Measuring the effects of reducing subsidies for private insurance on public expenditure for health care

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1 Measuring the effects of reducing subsidies for private insurance on public expenditure for health care Terence Chai Cheng Melbourne Institute of Applied Economic and Social Research, The University of Melbourne, Melbourne, Australia Abstract This paper investigates the effects of reducing subsidies for private health insurance on public sector expenditure for hospital care. An econometric framework using simultaneous equation models is developed to analyse the interrelated decisions on the intensity and type of health care use and private insurance. The framework is applied to the context of the mixed public-private system in Australia. The simulation projections show that reducing premium subsidies is expected to generate net cost savings. This arises because the cost savings achieved from reducing subsidies are larger than the potential increase in public expenditure on hospital care. JEL classifications: I11, H42, C31, C15 Keywords: Private health insurance; Subsidies; Public and private finance; Simultaneous equation models Contact information: Tel ; Fax ; address: techeng@unimelb.edu.au. I am especially grateful for the comments and suggestions from Deborah Cobb-Clark, John Deeble, Guyonne Kalb, Elizabeth Savage, two anonymous referees, as well as participants at the 3 rd Australasian Workshop on Econometrics and Health Economics, the 8 th World Congress on Health Economics, and seminars at the University of Melbourne and Monash University. This paper uses unit record data from the in-confidence version of the Household, Income and Labour Dynamics in Australia (HILDA) survey. The HILDA project was initiated and is funded by the Australian Government Department of Families, Housing, Community Services and Indigenous Affairs (FaHCSIA) and is managed by the Melbourne Institute of Applied Economic and Social Research (Melbourne Institute). I gratefully acknowledge financial support from the Australian Research Council Discovery Project Grant (ID: DP ) and through grants provided by the Faculty of Business and Economics at The University of Melbourne. The findings and views reported in this paper are mine and should not be attributed to either FaHCSIA, Melbourne Institute or the funding organisations.

2 1 Introduction In many modern economies, the public sector plays an important role in the financing of health care. Nearly all OECD countries have universal health systems, where health care is funded either through taxation, or through publicly-sponsored or subsidised health insurance. Even in the market-oriented health system of the United States, health insurance is directly subsidised for individuals and families with low incomes and the elderly, while employment-based private health insurance is indirectly subsidised through the tax system. The extent of public involvement on health care financing in the United States is expected to rise with the implementation of the Patient Protection and Affordable Care Act which aims to ensure that all individuals have health insurance through a combination of mandates, premium regulations and subsidies. While there are generally strong justifications for the provision of subsidies for health care and health insurance, the arguments for subsidising duplicate private health insurance (PHI) in countries with universal health systems are less compelling. In these countries (e.g. Australia, Spain, United Kingdom), a private health care market coexists alongside the public sector providing health services already covered under the public system. Public subsidies for private insurance, either in the form of tax incentives or monetary rebates on premiums, have been a source of policy contention (Colombo and Tapay 2004). It is often argued that incentives for PHI can stimulate the private health care market, relieving both capacity and cost pressures off the public system, and improving access to and quality of public sector care. However, questions have been raised as to whether an expanding private sector diverts valuable resources away from the public sector. In addition, issues of equity arise as privately insured individuals, who usually have higher incomes, can bypass the public sector queues and obtain faster access to care. An important question in evaluating the effectiveness of subsidies for duplicate PHI is whether subsidies are self-financing if its introduction would lead to cost savings within the public health care system that exceed the cost of the subsidy program. The converse question, one that is pursued in this paper, is whether public savings achieved from reducing subsidies can more than offset the potential increase in public expenditure. Understanding the costs and benefits of subsidy programs for private insurance is important as it apprises the effectiveness of policy instruments avail to governments seeking to influence the public and private compo- 1

3 sition of health expenditures. This is especially relevant as policy makers look towards sources of private finance to pay for the health care demands of their populace in the face of rapidly growing public spending. A number of studies have examined the self-financing nature of subsidies for private insurance. Emmerson et al. (2001) and Frech and Hopkins (2004) investigate this issue through an ex-post policy evaluation for the United Kingdom and Australia respectively. The studies conclude that the cost of subsidising PHI exceeds the fiscal benefits on the public sector. López Nicolás and Vera-Hernández (2008), through an ex-ante policy simulation, arrive at a similar conclusion when simulating the effects of abolishing tax subsidies for private insurance in Spain. In addition to the significant cost involved in subsidising PHI, Colombo and Tapay (2004) highlight two other reasons why duplicate PHI is expected to have little cost-shifting effects (pp ). Firstly, relative to the public sector, the private health care sector usually focuses on elective treatments for patients with less complex and severe medical conditions. Secondly, privately insured individuals can continue to utilise the public sector. Following this, a question that is central to the debate is whether privately insured individuals opt out of the public system by substituting private for public health care, or top up and enlarge their use of health care without reducing their reliance on the public system (Fabbri and Monfardini 2011). This paper contributes to the literature investigating the self-financing nature of PHI subsidies. It develops a microeconometric framework to analyse the interrelated decisions on the intensity and type of health care use and PHI. The framework builds on the work by López Nicolás and Vera-Hernández (2008) who construct a discrete choice model to analyse the (binary) decisions surrounding public and private health care use and private insurance. The framework proposed here comprises of three simultaneous equation models which accommodate the count data nature of the health care utilisation measures (number of hospital admissions, length of overnight stay) and the binary nature of the measures of the type (public vs. private) of hospital care and PHI. The econometric framework is applied to the context of the mixed public and private health system in Australia. Australia is an interesting case study for examining the self-financing hypothesis. In the late 1990s a series of policy measures was introduced in the PHI market within a short time frame to encourage the purchase of private insurance. These measures 2

4 include a tax penalty on high income individuals without private health cover, a generous 30 percent rebate on premiums, and the introduction of entry-age adjusted premiums. To evaluate the self-financing nature of PHI, the estimates from the econometric models are used in an ex-ante simulation analysis in which the premium rebates are scaled back. This study combines two themes within the literature on the economics of health care and health insurance. The first concerns the effects of tax subsidies on the demand for health insurance, for which there have been considerable research in the United States (e.g. Gruber and Poterba 1994, Gruber and Washington 2005) and Canada (e.g. Stabile 2001, Finkelstein 2002). These studies, like most program evaluation research, focus on the ex-post evaluation of a policy or program. They exploit variation in the insurance price that arises from changes in the tax treatment on premiums and benefits affecting only a part of the population (e.g. defined by occupation types or geography), and examine how demand has changed relative to a subpopulation or control group not affected by the policy change. While this treatmentcontrol approach has its merits, it is not always feasible. For many important applications, it is often the case that the policy of interest affects the entire population, or that a comparable control group is not available. In some instances, a series of policies could have been introduced either concurrently or in close succession, as in the case of the PHI market in Australia, for which isolating the effects of a particular policy is difficult. Another limitation of the ex-post analytical techniques is that they do not allow the evaluation of the impacts of policies prior to their implementation. It is often important for governments to be able to assess the expected impacts, and costs, arising from a range of hypothetical policy options, hence facilitating the optimal design of policies to achieve the outcomes desired (Todd and Wolpin 2006). The second theme concerns the determinants of the demand for PHI, and the relationship between private insurance and health care use in the context of a National Health Service. On the former, the literature emphasises the role of public sector waiting times and quality, household income, and education attainment as important determinants of the decision to purchase PHI (See Barros and Siciliani (2012) for a comprehensive review). There is evidence from a variety of countries that individuals with private insurance consume more public and private health care. 1 In these studies, a key methodological issue that has to be addressed 1 This is the subject of substantial research in a number of countries such as Australia (Savage and Wright 2003); Germany (Riphahn et al. 2003); Ireland (Harmon and Nolan 2001); and Spain (Vera-Hernandez 1999). Jones et al. (2006) focuses on the use of specialist services in four European countries. 3

5 is that health insurance status is potentially endogenous to health care use, which arises as a result of the interdependency in the decisions to insure, and to consume health care (Cameron et al. 1988). The endogeneity problem is addressed using three simultaneous equation models that accommodate the mixed count-binary nature of the utilisation, type and insurance outcome variables. Traditional workhorse models for non-negative and integer-valued (count) outcomes such as the Poisson and Negative Binomial models have been extended to more advanced models with a variety of applications such as the multivariate count data models (e.g. Munkin and Trivedi 1999; Fabbri and Monfardini 2009; Hellström 2006), and count data models as a system of simultaneous equations (Deb and Trivedi 2006; Atella and Deb 2008; Cheng and Vahid 2011). A novel econometric model developed in this paper is a bivariate lognormal Poisson model with a common endogenous binary regressor, used to jointly analyse two hospital care utilisation measures (number of day and overnight hospital admissions) and the decision to purchase PHI. This novel model contributes to the growing literature on multivariate simultaneous equation count data models. The econometric results show that individuals with private health insurance are more likely to seek hospital care as a private patient compared to those without private insurance. However, the intensity of hospital admissions and length of overnight stay do not differ between the insured and uninsured groups. The simulation projections show that reducing premium subsidies is expected to generate net cost savings. This is because the cost of treating patients who drop private cover and rely on the public system is substantially lower than the cost of subsidising private insurance for the whole population. The savings are mainly driven by the inelastic demand for private insurance as only a small fraction of individuals are likely to respond to higher prices for insurance by dropping private health coverage. The remainder of the paper is organised as follows. Section 2 describes the institutional context in Australia. Section 3 presents the econometric framework, as well as discusses the estimation and identification strategies. Section 4 describes the data used in the empirical analysis. The results from the econometric analysis are discussed in Section 5 and those of the simulation analysis are discussed in Section 6. Section 7 assesses the sensitivity of the results. Finally, Section 8 concludes with a discussion of the key findings in the paper. 4

6 2 The Institutional Context in Australia Health care in Australia is funded through a combination of public and private sources of financing. Medicare, the universal tax-funded public health insurance scheme, subsidises medical services and technologies according to a schedule of fees referred to as the Medicare Benefit Schedule. Primary care is predominantly provided by general practitioners in private practice who are usually paid fee-for-service, and act as gatekeepers for specialist care as a referral is required to access the Medicare subsidy. Medicare also provides free access to public hospitals. Patients can choose hospital care as public (Medicare) patients in public hospitals and receive free treatment from doctors nominated by hospitals, as well as free (shared) accommodations and meals. Private care can be obtained from either private or public hospitals. Individuals who choose private care are entitled to their choice of treatment doctor, better amenities such as private rooms, and quicker access to treatment by avoiding public hospital waiting lists. Private medical specialists are free to charge patients what the market will bear, with a fixed subsidy resulting in a patient copayment. The difference is afforded either as out-of-pocket expenditure, or covered by insurance funds if individuals have PHI. Unlike private specialist fees, private hospital charges (e.g. room and theatre charges, medical expendables) do not attract any Medicare subsidy. Having PHI does not preclude the use of hospital care as a public patient, and individuals may do so if they perceive that there is no advantage in paying the copayments to be a private patient. The PHI industry in Australia is heavily regulated. The role of PHI, coverage and benefit requirements, and premium-setting behaviour by health insurance funds are constrained by legislation. There are two types of PHI cover, with the first being private hospital coverage which provides financial protection towards private hospital expenditures. The second type is ancillary or extra coverage which covers services such as dental care, allied health (e.g. physiotherapy), and items such as eye glasses which are not covered under Medicare. There is mandatory community rating on PHI premiums which stipulates that insurers must charge the same premium for a given insurance plan regardless of individuals age, gender, health status, and utilisation and claims history. For any given health fund, premiums are allowed to vary across different products, and across states, to reflect the costs of claims in local markets. The former allows insurers significant 5

7 flexibility in the product design, particularly to offer policies that explicitly exclude coverage for certain conditions or treatments (e.g. joint replacements for young adults) (Buchmueller 2008). A system of risk equalisation, in place since 2007, exists to partially compensate health funds with enrollees that have risker demographic profiles and higher claims experiences. Ministerial approval is required before health insurers can change the premiums charged. A series of three policy changes was introduced in the PHI market from the late 1990s with the aim of encouraging the uptake of PHI, which had been steadily declining since the introduction of Medicare in The then prevailing policy position supported a balanced public and private involvement in the delivery of health care, and the declining PHI membership was seen as threatening the financial viability of the private health care sector, which could eventually have spillover effects on the public hospital system. The first policy change in 1997 is the Private Health Insurance Incentive Scheme which involves the use of tax subsidies for low income individuals, and a tax levy for high income individuals and households without private insurance. Under this policy, singles and families with taxable income below $35,000 and $70,000 respectively are eligible for a subsidy, either in the form of a premium discount, direct payment, or tax offset. For the tax penalty, singles and families (inclusive of couples) with an annual household income greater than $50,000 and $100,000 respectively are liable for a tax levy amounting to one percent of their taxable income if they do not have private health insurance. This levy is known as the Medicare Levy Surcharge. By 1998, a second policy change was introduced, replacing the subsidy component with a nonmeans tested 30 percent rebate on premiums. A third policy is the Lifetime Health Cover, which involves the modification of the community rating regulations. Introduced in July 2000, this policy allows health funds to charge a premium loading on those without private health cover, which is applied when these individuals decide to purchase insurance in the future. The loading is calculated as 2 percent of the base premium for each year of age above 30, and applies over the remainder of individuals lifetimes. What followed the implementation of these three policies was a dramatic increase in percentage of the population with PHI, from a low of 30.1 percent in 1999 to 45.7 percent in September 2000, which has since stabilised at around 44 percent. 2 Hall et al. (1999) provide an excellent discussion of institutional environment and motivations that underpin the policy changes. See also Butler (2002) for a full description of the three policies. 6

8 3 Econometric Framework The key elements of a decision model of the demand for hospital care and PHI in a mixed system such as Australia s is described below to motivate the empirical modelling. This model is elaborated in Cheng (2011). The subject of interest is an individual who is an expected utility maximiser, who solves the following resource allocation problem max m, q, d π(s) U[C, h(m, q s)] (1) s with illness severity s that is distributed π(s), consumption C, and health status h. The inputs to the health production function h(m, q s), are hospital care services m of quality q. Here, m = (m y, m ov, st k ) is a three-dimensional vector where m y and m ov denote the number of day and overnight hospital admissions respectively. st k is the length of overnight stay (the number of nights in hospital) for the k-th overnight admission. The quality indicator vector q = (q y j, qov k ), where qy j, qov k {0, 1} and subscripts refer to the j-th day and k-th overnight admission respectively, are binary indices which assume the value of 0 if the individual chooses publicly (Medicare) funded hospital care, or 1 if private care is chosen. The individual may buy PHI, a decision denoted by d where d {0, 1}, which is available at nominal premium P. The effective premium P, defined as the nominal premium net a premium subsidy (r percent), and a tax levy of l percent of income which applies to individuals with incomes above Y T and who not have private insurance, is written as (1 r)p if Y Y T P = (2) (1 r)p + ly if Y > Y T The solution to the optimisation problem is given by the simultaneous equilibriums in the demands for day and overnight admissions; the length of overnight stay in each overnight admission; the choice of public or private admissions, and the choice to purchase PHI. These are represented by 7

9 m y = m y ( q, d, s) m ov = m ov ( q, d, s) st k = st k ( q, d, s) q y j (s) = arg max V qy j ( d, s) q y {0,1} q k ov (s) = arg max V qov k ( d, s) q ov {0,1} d = arg max d {0,1} EV d (3) where V qy j and V qy j are the indirect utilities associated with the admission type (i.e. public or private) strategies q y j and qov k ; and EV d the expected utility associated with insurance choice d. The joint estimation of the outcomes in equation (3) involves estimating an econometric model consisting of six non-linear equation which is a computationally intensive task. To simplify the econometric analysis, an econometric framework consisting of three distinct econometric models is developed. The first model jointly estimates the demands for day and overnight hospital admissions, and the demand for PHI (Section 3.1). The second model jointly analyses the admission type choice for day admission and the demand for PHI. The third model jointly estimates the admission type choice for overnight admission, the length of hospital stay, and the demand for PHI. There are two reasons why the econometric framework is specified in the manner described above. Firstly, this specification distinguishes between the frequency of admissions separately from outcomes that are conditional on admission, namely that of public-private choice and length of stay. Secondly, there is a data limitation in that the information of whether individuals chose to receive public or private care, and the length of overnight hospital stay, is only available for the most recent admission episode. Given this limitation, alternative specifications such as a bivariate model of public and private hospital admissions, or a joint model of day admissions and the total number of hospital nights, are not feasible. Below, the econometric framework is described which takes into account the simultaneity of the decisions on hospital care use and PHI, and is congruent with the count data nature of 8

10 hospital length of stay and binary nature of care type and insurance choice variables. 3.1 Demand for day and overnight hospital admissions Let m y i and m ov i i-th individual. be the observed frequencies for day and overnight hospital admissions for the Suppose conditional on the exogenous covariates X i1 and X i2, the endogenous variable d i, and random unobserved heterogeneity terms ε 1 and ε 2, m y i and m ov i have independent Poisson distributions, with mean parameters µ y i and µov i f(m y i X i1, d i, ε i1 ) = P o[µ y i ] (4) f(m ov i X i2, d i, ε i2 ) = P o[µ ov i ] (5) µ y i = exp(x i1β 1 + λ 1 d i + σ 1 ε i1 ) (6) µ ov i = exp(x i2β 2 + λ 2 d i + σ 2 ε i2 ) (7) where ε 1 and ε 2 are standardised and distributed standard normal, that is ε 1, ε 2 N(0, 1). The decision rule to purchase private hospital insurance is represented by the continuous latent variable d i, and the observed insurance choice d i is in turn related to d i by a dichotomous rule. These are written as d i = X i3β 3 + ε i3 (8) d i = 1[d i > 0] (9) where ε 3 N(0, 1). The RHS insurance variables d i in (6) and (7) are allowed to be endogenous by assuming that ε 1 and ε 2 are correlated with ε 3. A mixed bivariate Poisson lognormal model is adopted to gain efficiency, in which the unobserved heterogeneity terms ε 1 and ε 2 are allowed 9

11 to be correlated. More specifically, it is assumed that the unobserved variables, ε 1, ε 2 and ε 3, are distributed trivariate normal with zero means, unit variances, and correlation parameters ρ εjεk, j k, j, k = 1, 2, 3. The likelihood function of the model is shown in equation (A.1) in Appendix A. 3.2 Admission type choice for day hospital admission Suppose the decisions to seek day hospital care as a private patient and to purchase insurance are given by the continuous latent variable q y and d respectively where q y i = Z i1α 1 + δd i + v i1 ; q y i = 1[qy i > 0] (10) d i = Z i2α 2 + v i2 ; d i = 1[d i > 0] (11) The latent variables are related to the observed care type and insurance choices via the dichotomous rule given in (10) and (11). The RHS variable d i in (10) is allowed to be endogenous by assuming that v i1 and v i2 are distributed bivariate normal with zero means, unit variances and correlation parameter ρ v. The insurance outcome d is observed for all individuals, whereas q y is observed only for those for whom the number day hospital admissions are positive. The likelihood function for this model, shown in equation (A.2), accommodates this feature of the data. 3.3 Admission type choice and length of hospital stay for overnight admission Let st i denote the duration of hospital stay and q ov i the admission type binary variable which takes the value of 1 when private care was chosen and 0 otherwise. The binary variable indicating insurance status is given by d i as above. Suppose conditional on W i, q i, d i, and the unobserved heterogeneity ξ i1, st i follows a Poisson distribution with truncation at zero, with mean parameter µ i. 10

12 f(st i W i1, d i, q i, ξ i1 ) = exp µ i µ m i i m i! (1 exp µ ) (12) µ i = exp(w i1γ 1 + ψ 1 d i + ψ 2 q ov i + σ 3 ξ i1 ) (13) where ξ i1 is N(0, 1). The decision rules to seek private hospital care and to purchase insurance are given by the continuous latent variables q ov i by the respective decision rules and d i and are related to the observed outcomes q ov i = W i2γ 2 + ψ 3 d i + ξ i2 ; q ov i = 1[q ov i > 0] (14) d i = W i3γ 3 + ξ i3 ; d i = 1[d i > 0] (15) The RHS variables q ov i and d i in (13) and d i in (14) are allowed to be endogenous by assuming that ξ i1, ξ i2 and ξ i3 are distributed trivariate normal with zero means, unit variances and correlation parameters ρ ξjξk j k; j, k = 1, 2, 3. It is emphasised that the outcome variables m i, qi ov, d i are observed only for individuals who have been hospitalised for an overnight admission, and for non-hospitalised individuals only d i is observed. accommodates this feature of the data, and is shown in equation (A.3). The likelihood function 3.4 Estimation The likelihood functions for the econometric specifications in Sections 3.1 and 3.3 are complex and require the evaluation of integrals. Maximum simulated likelihood (MSL) techniques are used to approximate the likelihoods given that these functions do not have a closed-form expression. Quasi-Monte Carlo draws based on the Halton sequence were used in the simulations which have been shown to be more accurate and faster compared to the conventional random number generator (Bhat 2001, Train 2003). The number of simulations S has a considerable effect on the properties of the MSL estimator (Gouriéroux and Monfort 1996) simula- 11

13 tions were chosen, beyond which the estimation results obtained were very similar. The Berndt, Hall, Hall and Hausman (BHHH) quasi-newton algorithm was used to maximise the simulated likelihood using numerical derivatives. The variance of the MSL estimates was computed post convergence using the cluster-robust formula (Deb and Trivedi 2002, p.608), which takes into account the presence of multiple observations from each household, as well as the minimising the influence of simulation noise (McFadden and Train 2000). The model in Section 3.2 is estimated via maximum likelihood. 4 Data The empirical analysis uses data from the In-Confidence version of the Household, Income and Labour Dynamics in Australia (HILDA) survey. HILDA is a nationally representative longitudinal survey which collects extensive information on household and family formation, labour force participation and income, and life satisfaction, health and well-being. Every member of the household aged 15 and over are surveyed via a face-to-face interview and are requested to complete a self-completion questionnaire. The primary data source is from wave 4 (2004) of the HILDA survey, where data is available on individuals from 8280 households. A health module, in addition to the core survey questions, was included in wave 4 in which information on hospital care use and PHI status was collected. The data is combined with responses on self-assessed health status from wave 3 (2003) and information on households expenditure on PHI premiums from wave 5 (2005). In the analysis sample, respondents from multiple family households (N=2276) and those where the respondents age is below 25 years (N=5591) were excluded. Given the emphasis on the relationship between hospital care use and PHI, individuals with PHI policies that cover only ancillary services (cf. section 4.1) were coded as not having hospital insurance. After excluding observations with missing or ambiguous responses, 7089 observations remained in the sample. 3 3 The following are the variables (top five by frequency) and the corresponding the number of observations (in brackets) dropped due to missing or incomplete information: Private insurance and policy type (335); whether hospitalised for day (418) or overnight (59) admission; self assessed health (1026); daily alcohol consumption (353). 12

14 4.1 Private hospital insurance In the HILDA survey, individuals were also asked to provide information on whether they have PHI and the type of coverage. The three coverage types are hospital, ancillary or both. The focus of the paper is whether individuals have private hospital insurance, that is they possess either hospital only or combined cover. 4 Table 1 presents the proportion of individuals with private hospital insurance by coverage and income unit types. Overall, 50.9 percent of the sample have private hospital insurance. Respondents from couple only (56.3 percent) and couple family (55.9 percent) households are more likely to be privately insured compared with lone persons (39.1 percent) or lone parent (28.1 percent) households. Combined hospital and ancillary cover is more common compared to hospital-only cover, with 79.5 percent of insured individuals having policies of this type. The average annual expenditure on private hospital insurance premiums by coverage and income unit type for the HILDA data are shown in Table 1. 5 The expenditure on premiums is higher for individuals with combined cover compared with hospital-only and ancillary-only cover, and are generally higher for larger households (e.g. couples versus lone person). 6 Variations in premiums would also arise from the differences in the generosity of coverage, defined by the level of deductibles, percentage of copayment, as well as comprehensiveness in terms of the menu of services covered. For the purpose of benchmarking the data on premium expenditures, data from the Household Expenditure Survey on household expenditure on hospital, medical and dental insurance are presented at the bottom of Table 1. One would observe that the data on premiums are broadly consistent in both datasets. 4.2 Defining the price of insurance Estimating the demand elasticity for private insurance requires the specification of an insurance price. In this paper, the price of insurance is defined as the ratio of effective premium to the expected benefits received. To illustrate this definition, following Phelp (1997), suppose that the 4 In the original data set, 6.9 percent (N=428) of the 6183 respondents who indicated that they have PHI have ancillary-only policies. 5 Household expenditure data on premiums for PHI are obtained from Wave 5 (2005) of the HILDA survey and adjusted to account for the average growth in premiums of 7.6 percent between 2004 and 2005 (Private Health Insurance Administrative Council 2005). 6 Children under the 21 years of age and full-time students below 25 years may be covered under their parents policy without additional cost. 13

15 expected benefits from health insurance is E(B), which is a function of the prices and quantities of medical services, and patients cost sharing (e.g. copayments). The nominal premium is defined as P = (1 + L)E(B), where L is the percentage loading imposed by the insurer. The price of insurance is given by 1 + L = P/E(B), which is the ratio of nominal premium to the expected benefits. Given the financial incentives, the effective premium P faced by individuals is the nominal premium P net of the premium subsidy, and where applicable the tax levy. By substituting P for P, the price of insurance is expressed as P /E(B). This is interpreted as the effective price that is required for each dollar of expected benefits. Based on this definition, the observed variation in the insurance price arises from two main sources. The first source of variation is introduced through the Medicare Levy Surcharge. This is shown in equation (2) in Section 3. For a given insurance contract, variation in the effective premium arises from differences in the levy that individuals are liable to pay if they choose not to buy private insurance. For individuals above the income threshold, those with higher household income are required to pay a larger levy, and correspondingly face a lower effective premium. For those whose income are sufficiently high, the tax liability may exceed the nominal premium for the most generous policy available, resulting in a situation where the effective premium is less than zero. The second source of variation arises from differences in the expected benefits from insurance, which in turn depend on individuals characteristics such as age, gender and household composition. For instance, all else being equal, older individuals are expected to have higher use of hospital care compared to those who are younger. Females in their childbearing years are expected to have higher use compared with males. These utilisation patterns are illustrated in Figure 1 which shows the expected annual benefits per person for a hospital-only policy by sex, age (available in five-year bands) and states. In terms of household composition, households with children accrue higher expected benefits compared with those without children. This is because in Australia dependent children under 21 years of age, and fulltime students below 25 years, can be covered under their parents insurance contracts. An advantage of defining the insurance price in this manner is that it allows one to account for heterogeneity in policy types (e.g. hospital-only vs. combined cover) and household compositions (lone person vs. couple) that is observed in the data. For instance, individuals 14

16 with combined hospital and ancillary cover pay a larger premium, and receive expected benefits that are higher than those with hospital-only coverage. Furthermore, a couple household pays a larger premium and receives a higher level of expected total benefits (for insuring two individuals) as compared to a single-person household. Calculating the insurance price requires information on premiums. This is relatively straightforward for individuals with private insurance as one can use data on premium expenditure. For those without private insurance, premiums have to be estimated. This approach has been previously applied in studies that estimate the price elasticity of demand for private health insurance (e.g. Marquis and Long 2001; Costa and García 2003). For this paper, premiums for uninsured individuals are estimated using the predictions from a regression of premium expenditure observed from privately insured individuals in the sample. With data on premiums, one can calculate the effective premium, which forms the numerator in the price formula. For the denominator, the expected benefits are estimated using published data on benefits payouts. Here, information on age, sex and state of residence of respondents and their family members (where applicable), as well as data on respondents coverage types (hospital only, hospital and ancillary) and policy types (e.g. couple, family) are used to calculate the expected benefit accruing to each household. 7 Expected benefits are calculated using statistics published by the Private Health Insurance Administrative Council for the financial year (July 2004 to June 2005). For uninsured individuals, the insurance price is calculated using the estimated premiums and benefits of a combined hospital and ancillary policy as a benchmark. This is because the combined cover is the most common coverage type as shown in Table 1. For the subsample of individuals where observed premium expenditure is used to calculate the insurance price, the price may be inaccurate given that premiums reflect information on plan characteristics (e.g. deductibles and copayments) whereas benefits do not. As a result, the price may be understated (overstated) for individuals with more (less) generous coverage. This may affect the price elasticity estimate, and the direction and magnitude of any potential bias 7 The approach adopted in a number of studies estimating the price elasticity of private health insurance is to include premiums as a determinant of the insurance choice (see Kiil (2012) for a recent review). In addition, covariates such as age, gender, and household size are usually added as additional controls. These variables account for the expected benefits of insurance, although in a non-specific way. Hence the definition of the insurance price adopted in this paper provides a more structured interpretation in that these characteristics affect insurance choice by influencing individuals assessment on the expected benefits from insurance. The implied price elasticity estimates from both approaches are quite similar. These results are available upon request from the author. 15

17 will depend on the distribution of benefits payouts. 8 Unfortunately the lack of detailed data on these aspects does not allow one make reasonably accurate inference on how the elasticity estimate might be affected. 9 To address this potential problem, an alternative formulation of the insurance price is considered, where predicted premiums are used in place of observed premiums. Here, the insurance price is calculated from dividing predicted premiums by expected benefits. This formulation has the advantage that it does not over- or understate benefits (in relation to premiums) and the insurance price, and hence serves as a point of reference to assess the sensitivity of the price elasticity estimate. There are two disadvantages of using predicted premiums, the first of which is the general issue of efficiency loss given that information captured within observed premiums is not utilised. A second disadvantage is that endogeneity problems may be more severe given that plan-specific characteristics are neither incorporated within premium expenditures nor benefits, and these will be subsumed into the unobservables in the insurance equation. Endogeneity arises if these unobservables correlate with the unobserved characteristics that influence admission type choices and hospital use intensity, potentially leading to biased estimates. However, as with the case of observed premiums, such potential biases are mitigated with simultaneous equation estimation. Foreshadowing the results, the estimated price elasticities from using observed and predicted premiums are very similar (see Table 10), which suggest that the former is not significantly affected by unobserved plan characteristics. In addition, the regression estimates show a higher degree of correlation using predicted compared with observed premiums. This is consistent with expectations given that predicted premiums contain less information. 10 While the price formulation incorporates the premium subsidy and tax levy, the effect of the Lifetime Health Cover (LHC) policy is not explicitly modelled. Under this policy, individuals without private coverage are charged a premium loading which is applied when they decide to 8 The price of insurance would potentially be mismeasured if individuals with higher utilisation switch into plans with more generous coverage. This is a possibility given that data on premium expenditure is collected in the year after the hospitalisation data. If plan switching occurs, the price of insurance would be overstated (understated) if individuals with higher (lower) spending switch into more (less) generous plans. The extent to which plan switching takes place in the Australian context is unclear. Models of risk selection under community rating predict adverse selection while more recent research (e.g. Doiron et al. 2008) suggest advantageous selection. Hence whether the institutional context supports adverse or advantageous selection, and whether these factors drive plan-switching, remain open research questions. I am grateful to a referee for raising this issue. 9 Aggregate data on plan characteristics indicate that 96 percent of insurance contracts in-force at the end of 2004 have no exclusion conditions, and 59 percent have a front-end deductible. (Private Health Insurance Administrative Council 2004) 10 The results of the simulation analysis based on predicted premiums are presented as a sensitivity check in the paper, but not the regression estimates. These are available upon request. 16

18 buy private insurance in the future. To empirically model the effect of this policy requires the use of panel data given that the decision of whether and when to buy PHI would affect the premium cost. Ellis and Savage (2008) proposed a simple approach to analyse the effect of this policy by adding into the insurance equation an additional regressor measuring the difference between anticipated higher premiums under LHC, and actual premiums. This approach is used in a sensitivity analysis that is discussed in Section 7. Previewing the results, the estimated price elasticities are very similar with or without accounting for the LHC policy. 4.3 Estimating premium expenditure Premiums are estimated by fitting an ordinary least squares (OLS) regression to the logarithm of annual premium expenditure observed from individuals with private hospital insurance. Community rating requirements imply that individuals risk characteristics cannot be used as predictors of premiums. Instead, variations in premiums are explained by differences in coverage and policy types, as well as factors that influence claims experience and operating cost of health insurers across states. To this end, two sets of explanatory variables are included in the regression. The first is a set of binary indicators that represent individual-level information on coverage and policy types. The second is a set of state-level variables. For instance, the percentage of insurance policies with an excess across the different states is used as a proxy for plan characteristics, which is not collected in the data. To capture claims cost, state-level information on the percentage of population over 65 years is used as it has been shown that benefit payouts are significantly higher for older individuals. Claims are expected to be larger where professional fees charged by doctors are higher, the effect of which is captured by including the average price of an office-based consultation with a private specialist. The specialist-to-population ratio is also included which could be positively related to claim expenditures arising from higher activity rates, or negatively related if insurance funds are in a better position to negotiate for lower payments. Lastly, to capture economies of scale in the cost of administering private health insurance, the ratio of health insurance contracts to the number of individuals employed the general and health insurance industry is included as a regressor. 11 It should be pointed out that because of multicollinearity, state identifiers cannot 11 Data on the supply-side variables are obtained from a variety of sources: information on policies with excess and the number of health insurance contracts based on data published by the PHI Administrative Council; information on the number of individuals employed in the insurance industry and characteristics of 17

19 be included alongside the state-level covariates. Hence the estimates on these covariates also reflect heterogeneity across regions. The results from the OLS regression on log expenditure on premiums are shown in Table 2. The coefficients are mostly statistically significant and are consistent with expectations. Expenditure on premiums are higher for individuals with combined hospital and ancillary cover compared with hospital only cover, and are larger for family and couple only policies relative to single policies. The estimate on the fraction of policies with excess is statistically significant, albeit with an unexpected sign. Premiums are positively related to the percentage of individuals over 65 years and specialists fees, and have a U-shaped relationship with specialist density. Finally, premiums are negatively associated with the fraction of policies to individuals employed in the insurance industry. Studies have applied sample selection models to impute premiums which are otherwise not observed for the uninsured individuals. For example, Marquis and Long (2001) and Marquis and Louis (2002) used this approach on the grounds that selectivity correction removes the effects of omitted variables that influence both the health insurance premium as well as the decision (by firms) to offer insurance. The theoretical justification is based on a behaviorial model of firms decision to offer insurance to its employees whereby the problem of selectivity occurs when firms that do not offer insurance face higher premiums compared to those who offer insurance, for reasons such as higher perceived risk by insurers that are not observed by the researcher. In the Australian context, community rating regulations prohibit health insurers from setting premiums to discriminate based on individuals risk and hence the selectivity problems observed by the preceding studies are likely not to be relevant. 12 For high income individuals, the combination of the tax and subsidy programs results in a situation where the potential tax liabilities through the Medicare Levy Surcharge exceed the premium cost of PHI. When this occurs, the price of insurance is less than zero. In the sample of 7089 observations, 495 individuals have an effective price of insurance that is less than zero. 13 the Australian population is based on the 2006 Census; information on the number of specialists in Australia based on the sampling frame from wave 1 (2008) of the Medicine in Australia: Balancing Employment and Life (MABEL) longitudinal survey of doctors while the price of private specialists service is based on self-reported data also from the MABEL data. 12 The possibility of selectivity bias is investigated by estimating a regression of observed premiums using a Heckman selection model. The results obtained were counter-intuitive: predicted premiums were higher for insured individuals compare with those without insurance. 13 It is expected that these individuals would purchase private hospital insurance given they would be financially better off, although it is observed that a small percentage (4.9 percent) are not privately insured. This may be 18

20 These observations are excluded from the regression analysis but are included in the simulation analysis. The subsequent sections describe the characteristics of the 6594 observations in the sample. 4.4 Measures of hospital care use In the survey, individuals were asked about the number of occasions they had been admitted to hospital as a day patient and for an overnight stay in the twelve months preceding the survey. Individuals who have been hospitalised were further queried on the duration of hospital stay and whether they were admitted as a Medicare (public) or private patient on the most recent day and overnight admission. The descriptive statistics for the hospital care utilisation measures are summarised in Table 3. The count data utilisation measures are the number of day admissions, overnight admissions, and the number of hospital nights. The measures have mass points at 0 and 1 and exhibit overdispersion where the unconditional variance (Sy) 2 is larger than its mean (ȳ). The number of hospital nights, and the binary outcome of whether individuals chose to be admitted as private patients in their last overnight hospital stay, are observed only for the 881 individuals in the analysis sample who have been admitted for an overnight stay. On the latter, 46.9 percent of individuals chose private care. Of the 800 individuals who had at least one day hospitalisation episode, 58.6 percent chose to be admitted as private patients in the last day admission. 4.5 Remaining explanatory variables The remaining explanatory variables that are used in this study can be classified into the following categories: demographics and socioeconomic characteristics (e.g. age, gender, household income), health status measures (presence of chronic conditions), health risk factors (drinker, smoker) and geographical information (state/territories, remoteness). The choice of variables is similar to that in Cameron et al. (1988), Cameron and Trivedi (1991), Savage and Wright (2003) and Propper (2000). In addition to variables that are available in the survey, two variables that are obtained through external data sources are incuded. The first is the number of individuals employed in the general and health insurance industry within the intermediexplained by a variety of factors, including the presence of measurement error in household income. For these uninsured individuals, the magnitude of the effective outlay on insurance premiums is small (median=-$451, mean=-$705) which suggest that the effects of measurement error, if any, is not likely to be significant. 19