Capital Ratio, Product Risk and Asset Risk Relationships in the U.S. Health Insurance Industry
Dr. Etti G. Baranoff, FLMI Associate Professor of Insurance and Finance Department of Finance, Insurance and Real Estate School of Business Virginia Commonwealth University Snead Hall, 301 West Main Str., Suite B4167 Richmond VA 23284-4000 Tel: 804-828-3187, Fax: 804-828-3972 Cell: 512-750-6782 www.professorofinsurance.com
[email protected] or
[email protected]
Thomas W. Sager Professor of Statistics Department of Information, Risk, and Operations Management The University of Texas at Austin, CBA 5.202 Austin, Texas 78712-1175 (512) 471-3322
Bo Shi Department of Information, Risk, and Operations Management The University of Texas at Austin, CBA 5.202 Austin, Texas 78712-1175 (512) 471-3322
Capital Ratio, Product Risk and Asset Risk Relationships in the U.S. Health Insurance Industry Abstract As financial intermediaries in the health care delivery system, U.S. health insurers will be strongly affected by sweeping legislative reforms adopted in 2010, both in health care and in financial regulation. In this paper, we provide useful context or benchmarks for interpreting these reforms and for understanding the financial behavior of health insurers more generally. In particular, we extend capital/risk studies to the U.S. Health insurance industry by modeling the interrelationship between health insurers’ capital and asset risk as endogenously interacting variables. We test whether the industry manages its capital vis-à-vis investments in a risklimiting or risk-seeking manner and assess the strengths of those relationships. We also examine evidence for the business-strategy hypothesis that choices of capitalization and investment risk can be viewed as flowing from a prior choice of product risk level. Using the rich data of these insurers we devise asset risk and product risk proxies tailored to the health insurance industry. We find that for the 2001-2008 period, our panel of health insurers acted to limit risk by balancing an increase of risk in one area with a decrease in another. The elasticity of capital with respect to asset risk is low, suggesting that the capital structure of health insurers is relatively insensitive to significant change in asset risk. We also find support for the business-strategy hypothesis.
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Capital Ratio, Product Risk and Asset Risk Relationships in the U.S. Health Insurance Industry
I. Introduction The health care delivery system in the United States partners with insurers, HMOs and Blue Cross and Blue Shield plans. (Henceforth we refer to these insurers, HMOs, and BCBS plans collectively as health insurers). Health insurers act as financial intermediaries and as managers of access to health care. The majority of the funds for health care flow from consumers to health care providers through health insurers, who may approve or disapprove payment for services. Health insurers retain their position as intermediaries and care managers under the Patient Protection and Affordable Care Act (PPACA) and the reconciliation bill signed in March 2010. Therefore, the financial well being of these partners is critical to the sustainability of the current health care system. It is of great importance to understand how health insurers will react to changes in their risks imposed by reform legislation, in particular, and how they manage financial risk, in general. In this study, we extend studies of the interrelationship between capital and risks to the health insurance industry in the U.S. Similar studies have been conducted for the U.S. propertyliability insurance industry (Cummins and Sommer, 1996, and Shim, 2010), the U.S. life insurance industry (Baranoff and Sager, 2002 and 2003, and Baranoff, Papadopoulos and Sager, 2007) and the U.S. banking industry (Shrieves and Dahl, 1992, and Jacques and Nigro, 1997). Our extensive literature reviews of the health insurance industry and of health economics failed -2-
to find similar studies of capital/risks interrelations for the health insurance industry. The literature concentrates on other important issues, as will be noted briefly in section II. More specifically, in this study we evaluate whether U.S. health insurers operate within a “finite-risk” paradigm, in which taking greater risk in one area is accompanied with lowering the risk in another area – or whether the industry operates in a mode of “excessive-risk” undertaking. Moreover, following Baranoff and Sager (2003), we develop our model informed by the business strategy hypothesis, which regards the choice of business product (health insurance specialty) as a foundation for other decision making, such as the choices of capital structure and asset risk. We model capital and asset risk as endogenously interacting variables. In keeping with the business strategy hypothesis, we model product risk as predetermined, since it is viewed as a driver of other decisions. Our model also includes many other proxies of risks and controls. We argue that most health insurance activities incur high product risk. As a consequence, the health insurance industry is predisposed toward use of capital structure as a tool to manage product risk, and only to a lesser degree to manage other risks, such as asset risk. In other insurance sectors, such as life insurance and annuities, for which the product risk is much less and other risks relatively greater, we would expect to find greater use of capital to manage non-product risks, although we do not pursue that idea here. Our findings provide context and benchmarks for interpreting important legislative changes imposed by PPACA, which are anticipated to increase the product risk of health insurers. We find positive values for the elasticity of capital with respect to both product and asset risk, which suggest that health insurers operated within the finite-risk (risk-limiting) mode, rather than the excessive-risk (risk-seeking) mode. But our findings also suggest that more product risk, -3-
such as elimination of benefit caps, guaranteed insurability, and loss ratio minima under PPACA, will impel health insurers to seek more capital as a risk-balancing offset. Insurers may also seek to raise premiums to price their increased product risks at true value. But some adjustments may be blocked. Access to the capital markets may not be assured. Pricing power may be limited by regulation, competition, and/or consumer resistance. Given sufficient roadblocks, health insurers may be driven away from finite-risk and toward excessive-risk behaviors, in a “go-for-broke” mode – a notion of importance to both Federal and State insurance regulators. Scenario analysis of future impacts of various PPACA elements can use this study as a benchmark tool for the industry’s risk/capital attributes if expectations about risk attitudes remain the same. The next section of the paper provides a brief overview of the place of the health insurance industry in the U.S. health care system before the 2010 health care reform and afterwards. We also provide very brief literature review regarding this system. Section III provides the theoretical foundation for the interplay between the capital and asset risk of health insurers, followed by the data section (Section IV) where the rich variables available are discussed. This is followed by the Methodology (section V) and the results (section VI). The paper concludes with a Summary (section VII).
II. The U.S. Health Insurance System
Figures 1 and 2 below provide a graphical depiction of major features of the health care system in the U.S., before and after the 2010 reforms.1 Health insurers (in green) are financial
1
These are original models developed by the authors to explain the system.
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intermediaries in the system. Money flows from consumers/patients/employers to health care providers through health insurers. As a result, health insurers have developed a role as managers of access to health care through their ability to approve or to disapprove payment for services. Before the Patient Protection and Affordable Care Act (PPACA) of 2010, the evolution of managed care techniques excluded more than 40 million American for various reasons. As shown in Figure 1, the excluded group has not been part of the managed care system and has used the health care system mostly on an emergency basis without discounts. Traditionally, U.S. insurance regulation of insurers has been in the domain of the States, rather than the Federal government, and has emphasized insurer solvency and consumer protection, along with guarantee funds, which provide payment for the claims of insolvent insurers. Reimbursement limits for guarantee funds are set by each state and vary from $100,000 to $500,000 per claimant.2 The effect of the PPACA is shown in Figure 2. PPACA brings the uninsured population into the system and the Federal Government plays a larger regulatory and participatory role. The States still regulate the health insurance industry within the requirements of the new law (yet to be completely clarified).3 The consumer group (in orange) grows with the addition of the formerly uninsured. Persons with pre-existing conditions are expected to flow into high risk pools subsidized by the Federal government and implemented by the States. Since PPACA mandates coverage for all, Exchanges are established to insure coverage for persons otherwise lacking easy access to the system. Under PPACA, the health insurance industry retains its
2
See NOLHGA, the Life and Health Insurance Guaranty System, and the Financial Crisis of 2008-2009” by Peter G. Gallanis, June 5, NY, NY at the American Bar Association Tort Trial & Insurance Practice Session. 3
The detailed implementation of PPACA evolves daily, and is not discussed here.
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position as financial intermediary and the “holder” of the managed care methods for utilization and apportionment of claims payments.
Figure 1 - Health Care Delivery System Before The Patient Protection Act of 2010 State Regulation Financial oversight, Consumer Protection and Guarantee Funds
Minimal or no Federal Regulation
Insurers= Financial Intermediaries
Managed Care
Consumers
Health Care Providers
[via employers and individuals]
No Managed Care
Consumers [Not in the system]
Figure 2 - Health Care Delivery System With Patient Protection and Affordable Care Act of 2010 Federal Regulatory Oversight
States Exchanges State Regulation
Insurers= Financial Intermediaries
Federal High Risk Pool
Managed Care
Health Care Providers
All Consumers [via employers and individuals]
Many insurers are diversified and may provide life, annuity, reinsurance, property and casualty and other products as well as health insurance. In the U.S., each insurer files an annual report with the National Association of Insurance Commissioners (NAIC) in one and only one -6-
category as a Life, Health, Property and Casualty insurer (etc.), based upon its primary identification. The Life category is especially diverse and includes many insurers with substantial health business. But our focus in this study is on insurers whose predominant business is health insurance and who identify themselves as such and file with the NAIC as Health insurers. These insurers covered about 151 million insured members and collected premium income of $298 billion in 2006. The corresponding figures for 2008 were about 157 million insured members and $346 billion in premium income. Although there is a vast literature on health care, we did not find health insurance research on the topic of capital structure and risks. However, the health care literature does include work that is related to some of the themes of our paper. We mention a few briefly. The literature regarding the demand for health insurance and health care is of interest since it supports the notion that health care is a product with inelastic demand (see Ahking, Giaccotto and Santerre, 2009; Marquis and Long, 1995; and Liu and Christianson, 1998). Since our study period includes the recession of 2007-2009, studies that relate health care usage to recession factors such as unemployment are of interest. For example, Cawley and Simon (2003) find a negative relationship between unemployment and use of health care/insurance. Others studies relate to the product risk of health insurance. For example, growth in per capita real income, technology changes, and wage increases in excess of productivity growth help drive the increase in health care expenditures (see Okunade and Murphy, 2002; and Hartwig, 2008). In addition, the impact of health insurance on health care utilization and increase in insurers’ product risk can be seen in Buchmueller, Grumbach, Kronick and Kahn (2005), and Freeman, Kadiyala, Bell and Martin (2008). Since HMOs attempt to limit their product risk with managed care, the finding by
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Brockett, Chang, Rousseau, Semple, and Yang (2004) that more restrictions in managed care lower the efficiency in HMOs is also of interest. Health insurers in the U.S. operate under various organizational structures, which include profit and non-profit; mutual and stock (most of which are not publicly traded). Another structure, unique to health insurers, is the HMO.4 In the HMO, providers are not reimbursed on the basis of fee for service and the insured members have greater restrictions on their choice of provider and services. Insurers deliver various lines of health care coverage. Some provide specialized health care coverage such as vision, dental, comprehensive coverage, or Medicare supplement as shown in Table 1 for 2008. Table 1 includes overlaps as many insurers serve more than one line of business. The same members may be insured for various lines, such as comprehensive coverage, dental and vision. In 2008, 109 insurers sold only comprehensive coverage (which includes serving the Federal employees) while 142 sold only dental insurance. There were 105 insurers that sold comprehensive insurance plus one more line of insurance, and 150 insurers that added multiple lines to the comprehensive business (not shown in Table 2)
4
There are also various subspecies of HMO. In some, the providers are employees of the HMOs. In others, the structure is more open and physicians are paid fees for service and capitation. For more information, see Chapter 22 in Baranoff, Brockett and Kahane (2009) “Risk Management for Enterprises and Individuals.”
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Table 2. Health Insurance Industry by Line of Business in 2008† Variable
Comprehensive
Medicare Supplement
Dental
Federal Employee Benefit Plans
Vision
Medicare
Other Health Plans
Medicaid
445
109
236
73
164
338
183
145
Total Premium Income (in $M)
$ 186,456
$7,546
$ 7,624
$ 1,337
$ 26,692
$ 65,962
$ 42,265
$ 8,244
Total Covered Members
57,848,959
3,840,297
29,200,731
21,206,913
6,285,046
6,247,221
16,752,154
15,127,177
(umber of Insurers
† For insurers reporting to the NAIC in the “Health insurer” category. Insurers involved in multiple lines of business are tallied in each line. Members covered under multiple lines are tallied in each line. However, premiums are specific to each line.
As noted above, the comprehensive coverage is regarded as the riskiest product.
III. Theoretical Foundation Business-Strategy Hypothesis Following Baranoff and Sager’s (2003) business-strategy hypothesis for the life insurance industry, we now apply this foundation to the U.S. health insurance industry. Under the business-strategy hypothesis, an insurer first chooses the line of business in which it wishes to operate. The choice of business product is fundamental. Other financial and corporate decisions flow from that basic choice, including the interplay between capital and asset risk that would be deemed appropriate to balance the risks of the business choice.5 Since an insurer – or any firm, in general – would not be expected to change its fundamental business strategy very often, it is appropriate that the product risk derived from the business decision would be a pillar undergirding other decisions. Within health insurance, the firm may specialize or diversify. 5
Baranoff and Sager (2003) advance transactions-cost economics arguments as theoretical support for the businessstrategy hypothesis.
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Table 2 shows a number of different health product lines for specialization or diversification. An insurer that sells primarily one type of coverage with limited benefits, such as dental care or vision care, should have limited product risk. The dental and vision insurance coverage contract is very explicit with major limits on procedures and maximum benefit amounts. For example, coverage for dental insurance may not exceed $2,000 per year regardless on the number of procedures. On the other hand, an insurer that sells comprehensive coverage is much more susceptible to product risk since the contract promises coverage for a multitude of illnesses and conditions up to very large limits. Moreover, medical innovation introduces new treatments and procedures not anticipated by the parties to the contracts. Legislation and court rulings may expand or contract coverage. Under PPACA, there can be no limit on lifetime benefit amounts. Comprehensive coverage contracts are incomplete and relational in the language of transaction costs economics (see Williamson, 1985). The contracts are implicit and open to interpretation.6 Therefore, we expect that substantial exposure to comprehensive health coverage should confer greater product risk than substantial exposure to dental coverage. Consistently with the business-strategy hypothesis, we adopt the working hypothesis that product risk is a predetermined variable in the sense of econometric modeling.7 We also use other risk measures and control variables to help isolate the impact of the product risk on the capital and asset risk decisions. These additional variables include loss ratios and utilization values. We then consider whether these choices in fact affect logically subsequent choices of
6
The media often report on consumers’ fights with health insurers over coverage. A much broader source for disputed claims adjustments may be found in the complaint data filed with the various states’ insurance regulators. 7
A predetermined variable may be distinguished from an exogenous variable conceptually by asking whether the variable values are really set externally to the firm (exogenous), or are merely treated as given (predetermined). For estimation purposes, both cases are treated the same.
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capital and asset risk levels, which we view as mutually interacting endogenous variables, as per prior capital-risk interrelationship literature in the banking and insurance industry. In a sense we pick up the action after the insurer has decided on its business strategy (and hence product risk), and see if product risk plays a role in the capital and asset risk “dance.” Theories of insurer risk behavior. Two hypotheses have been advanced to explain the capital accumulating and investing behaviors of insurers. The literature entertains two opposing hypotheses about the relationship between capital and risk for insurers. One set of theories predicts that the relationship between capital and asset risk is positive. If an insurer acts to limit its overall risk, then maintaining a high level of capital (low financial risk) would lead it to pursue a conservative investment policy (low asset risk), and vice-versa. In this scenario, we would expect a positive correlation between capital and asset risk. Because such theories imply that firms balance greater risk in one activity with lower risk in another, we refer to these theories collectively as the finite risk hypothesis. They include agency theory (starting with Jensen and Meckling, 1976), transactions cost economics (Williamson, 1985 and 1988), bankruptcy and regulatory cost, and complete markets. For example see Cummins and Sommer (1996) for the property casualty industry, Baranoff and Sager (2002 and 2003) and Shrieves and Dahl (1992) and Berger (1995) for the banking industry. On the other hand, if an insurer does not act to limit its overall risk, then there may be situations in which the insurer seeks to increase its overall risk. Thus, maintaining a low level of capital (high financial risk) might lead it to pursue an aggressive investment policy (high asset risk), and vice-versa. In this scenario, we would expect a negative correlation between capital and asset risk. In the literature, some theories have predicted this outcome. Because they imply -11-
that greater risk in one activity may lead to greater risk in another, we refer to these theories collectively as the excessive risk hypothesis. The risk subsidy of guaranty funds provides one possible mechanism for the operation of this moral hazard. Others include asymmetric information, “go for broke”, signaling and adverse selection. See, for example, Cummins (1988), Berger, Herring and Szego (1995) and Downs and Sommer (1999). If the finite risk hypothesis (or risk-limiting or risk-averse hypothesis) describes the behavior of health insurers, then we expect to find that health insurers that assume high asset risk through their choice of investments would accumulate large amounts of capital as a counterbalance and vice versa. On the other hand, if the excessive risk hypothesis (or riskseeking hypothesis) prevails, then we expect to find high asset risk associated with low capital accumulations and vice versa. In our models, we examine evidence for these two hypotheses in the interrelationship between capital and asset risk as simultaneously interacting endogenously determined variables. IV. Data The dataset was extracted from the annual statements filed by U.S. insurers with the National Association of Insurance Commissioners for 2001 – 2008. We used all insurers that file in the NAIC Health category. As we noted previously, many diversified insurers that file in other NAIC categories may write substantial health business. The NAIC Health category encompasses insurers that identify primarily as health insurers and that write the majority of health business. There are 6,487 firm-years of data.8 A partial profile of the panel of insurers is shown in Table 1.
8
For this paper, we include only insurers with capital ratio between 0 and 1, which excludes 56 firm-years and arrives at 6,431 firm-years.
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Capital ratio For capital, we use the ratio of total book capital to total assets. A high capital ratio is associated with low risk; a low capital ratio is associated with high risk. For nonfinancial firms, the debt-to-equity ratio is often used to assess this source of risk. However, insurers typically have little conventional debt, since most liabilities are in the form of actuarially calculated reserves for paying future claims.
Risk Proxies Product Risk We have argued that health insurance is a riskier product than other lines of insurance, in general. Within health insurance, comprehensive lines embody the most risk for the incompleteness of their contracts, whereas vision and dental embody the least risk for their limited and more definite scopes. We selected two product risk proxies to represent the range of health insurance risks. Both proxies are exposure measures, based on the relative amount of coverage written in the lines of each. To proxy the riskier lines, we took the ratio of premiums from comprehensive and Federal employee lines to total insurer assets. Since Federal employee coverage is also comprehensive coverage, we call this proxy the comprehensive product risk. Dividing by total assets scales the measure to remove the effect of firm size. To proxy the less risky lines, we computed the ratio of premiums from dental coverage to total insurer assets and call the result dental product risk.
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Asset Risk To proxy asset risk, we use a volatility-of-returns measure that comports with notions of asset risk in finance. Monthly returns are calculated for each of 16 asset classes by applying an appropriate market index to each of the asset classes. For each insurer, we use the value of the asset class as reported in the insurer’s annual statement. We multiply the value of the asset class by a corresponding monthly return obtained from a public market index. For example, for stock holdings we use the monthly return of the S&P500. Then returns are summed across the 16 asset classes to give a total portfolio return for each of the 12 months in a given year. The result is not necessarily the total portfolio return that the insurer actually earned, but a hypothetical return that the insurer could have earned by investing its portfolio in the assets represented by our 16 market indices. Actual individual insurer returns are not available to us. The computation of the asset risk proxy is completed by calculating the standard deviation of the 12 monthly returns in each year and dividing by total invested assets. This computation follows Baranoff, Papadopoulos and Sager (2007), who call the result opportunity asset risk (OAR) because it represents the asset risk that the insurer could have achieved by investing its portfolio in the assets of the 16 market indices. Dividing by total invested assets scales the measure and removes the effect of insurer size. In this paper, we use OAR in logarithm scale to proxy asset risk. Figure 3 shows the composition of the portfolios for our panel of health insurers by the 16 asset classes.
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Figure 3 Health insurers’ invested asset allocation in 2004 and 2008 †
Index: Gov1 = ratio of government bonds 20 yrs yrs to invested assets. MuniHi = ratio of high quality municipal bonds to invested assets. MuniLo = ratio of low quality municipal bonds to invested assets. Util = ratio of utility bonds to invested assets. Corp12 = ratio of high quality corporate bonds to invested assets. Corp3 = ratio of quality 3 corporate bonds to invested assets. Corp4 = ratio of quality 4 corporate bonds to invested assets. Corp56 = ratio of lowest quality corporate bonds to invested assets. Stocks = ratio of common stocks to invested assets. Mortgages = ratio of mortgages to invested assets. RealEstate = ratio of all real estate to invested assets. CashSTinvest = ratio of cash and short term investments to invested assets. † For each asset class, the bar represents the sum of the values of the asset class across all insurers, divided by the sum of total invested assets across all insurers, expressed as a percent.
Control Variables Table 2 lists the definitions of all variables used in our model. The predetermined/exogenous controls include firm size, which has been implicated in many studies as an important factor for capital and risk. In this study, many of the key variables have already been adjusted for size by conversion to ratios (CAP = capital-to-asset ratio, RBCratio, RetOnCap = net income / capital, Product Risk and Asset Risk are as described above). But we include size explicitly to mop up remaining unadjusted effects. Three obvious size proxies are total assets, -15-
total liabilities, and total premiums collected. These three are rather highly correlated with each other, however, and their inclusion as a group in a regression model may induce collinearity issues. Therefore, we decided to combine them by taking the logarithm of their geometric mean and calling the result Size.9 Since the insurance industry is highly regulated, we use the risk-based capital ratio (RBCratio = 100 * Total market capital / (2 * total authorized risk capital)) as an indicator of regulatory forbearance. Return on capital (total income / total market capital) is also included as an indicator of earnings and performance (Berger, 1995; and Berger and Patti, 2006). Agency theory predicts that the governance type of insurance companies (stock or mutual) affects their risk taking behavior. So an indicator variable (Stock insurer? = 1 if stock company, = 0 if not) is used to represent the governance type. If an insurer belongs to an affiliated group of companies, access to the resources of sister firms might affect the insurer’s risk taking behavior. Another indicator variable (In group? = 1 if a member of an affiliated group, = 0 if not) is included for this reason. Use derivatives? (= 1 if there is derivative activity, = 0 if not) is taken as an indicator for sophistication of health insurers. The number of states in which a health insurer is licensed to conduct business (States of licensure) may also affect its risk management behavior, because health insurance product risk is related to geographic and demographic factors. In addition to the above generic exogenous variables, we also include two predictor variables that are specific to the health insurance industry. The health loss ratio is defined as the sum of total hospital and medical expenses, claims adjustment expenses, administrative expenses, 9
Supporting this approach is the fact that a principal components analysis showed that the first principal component explains 95% of the variation of the group. Furthermore, the factor loadings of the three are about equal, which supports the equal weighting implied by the geometric mean.
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and the increase in reserves, divided by total premium income from health insurance. It represents the fraction of health insurance income attributable to claims and other charges that originate from health insurance underwriting. The health loss ratio is an important indicator of health insurers’ underwriting performance or profitability. A high loss ratio means low profitability. Utilization of health services is defined as (number of provider encounters + number of hospital patient days + number of inpatient admissions) / total health premiums. Insurers with high utilization rates may suffer impaired profitability.
Endogenous Variables
Variables
Table 2. Variable Definitions Description
Capital
Capital / Total Assets
Asset Risk
Opportunity Asset Risk (see discussion in the text)
(Comprehensive Premium Income + Federal Employee Benefits Plans Premium Income) / Total Assets Comprehensive product risk Dental product risk
Utilization Predetermined Health Loss or Exogenous Ratio Variables Size RBCratio
Dental Premium Income / Total Assets
(number of provider encounters + number of hospital patient days + number of inpatient admissions) / total health premiums (total hospital and medical expenses + claims adjustment expenses + administrative expenses + increase in reserves) / total premium income from health insurance Geometric Mean of (Total Assets + Total Liabilities + Total Writings) Risk-Based Capital Ratio = 100 * Total book capital / (2 * total authorized risk capital)
Return on capital
Return on Capital = Total Income / Total Book Capital
In group?
In Affiliated Group (1), Not in Affiliated Group (0)
Stock insurer? Use derivatives? States of licensure
Stock Firm (1), Non-Stock Firm (0) Indicator of Derivative Activity (1=Yes) Number of States of Licensure -17-
V. Methodology Since we view capital and asset risk as mutually interacting and endogenous, we deploy a simultaneous equation model with two structural equations, one for capital and one for asset risk. Each structural equation has its own set of predetermined/exogenous control variables, including our product risk index. One of the issues for our analysis is whether the business strategy hypothesis is in play for health insurers. This hypothesis views capital and asset risk choices as flowing from the choice of business lines, represented in our model by the product risk index. To test the business strategy hypothesis, the product risk index logically must be treated as predetermined rather than as endogenous.10 Confirmation of the business-strategy hypothesis would be represented by statistical significance of the product risk index in our model. Our structural model is: Ct = β 0C + β CC Ct −1 + β AC At + β PC Pt + β1C X 1t + L + β kC X kt + ε tC
(3) A 0
A C
A A
A P t
A 1
A k
At = β + β Ct + β At −1 + β P + β X 1t + L + β X kt + ε
A t
where C is the insurer capital-to-asset ratio, A is the asset risk index, and P is the product risk index. Although P is singled out to emphasize its special role in the business-strategy hypothesis, P is treated the same for estimation as any other predetermined/exogenous variable X. A appears in the structural equation for C, and C appears in the structural equation for A. This aspect of the model represents the assumed mutual interaction between A and C. The role of the lags Ct −1 and
10
Therefore, our treatment of product risk here differs from the treatment of Baranoff and Sager (2002), who accord product risk a third equation as an endogenous variable. There is no inconsistency between our treatment and theirs, since they do not test the business-strategy hypothesis.
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At −1 is to capture effects on C and A that are not isolated by other predictors and that are strong enough to linger on into the next year. Both A and C are used in logarithm scale in the model. This transformation makes them more nearly normal and enables the interpretation of their coefficients as elasticities. The estimation methodology is two-stage least squares with instrumental variables and correction for autocorrelation. In the first stage, the reduced-form model is estimated: Ct = α 0C + α1C X 1t + L + α kC X kt + ε tC
(4) At = α 0A + α1A X 1t + L + α kA X kt + ε tA
Each reduced form equation is estimated separately and uses the complete set of predetermined/exogenous variables from Table 2, except for product risk. Of course, all endogenous variables and their lags are also excluded from the right-hand sides of (4). Since we have a panel dataset, the covariance matrix of the errors in (4) is block-diagonal, so OLS estimation should not be used. Instead we use the Generalized Estimating Equations (GEEs) methodology (Liang and Zeger, 1986) for autoregressive errors, as implemented in SAS. The *
*
resulting estimated values ( Ct and At ) of Ct and At , respectively, are instruments for use in the second stage of the two-stage least squares methodology. Substituting the first stage instruments into the right-hand side of (3), we then estimate the second-stage model: *
Ct = β 0C + β CC Ct −1 + β AC At + β PC Pt + β1C X 1t + L + β kC X kt + ε tC (5) A 0
A C
*
A A
A P t
A 1
A k
At = β + β Ct + β At −1 + β P + β X 1t + L + β X kt + ε -19-
A t
Each equation is again estimated separately. Use of the instruments permits asset risk to “participate” in the capital equation, and vice-versa, while removing the correlation between the endogenous predictors and the errors that makes OLS inconsistent in (3). Because of the panel data structure, we again have autocorrelated errors in (5), so we again employ GEE. Variable selection for the stage 2 models was informed by the need to insure identifiability of parameters, by the importance attached to variables by previous research, and by stepwise regression to achieve parsimonious models. The results of the second stage analysis are discussed in the next section. VI. Results 1. Summary Statistics Table 3 shows the summary statistics for all the endogenous and exogenous variables used in our analysis. Health insurers with capital-to-asset ratio below 0 or above 1 are omitted. To save space, we supply summary statistics for even-numbered years only. Table 3 shows some striking facts about the US health insurance industry. The mean capital ratio grew from 52.7% in 2002 to more than 59% in 2006 and 2008. Compared with the life insurance industry (see Baranoff and Sager, 2002 and 2003), the health insurance industry is more capitalized. The mean asset risk grew in 2008, as would be expected for the period of the financial crisis and volatility in the financial markets. Health insurers have much more exposure to the most risky product (comprehensive) than to the least risky product (dental).
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Table 3. Summary Statistics for (AIC Health Insurers 2001 – 2008 Variable
(
Mean
Median
Std Dev
(
Mean
2002 0.527
Median
Std Dev
2004
Capital ratio
728
Asset risk
761
0.004
0.003
0.005
758
0.005
0.004
0.003
Comprehensive product risk
759
1.353 11
0.673
1.608
755
1.233 11
0.568
1.504
Dental product risk
759
0.515
0.000
1.394
756
0.521
0.000
1.402
Utilization
715
12
112
0.002
0.008
Health Loss Ratio
701
Size
764
RBCratio
727
Return on capital
0.005
0.482
0.244
727
0.585
0.004
0.549
0.212
0.003
0.020
708
0.987
0.984
0.287
685
0.996
0.970
0.240
16.432 13
16.850
2.537
760
16.572 113
17.014
2.557
4545.770
224.210
52164
728
6581.990
273.294
106397
730
0.078
0.113
0.645
728
0.152
0.138
0.471
In group? (1/0)
764
0.657
1
0.475
760
0.689
1
0.463
Stock insurer? (1/0)
764
0.729
1
0.445
760
0.725
1
0.447
Use derivatives? (1/0)
764
0.003
0
0.051
760
0.009
0
0.096
States of licensure
764
1.410
1
2.587
760
1.588
1
3.611
Capital ratio
819
0.594
0.572
0.223
824
0.592
0.562
0.211
Asset risk
863
0.003
0.002
0.002
867
0.008
0.006
0.009
Comprehensive product risk
862
11
0.040
1.470
865
0.979
0.021
1.350
Dental product risk
863
0.457
0.000
1.298
865
0.417
0.000
1.194
Utilization
783
0.003 12
0.002
0.006
813
0.004 112
0.002
0.035
Health Loss Ratio
758
1.000
0.975
0.255
797
1.012
0.986
0.260
866
16.627
13
17.008
2.590
868
16.839
113
17.178
2.520
2006
Size
1.065
2008
RBCratio
816
21667.820
289.348
304992
821
14476.090
271.258
345712
Return on capital
820
0.099
0.120
0.504
826
0.039
0.059
0.660
In group? (1/0)
866
0.703
1
0.457
868
0.712
1
0.453
Stock insurer? (1/0)
866
0.730
1
0.444
868
0.735
1
0.442
Use derivatives? (1/0)
866
0.007
0
0.083
868
0.008
0
0.089
States of licensure
866
2.066
1
5.364
868
2.552
1
6.942
11
Comprehensive product risk may exceed 1 because comprehensive premium income (the numerator) may exceed total assets (the denominator). Health insurers experience large inflows and outflows of cash in relation to their assets.
12
Utilization is defined as the number of medical care events (see Table 2) per premium dollar. So it may appear to be low in absolute terms. 13
Size is in log scale. Thus, a size of 16.5 corresponds to a geometric mean of assets, premiums, and liabilities of about $14.5 million.
-21-
2. Results for the statistical models Table 4 presents results for stage two of the two-stage least squares estimation methodology sketched in the methodology section. The main issues for analysis are the businessstrategy, finite risk, and excessive risk hypotheses. The results provide support for the businessstrategy hypothesis. The product risk is significant in the capital model and the asset risk model.
Table 4. Simultaneous equation estimates for stage 2 of the two-equation model for capital-to-asset and asset risk PVariables (Parameters) Estimates Value Estimates P-Value Structural equation for the log of asset Structural equation for logarithm of capital-to-asset ratio risk -0.215 0.475 -1.716 0.000 Intercept 0.048
