Blessing or Curse from Health Insurers Mergers and Acquisitions? The Analysis of Group Affiliation, Scale of Operations, and Economic Efficiency

Blessing or Curse from Health Insurers Mergers and Acquisitions? The Analysis of Group Affiliation, Scale of Operations, and Economic Efficiency Abstract This research examines the potential effects of health insurance mergers and acquisitions through analyzing the impact of insurers scale of operations and affiliation status on benefits, costs, and the efficiency of all stakeholders, aiming to provide insights to federal and state governments antitrust scrutiny and regulations and inform the public debate over mergers and acquisitions in the health insurance industry. Ceteris paribus increasing the scale of operations leads to lower premiums, more profits, and reduced payments to providers and administrative expenses; the affiliation with top s increases premiums and profits but does not lower hospital & medical expenses or administrative expenses. The stakeholders are inconsistent regarding the impact of the scale of operations and the affiliation status on their overall efficiency. The result also suggests, in compromise, the (sub-)optimal health insurance market be dominated by medium-sized s with big-sized insurers, and health insurance megamergers be carefully crafted to small members into big-sized insurers and simultaneously reduce the number of members. Additionally, most insurers are scale inefficient. The analysis of scale (dis)economies provides some guidelines regarding the appropriate scale of operations for the scale efficiency. Keywords: health insurance, scale of operations, affiliation JEL classifications: I13, G34, D24, L22, G22 1

Blessing or Curse from Health Insurers Mergers and Acquisitions? The Analysis of Group Affiliation, Scale of Operations, and Economic Efficiency 1. Introduction Among the ongoing health care merger frenzy, the recent proposed multi-billion megamergers of the top health insurers Aetna/Humana and Anthem/Cigna have raised considerable antitrust concerns for the already much concentrated health insurance markets. Critics, including consumer advocates, physicians and hospitals s, insist that further industry consolidation will result in more monopolistic bargaining power of a handful of nationwide health insurers, even less competition, reduced payments to providers, and leave consumers with fewer choices and potential premium increases. However, proponents such as health insurers claim that newly achieved synergies and economies of scale/scope will eliminate redundancies, drive greater efficiency and affordability, accelerate improvements of cost savings, and expand access to quality health care. Two of the direct changes from mergers and acquisitions (M&As) are the affiliation status and the size of operations of health insurers. This research uses the Data Envelopment Analysis (DEA) and regression models to examine the impact of these two factors on health insurers economic efficiency from different perspectives and the benefits/costs to all stakeholders consumers, providers, health insurers, and the whole society, and aims to provide important insights regarding federal and state governments antitrust scrutiny and regulations, the structure of the health insurance market, health insurers performance improvement, and inform the public debate over mergers and acquisitions in the health insurance industry. Different parties, such as consumers, providers, insurers, and the society, have different perspectives of what constitutes their inputs and outputs, and different goals of what constitutes 2

the best performance. Mergers and acquisitions, for example, may benefit insurers but at the cost of consumers, or vice versa. In the recent literature, regarding the efficiency analysis from different perspectives, Brockett et al. (2004) apply the game-theoretic DEA model to evaluate the relative overall efficiency of HMOs (health maintenance organizations) from two perspectives: that of consumers and that of the society. Yang (2014) uses the input-oriented Data Envelopment Analysis (DEA) approach to examine the medical services efficiency of the U.S. health insurers from the societal perspective. To accommodate the interests of different parties, Brockett et al. (2005) acknowledge that interests potentially conflict and the strategic decision makers must balance one concern versus another, and investigate the efficiency of insurance companies using data envelopment analysis (DEA) having the combination of solvency, claimspaying ability, and return on investment as outputs. As to insurers performance and the scale of operations, Cummins and Xie (2013) provide an analysis of economies of scale of the U.S. property/liability insurance industry and examine firm characteristics that are associated with their returns to scale. They find that firms below median size operate with increasing returns to scale, and the majority of firms above median size operate with decreasing returns to scale. With regard to M&As and insurance efficiency, Cummins and Xie (2008) analyze the productivity and efficiency effects of mergers and acquisitions in the U.S. property-liability insurance industry for both acquirers and targets and find that M&As were value-enhancing in this industry, but they find no evidence of improvement in scale economies. Related to the benefits and costs analysis of this current research, Karaca-Mandic, Abraham, and Simon (2015) examine how premiums and expenses are related to insurer and market characteristics and whether the medical loss ratio can serve as a good target measure of market power in regulating the individual health insurance market. 3

Specifically, this current research uses two DEA models (the variable benchmark model and the regular envelopment model) and two regression models (the linear regression model and the logistic regression model) to analyze the impact of the scale of operations and the affiliation status on insurers efficiency, scale economies and diseconomies, and benefits/costs for all the stakeholders from five different perspectives: the consumers perspective, the providers perspective, the societal perspective, the insurers perspective, and the composite perspective which combines the societal and the insurers perspectives. For each of the five perspectives, the overall efficiency is compared among small insurers, medium insurers, and big insurers, and among different s: big s, small s, and single insurers. Secondly, the insurer s returns to scale (RTS) and scale (dis)economies are investigated. The logistic regression is conducted to provide some evidence on the impact of the size, the affiliation status, and other factors on the RTS of insurers. In addition, the linear regression model is utilized to examine the impact of the size and affiliation on the benefits and costs of stakeholders, including premiums, hospital & medical expenses, general administrative and claim adjustment expenses, and net underwriting and investment gain/loss. 2. Data, methodology, and research design This research examines the impact of the size and the affiliation status on insurers overall efficiency by comparing the insurers of different sizes and different s and also on scale economies and diseconomies indicated by returns to scale. For this purpose, two DEA models are adopted: the variable benchmark model and the regular envelopment model. The regular envelopment model pools all DMUs (decision-making units) together performing a joint collective-frontier analysis. Given n DMUs, each with m inputs and s outputs, the relative 4

efficiency score of a test DMU 0 is determined by solving the following program assuming constant-returns-scale (Charnes, Cooper, and Rhodes, 1978; Brockett et al., 2004): T y0 v Max u, v x T u 0 T y j v s.t. 1, j = 1, 2,, n (1) T x u j u, v 0 where the subscript 0 denotes any one of the n DMUs whose efficiency is being evaluated. y T and x T denote the vector of the outputs and inputs of DMU j respectively (T denotes the transpose of a vector). And u and v are the input and output weights. Using the duality in linear programming, one can derive an equivalent envelopment form of the problem: min j Subject to X x j j y j j 0 j j Y (2) where Y is an n x s output matrix and X a m x n input matrix for all firms in the sample, y j is a n x 1 output vector and x j an m x 1 input vector for firm j, and j is an n x 1 intensity vector for firm j. The constraint 0 imposes CRS (constant returns to scale). For a variable returns j to scale (VRS), add an additional constraint 1 n n j 1, 1 j n j 1 for a non-increasing returns to scale (NIRS), and 1 for a non-decreasing returns to scale (NDRS). The scale j 1 j efficiency ( efficiency scale ) is defined as the efficiency under CRS ( efficiency CRS ) divided by 5 j

the efficiency under VRS ( efficiency VRS ). Thus, if efficiency CRS = efficiency VRS, i.e., the CRS and VRS efficiency estimates are equal, then efficiency scale = 1 and CRS is indicated. If efficiency 1and the NIRS efficiency measure = efficiency VRS, DRS is present; whereas scale if efficiency 1and the NIRS efficiency measure efficiency VRS, then IRS is indicated scale (Aly et al., 1990). The variable-benchmark model (Zhu, 2009) or the Game-Theoretic Model (Brockett et al., 2004) is used to compare one of DMUs with another instead of pooling all the DMUs together. The efficiency score of a test DMU k ( k G ) is obtained by solving the following program: T yk v Max u,v x u T k T y j v s.t. 1 T x u j C j G (3) u, v 0 where G and G C represent two different s of DMUs. The above DEA optimization problems are solved by using the DEA software developed by Joe Zhu (http://www.deafrontier.net/software.html). More details of the DEA models can be found in Charnes, Cooper, and Rhodes (1978), Brockett et al. (2004), and Zhu (2009). The DEA efficiency analysis should start with picking a perspective. Different parties have different perspectives which determine their different inputs and outputs. This current research examines the efficiency of health insurers from different perspectives of all stakeholders respectively: the consumers perspective, the providers perspective, the societal perspective, the insurers perspective, and the composite perspective. The inputs and outputs for all the five 6

perspectives are presented in Table 1. Some justifications for the selection of some of the inputs and outputs are available in Brockett et al. (2004), Kao and Hwang (2008), Xie (2010), and Yang (2014). The composite model is the combination of the societal and the insurers models to accommodate the interests of more than one party in a single model. The services received by consumers (consumers outputs: ambulatory encounters and hospital patient days) are provided by providers, therefore they serve as the inputs for the providers model. The hospital & medical expenses, inputs of the societal and the insurers models, are paid to providers thus serve as the outputs of the providers model. Table 1. Inputs and Outputs of DEA (Data Envelopment Analysis) Models DEA model Inputs Outputs The consumers' model Total premiums Ambulatory encounters Hospital patient days Total hospital & medical Ambulatory encounters The providers' model expenses Hospital patient days Total hospital & medical expenses Total member months The societal model Claim adjustment expenses Ambulatory encounters General administrative expenses Hospital patient days Total hospital & medical expenses Net underwriting gains/losses Claim adjustment expenses net investment gains/losses The insurers' model General administrative & investment expenses Capital & surplus Total hospital & medical expenses Net underwriting gains/losses Claim adjustment expenses net investment gains/losses The composite model General administrative & investment expenses Total member months Capital & surplus Ambulatory encounters Hospital patient days This current research also analyzes the determinants of insurers returns to scale and the benefits and costs of stakeholders by using two regression models: the logistic regression model 7

for the analysis of returns to scale, and the linear regression model for the impact of different factors on the benefits and costs including premiums, expenses, and the net underwriting and investment gain/loss. The explanatory variables are selected following relevant literature such as Cummins and Xie (2013), Yang (2014), and Karaca-Mandic, Abraham, and Simon (2015), which include the size of the insurer, the affiliation status (a dummy denoted by Group, 1 if affiliated with a big in one model and 1 if affiliated with a top 5 in the other), the product type, the organization type (a dummy denoted by Stock, 1 for stock insurers), the number of states the insurer serves (a dummy, 1 for multi-state insurers), the line of business, and the payment methods. The size of the insurer is measured by the logarithm of member months. Size is conceptually an important factor determining a firm s returns to scale. Some existing studies on efficiency find that larger firms tend to be more cost and revenue efficient (Ma, Pope, Xie, 2014). The second variable of focus is affiliation. The existence of internal capital market and resource sharing opportunities may enable firms affiliated with big s to operate more efficiently. Some studies show that the organizational type has some effect on insurers efficiency (Chen, Lai, and Wang, 2011; Jeng, Lai, and McNamara, 2007). Cummins and Xie (2013) find that geographical diversification is related with an insurer s scale economies, a dummy variable number of states the insurer operates in is included. Additionally, the product type, the line of business, and the payment methods are all important factors affecting the health insurance business (Yang, 2014). Therefore, some related variables are included: the product type (HMO, percent of total member months), the line of business (Medicare, Medicaid, percent of total member months respectively), and the payment methods (contractual fee payments, percent of total payments). Other variables of product types, lines of business, and payment methods are excluded because of collinearity or too many zero values. 8

This current research is based on the health insurers financial statements of 2014, filed with the National Association of Insurance Commissioners (NAIC). Insurers with missing and/or inappropriate data are excluded, so are the very small insurers. Additionally, the health insurance CO-OPs (consumer operated and oriented plans) are also excluded because of their abnormal performance in the first year of operation. There are 417 insurers in the final sample. Most insurers are affiliated (358 out of 417, 85.9%) (Table 2), only 59 (14.1%) single insurers. The insurers affiliated with big s and top 5 s (by the number of member insurers) are compared with other insurers respectively. In the sample, there are nine big s each of which includes nine or more insurers, and 171 insurers in other s ( small s for simplicity) each of which includes six of fewer insurers. The t-test shows that the average sizes of the insurers are not significantly different between small s and big s (the p-value is 0.956). Table 2. Some Summary Statistics of Member Months by the Insurer s Group Affiliation Status # of insurers Minimum Maximum Mean Median StDev Single insurers 59 10,927 22,427,397 1,473,573 339,931 3,212,715 Small s 171 16,062 113,187,473 3,195,533 908,394 9,418,338 Big s 187 11,748 100,847,661 3,144,252 1,259,023 8,144,364 Top 5 s 145 11,748 100,847,661 3,366,723 1,238,885 9,166,897 The whole sample 417 10,927 113,187,473 2,928,902 1,035,526 8,227,798 3. Analyses from the consumers perspective To address the consumers concern that mergers and acquisitions may drive up consumers costs, the determinants of total premiums are analyzed with an emphasis on the scale of operations and the insurer s affiliation status. The consumers scale economies or diseconomies are examined, as well as whether the consumers overall efficiency is improved 9

with the increasing scale of operations and the insurer s affiliation with a big. From consumers perspective, the input is total premiums, and the outputs are ambulatory encounters and hospital patient days (Brockett et al., 2004). For the consumers efficiency to be comparable among different insurers, total premiums are adjusted for the regional cost difference (Yang, 2014). The input-oriented DEA model is adopted to minimize the cost of consumers (total premiums) conditional on the level of outputs. Firstly, consumers efficiency is compared by the size of the insurer based on member months enrolled with the insurer. The variable benchmark model is utilized to obtain consumers efficiency scores with small insurers, medium insurers, and big insurers. By member months, the top 30% (125 insurers) are selected as big insurers, the middle 30% (125 insurers) medium insurers, and the bottom 30% (125 insurers) small insurers. The Mann-Whitney rank test is then used to compare the efficiency ranks of any two s. For example, to compare the consumers efficiency between big and small insurers, the alternative hypothesis is that big insurers are more efficient than small insurers. The test supports the alternative hypothesis with a p-value of 0.001 (the significance level is around 10% or lower throughout the article). Medium insurers are then compared with big and small insurers. The results show that medium insurers are more efficient than both big insurers (p-value 0.068) and small insurers (p-value <0.0001). In summary, medium insurers are the most efficient from the consumers perspective, and small insurers are the least efficient. Therefore, if a merger or acquisition will increase the scale of insurers above the medium size, consumers would not be benefited the most in economic efficiency. However, it does not mean that such merger or acquisition should be blocked, but the size of insurers should be kept at an optimal level as far as consumers efficiency is concerned. Additionally, consumers are just one of stakeholders, so lower consumers efficiency 10

might not be enough support to disapprove any merger or acquisition based on the holistic goal to balance the interests of all the parties involved. Furthermore, the impact of the scale of operations on consumers efficiency is examined by investigating consumers scale efficiency and returns to scale. The insurers with constant returns to scale (CRS) are fully scale efficient, and those with increasing returns to scale (IRS) and decreasing returns to scale (DRS) are scale inefficient. The DEA model is run three times with CRS, VRS, and NIRS (non-increasing returns to scale) frontiers respectively, to obtain the insurer s returns to scale. The results show that very few insurers are scale efficient from the consumers perspective (only five out of 417 insurers, 1.2%), and most insurers are scale inefficient: 111 DRS (26.6%) and 301 IRS (72.2%) (Table 3). Interestingly, the majority of insurers need to increase the scale of operations (72.2%). For the insurers with an enrollment below 2,211,431 member months (292 insurers), 94.2% (275 insurers) have increasing returns to scale. Therefore, generally the enrollment of an insurer should not be lower than 2,211,431 from the consumers perspective. On the other hand, overall 26.6% of the insurers need to decrease their size to. For the insurers with an enrollment above 3,585,532 member months (84 insurers), 86.9% (73 insurers) have decreasing returns to scale, as indicates that the enrollment of the insurers generally should not be more than 3,585,532 from the consumers perspective. However, it shows that from the consumer s perspective, it is very difficult to achieve constant returns to scale to be fully scale efficient which might not be a realistic objective for the insurers. 11

Table 3. Distribution of Insurers by Returns to Scale and Enrollment (Member Months): the Consumers Model # of insurers % of insurers Member months Decile Total CRS DRS IRS CRS DRS IRS 1 [113187473, 6412585) 42 1 39 2 2.4% 92.9% 4.8% 2 [6412585, 3585532) 42 0 34 8 0.0% 81.0% 19.0% 3 [3585532, 2211431) 41 1 24 16 2.4% 58.5% 39.0% 4 [2211431, 1459462) 42 0 6 36 0.0% 14.3% 85.7% 5 [1459462, 1035526) 41 2 6 33 4.9% 14.6% 80.5% 6 [1035526, 625718) 42 0 2 40 0.0% 4.8% 95.2% 7 [625718, 388028) 42 0 0 42 0.0% 0.0% 100.0% 8 [388028, 212418) 41 0 0 41 0.0% 0.0% 100.0% 9 [212418, 78262) 42 1 0 41 2.4% 0.0% 97.6% 10 [78262, 10927] 42 0 0 42 0.0% 0.0% 100.0% Total 417 5 111 301 1.2% 26.6% 72.2% Next the logistic regression analysis is conducted to analyze the determinants of scale economies and diseconomies, with returns to scale as the dependent variable. Independent variables include size, affiliation, product type, organization type, number of states the insurer serves, line of business, and payment methods (Table 4). In one model, the dummy takes the value of 1 if affiliated with a big, while in the other model it takes the value of 1 if affiliated with a top 5. There are only five insurers with CRS so this analysis only focuses on the determinants of DRS and IRS. As expected, the size of health insurers is negatively related to the probability of IRS (positively related to the probability of DRS correspondingly). This provides further evidence that big insurers tend to have DRS while small insurers tend to have IRS. The result also indicates that the affiliation status has no significant impact on scale economies or diseconomies, that is, insurers affiliated with a big are not necessarily operating with DRS or IRS, neither are the insurers affiliated with a small. 12

Table 4. The Logistic Regression Model of Health Insurers Returns to Scale from the Consumers Perspective: Decreasing Returns to Scale (DRS) 0, Increasing Returns to Scale (IRS) 1 affiliated with a big affiliated with a top 5 Coefficient P-value Coefficient P-value Intercept 86.66 < 0.0001 87.73 < 0.0001 Size -12.52 < 0.0001-12.67 < 0.0001 Group -0.02 0.97 0.26 0.64 HMO -2.45 0.00-2.44 0.00 Stock -0.77 0.28-0.92 0.14 Number of states -0.02 0.98-0.07 0.91 Medicare -6.20 < 0.0001-6.42 < 0.0001 Medicaid -0.50 0.57-0.53 0.53 Contractual fee payments -3.96 0.00-4.03 0.00 R²(McFadden) 0.74 0.74 R²(Cox and Snell) 0.58 0.58 R²(Nagelkerke) 0.84 0.84 The following analysis examines the impact of the affiliation status on consumers overall efficiency of which the scale efficiency is just one component. Firstly the insurers affiliated with big s are compared with other insurers. As stated, big s are those with nine or more insurers, and there are nine big s which include 187 insurers. Other insurers consist of the 230 small (a with 6 insurers or fewer) and single insurers. The efficiency scores are also obtained using the variable benchmark model, and the Mann-Whitney rank test is used to test the hypothesis. The alternative hypothesis is that insurers in big s are less efficient than small and single insurers. The test supports the alternative hypothesis at the 1% significance level (the p-value is <0.0001). Furthermore, the insurers in the top five s are compared with all other insurers. There are 145 insurers in the top five s, and 272 other insurers. The alternative hypothesis 13

is that insurers in the top five s are less efficient than other insurers. The test supports the alternative hypothesis at the 1% significance level (the p-value is <0.0001). In addition, single insurers are compared with small insurers. There are 59 single insurers, and 171 small insurers. The alternative hypothesis is that single insurers are more efficient than insurers in small s. The test supports the alternative hypothesis at the 1% significance level (the p- value is 0.002). In summary, single insurers are the most efficient from the consumers perspective, and insurers affiliated with big s are the least efficient. Therefore, megamergers, for example, Aetna/Humana and Anthem/Cigna, may not be in favor of consumers as far as their overall efficiency is concerned. However, a balance of the interests of different parties is more appropriate in evaluating any mergers or acquisitions. One big concern from consumers is potential premium increases resulted from mergers and acquisitions. To address this concern, the linear regression analysis is conducted to analyze the determinants of the premium, with the premium per member month as the dependent variable (Table 5). Independent variables are the same as those of the logistic regression. It shows that the size is negatively related to the premium which suggests increasing the scale of operations actually results in lower premiums, ceteris paribus. As to the effect of the affiliation status, the premium is significantly higher from insurers affiliated with the top 5 s than other insurers, other things being the same. 14

Table 5. The General Linear Regression Model of the Premium per Member Month of Health Insurers affiliated with a big affiliated with a top 5 Coefficient P-value Coefficient P-value Intercept 734.64 < 0.0001 743.96 < 0.0001 Size -64.23 0.00-66.26 0.00 Group 34.52 0.25 59.59 0.04 HMO 92.51 0.01 91.93 0.01 Stock -59.82 0.07-65.81 0.04 Number of states 12.07 0.70 11.80 0.71 Medicare 640.76 < 0.0001 637.66 < 0.0001 Medicaid 52.21 0.22 64.32 0.13 Contractual fee payments -9.86 0.82-9.91 0.81 Adjusted R² 0.49 0.49 4. Analyses from the providers perspective Providers believe that further health insurance industry consolidation through mergers and acquisitions will result in more monopolistic power of top health insurers and reduced payments to providers. To address this concern, this section analyzes the impact of the scale of operations and the insurer s affiliation status on providers efficiency, and the determinants of the providers scale economies, diseconomies, and their benefits. The services that consumers receive are provided by providers. From the providers perspective, the inputs are ambulatory encounters and hospital patient days, the outputs of the consumers model. The output is total hospital & medical expenses that the insurer pays providers. Similarly, total hospital & medical expenses are adjusted for the regional cost difference. The output-oriented DEA model is adopted to maximize payments that providers receive given all the inputs. As in the consumers model, the providers efficiency scores are obtained using the variable benchmark DEA model, and the Mann-Whitney rank test is utilized to test the 15

hypothesis. The results show that big insurers are less efficient than small insurers from the providers perspective (the p-value is <0.0001), medium insurers are more efficient than big insurers (p-value <0.0001), equally efficient as small insurers (p-value 0.864, the alternative hypothesis is medium insurers are not equally efficient as small insurers). That is, big insurers are the least efficient from the providers perspective, and medium and small insurers are more efficient. In agreement with consumers, medium-sized insurers should benefit providers more than big insurers. However, rising health care costs are among the most acute challenges in the U.S. health care system, and if any attempt to improve providers efficiency is accompanied by increasing payments or health services costs, providers might have to lose the battle. The providers better stand in the debate against health insurers megamergers should root for reasonable payments to providers instead of going against reduced payments to providers. If the health care costs were too high (they actually are), they would have to be reduced to a reasonable level, but definitely not below the reasonable level so that no disgruntled providers would reduce the supply or the quality of health services. Furthermore, if any mergers or acquisitions would help keep the health care costs at a reasonable level, it should a big plus on the list for regulators approval even with some sacrifice of providers benefits. To analyze the impact of the scale of operations from the providers perspective, the returns to scale of the insurers are also presented. Similar to the consumers analysis, there are also very few insurers (four out of 417, 1.0%) with constant returns to scale (CRS) (Table 6). Most insurers are not fully scale efficient: 358 DRS (85.9%) and 55 IRS (13.2%). The majority of the insurers need to decrease their scale of operation, for example, among the 250 insurers with an enrollment of more than 625,718 member months, 96.4% (241 insurers) operate with DRS. Even a lot of small insurers also operate with DRS: among the 167 insurers with an 16

enrollment below 625,718 member months, 70.1% have DRS. Correspondingly, only 2.8% (28.7%) of the insurers above (below) 625,718 member months have IRS. The results show that, from the providers perspective, unrealistically, most insurers, big or small, should decrease their scale of operations to be fully scale efficient, big to small, small to smaller. Therefore, it is understandable that providers are not in favor of mergers and acquisitions of health insurers which generally increase the scale of operations. However, as discussed, the providers efficiency should not be the top priority in evaluating any health insurers mergers or acquisitions. Table 6. Distribution of Insurers by Returns to Scale and Member Months: the Providers Model Decile Member months # of insurers % of insurers Total CRS DRS IRS CRS DRS IRS 1 [113187473, 6412585) 42 0 42 0 0.0% 100.0% 0.0% 2 [6412585, 3585532) 42 0 42 0 0.0% 100.0% 0.0% 3 [3585532, 2211431) 41 0 39 2 0.0% 95.1% 4.9% 4 [2211431, 1459462) 42 0 42 0 0.0% 100.0% 0.0% 5 [1459462, 1035526) 41 1 39 1 2.4% 95.1% 2.4% 6 [1035526, 625718) 42 1 37 4 2.4% 88.1% 9.5% 7 [625718, 388028) 42 1 31 10 2.4% 73.8% 23.8% 8 [388028, 212418) 41 0 33 8 0.0% 80.5% 19.5% 9 [212418, 78262) 42 0 27 15 0.0% 64.3% 35.7% 10 [78262, 10927] 42 1 26 15 2.4% 61.9% 35.7% Total 417 4 358 55 1.0% 85.9% 13.2% Furthermore, the logistic regression is conducted to analyze the determinants of scale economies and diseconomies from the providers perspective, with returns to scale as the dependent variable (Table 7). Since there are only seven insurers with CRS, the regression focuses on the determinants of DRS and IRS. It shows that the size and are both negatively related to the probability of IRS and positively related to the probability of DRS. That is, big insurers have a higher probability of operating at DRS while small insurers a relatively higher 17

probability of IRS. Different from the consumers model, the affiliation with a big leads to a higher probability of DRS for providers. Therefore, mergers and acquisitions to create bigger s and increase the scale of operations should be discouraged as far as providers scale economies are concerned. Table 7. The Logistic Regression Model of Health Insurers Returns to Scale from the Providers Perspective: Decreasing Returns to Scale (DRS) 0, Increasing Returns to Scale (IRS) 1 affiliated with a big affiliated with a top 5 Coefficient P-value Coefficient P-value Intercept 12.18 < 0.0001 12.29 < 0.0001 Size -2.18 < 0.0001-2.19 < 0.0001 Group -0.96 0.04-0.71 0.12 HMO -0.65 0.16-0.72 0.12 Stock 0.42 0.33 0.34 0.43 Number of states -0.33 0.47-0.30 0.50 Medicare -2.83 < 0.0001-2.87 < 0.0001 Medicaid -1.34 0.06-1.48 0.04 Contractual fee payments -0.56 0.27-0.66 0.20 R²(McFadden) 0.36 0.35 R²(Cox and Snell) 0.24 0.24 R²(Nagelkerke) 0.45 0.44 The impact of the affiliation status on insurers overall efficiency is further analyzed using the variable benchmark DEA model and the Mann-Whitney rank test. The results show that, from the providers perspective, insurers affiliated with big s are less efficient than small and single insurers (the p-value is <0.0001); insurers affiliated with the top five s are less efficient than other insurers (the p-value is 0.001); single insurers are more efficient than small insurers (the p-value is 0.0004). In summary, from the providers perspective, single insurers are the most efficient, while big insurers are the least efficient. 18

This provides further evidence that big s are not the favorite of providers. However, following the providers demand to restructure the health insurance market and dismantle the potential bargaining power of top health insurers might further increase health care costs which should be avoided from the consumers and the societal view. To address the providers concern that health insurers mergers and acquisitions might result in potential reduction to their payments, the linear regression analysis is conducted with hospital & medical expenses per member month as the dependent variable (Table 8). As expected, the size of the insurer is negatively related to hospital & medical expenses, the payments received by providers. It shows that ceteris paribus increasing the scale of insurers really cuts providers benefits, as should be desirable for lower health care costs. Contrary to the claims of some providers, the affiliation with big s does not significantly lead to reduced payments to providers. Table 8. The General Linear Regression Model of Hospital & Medical Expenses per Member Month of Health Insurers affiliated with a big affiliated with a top 5 Coefficient P-value Coefficient P-value Intercept 710.88 < 0.0001 727.53 < 0.0001 Size -65.85 0.00-68.27 0.00 Group -0.43 0.99 23.87 0.37 HMO 67.31 0.04 65.09 0.05 Stock -58.36 0.06-67.46 0.02 Number of states 12.62 0.67 13.32 0.65 Medicare 575.58 < 0.0001 572.27 < 0.0001 Medicaid 56.43 0.16 59.62 0.14 Contractual fee payments -2.19 0.96-7.00 0.86 Adjusted R² 0.47 0.47 19

5. Analyses from the societal perspective One important objective of the health care reform or any health care system is the universal coverage. To incorporate this component into the efficiency analysis creates another perspective the societal perspective (Brockett et al, 2004 and Yang, 2014). This section examines the impact of the affiliation status and the size of operations on the efficiency from the societal view, aiming to provide some insights on whether health insurers mergers and acquisitions benefit the society, with an emphasis on enrollment and quality medical services at reasonable costs. From the societal perspective, the inputs are total hospital & medical expenses, general administrative expenses, and claim adjustment expenses, and the outputs are total member months, ambulatory encounters, and hospital patient days. To be comparable among the insurers, the inputs are adjusted for the regional cost difference. The input-oriented DEA model is adopted to minimize the cost providing health care services given the output level. Firstly, from the societal perspective, the impact of the scale of operations on the overall efficiency is examined by comparing the three different s of insurers: small insurers, medium insurers, and big insurers. It shows that, from the societal perspective, big insurers are more efficient than small insurers (the p-value is <0.0001); big insurers are more efficient than medium insurers (the p-value is <0.0001); and medium insurers are more efficient than small insurers (the p-value is <0.0001). In summary, from the societal perspective, big insurers are the most efficient, and small insurers are the least efficient, as is different from the preference of consumers and providers. The implication is that mergers and acquisitions to increase the scale of operations should be beneficial from the societal perspective even though they might be detrimental to the benefits of consumers and providers. This result is as expected because the 20

societal model incorporates the enrollment (the measure of the scale of operations) as one of the outputs. Next, scale economies and diseconomies are analyzed by examining returns to scale from the societal perspective. Compared to the consumers and the providers models, there are more insurers which are fully scale efficient: 19 of the 417 (4.6%) insurers have constant returns to scale (CRS) (Table 9). Still, most insurers are scale inefficient: 175 DRS (42.0%) and 223 IRS (53.5%). A big majority of insurers (92.0%) operate with DRS among the insurers with an enrollment above 2,211,431 member months, while a big majority of insurers (92.8%) operate with IRS among the insurers with an enrollment below 625,718 member months. Therefore, generally the size of the insurer should not be bigger than 2,211,431 member months or smaller than 625,718 member months from the societal perspective. Table 9. Distribution of Insurers by Returns to Scale and Member Months: the Societal Model Decile Member months # of insurers % of insurers Total CRS DRS IRS CRS DRS IRS 1 [113187473, 6412585) 42 2 40 0 4.8% 95.2% 0.0% 2 [6412585, 3585532) 42 1 40 1 2.4% 95.2% 2.4% 3 [3585532, 2211431) 41 4 35 2 9.8% 85.4% 4.9% 4 [2211431, 1459462) 42 1 28 13 2.4% 66.7% 31.0% 5 [1459462, 1035526) 41 2 20 19 4.9% 48.8% 46.3% 6 [1035526, 625718) 42 2 7 33 4.8% 16.7% 78.6% 7 [625718, 388028) 42 1 5 36 2.4% 11.9% 85.7% 8 [388028, 212418) 41 1 0 40 2.4% 0.0% 97.6% 9 [212418, 78262) 42 4 0 38 9.5% 0.0% 90.5% 10 [78262, 10927] 42 1 0 41 2.4% 0.0% 97.6% Total 417 19 175 223 4.6% 42.0% 53.5% The logistic regression analysis is conducted to analyze the determinants of scale economies and diseconomies, with returns to scale as the dependent variable (Table 10). This analysis only focuses on the determinants of DRS and IRS. As expected, the size is negatively 21

related to the probability of IRS (positively related to the probability of DRS). The dummy is not significant, and the affiliation with big s or small s makes no significant difference on whether the insurer is operating with DRS or IRS, ceteris paribus. Table 10. The Logistic Regression Model of Health Insurers Returns to Scale from the Societal Perspective: Decreasing Returns to Scale (DRS) 0, Increasing Returns to Scale (IRS) 1 affiliated with a big affiliated with a top 5 Coefficient P-value Coefficient P-value Intercept 46.88 < 0.0001 46.54 < 0.0001 Size -7.45 < 0.0001-7.41 < 0.0001 Group 0.24 0.61 0.08 0.84 HMO -0.91 0.11-0.91 0.11 Stock -0.13 0.80-0.04 0.93 Number of states -0.23 0.60-0.25 0.57 Medicare -0.89 0.22-0.83 0.25 Medicaid 0.55 0.40 0.62 0.32 Contractual fee payments -0.96 0.20-0.85 0.24 R²(McFadden) 0.64 0.64 R²(Cox and Snell) 0.59 0.59 R²(Nagelkerke) 0.79 0.79 The impact of the affiliation status is further analyzed by comparing the overall efficiency of different s from the societal perspective. It shows that insurers affiliated with big s are less efficient than small and single insurers (the p-value is <0.0001); the insurers in the top five s are less efficient than other insurers (the p-value is <0.0001); and there is no significant difference between single insurers and small insurers (the p-value is 0.563). In summary, from the societal perspective, insurers in big s are the least efficient, single insurers and those in small s are equally efficient statistically. Therefore, mergers and acquisitions to create big s are not beneficial from the societal perspective, even though big-sized insurers are. 22

Potentially reduced administrative expenses are what most merging insurers emphasize. Since administrative expenses are first introduced in the societal model, the linear regression analysis is conducted to analyze the determinants of administrative expenses (as well as claim adjustment expenses) in this section, with administrative expenses (claim adjustment expenses) per member month as the dependent variable (Tables 11 and 12). It shows that the scale of operations is negatively related to administrative expenses, which suggests that increasing the scale of operations reduces administrative costs. However, the dummy is positively related to administrative expenses, as does not support the claim that mergers and acquisitions to create big s save administrative costs through synergies and elimination of redundancies. Similarly, increasing the scale of operations incurs lower but the affiliation with big s leads to more claim adjustment expenses. Table 11. The General Linear Regression Model of General Administrative Expenses per Member Month of Health Insurers affiliated with a big affiliated with a top 5 Coefficient P-value Coefficient P-value Intercept 157.28 < 0.0001 151.31 < 0.0001 Size -18.98 < 0.0001-18.30 < 0.0001 Group 10.14 0.02 4.72 0.27 HMO 8.01 0.12 9.00 0.08 Stock -1.85 0.70 1.16 0.80 Number of states -0.25 0.96-0.69 0.88 Medicare 43.26 < 0.0001 44.09 < 0.0001 Medicaid -3.46 0.58-1.63 0.80 Contractual fee payments -5.01 0.43-2.52 0.69 Adjusted R² 0.32 0.31 23

Table 12. The General Linear Regression Model of Claim Adjustment Expenses per Member Month of Health Insurers affiliated with a big affiliated with a top 5 Coefficient P-value Coefficient P-value Intercept 34.79 < 0.0001 34.39 < 0.0001 Size -3.74 0.00-3.73 0.00 Group 2.59 0.13 2.85 0.08 HMO -2.84 0.16-2.74 0.17 Stock -3.59 0.05-3.43 0.05 Number of states 0.46 0.80 0.40 0.82 Medicare 20.57 < 0.0001 20.56 < 0.0001 Medicaid 6.68 0.01 7.37 0.00 Contractual fee payments 2.36 0.34 2.68 0.27 Adjusted R² 0.21 0.21 6. Analyses from the insurers perspective In defending proposed mergers and acquisitions, health insurers usually claim that newly achieved synergies and economies of scale will eliminate redundancies, drive greater efficiency and affordability, accelerate improvements of cost savings, and expand access to quality health care. Another important motivation is that mergers and acquisitions will hopefully bring insurers more profits, which is definitely a very rightful endeavor just like other businesses and should not serve as an attacking target especially when it is not accompanied by much sacrifice of consumers and the society. This section analyzes the impact of the scale of operations and the affiliation status on the efficiency from the insurers perspective, and the determinants of insurers scale economies, diseconomies, and their benefits. From the insurers perspective, the inputs are total hospital & medical expenses, general administrative expenses, claim adjustment expenses, and capital and surplus. The outputs are the net underwriting gain/loss and the net investment gain/loss, two profitability measures. To test scale (dis)economies, the DEA model 24

has to run at CRS, VRS, and NIRS frontiers respectively. Therefore, the insurers with nonpositive outputs cannot be included. In other words, the sample for the insurers model only includes the insurers with positive outputs (225 insurers). Different from the providers and the consumers models, it is not necessary to adjust the inputs or outputs for the insurers model. The output-oriented DEA model is adopted to maximize the outputs given the inputs. Firstly, the insurers efficiency is compared by the size of the insurer. Since this sample is smaller (225 vs. 417 insurers) and there is also less difference in member months of the 225 insurers, the top 20% (45 insurers) by member months are selected as big insurers, middle 20% (45 insurers) medium insurers, and bottom 20% (45 insurers) small insurers. It shows that, from the insurers perspective, big insurers are more efficient than small insurers (the p-value is 0.02), big insurers are equally efficient as medium insurers (p-value 0.508), and medium insurers are more efficient than small insurers (p-value 0.116). In summary, from the insurers perspective, small insurers are the least efficient; however, there is no significant difference in the insurers overall efficiency between medium and big insurers. One of the preferred by providers, the small scale of operations is definitely not the choice from the insurers perspective; the medium scale of operations is acceptable to consumers, providers, and insurers as far as the efficiency is concerned. However, the efficiency analysis incorporates the impact of both inputs and outputs. If the insurer focuses on one side, the profitability, a different scale such as the big scale of operations might be preferred. The following analysis examines scale economies and diseconomies from the insurers perspective. It shows that, still very few (10 of the 225 insurers, 4.4%) have constant returns to scale, while most are not fully scale efficient: 125 DRS (55.6%) and 90 IRS (40.0%) (Table 13). The majority of the insurers (93.3%) with an enrollment above 3,838,999 member months 25

operate with DRS. Between 991,949 and 3,838,999 member months, 65.6% (30.0%) insurers operate with DRS (IRS). Between 229,156 and 991,949 member months, 35.8% (58.2%) insurers operate with DRS (IRS). Surprisingly, there is not a clear cutoff enrollment below which a big majority (like more than 80%) of the insurers are operating with IRS except for the lowest decile with an enrollment between 11,748 and 229,156 member months where all the insurers have IRS. Even though there is a trend that the number of IRS insurers increases with the decreasing scale, they are spread out in most of the enrollment levels. This suggests that, from the insurers perspective, a decent number of insurers operate with IRS (DRS) at a much bigger (smaller) enrollment than from the consumers and the providers perspective. This provides insurers more flexibility in the defense of increasing or decreasing their scale of operations unless it is too big or too small. Table 13. Distribution of Insurers by Returns to Scale and Member Months: the Insurers Model Decile Member months # of insurers % of insurers Total CRS DRS IRS CRS DRS IRS 1 [100847661, 6907026) 23 1 22 0 4.3% 95.7% 0.0% 2 [6907026, 3838999) 22 1 20 1 4.5% 90.9% 4.5% 3 [3838999, 2654951) 23 0 18 5 0.0% 78.3% 21.7% 4 [2654951, 1740807) 22 1 14 7 4.5% 63.6% 31.8% 5 [1740807, 1265700) 22 0 14 8 0.0% 63.6% 36.4% 6 [1265700, 991949) 23 3 13 7 13.0% 56.5% 30.4% 7 [991949, 677149) 22 1 7 14 4.5% 31.8% 63.6% 8 [677149, 413007) 23 1 11 11 4.3% 47.8% 47.8% 9 [413007, 229156) 22 2 6 14 9.1% 27.3% 63.6% 10 [229156, 11748] 23 0 0 23 0.0% 0.0% 100.0% Total 225 10 125 90 4.4% 55.6% 40.0% Furthermore, the logistic regression is conducted to analyze the determinants of scale economies and diseconomies from the insurer s perspective (Table 14). As expected, the size is negatively related to the probability of IRS (positively related to the probability of DRS). This 26

provides further supports that big insurers tend to have DRS while small insurers tend to have IRS even though a decent number of insurers in most of the different enrollment levels operate with DRS or IRS as shown above. The result also indicates that the affiliation with big s has no significant effect on the probability of the insurer s scale (dis)economies. Table 14. The Logistic Regression Model of Health Insurers Returns to Scale from the Insurers Perspective: Decreasing Returns to Scale (DRS) 0, Increasing Returns to Scale (IRS) 1 affiliated with a big affiliated with a top 5 Coefficient P-value Coefficient P-value Intercept 28.11 < 0.0001 27.94 < 0.0001 Size -4.15 < 0.0001-4.11 < 0.0001 Group -0.30 0.50-0.62 0.14 HMO 0.09 0.88-0.01 0.98 Stock -1.23 0.04-1.14 0.05 Number of states -0.16 0.74-0.16 0.73 Medicare -2.81 0.00-2.71 0.00 Medicaid -0.99 0.15-1.03 0.12 Contractual fee payments -1.42 0.06-1.38 0.06 R²(McFadden) 0.40 0.41 R²(Cox and Snell) 0.42 0.43 R²(Nagelkerke) 0.57 0.58 The following analysis examines the effect of the affiliation status on the overall efficiency from the insurers perspective. In the sample of 225 insurers, 135 insurers are affiliated with the nine big s, and there are 90 small and single insurers. It shows that insurers affiliated with big s are more efficient than small and single insurers (the p- value is <0.0001). In addition, the insurers in the top five s are compared with other insurers. There are 111 insurers in the top five s, and 114 other insurers. The result indicates that the insurers of the top five s are more efficient than other insurers (the p- value is <0.0001). Single insurers are also compared with small insurers. There are 22 27

single insurers, and 68 small insurers. It finds that single insurers are less efficient than small insurers (the p-value is 0.002). In summary, from the insurers perspective, the insurers in the big s are the most efficient, single insurers are the least efficient, exactly opposite to the preference of consumers and providers. This somehow explains the furious argument between health insurers, consumers and providers regarding the proposed megamergers which probably enhance the efficiency of insurers but not consumers or providers. The linear regression is conducted to analyze the determinants of the insurer s profits, with the net underwriting and investment gain/loss per member month as the dependent variable (Table 15). This regression analysis uses the original sample of 417 insurers. The results indicate that the size and the dummy are both positively related to the profit of the insurer which increases with bigger scales of operations and bigger s. To combine all the results of this section together, from the insurers perspective, big size and big should be their best choice. With the conflicting interests from consumers, providers, and insurers, the regulatory power should be exercised carefully to strike a satisfactory balance depending on some appropriate objectives of the health care system. 28

Table 15. The General Linear Regression Model of the Net Underwriting and Investment Gain/Loss per Member Month of Health Insurers affiliated with a big affiliated with a top 5 Coefficient P-value Coefficient P-value Intercept -202.25 < 0.0001-201.60 < 0.0001 Size 30.26 < 0.0001 29.88 < 0.0001 Group 14.43 0.02 20.14 0.00 HMO 24.54 0.00 24.73 0.00 Stock 3.12 0.64 2.40 0.71 Number of states -2.90 0.66-3.15 0.62 Medicare -2.92 0.74-3.56 0.69 Medicaid -19.73 0.03-15.31 0.08 Contractual fee payments 7.66 0.39 8.57 0.32 Adjusted R² 0.17 0.18 7. Analyses from the composite perspective So far, from the four models examined above, it shows that the impact of the scale of operations and the affiliation status and the preference for the size of an insurer and the size of an insurer are inconsistent among all the stakeholders consumers, providers, insurers, and the society. This section discusses the composite model trying to accommodate the interests of different parties, but not all the parties involved. The composite model combines the societal and the insurers models but leaves out the providers model. The rationale is that quality medical services at reasonable costs should be the first priority, but the insurers profitability should also be considered, otherwise they might exit the market. The providers are left out of the composite model because it might not be very convincing to maximize hospital & medical expenses now that rising costs has been a considerable concern in the health care system. From the composite perspective, the inputs are total hospital & medical expenses, general 29