, efficiency scores estimated by DEA are expected to be correlated with each other, as the calculation of efficiency of one firm incorporates observation of all other firms in the same data set. Therefore, direct regression analysis is invalid because of the dependency of the efficiency scores. Similarly, in small samples, a strong correlation is expected between the input/output variables and environmental variables, therefore, violating the regression assumption that ei are independent of zi . To overcome the above problem, Simar and Wilson (2007) proposed the double bootstrapping procedure, in which the bootstrap estimators are substituted from the estimators in the regression stage to calculate the standard error of the estimates. In this way, it is possible to solve the dependency problem and produce valid estimates for the parameters in the second stage regression. More details on the bootstrap procedure used in this stage refer to Simar and Wilson (2007). ^i for i. Calculate the DEA output-orientated efficiency score d each firm, using the linear programming problem in (1). ii. Use the maximum likelihood method to estimate the trun^ of b cated regression of ^ di on zi , to provide and estimate b ^ e of re . and an estimate r iii. For each insurance company i ¼ 1; . . . ; n, repeat the next four steps (1–4) B times oto yield a set of bootstrap n estimates ^ di;b ; b ¼ 1; . . . ; B . ^ 2e Þ distribution with left trunca1. Draw ei from the Nð0; r ^ i Þ. tion at ð1 bz ^ i þ ei . 2. Compute di ¼ bz 3. Construct a pseudo data set ðxi ; yi Þ, where xi ¼ xi and di =di . yi ¼ yi ^ 4. Compute a new DEA estimate di on the set of pseudo data ðxi ; yi Þ, i.e. iv. For each insurance company, compute the bias corrected ^ ^si , where bia ^s is the bootstrap estimadi bia estimate ^ di ¼ ^ Pi di;b ^ di . tor of bias obtained as: b^iasi ¼ 1B Bb¼1 ^ 2 These are variables that are neither inputs nor outputs but are used to mainly explain the variation in the efficiency scores.
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Table 1 Summary of previous research. Papers
Method
Units
Inputs
Outputs
Barros and Barroso (2005) Ennsfellner et al. (2004)
DEA-Malmquist
27 Portuguese insurance companies
Wages, capital, total investment income and premiums issued
Claims paid and profits
Bayesian stochastic frontier
Health, life and non-life: net operating expenses, equity capital and technical provisions net of reinsurance
Cummins et al. (2004)
DEA input distance function
Austrian health, life and non-life insurance companies, 1994–1999 Spanish stock and mutual insurance companies, 1989– 1997
Health and life: incurred benefits net of reinsurance, changes in reserves net of reinsurance, total invested assets. Non-life: claims incurred net of reinsurance, total invested assets Total output, non-life output, life output
Mahlberg and Url (2003)
DEA-Malmquist index
Austrian insurance companies, 1992– 1999
Diacon et al. (2002)
DEA–CRS and DEA–VRS
Noulas et al. (2001)
DEA–CRS model
Total operating expenses net of reinsurance commissions, total capital, total technical reserves, total borrowings Direct cost (claims) and indirect costs (salaries and other expenditures)
Cummins et al. (1999)
DEA input oriented distance function, DEAMalmquist index Deterministic cost frontier, DEA– CRS, DEA–VRS and DEA–NIRS DEA-Malmquist index
Standard & Poor’s Eurothesys data base, 1996–1999 11 Greek insurance companies, 1991– 1996 USA insurers 1981– 1990
Labour costs, materials, policy holders supplied debt capital and equity capital and real invested assets
Short tail personal lines, short tail commercial lines, long tail personal tail, long tail commercial tail, return on assets
USA insurance companies, 1988– 1992
Labour, financial capital and materials
Incurred benefits desegregated into ordinary life insurance, group life insurance and individual annuities, addition to reserves
25 Japanese life insurance companies, 1988–1993 17 Italian life, 58 non-life and 19 mixed insurance companies, 1985– 1993 84 life and 243 nonlife French insurance companies, 1984– 1989 From 38 to 134 USA insurance companies, 1980–1988
Asset value, number of workers and tied agents or sales representatives
Insurance reserves, loans
Wages, administrative wages, fixed capital, equity capital and other ratios
Life insurance benefits and changes in reserves, non-life incurred losses in auto property, in auto liability, in other property and in other liability, and invested assets
Wages, other outlays, distribution ratio, reinsurance ratio and claims ratio
Gross premiums, desegregated by sectors and the sum of dividends, coupons and rents
Labour, capital and intermediate expenditures
561 USA life insurance companies, 1985–1990
Labour, physical capital and miscellaneous items
Discounted long tail incurred losses for unregulated and regulated states; discounted long tail incurred losses for unregulated and regulated states, the sum of loss reserves, loss adjustment expense reserve and unearned premium reserve and the sum of loss adjustment expenses Ordinary life insurance premiums, group life insurance premiums, ordinary annuity, group annuity, group accident and health premiums
Cummins and Zi (1998)
Fukuyama (1997) Cummins et al. (1996)
DEA input distance function and DEAMalmquist index
Fecher et al. (1993)
DEA–BCC and stochastic Cobb– Douglas frontier
Cummins and Weiss (1993)
Translog stochastic frontier
Gardner and Grace (1993)
Deterministic Cobb–Douglas frontier
Price of non-life output, price of life output, labour input, materials, equity capital, debt capital, price of labour, price of materials, price of equity capital, price of debt capital, total costs, total assets, non-life premiums, life premiums, net income, reserves/total assets, net income/equity income, debt capital/total capital, equity capital/ total assets, net income/total assets Administration and distribution costs and costs of capital investments
v. Use the maximum likelihood method to estimate the trun^ ^ ^ ^ r ^ Þ of cated regression of ^ di on zi , providing estimates ðb; ðb; re Þ. vi. Repeat the next three steps (1–3) B2 times to obtain a set of n o ^ ^ ; b ¼ 1; . . . ; B ^ ; r ^ . bootstrap estimates b 2 b b ^ ^ with left trun1. For i ¼ 1; . . . ; n; ei is drawn from N 0; r ^ ^ i . cation at 1 bz ^ ^ i þ ei . 2. For i ¼ 1; . . . ; n, compute d ¼ bz i
3. The maximum likelihood method is again used to estimate the truncated regression of d i on zi , providing esti^ ^ ^ ; r ^ Þ. mates ðb vii. Use the bootstrap results to construct confidence intervals, Zelenyuk and Zheka (2006).
Aggregate value of: expenditure on claims incurred, net change in technical provisions and the amount of returned premiums desegregated on Health insurance, Life insurance, property– liability insurance General insurance net earned premiums, long term insurance net earned premium, total investment income Premium income and revenue from investments
5. Data and results To estimate the production frontier, we used panel data for the years 1994–2003, obtained from the Association of Insurance Companies of Greece, on 71 insurance companies, (10 years 71 companies = 710 observations).The sample consists of 17 life insurers, 41 non-life insurers, and 10 mixed insurance companies. The insurance companies that are considered in this analysis represent almost 90% of the market, thus being abundantly representative of the Greek insurance market. We respected the DEA convention that the minimum number of DMUs is greater than three times the number of inputs plus output (Vassiloglou and Giokas, 1990; Dyson et al., 2001). Determination of inputs and outputs was based on the literature review section. Therefore we measured output by: (i) invested
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Table 2 Average CRS relative efficiency observed in Greek insurance companies: 1994–2003. Name of insurance company
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Average efficient scores
INTERAMERICAN INT. LIFE SCOPLIFE EXPRESS SERVICE NON-LIFE ELLINOBRETANIKI LIFE HELVETIA/POSEIDON LIFE PROODOS NON-LIFE INTERAMERICAN ROAD ASSISTANCE NON-LIFE INTERSALONICA LIFE METROLIFE LIFE IMPERIO LIFE EVROPAIKI PISTI NON-LIFE ELLINOBRETANIKI NON-LIFE COMMERCIAL UNION LIFE DAS NON-LIFE GENIKI EPAGELMATIKI NON-LIFE OLYMPIAKI/VICTORIA LIFE INTERNATIONAL LIFE INTERAMERICAN ASSISTANCE AMYNA NON-LIFE AKMI NON-LIFE AKMI/EFG LIFE NORDSTERN LIFE AEGAION NON-LIFE UNIVERSAL LIFE INTERAMERICAN LIFE HELVETIA NON-LIFE EGNATIA NON-LIFE SKOURTIS NON-LIFE PHOENIX MIXED IMPERIAL NON-LIFE EVROPAIKI PRONOIA NON-LIFE INTERNATIONAL NON-LIFE INTERAMERICAN NON-LIFE GENERALI LIFE EUROSTAR NON-LIFE ASPIS PRONOIA MIXED ALPHA NON-LIFE AGROTIKI NON-LIFE AGROTIKI LIFE YDROGEIOS NON-LIFE POSEIDON NON-LIFE PIGASOS NON-LIFE NORDSTERN NON-LIFE METROLIFE NON-LIFE MAGDEMBOURGER NON-LIFE INTERSALONICA NON-LIFE INTERLIFE NON-LIFE GENIKI PISTI NON-LIFE EVROPAIKI PISTI MIXED EVROPAIKI ENOSIS MIXED ESTIA MIXED DYNAMIS NON-LIFE ASPIS PRONOIA NON-LIFE ARGONAYTIKI NON-LIFE SYNETAIRISTIKI MIXED OIKONOMIKI NON-LIFE GOTAER MIXED GENERALI NON-LIFE GALAXIAS NON-LIFE EVROPI NON-LIFE ETHNIKI MIXED DIETHNIS ENOSIS NON-LIFE ALLIANZ LIFE PERSONAL NON-LIFE ORIZON MIXED OLYMPIAKI/VICTORIA NON-LIFE GENERAL UNION NON-LIFE ELLAS NON-LIFE SIDERIS NON-LIFE ALLIANZ NON-LIFE ATLANTIKI ENOSIS MIXED
0.9 1 1 0.92 0.94 1 1 0.98 0.98 1 0.99 0.92 1 0.96 0.97 0.99 1 1 1 1 1 0.9 0.97 0.99 0.89 0.92 1 0.97 0.91 1 1 0.93 0.9 0.9 0.92 0.95 0.98 0.92 0.92 0.96 0.91 0.91 0.93 0.94 0.89 0.91 0.96 1 0.94 0.93 0.94 0.95 0.99 0.99 0.95 0.9 0.91 0.95 0.9 0.97 0.89 0.87 0.92 0.9 0.99 0.94 0.93 0.86 0.9 0.93 0.88
1 0.96 1 0.84 0.89 1 1 0.89 0.93 1 0.89 0.87 0.98 0.91 0.89 0.9 0.93 0.95 0.92 0.92 0.97 0.87 1 0.87 0.85 0.88 0.96 0.91 0.9 0.9 1 0.89 0.86 0.87 0.88 0.88 0.91 0.91 0.87 0.88 0.89 0.83 0.88 0.88 0.83 0.87 0.89 0.89 0.87 0.91 0.85 0.89 0.94 0.9 0.89 0.86 0.88 0.9 0.84 0.89 0.83 0.87 0.87 0.87 0.87 0.87 0.87 0.86 0.86 0.88 0.85
1 1 1 1 0.95 1 1 0.93 0.97 1 0.94 0.91 1 0.94 0.92 0.92 0.94 1 0.94 0.97 0.97 0.94 1 0.93 0.92 0.91 1 0.95 0.94 0.93 1 0.93 0.91 0.92 0.93 0.95 0.95 0.94 0.92 0.94 0.91 0.87 0.92 0.91 0.86 0.93 0.92 0.93 0.91 0.94 0.95 0.93 0.93 0.94 0.9 0.91 0.92 0.93 0.9 0.91 0.96 0.93 0.9 0.92 0.9 0.91 0.93 0.94 0.9 0.9 0.9
1 1 1 1 0.99 1 1 0.98 1 1 1 0.92 1 0.97 0.97 0.99 0.97 1 0.96 0.96 0.94 0.92 0.96 1 1 0.91 0.94 0.97 0.97 0.97 0.97 0.95 0.93 0.97 0.93 0.98 0.94 0.97 0.97 0.99 0.93 0.89 0.9 0.93 0.89 0.96 0.94 0.93 0.96 0.96 0.99 0.94 0.95 0.93 0.92 0.92 0.92 0.97 0.94 0.92 1 0.94 0.93 0.95 0.9 0.93 0.92 0.91 0.89 0.92 0.92
1 1 1 1 0.9 1 1 0.92 0.9 0.93 1 0.85 0.99 0.93 0.9 0.86 0.86 0.91 0.88 0.89 0.89 0.84 0.85 0.86 0.96 0.85 1 0.86 0.86 0.87 0.84 0.88 0.86 0.89 0.88 0.88 0.93 0.9 0.88 0.85 0.85 0.75 0.85 0.89 0.84 0.88 0.82 0.87 0.88 0.87 0.86 0.87 0.85 0.86 0.87 0.88 0.89 0.9 0.81 0.85 0.91 0.89 0.84 0.84 0.85 0.86 0.87 0.88 0.82 0.83 0.86
1 0.9 1 1 1 1 0.78 0.96 0.88 1 1 1 0.9 0.86 0.91 0.9 0.83 0.81 0.9 0.88 1 0.81 0.82 0.83 0.86 0.8 1 0.78 1 0.89 0.81 0.8 1 0.76 0.8 0.78 0.82 0.83 0.86 0.78 0.81 0.78 0.77 0.78 0.79 0.78 0.82 0.8 0.79 0.84 0.8 0.79 0.8 0.8 0.79 0.77 0.77 0.81 0.76 0.81 0.81 0.8 0.79 0.68 0.82 0.78 0.79 0.79 0.82 0.77 0.82
1 0.92 0.88 1 1 1 0.83 1 0.94 1 0.83 1 0.95 1 0.93 0.89 0.95 1 0.95 0.96 0.95 0.75 0.87 0.91 0.87 1 0.89 0.85 1 0.83 0.86 1 0.85 0.89 0.89 0.85 0.84 0.87 0.9 0.81 0.89 0.87 0.8 0.92 0.83 0.98 0.84 0.83 0.83 0.85 0.85 0.83 0.83 1 0.91 0.81 0.82 0.95 0.82 0.83 0.84 0.86 0.82 0.84 0.78 0.81 0.82 1 0.8 0.75
1 0.97 1 1 1 0.97 1 1 0.88 0.88 0.99 1 0.88 0.84 0.91 0.9 0.89 0.86 0.78 0.83 0.85 0.85 0.84 0.83 0.89 0.88 0.81 0.82 0.82 1 0.81 0.79 0.82 0.85 0.83 0.82 0.79 0.81 0.85 0.82 1 1 0.77 0.8 0.89 0.83 0.8 0.8 0.82 0.8 0.78 0.81 0.79 0.8 0.8 0.78 0.82 0.78 0.77 0.78 0.74 0.8 0.8 0.87 0.78 0.79 0.77 0.79 0.8 0.75 0.77
1 1 0.99 1 1 1 1 1 1 0.68 1 1 0.87 1 0.77 0.89 0.89 0.81 0.96 0.86 0.76 1 0.83 0.82 0.8 1 0.94 0.81 0.78 0.77 0.76 0.74 0.73 0.83 0.79 0.75 0.74 0.77 0.74 0.76 0.76 0.81 0.79 0.72 0.82 0.79 0.7 0.74 0.76 0.74 0.71 0.76 0.73 0.73 0.75 0.73 0.73 0.72 1 0.77 0.7 0.74 0.76 0.75 0.7 0.73 0.71 0.76 0.74 0.7 0.73
1 1 1 1 1 0.91 1 0.74 0.82 0.81 0.76 0.89 0.74 1 1 0.71 0.71 0.73 0.74 0.71 0.64 1 0.74 0.73 0.73 0.69 0.72 0.72 0.74 0.69 0.7 0.69 0.73 0.69 0.71 0.74 0.7 0.71 0.68 0.69 0.7 0.76 1 1 0.77 0.74 0.66 0.7 0.71 0.7 0.74 0.73 0.68 0.71 0.7 0.7 0.73 0.68 0.71 0.68 0.72 0.71 0.68 0.72 0.67 0.71 0.68 0.72 0.69 0.68 0.68
0.99 0.98 0.98 0.98 0.97 0.96 0.95 0.94 0.93 0.93 0.93 0.93 0.93 0.92 0.91 0.9 0.9 0.9 0.9 0.9 0.9 0.89 0.89 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.87 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.83 0.83 0.83 0.83 0.83 0.82 0.82 0.81
Average efficiency (over firms) Median St. dev.
0.95 0.94 0.04
0.90 0.89 0.05
0.94 0.93 0.03
0.95 0.96 0.03
0.89 0.88 0.05
0.85 0.81 0.08
0.89 0.87 0.07
0.85 0.82 0.08
0.82 0.77 0.11
0.76 0.72 0.11
0.88 0.86 0.04
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assets; (ii) losses incurred; (iii) reinsurance reserves and (iv) own reserves; and measured inputs by (v) labour cost, (vi) non labour cost and (vii) equity capital. We may note that for the life insurance companies the term ‘‘losses incurred” is the sum of ‘‘life benefits” plus ‘‘change in reserves”. All variables have been deflated, using the GDP deflator (1994 = 100) obtained from the Annual Report of the Central Bank of Greece.
Table 3 Truncated bootstrapped second stage regression. Model 1 Const Life Non-Life M_A Foreign Big Quoted Log(MktShare) Log(CastNew) Variance
5.1. Results Table 3 presents the CRS efficiency scores for the sample insurance companies in a ranking order. Certain conclusions may be derived from Table 3. First, the analysis is based on a period by period; the overall inefficiency gap for the Greek insurance industry is 0.12. It should be noted, however, that this gap was only 0.05 in 1994, started decline after 1997 and reached a value of 0.24 in 2003. This finding implies that some units moved rapidly ahead following deregulation, leaving others behind in relative term. Second, fifteen insurance companies (7 life and 8 non-life) managed to maintain their competitive positions during the sample period, having on average efficiency scores above 0.90. It seems that life insurers (7 out of 17) and a smaller proportion of non-life companies (8 out of 44) were able to withstand the pressures of deregulation, whereas all mixed insurers proved to be less prepared for the difficulties of the period. Note, that in further analysis we have also checked the robustness of the results, by estimating the VRS and NIRS models. We verified that the ranks are preserved by the three methods adopted, signifying that the results are robust to alternative methods of estimation (see Table 2). 6. Determinants of efficiency In order to examine the hypothesis that insurance efficiency is determined by different contextual variables, we followed the two-step approach, as suggested by Coelli et al. (1998), estimating the regression shown below. It is recognised in the DEA literature that the efficiency scores obtained in the first stage are correlated with the explanatory variables used in the second term, and that the second stage estimates will then be inconsistent and biased (Efron, 1979). A bootstrap procedure is needed to overcome this problem (Efron and Tibshirani, 1993). Therefore, we set:
^dit ¼ b þ b Life þ b Non Life þ b M&Ait þ b Foreign 1 2 3 4 5 it it it þ b6 Big it þ b7 Quotedit þ b8 logðMKShareÞit þ b9 LogðCastNewÞit þ eit
ð3Þ
where ^ d represents the CRS efficiency score. Life is a dummy variable, which is one for life insurance companies. Non-life is a dummy variable which is one for non-life insurance companies. M&A is a dummy variable which is one for enterprises linked to mergers and acquisitions, aiming to capture the effect of mergers and acquisitions in the efficient score. Foreign is a dummy variable, which is equal to one for foreign insurance companies in the sample. The inclusion of this variable is based on the assumption that foreign companies may exhibit higher efficiency due to advanced knowhow. Big is a dummy variable which is one for big companies measured by the total value of assets. Quoted is a dummy variable which is one for companies quoted in the stock market, aiming to capture the effect of transparency due to the stock market governance requirements. Log(MkShare) is the logarithm of the market share of the insurance companies analysed. Log(CastNew) is the logarithm of the ratio equity/invested assets, aiming to capture the effect of capital structure. Following Simar and Wilson (2007) we employ a MATLAB program developed by Valentin Zelenyuk to bootstrap the
** ***
***
1.16 0.11*** 0.03 0.03 0.03 0.16*** 0.01 0.06*** 0.02** 0.03
Model 2 ***
1.10 0.09** 0.07** 0.00 0.00 0.13*** – 0.07*** 0.04*** 0.03
Model 3 ***
1.16 0.19*** 0.07 – 0.04 0.15*** – 0.06*** 0.04*** 0.04
Model 4 ***
1.09 0.19*** 0.01 – 0.09*** – 0.05*** 0.07*** 0.03
Model 5 1.14*** 0.14*** – – – 0.15*** – 0.07*** 0.05*** 0.03
Statistically significant parameters at the 5% level. Statistically significant parameters at the 1% level.
confidence intervals, with 2000 replications. The results are presented in Table 3. Several models are estimated for comparative purpose. The results are quite robust since the variables that were significant in the starting model 1, remained significant after dropping the insignificant variables. A first conclusion is that ‘‘life” companies contribute negatively to efficiency, signifying that this type of companies face different constraints in the Greek insurance market. Second, the variable ‘‘big”(determined on the basis of invested assets) has, also, a negative influence on efficiency; a result associated with the inefficiency of the big(mainly ‘‘mixed”) insurers in the local market. Third, the variable log(market share) has a positive impact on efficiency, implying that consolidation and scale are desirable characteristics of the local market. Finally, the variable log(equity/invested assets) shows that the specific capital structure of Greek insurance companies exercises a negative influence on efficiency. 7. Concluding remarks In this paper, we have analysed technical efficiency in a representative sample of Greek insurance companies between 1994 and 2003, a period of intense volatility due to the deregulation of the market. The analysis is based on a two-stage procedure proposed by Simar and Wilson (2007). Benchmarks are provided for improving the operations of poorly performing insurance companies. It is important to note that a major finding of this study was that competition for market share is the main driver of efficiency in the Greek insurance market. However, the degree of consolidation has not been adequate enough to improve the efficiency of the market. After 1997, the majority of insurance companies operated on declining efficiency, obviously due to inadequacies in management, scale, and technology. What should the managers of inefficient Greek insurance companies do to improve efficiency? First, they should adopt a benchmark management procedure in order to evaluate their relative position and to adopt appropriate managerial procedures for catching up with the frontier of ‘‘best practices”. Second, they should upgrade the quality of their management practices, responding to the results of the present research. Third, they should adopt human resources policies that limit the principal-agent relationship, as well as eliminating collective action problems. Finally, they should pursue market-oriented strategies which increase outputs and decrease inputs. Moreover, the regulatory authority has an important role to play in improving the efficiency of insurance companies by (1) abandoning complacency in enforcing its regulatory duties, (2) publishing information on individual companies in order to introduce greater transparency into the market, and (3) enforcing ‘best practices’ adopted by other regulatory authorities in protecting consumer rights.
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Acknowledgements The authors thanks two anonymous referees for their comments, which contributed to improving the paper. Any remaining errors are our own. References Altunbas, Y., Gardener, E.P.M., Molyneux, P., Moore, B., 2001. Efficiency in European banking. European Economic Review 45, 1931–1955. Barros, C.P., Barroso, N., 2005. Evaluating the efficiency and productivity of insurance companies with a Malmquist index: A case study for Portugal. Geneva Papers on Insurance: Issues and Practice 30 (2), 244–267. Coelli, T.J., Perelman, S., 1999. A comparison of parametric and nonparametric distance functions: with application to European railways. European Journal of Operations Research 117 (2), 326–339. Coelli, T.J., Perelman, S., 2000. Technical efficiency of European railways: A distance function approach. Applied Mathematics 32 (15), 1967–1976. Coelli, T.J., Rao, P., Battese, G.E., 1998. An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Press. Cummins, J.D., Weiss, M.A., 1993. Measuring cost efficiency in the property–liability insurance industry. Journal of Banking and Finance 17, 463–481. Cummins, J.D., Zi, H., 1998. Comparison of frontier efficient methods: An application to the US life insurance industry. Journal of Productivity Analysis 10 (2), 131– 152. Cummins, J.D., Turchetti, G., Weiss, M.A., 1996. Productivity and Technical Efficiency in the Italian Insurance Industry. Working Paper 96-10, Wharton School. Cummins, J.D., Weiss, M.A., Zi, H., 1999. Organizational form and efficiency: The coexistence of stock and mutual property–liability insurers. Management Science 45 (9), 1254–1269. Cummins, J.D., Rubio-Misas, M., Zi, H., 2004. The effects of organisational structure on efficiency: evidence from Spanish insurance industry. Journal of Banking and Finance 28, 3113–3150. Diacon, S.R., Starkey, K., O’Brien, C.O., 2002. Size and efficiency in European longterm insurance companies: An international comparison. Geneva Papers on Risk and Insurance 27, 444–466. Dyson, R.G., Allen, R., Camanho, A.S., Podimovski, V.V., Sarrico, C., Shale, S., 2001. Pitfalls and protocols in DEA. European Journal of Operational Research 132 (2), 245–259.
Efron, B., 1979. Bootstrap methods: another look at the Jackknife. Annals of Statistics 7, 1–26. Efron, B., Tibshirani, R.J., 1993. An Introduction to Bootstrap. Chapman and Hall, London. Ennsfellner, Karl C., Lewis, D., Anderson, Randy I., 2004. Production efficiency in the Australian insurance. The Journal of Risk and Insurance 71 (1), 135–159. Fecher, F., Kessler, D., Perelman, S., Pestieu, P., 1993. Productive performance of the French industry. Journal of Productivity Analysis 4, 77–93. Fukuyama, H., 1997. Investigating productive efficiency and productive changes of Japanese life insurance companies. Pacific-Basin Finance Journal 5 (4), 481–509. Gardner, L.A., Grace, M.F., 1993. X-efficiency in the US life insurance industry. Journal of Banking and Finance 17, 410–497. Mahlberg, B., Url, T., 2003. The effects of the single market on the Austrian insurance industry. Empirical Economics 28, 813–838. Nektarios, M., Barros, C.P., Forthcoming. A Malmquist index for the Greek insurance industry. Geneva Papers on Insurance: Theory and Practice. Noulas, A.G., Hatzigayios, T., Lazaridis, J., Lyroudi, K., 2001. Non-parametric production frontier approach to the study of efficiency of non-life insurance companies in Greece. Journal of Financial Management and Analysis 14 (1), 19– 26. Russell, R.R., 1990. Continuity of measures of technical efficiency. Journal of Economic Theory 51, 255–267. Russell, R.R., 1997. Distance functions in consumer and producer theory. In: Index Number Theory: Essays in Honor of Sten Malmquist. Kluwer Academic Publishers, Boston, pp. 7–90. Simar, L., Wilson, P., 1998. Sensitivity analysis of efficiency scores: how to bootstrap in non-parametric frontier models. Management Science 44 (1), 49–61. Simar, L., Wilson, P.W., 1999. Estimating and bootstrapping Malmquist indices. European Journal of Operational Research 115, 459–471. Simar, L., Wilson, P.W., 2000. Statistical inference in nonparametric frontier models: The state of the art. Journal of Productivity Analysis 13, 49–78. Simar, L., Wilson, P.W., 2007. Estimation and inference in two-stage, semiparametric models of production processes. Journal of Econometrics 136, 31– 64. Vassiloglou, M., Giokas, D., 1990. A study of the relative efficiency of banks branches: An application of data envelopment analysis. The Journal of Operational Research Society 41 (7), 591–597. Zelenyuk, V., Zheka, V., 2006. Corporate governance and firm’s efficiency: The case of a transitional country, Ukraine. Journal of Productivity Analysis 25, 143–168.