Efficiency and Profitability in the Global Insurance Industry. Martin Eling, Ruo Jia + (September, 2018)

Transcription

1 Efficiency and Profitability in the Global Insurance Industry Martin Eling, Ruo Jia + (September, 2018) Abstract We examine the relationship between firm efficiency (E) and profitability (P) with a global dataset of 5,000 insurance companies. Consistent with previous studies in banking and insurance, we document a significantly positive correlation between the efficiency measures and returns on equity and assets. Beyond the extant evidence, we find significant industry dependency in the E-P relationship driven by industry idiosyncrasies, whereas efficiency is more critical to the profitability of life insurers than to that of nonlife insurers. We also show that the E-P relationship is nonlinear: the marginal impact of efficiency on profitability decreases as the insurer s efficiency is close to the best practice. Keywords Insurance, Data envelopment analysis (DEA), Frontier efficiency analysis, Firm performance, Industry dependency JEL Classification: G22, L21 + Martin Eling (martin.eling@unisg.ch, +41 (0) ), the corresponding author, is affiliated with the Institute of Insurance Economics, School of Finance, University of St. Gallen, Girtannerstrasse 6, 9000 St. Gallen, Switzerland. Ruo Jia (ruo.jia@pku.edu.cn, +86 (0) ) is affiliated with the Department of Risk Management and Insurance, School of Economics, Peking University, Yiheyuan Rd. 5, Beijing, China.

2 1. Introduction The measurement of firm performance is central to the business research. Previous studies have demonstrated that emphasis on purely financial measures (e.g. return on equity) may overlook a firm s competitive advantage embedded in its efficiency in transforming resources (Chen, Delmas, and Lieberman, 2015). Frontier efficiency measures reveal this productive dimension and thus constitute an important element of overall firm performance. With the two measures of different focuses, an important question is to what extent a firm s efficiency in converting inputs to outputs translates into its financial profit. In other words, what is the link between what firms do (efficiency) and what their shareholders get (profitability)? The intention of this paper is to analyze the alignment and differences between the frontier efficiency and financial profitability measures. This question has been investigated in manufacturing (see e.g., Chen et al., 2015), banking (see e.g., Olsen and Zoubi, 2011), as well as life (Greene and Segal, 2004) and nonlife insurance (Leverty and Grace, 2010) industries. The extant results in general reveal a positive E-P relationship in various industries, however, do not discuss that the magnitudes of such impact differ from industry to industry. Some industries efficiency of transmitting resources may be more critical to their financial profitability than others. For example, Sherman and Gold (1985) and Oral and Yolalan (1990) suggest that efficiency is only a secondary determinant of profitability in the banking industry, while Greene and Segal (2004) argue that efficiency is of paramount importance to the life insurers profitability. Thus, the E-P relationship is industry dependent. Moreover, the E-P relationship may not be necessarily linear, that is the impact of efficiency on profitability may be contingent on the degree of efficiency. While the general positive E-P relationship is well documented, these latter two questions (potential industry dependence and nonlinearity) have not yet been answered in the literature. The insurance industry provides a unique context to investigate the industry dependency of E-P relationships with its two sub-industries life and nonlife insurance operated by separate legal entities in most markets. Moreover, with its large variation of efficiency degrees in different markets, the global insurance industry is also ideal to reveal the nonlinear E-P relationship, if any. The optimization principle in microeconomics suggests that firms minimize costs and maximize profits subject to existing technologies and expertise; competition will drive firms that are not attaining the optimization out of the market in the long run (Bauer, Berger, Ferrier, and Humphrey, 1998; Cummins and Weiss, 2013). Various theories explain why inefficient firms can also survive in the long run due to insufficient competition (Motta, 2004), management motivations (Leibenstein, 1966), and behavioral reasons (Stein, 1989). In business practice, managers and regulators focus on identifying non-optimized production units by benchmarking them with peers in the industry (Kaplan and Norton, 2005). Farrell (1957) develops the modern framework of frontier efficiency analysis following the concept of optimization in microeconomics and aims to identify firms that do not succeed in optimization and to measure how far they are from the best practice firms. The frontier efficiency analysis aggregates multiple inputs and outputs to a single efficiency measure. Since the methodological contribution of Aigner, Lovell, and Schmidt (1977) and Charnes, Cooper, and Rhodes (1978), the academic studies on the performance of financial institutions have increasingly focused on the frontier efficiency methods (Bauer et al., 1998), first in the banking industry (see Berger and Humphrey, 1997 for a review), and shortly afterwards also in the insurance industry (see Eling and Luhnen, 2010a; Cummins and Weiss, 2013 for reviews). 1

3 The E-P relationship is important to better understand the linkage between the profitability and the operational process of input-output-transformation (Kaplan and Norton, 2005). This is particularly true for those organizations focusing on non-tangible services, innovations, and learning, such as financial institutions. However, the frontier efficiency measures have not yet been prevalent in business as it is in academia. Bauer et al. (1998) discuss six conditions that may affect the application of frontier efficiency measures by regulators and managers. One of them is the consistency between frontier efficiency measures and conventional financial measures. This criterion is critical because the financial ratios are the present language of managers, investors, and regulators, which thus define the reality. As a relatively new performance concept, the frontier efficiency measure has to demonstrate its consistency with conventional measures, i.e. it is not just artifact of the efficiency approach assumptions (Bauer et al., 1998; Laverty and Grace, 2010). 1 Thus, we are motivated to analyze the relationship between firm efficiency and profitability (E-P relationship) in financial services, in our case the global insurance industry. Our analysis is novel and informative in the following aspects: (1) insurance is one of the most rapidly growing fields of frontier efficiency analyses, with over one hundred peer-review journal articles published in the past decade (see Eling and Luhnen, 2010a; Cummins and Weiss, 2013 for reviews). However, the evidence on the E- P relationship in the insurance industry is limited to the U.S. life (Cummins and Zi, 1998; Greene and Segal, 2004) and nonlife (Leverty and Grace, 2010) insurance markets. We extend the analysis to non-u.s. markets and found support for the global validity of the E-P relationship. 2 (2) We go beyond the existing literature and contribute to the understanding of E-P relationship s nature in terms of nonlinearity and industry dependency. The importance of a firm s efficiency in determining its profitability depends on the level of its own efficiency and on the industry idiosyncrasies. (3) We expand the methods that Cummins and Zi (1998), Greene and Segal (2004), and Leverty and Grace (2010) use to examine the E-P relationship by using the rank-order correlation measures, Spearman s Rho and Kendall s Tau; another innovation on the methodological side is our attempt to also assess the relationship between profit efficiency and profitability ratios in the insurance industry. Furthermore, the strength of our analysis lies with a large sample of around 5,000 insurers and 27,000 firm-year observations over 11 years, which covers more than 50% of premium volume outside North America (Swiss Re, 2014). By way of preview, we document a significantly positive correlation between firm efficiency and profitability. This E-P correlation is economically significant and comparable to Greene and Segal s (2004) results for the U.S. life and Leverty and Grace s (2010) results for the U.S. nonlife insurance industry. Moreover, we show that the E-P correlation is nonlinear and industry dependent; the positive impact of efficiency becomes smaller as the 1 Other reasons for the lack of use of frontier efficiency measures in financial services include the higher complexity of multi-dimensional inputs and outputs and the unclear definition of output. For example, in the insurance industry, it may not be straightforward that higher insurance losses are good in terms of productivity and thus efficiency. From a business management point of view, one might expect to see profit or premium as output of the firm. However, from a microeconomic point of view, then insurance losses that is the main type of service given to the customer are a meaningful output measure. Moreover, the premium represents the price times service quantity instead of the quantity and thus cannot be used as an output measure (Yuengert, 1993). In the manufacturing industries, e.g. coal mine or power plants, the outputs are clearer and thus have a broader application of the efficiency measures (Yang and Pollitt, 2009). 2 The use of a global dataset helps to identify whether the E-P relationship is a market specific phenomena; particularly also, whether the E-P relationship is robust across different regions (EU vs. non-eu) and different market development phases (e.g. matured vs. emerging markets). 2

4 firm approaches to the best practice, and efficiency is more critical to the profitability of life insurers than to that of nonlife insurers; the latter result is probably due to higher degree of competition and more difficult general market conditions (e.g. tougher regulation, low interest rates). The remainder of this paper is organized as follows. We first review the extant E-P relationship literature to develop our hypotheses. Then, we introduce our sample, methodology, and empirical models, followed by results and robustness tests. Finally, we conclude. 2. Hypotheses development Berger and Humphrey (1997) summarize three basic usages of frontier efficiency analysis: (1) to address research questions by describing the efficiency of an industry and ranking its firms; (2) to improve managerial performance by identifying best practices and worst practices associated with high and low measured efficiency, respectively, and encouraging the former practices while discouraging the latter; (3) to inform regulators and policy makers by assessing the effects of deregulation, mergers, or market structure on efficiency. The frontier efficiency measures are superior to the conventional financial measures in many aspects for most regulatory and managerial purposes (Bauer et al., 1998; Leverty and Grace, 2010). This is because (1) frontier efficiency measures remove the effects of differences in input prices and other exogenous market factors affecting the conventional financial measures 3, and thus are better estimates of the underlying performance of the managers and operations (Bauer et al., 1998); (2) conventional financial measures fail to consider the value of management actions (e.g. investment decisions) that will affect the future as opposed to current performance (Sherman and Gold, 1985; Kaplan and Norton, 2005), and thus may not be appropriate to reflect a firm s real performance in the long run (Oral and Yolalan, 1990). Therefore, frontier efficiency measures dominate conventional financial measures in terms of developing meaningful and reliable measures of performance (Cummins and Weiss, 2013). Efficiency estimated by frontier efficiency analysis and profitability measured by conventional financial ratios are two connected concepts. The efficiency captures a firm s outputs/inputs ratio relative to the best practice firms. It integrates multiple inputs and outputs into a single measurement of efficiency and defines a frontier of best practices with firms at different size. The same is true for conventional financial measures such as return on equity or assets, which are also size neutral and reflect the integrated result of various firm activities. Cost efficiency affects profits through the negative effect of wasted resources on earnings and cash flows (Greene and Segal, 2004). More efficient insurers are expected to earn higher profit, because they have lower operating costs for given amount of outputs. These similarities and connections establish the basis of consistency between frontier efficiency measures and conventional profitability measures. The differences of the two concepts are also significant. First, the efficiency is a relative measure against a group of best practice firms operating on the efficient frontier and thus is bounded between 0 and 1; 4 while the 3 The frontier efficiency measures may successfully remove the market factors for a single market (e.g. industry growth, industry profitability) because efficiencies are measured against the best practice in the same market. However, in our cross-market setup, different market environments may affect the efficiency of firms in respective markets differently (Eling and Huang, 2013; Eling and Schaper, 2016). 4 We adopt Farell s (1957) efficiency measures that are bounded between 0 and 1. Some scholars (e.g. Greene and Segal, 2004) also use inefficiency scores (i.e. 1-[efficiency score]). 3

5 profit ratios are absolute ratios that are in principle not bounded. Second, the profitability reflects the results of all activities of a firm including the exogenous price and market fluctuations that managers have little or no control; while the efficiency focuses on the key inputs and outputs and those elements that managers are able to influence on operational and/or capital wise (Leverty and Grace, 2012). For example, a financial crisis shall result in immediate low financial returns reflecting on profit ratios, but the output or input adjustments take longer time and all firms operating in the market may adjust in the same direction. Therefore, the efficiency of a firm may vary less than its profitability, i.e. less sensitive to the exogenous market factors which affect the whole industry. For example, from late 1970s to early 1990s, the U.S. car manufacturers had persistently lower cost efficiencies but higher profitability than Japanese ones due to the U.S. market entry barriers (Chen et al., 2015). An insurer may also have a good overall profit even if it has poor operations (high expense ratio and low efficiency) but a good luck (low loss ratio). In the banking performance literature, Sherman and Gold (1985) and Oral and Yolalan (1990) argue that a bank s operating efficiency is one of the determinants of profitability, but only a secondary one. 5 Bauer et al. (1998) and Eisenbeis, Ferrier, and Kwan (1999) present evidence from the U.S. banking industry showing a low but significantly positive correlation between bank efficiency and its profitability. The Pearson correlation coefficients between cost efficiency and ROA are mostly 10% to 25% (Bauer et al., 1998). Casu and Molyneux (2003) document similar small magnitude considering European banks. 6/7 In the insurance performance literature, Cummins and Zi (1998) find that in almost all cases, frontier efficiency measures derived from various techniques have significantly positive correlation with conventional profitability measures. The Pearson correlation coefficients between cost efficiency and the ratio of revenue (net income plus benefits) to equity are mostly 12% to 35%. Greene and Segal (2004) reinforce the E-P link in the U.S. life insurance industry by using a regression model controlling for other factors that influence the financial returns. They document a statistically positive and economically significant impact of cost efficiency on returns. Leverty and Grace (2010) confirm this positive E-P relationship in the U.S. nonlife insurance industry. It would be interesting to directly compare the magnitude of E-P relationship between Greene and Segal s (2004) U.S. life insurance results and Leverty and Grace s (2010) U.S. nonlife insurance results. However, this is difficult because (1) Greene and Segal (2004) use SFA to derive cost inefficiency scores (one minus efficiency), while Leverty and Grace (2010) use DEA to derive the efficiency scores; (2) Leverty and Grace (2010) only present the results for the decompositions of cost efficiency (i.e. pure technical efficiency, scale efficiency, and allocative efficiency) rather than the results for aggregated cost efficiency-profitability relationship. We are thus 5 Sherman and Gold (1985) suggest that marketing new services to attract new funds may for example be more prominent focus of bank managers, comparing to the operational efficiency. 6 Casu and Molyneux (2003) consider return on equity as a determinant of cost efficiency and use return on equity as the independent variable. Thus the results are not directly comparable with others. Their coefficient between return on equity and cost efficiency is Looking into other industries, the direct evidence on E-P relationships in manufacturing is limited. Wagner (2004) show that in four German manufacturing industries (automotive, chemical, machinery, and metals), the cost efficiency mediates the relationship between internationalization and firm profitability, implying a positive E-P relationship. With a sample of 57 North American manufacturing plants, Swink, Narasimhan, and Kim (2005) show that cost efficiency mediates the influence of strategy integration on market-based performance, also implying a positive E-P relationship. 4

6 motivated to compare the E-P relationship in life and nonlife industries with our sample and to compare our non-u.s. results with those from the U.S. markets. Considering the connections and differences in efficiency and profitability, one should expect a positive correlation between frontier efficiency measures and conventional profitability ratios, but should not expect the correlation to be close to one (Bauer et al., 1998) as the efficiency only explains a part of the profit. Consistent with the extant evidence in banking and insurance literature, we hypothesize that: Efficiency and profitability are positively correlated in the global insurance industry (H1). Comparing the two industries within financial services, i.e. banking vs. insurance, extant evidence suggests that an industry dependency might exist in the E-P relationship, which is stronger in insurance than in banking. The management of operations is a secondary concern and less critical to the profitability of the banking industry (Sherman and Gold, 1985; Oral and Yolalan, 1990) but of paramount importance to the profitability of the life insurance industry (Greene and Segal, 2004). Following this line of thought, the industry dependency may also exist within the insurance industry, i.e. between life and nonlife insurance. 8 The insurance industry provides a unique context to investigate the industry dependency of E-P relationships with its two sub-industries life and nonlife insurance operated by separate legal entities in most markets. Comparing the idiosyncrasies of life and nonlife insurance, life risks are largely homogeneous and predictable but nonlife risks are more diverse and often more difficult to underwrite (Biener, Eling, and Jia, 2016). Thus, the majority of life insurance products are also more homogenous than the majority of nonlife products. The innovation of a life insurance product is easily copied by other insurers (Greene and Segal, 2004). Then relatively cost and operational competition is more important to life insurers than to nonlife insurers. Moreover, the impact of interest rates is different for life and nonlife insurers. In our sample period, the interest rate on average went down imposing pressure on long-term life insurance products with long-term guaranteed investment returns. These life insurers have to compensate the deficiency between the current market returns and the guaranteed returns by for example cost reduction or efficiency improvement (Eling and Schaper, 2017). Therefore, we would expect that cost efficiency plays a more important role for life insurers profitability than for nonlife insurers. In addition, life insurers do not only compete within the industry but also compete with other players in wealth management market such as banks and pension funds; while nonlife insurers do not have such competing pressure from other industries. For this reason, life insurance market may be more competitive and thus operating efficiency is more critical. Therefore, competition among life insurers more focuses on cost management (Greene and Segal, 2004) as opposed to nonlife insurers, where other factors might be important. We thus hypothesize that: The impact of efficiency on profitability is stronger for life insurers than that for nonlife insurers (H2). The principle of diminishing marginal returns in microeconomics suggests that holding other factors of production constant, the marginal increase of a single input factor yields marginal decreased (though positive) returns. Following this line of thought, if we consider firm efficiency as one input factor of the profitability, will firm efficiency have similar effects on profitability? The marginal profit increase may be lower for insurers that 8 For example, in the internationalization-performance relationship, the internationalization strategy works better for nonlife insurers than for life insurers due to industry idiosyncrasies (Biener, Eling, and Jia, 2016). 5

7 are already very efficient and higher for insurers that are far from best practice. From the management perspective, the first marginal increase of cost efficiency may be more valuable and can translate into more profits than the second marginal increase. If we consider a multi-period setting, continuous cost management programs every year may significantly reduce employees and managers motivation to optimize other aspects of business. With the above consideration, the correlation between efficiency and profitability might be nonlinear with a positive first order and a negative second order derivative. We thus hypothesize that The impact of efficiency on profitability follows the law of diminishing marginal returns (H3). 3. Data and methodology 3.1. Sample We use the A.M. Best s Non-US Insurance Reports (A. M. Best, ), which are a comprehensive source for information of insurance companies and widely used in insurance efficiency research (see e.g., Eling and Luhnen, 2010b; Pasiouras and Gaganis, 2013). We use all insurers from the database but exclude entities that are branches, special purpose vehicles, Lloyds syndicates, captives, reinsurers, composite insurers 9, and firms that operate insurance as minor business according to A.M. Best (e.g., banks, manufacturers, and healthcare providers). We trim insurers key ratios at the 0.5 and 99.5 percentiles for life and nonlife insurers separately in order to reduce the potential bias driven by extreme values (Olesen and Peterson, 2002; Zelenyuk and Zheka, 2006). 10 The key ratios are those used in the later DEA and regression analyses: return on equity (ROE), return on assets (ROA), life benefits ratio (benefits paid divided by net premiums written), nonlife loss ratio (loss incurred divided by net premiums earned), leverage ratio (total liabilities divided by total capital and surplus), liquidity ratio (liquidity assets divided by total liabilities), premium retention ratio (inverse reinsurance ratio, net premiums written divided by gross premiums written), and yearly real net premium growth. Our final sample comprises 1,786 life insurers with 9,597 firm-year observations and 3,214 nonlife insurers with 17,338 firmyears. The sample spreads over 91 markets and covers more than 50% of premiums outside the U.S. (Swiss Re, 2014). 11 Table 1 reports the summary statistics. We observe that the ROAs of life insurers (with a mean of 0.012) are much lower than the ROAs of nonlife insurers (with a mean of 0.039), 12 though their ROE means are much closer (0.098 vs. 0.11). This is because life insurers have on average much higher leverage ratios (23.7) than 9 Composite insurers offering both life and nonlife insurance amount for 12.8% of all firm-year observations. Some of them are simply the consolidation of life and nonlife insurers financial results. This practice also helps to construct the comparison between life and nonlife insurers. 10 Outliers are present in the A. M. Best dataset because of startups that do not yet underwrite business and runoff insurers that are not comparable to and not in competition with regular insurers (Biener, Eling, and Jia, 2016). We alternatively trim the key ratios at the 1st and 99th percentiles and the 2nd and 98th percentiles. In addition, we conduct a robustness test by winsorising these key ratios (see. e.g., Leverty and Grace, 2010). The different trimming or winsorising methods are consistent in results and do not change our conclusions. The results are available from the authors upon requests. 11 We carefully consider the potential heterogeneity across the 91 countries. When estimating efficiencies, we consider three efficiency frontiers: EU, emerging markets, and developed markets outside EU countries. In the section of robustness tests, we present a number of specifications to control for country fixed effects and also present results for a subsample considering the EU countries only, which are more homogenous. All these tests confirm the general findings of the paper. 12 The ROA difference is also statistically significant subject to mean comparison T-test (T=34.28, p- value=0.000). 6

8 nonlife insurers (2.85), driven by the different business models of life and nonlife insurance. Life insurance is usually long term and a large portion of insurance reserves are booked under the life insurer s liability resulting in high leverage and small ROAs. The different capital structure of life and nonlife insurers may also be driven by that life risk portfolios are more predictable than nonlife, thus ceteris paribus less capitalization and higher leverage are possible. From the management perspective, ROE can be decomposed into two elements as shown in Equation (1), the operational profitability measured by the ratio of profit over the risk volume (liability) and the capital efficiency measured by the leverage ratio (liability over equity). ROE = Profit = Profit Liability = Operational profitabilty Leverage ratio (1) Equity Liability Equity The ROA (profit over the sum of liability and equity) cannot fully capture the component of capital efficiency. Thus, ROE is a better measurement of profitability than ROA, when comparing the profitability and the E-P relationship between life and nonlife insurers. 13 Moreover, the summary statistics in Table 1 also suggest that the ROAs in the life insurance industry are significantly lower than the ROAs in the nonlife insurance industry, suggesting systemic difference between life and nonlife capital structure. The frontier efficiency analysis captures the operational efficiency and capital efficiency because (1) equity capital and debt capital are used as separate inputs and (2) risk volume (premium or loss) and invested assets are used as outputs. The input of equity together with the output of risk volume (premium or loss) shares the essence of capital efficiency. Moreover, as we use a sample across multiple markets with different tax systems, ROE before tax is used as the primary profitability measure. The Panel B of Table 1 presents the following firm specific characteristics: firm size in terms of total assets (inflation adjusted at 2013), yearly real growth of net premiums written, premium retention ratio, leverage ratio, liquidity ratio, a mutual dummy, and an unaffiliated single firm dummy. The three dummy variables of EU, other Emerging, and other Developed describe the geographical distribution of our sample in three exclusive regions. 14 In later regression analyses, we always control for Emerging and Developed, and use the EU companies as the reference group. Insurance penetration (life or nonlife premium over GDP) captures the maturity of an insurance market. Real GDP growth captures the economic environment in an insurer s home market. Our sample has a great variety to cover both small and large, both high and low growth, and both developing and developed markets. 13 For this reason we focus on ROE in the main part of the analysis, but in later tests also present the findings for ROA which yield consistent results. 14 The European Union has been establishing single insurance market since 1994, and thus we consider EU as one large insurance market and as one standalone region. Outside the EU, we are not able to derive frontiers for each market due to the small number of observations in many markets. We then estimate two frontiers for insurers in developed markets and emerging markets separately to reflect the operational efficiency gap and different business orientations (profitability in developed markets vs. growth and market share in emerging markets). 7

9 Table 1 Summary statistics Sample Life (N=9,597) Nonlife (N=17,338) Unit Mean Std. dev. Median Mean Std. dev. Median Panel A: Profitability ROE before tax ROE after tax ROA before tax ROA after tax Panel B: Firm- and country-specific characteristics Total assets a 1,000 9,071, ,804, ,181, ,083, ,796, ,354.4 Real premium growth Premium retention ratio Leverage ratio Liquidity ratio b Mutual Dummy Unaffiliated Dummy Emerging Dummy Developed Dummy EU Dummy Life or nonlife insurance penetration Real GDP growth Panel C: Inputs, inputs prices, and outputs Labor (approximate number of employees) 1 5, , , , Equity capital (capital and surplus) a 1, , ,709, , , ,744, ,173.7 Debt capital (total liabilities) a 1,000 8,484, ,591, ,069, , ,361, ,178.1 Labor price (Wage) a 1 56, , , , , ,092.9 Equity price (MSCI yearly returns) Debt price (IMF long-term govt. bond rates) Benefits paid plus reserve changes (life) or smoothed loss 1,000 1,637, ,835, , , , ,068 (nonlife) a Total invested assets a 1,000 8,346, ,516, ,054, , ,910, ,207.0 Panel D: Cost efficiency scores Cost efficiency (regional frontiers) Cost efficiency (global frontier) Pure technical efficiency (regional frontiers) Scale efficiency (regional frontiers) Allocative efficiency (regional frontiers) Panel E: Changes in efficiency and profitability Changes in ROE before tax Changes in cost efficiency (regional frontiers) Notes: a In USD and inflation adjusted for b The liquid assets in the A.M. Best database include cash, bonds, shares, and assets held to cover linked liabilities. With this broad definition, liquidity ratio is thus large. 8

10 3.2. Frontier efficiency methodology Two primary approaches have been used to estimate efficiency: the parametric approach, most prominently Stochastic Frontier Analysis (SFA), and the non-parametric approach, most prominently Data Envelopment Analysis (DEA), among others (Bauer et al., 1998; Cummins and Weiss, 2013). In the banking literature, SFA seems to have a better consistency with the conventional profit ratios than DEA (Bauer et al., 1998; Eisenbeis et al., 1999); while in the insurance literature, DEA shows the highest correlation with the profit ratios (Cummins and Zi, 1998; Leverty and Grace, 2010). We choose DEA to estimate the efficiency scores because (1) extant evidence for insurance suggests that DEA efficiencies are superior to other frontier efficiency measures, including for example the stochastic frontier analysis and the financial intermediary approach, in terms of their consistency with the profitability measures (Cummins and Zi, 1998; Leverty and Grace, 2010); 15 (2) DEA is the most prevalent frontier efficiency method applied to insurance data in the past two decades, which has much higher proportion of applications than SFA (Eling and Luhnen, 2010a; Cummins and Weiss, 2013). We follow the state-of-the-art procedure of DEA in the insurance industry (Eling and Luhnen, 2010a; Cummins and Weiss, 2013) to estimate insurer efficiency with relative cost efficiency scores. DEA cost efficiencies are the representation of firms distances to the best-practice efficient frontiers and are bounded between 0 and 1 (Farrell, 1957). The best-practice frontier is defined by firms that use the minimum amount and optimal combination of inputs to produce certain amount of outputs. We estimate cost frontiers separately for life and nonlife insurers, separately for each year between 2003 and 2013, and separately for each of the three regions: European Union, other developed markets and other emerging markets. One important assumption of DEA efficiency estimates is that firms are employing similar technologies. The assumption that all insurers employ similar technologies worldwide is strong. Therefore, we group insurers in our sample into three regions according to their domiciliary countries considering the operational similarities and the balance of observations in each region (Biener, Eling, and Jia, 2016). Cost efficiency scores estimated relative to a single global frontier are used as a robustness test, the results of which are consistent with our conclusions. Bootstrapped biascorrected efficiency scores are used to account for the sensitivity of efficiency measures to sampling variation (Simar and Wilson, 2000). There are other efficiency measures that can be derived from DEA method, e.g. production, technical, revenue, and profit efficiencies. We use cost efficiency because it is the most prevalent efficiency measure in the existing literature and also supported by other frontier efficiency methods (e.g., SFA). Thus, the cost efficiency measure enables us to compare our results with results of other papers (e.g. Greene and Segal, 2004; Leverty and Grace, 2010). As additional tests and for comparison purpose with Leverty and Grace (2010), in later part of the discussion, we estimate revenue efficiency and decompose the cost efficiency into three components as scale, pure technical, and allocative efficiency that capture different aspects of cost efficiency. Moreover, it is intuitive to link the profit efficiency with the profit ratio. Profit efficiency incorporates both cost and revenue aspects of efficiency and thus more comprehensively captures the overall performance of a firm from both business development and 15 Cummins and Zi (1998) show that the Pearson correlation coefficient (0.35) is the highest between DEA cost efficiency and the profitability; while most other correlation coefficients based on other efficiency measures, including the SFA measures, are below Leverty and Grace (2010) demonstrate that DEA efficiencies are much more consistent with ROA and ROE than financial intermediation approach (the flow approach). 9

11 cost management perspectives. As an additional test, we present the first piece of evidence in the literature to link DEA profit efficiency with the profit ratio. The inputs, outputs, and prices used to obtain the efficiency scores follow the common practice of DEA analysis in insurance industry (Eling and Luhnen, 2010a; Cummins and Weiss, 2013). We use three input quantities: labor (i.e., approximated number of employees), equity capital (i.e., capital and surplus, in real values in 2013), and debt capital (i.e., total liabilities, in real values in 2013). Labor is approximated by operating expenses divided by the annual wage for the insurance sector in respective country-years. We use annual wages (in real values in 2013) for the insurance sector in respective country-years as the price for labor. The wage information is obtained from the ILO Main Statistics and October Inquiry databases. 16 We use the 10-year rolling window moving averages of yearly total return rates, based on Morgan Stanley Capital International (MSCI) indices in the respective countries as the price for equity capital. 17 We use the two-year rolling window averages of International Monetary Fund (IMF) long-term government bond yearly interest rates in respective countries as the price for debt capital. 18 The long-term government bond rates are used to match the long duration of life insurers liabilities. The MSCI indices and IMF interest rates are obtained from the Thomson DataStream database. We use two output quantities, total invested assets and insurance benefits or losses (all in real values in 2013). The two outputs represent insurers two major functions financial intermediation and risk pooling, respectively. For life insurers, the insurance benefits are captured by net benefits paid plus net reserve changes 19, as reserves reflect the accumulation of unpaid cash values of life insurance policies (Cummins and Weiss, 2013). For nonlife insurers, the insurance losses are captured by the smoothed loss, which is calculated following the loss-smoothing procedure in Cummins and Xie (2008; 2013). 20/21 16 If missing, we adjust the nearest available data point of ILO annual wage to the previous or later years by using changes in general price levels represented by the consumer price indices (CPI). 17 To impute missing values and replace negative values in MSCI indices, we use the rolling window two-year averages of realized country-average ROEs in respective country-years (see Cummins and Weiss, 2013, for a discussion of capital price proxies). We use two-year moving average values because we only have the data that date back to We use country-average ROEs because many firms may have negative ROEs due to the volatile nature of the insurance business. Less than 10% of our sample is affected by this procedure. 18 If missing, we use the IMF central bank policy rate or deposit rate in respective country-years. 19 The net benefits paid plus net reserve changes (NBPNRC) could exhibit negative values; therefore, we follow the standard DEA practice of shifting all values by adding the minimum NBPNRC (Cummins and Weiss, 2013). Alternatively, we added other random positive numbers to NBPNRC in order to eliminate the negative values. This practice has no impact on the DEA results. 20 Leverty and Grace (2010) compare different output measures of the risk pooling function. They show that measures accounting for the volatilities of losses are better than that using the actual losses. From the theoretical perspective, Brockett et al. (2004, 2005) also criticize the use of actual incurred loss as output because unexpected large losses due to unforeseen catastrophes or other random fluctuations could be artificially efficiency enhancing as the output is higher. Premiums are sometimes applied as an output to replace the insurance benefits or losses, since premiums capture the business volume generated by insurers. However, the concerns arise as premiums do not only captures the quantity of outputs but also the price; it represents the price times the output quantity (Yuengert, 1993). 10

12 The DEA inputs, input prices, outputs, and estimated efficiency scores are presented in the Panel C-F of Table 1, respectively. As expected, the life insurers have a much larger size than nonlife insurers in terms of debt capital and invested assets. The input prices are at the similar level for both life and nonlife insurers. The efficiency scores estimated based on one global frontier are lower than those estimated based on three regional frontiers. The average efficiency scores are lower than previous studies (Greene and Segal, 2004; Leverty and Grace, 2010) because the difference in operations across markets within one region (regional frontier) is larger than the difference in operations across states within the U.S. (country frontier); thus the inefficient insurers tend to have lower cost efficiency scores and larger diversities in our global sample than in the U.S. sample Regression model We follow Greene and Segal (2004) to test the correlation between cost efficiency and profitability with firm random effects models (Equation 2). We use random effects models because firm fixed effects do not allow for time invariant independent variables (e.g., the life insurer dummy) and thus are not able to identify the different impact of cost efficiency on ROE between life and nonlife insurers. 22 We use firm fixed effects models and OLS mean regression as robustness tests, the results of which are consistent with our conclusions. The mean regression helps to smooth out the year-to-year fluctuation in ROE and ROA and thus is expected to have a higher correlation with the efficiency measures (Greene and Segal, 2004). Moreover, considering the cost efficiency scores are estimated separately for each year, in a robustness test, we include the interaction terms between CE and the year dummies, the results are consistent with our conclusions. To allow for the hypothesized nonlinear correlation (H3) between cost efficiency (CE) and ROE, we include the square term of cost efficiency scores. 23 A life insurer dummy is included in the regression as well as its interactions with cost efficiency to capture the hypothesized different E-P relationship between life and nonlife insurers (H2). X i,t is a vector of control variables including dummy variables of mutual, unaffiliated, emerging, and developed (the dummy EU is not included to avoid multicollinearity); including continuous variables of the natural logarithm of firm total assets, real growth of net premiums written, premium retain ratio (inverse reinsurance ratio), leverage ratio, liquidity ratio, life or nonlife insurance penetration, and real GDP growth of the firm domiciliary market. The variance inflation factors are all below 5, indicating no serious multicollinearity problem. ROE i,t = β 0 + β 1 CE i,t + β 2 CE 2 i,t + β 3 CE i,t Life i + β 4 CE 2 i,t Life i + β 5 X i,t + β 6 Year t + ε i,t (2) Based on our hypotheses, we expect a positive coefficient of cost efficiency (positive β 1 ), a negative coefficient of cost efficiency 2 (negative β 2 ), and a positive coefficient of the interaction term of CE Life (positive β 3 ). The coefficient of CE 2 Life (β 4 ) can be positive, negative, or insignificant. To further test the robustness of the 21 The smoothing procedure is as follows. First, we rank the nonlife insurers by their net premiums written in each year. We then determine the 10th and 90th percentiles of the loss ratio of the largest 80% nonlife insurers in each year and winsorize the loss ratios beyond 10th and 90th percentiles, respectively. Second, for each firm in the sample, we fit a linear time trend to the winsorized loss ratios. The linear trend regression for each firm-year is Loss Ratio(i,t)=β 1 +β 2 T+ε(i,t), where i represents the nonlife insurer and t represents the year. We then use the predicted loss ratio values as smoothed loss ratios and use the smoothed loss ratio multiplied by the net premiums written of respective firm-years to generate the smoothed loss. 22 It has been acknowledged that with panel data, random effects models better capture the cross-sectional effects among firms; while firm fixed effects models better capture the dynamics of one firm over years. Thus, the use of random effects models is also in line with the relative nature of cost efficiency scores. 23 We conduct additional tests to reveal the shape of nonlinear EP relationship, which will be discussed in the section of Results. 11

13 nonlinear E-P relationship, if any, we further look at the E-P relationship in four subsamples based on quartiles of cost efficiency scores. We standardize ROEs bounded between 0 and 1 in a robustness test, to account for the potential measurement bias considering CE is bounded between 0 and 1, while ROE is not. The results are consistent with our conclusions. The CE is centered to avoid multicollinearity with its squared term Rank-order correlation One concern regarding the parametric regression models to identify the E-P relationship lies with the complexity and nonlinearity of this relationship. This is particularly true considering that the profit measures are absolute ratios for one firm itself; while the efficiency measures are relative scores to the best practice firms. Therefore, in addition to the quadratic term included in the parametric models, we are interested in examining the rankorder correlation between efficiency and profitability. The rank-order correlation captures whether a firm having a relatively high rank of cost efficiency is associated with its high rank in ROE. It excludes the effects of different scale of efficiency and profit measures, matches with the relative nature of frontier efficiency measure, and minimizes the model misspecification risk. The rank-order test is new to the E-P relationship studies in the insurance industry. 24 We calculate Spearman s Rho and Kendall s Tau rank correlation statistics. These statistics are informative in two aspects: (1) they tell whether the rank of efficiency and the rank of profitability are independent; (2) the values of correlation statistics tell how important the efficiency in determining the relative position of a firm s profitability is. As suggested by Bauer et al. (1998), one should expect a positive rank-order correlation between the efficiency measures and the conventional profit ratios. However, the correlations should be far from one because the conventional profit measures embody not only the efficiencies, but also the effects of differences in input prices and other exogenous variables, over which financial institution managers have little or no control. 4. Results 4.1. Regression analyses Table 2 reports the results of estimating Equation (2). Columns 1-2 are from the full sample; Columns 3-4 are from the life and nonlife subsample, respectively. To reveal the shape of the nonlinear EP relationships, we conduct subsample regressions based on the quartiles of cost efficiency scores. The results are then presented in Columns 5-8 from the least efficient quartile to the most efficient quartile. Columns 9 and 10 are from the European Union (EU) and non-eu subsample, respectively. The positive coefficients of cost efficiency (β 1 ) and the negative coefficients of cost efficiency 2 (β 2 ) indicate that the positive impact of cost efficiency on profitability is smaller for cost efficient firms than for cost inefficient firms in both life and nonlife insurance industries. 25 The positive coefficient of the interaction term CE life (β 3 ) suggest that the cost efficiency has a stronger positive impact on life insurers profitability than on nonlife insurers profitability. We further compare the magnitude of cost efficiency coefficients in the life and nonlife subsamples (Columns 3-4). The impact of cost efficiency in the life sample is significantly larger than that in the nonlife sample at 99% confidence level, subject to the Z test. The results thus support Hypotheses 1 and 2. This interpretation is confirmed by the CE quartile regressions in Columns 5-8, Table 2, and by the log- 24 Bauer et al. (1998), Eisenbeis et al. (1999), and Weill (2004) apply the rank-order tests in the banking industry. Leverty and Grace (2010) apply it for the comparison of different efficiency measures. 25 The magnitudes of coefficients do not suggest an inverted-u shape because the E-P relationship is always positive in the efficiency score range between 0 and 1. The maximum profit is likely to reach at CE is around 2, which, however, is not possible. 12

14 transformed regression as a robustness test shown in Column 3, Table 6. We compare the overall marginal effects of cost efficiency on ROE at the means of all covariates, considering both the term cost efficiency and the interaction term cost efficiency life. The overall marginal effect of a variable at the means of all covariates is different from the coefficients of that variable, because it shows the combined effects of all linear, higher order, and interaction terms of that variable, which can be computed in a second step after regression with standard statistical tools. From the least efficient quartile to the most efficient quartile (i.e. from Column 5 to Column 8), if the cost efficiency increases 1 percentage point, then the ROE on average increases 0.44***, 0.31***, 0.093*, 0.086** percentage points for all life and nonlife insurers, respectively. Such nonlinearity is also reflected in the elasticities of E-P relationship, from the least efficient quartile to the most efficient quartile, the elasticities of cost efficiency are 1.12***, 0.78***, 0.33*, 0.46**, respectively. The efficiency gains for low efficiency firms are more likely to realize in profit than firms that are already highly efficient. These results support Hypothesis 3. In Columns 9 and 10, we separate our sample to European Union (EU) insurers and Non-EU insurers. The EU insurers take around two thirds of our observations. The results suggest that the positive E-P relationships and the difference between life and nonlife segments are valid in both EU and insurance markets outside EU/US. Looking at the magnitude of the E-P correlation, the coefficients in the life sample (Column 3) suggest that at the means of all covariates, as the cost efficiency increases by 1 percentage point, the ROE shall increase by 0.21 percentage point; the (semi-) elasticity of cost efficiency at the means of all covariates is 0.91 (0.11), meaning that 1% increase in cost efficiency shall increase the ROE by 0.91% or by 0.11 percentage point in absolute term. For nonlife insurers (Column 4), 1 percentage point increase in cost efficiency only corresponds to 0.17 percentage point increase in ROE and the (semi-) elasticity of cost efficiency is 0.44 (0.049), meaning that 1% increase in cost efficiency only increases the ROE by 0.44% or by percentage point in absolute term. 13