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 onpublic sector expenditure for hospital care. An econometric framework using simultaneousequation models is developed to analyse the interrelated decisions on the intensity and typeof health care use and private insurance. The framework is applied to the context of themixed public-private system in Australia. The simulation projections show that reducingpremium subsidies is expected to generate net cost savings. This arises because the costsavings achieved from reducing subsidies are larger than the potential increase in publicexpenditure on hospital care.

JEL classifications: I11, H42, C31, C15Keywords: Private health insurance; Subsidies; Public and private finance; Simultaneousequation models

∗Contact information: Tel. +61 3 83442124; Fax. +61 3 83442111; Email address: techeng@unimelb.edu.au.I am especially grateful for the comments and suggestions from Deborah Cobb-Clark, John Deeble, GuyonneKalb, Elizabeth Savage, two anonymous referees, as well as participants at the 3rd Australasian Workshop onEconometrics and Health Economics, the 8th World Congress on Health Economics, and seminars at the Univer-sity of Melbourne and Monash University. This paper uses unit record data from the in-confidence version of theHousehold, Income and Labour Dynamics in Australia (HILDA) survey. The HILDA project was initiated andis funded by the Australian Government Department of Families, Housing, Community Services and IndigenousAffairs (FaHCSIA) and is managed by the Melbourne Institute of Applied Economic and Social Research (Mel-bourne Institute). I gratefully acknowledge financial support from the Australian Research Council DiscoveryProject Grant (ID: DP0880429) and through grants provided by the Faculty of Business and Economics at TheUniversity of Melbourne. The findings and views reported in this paper are mine and should not be attributedto either FaHCSIA, Melbourne Institute or the funding organisations.

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 involve-

ment 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

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 insur-

ance. 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. Lopez

Nicolas and Vera-Hernandez (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) high-

light two other reasons why duplicate PHI is expected to have little cost-shifting effects (pp.

193-194). 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 sub-

sidies. 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 Lopez

Nicolas and Vera-Hernandez (2008) who construct a discrete choice model to analyse the (bi-

nary) 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

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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 treatment-

control 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

1This is the subject of substantial research in a number of countries such as Australia (Savage and Wright2003); 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

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 accom-

modate 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; Hellstrom 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.

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2 The Institutional Context in Australia

Health care in Australia is funded through a combination of public and private sources of fi-

nancing. 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 Medi-

care 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 leg-

islation. 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 com-

munity 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

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 1984.2 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 non-

means tested 30 percent rebate on premiums.

A third policy is the Lifetime Health Cover, which involves the modification of the commu-

nity 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.

2Hall et al. (1999) provide an excellent discussion of institutional environment and motivations that underpinthe policy changes. See also Butler (2002) for a full description of the three policies.

6

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

maxm,q, d

∑s

π(s)U [C, h(m,q | s)] (1)

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 = (my,mov, stk) is a three-dimensional vector where my and mov denote the number of

day and overnight hospital admissions respectively. stk is the length of overnight stay (the

number of nights in hospital) for the k-th overnight admission. The quality indicator vector

q = (qyj , qovk ), where qyj , q

ovk ∈ {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 YT and who

not have private insurance, is written as

P =

(1− r)P if Y ≤ YT

(1− r)P + ℓY if Y > YT

(2)

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

my = my(q, d, s)

mov = mov(q, d, s)

˜stk = stk(q, d, s)

qyj (s) = argmaxqy∈{0,1}

V qyj (d, s)

qovk (s) = argmaxqov∈{0,1}

V qovk (d, s)

d = argmaxd∈{0,1}

EVd (3)

where V qyj and V qyj are the indirect utilities associated with the admission type (i.e. public or

private) strategies qyj and qovk ; and EVd 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 sim-

plify the econometric analysis, an econometric framework consisting of three distinct economet-

ric 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

hospital length of stay and binary nature of care type and insurance choice variables.

3.1 Demand for day and overnight hospital admissions

Let myi and mov

i be the observed frequencies for day and overnight hospital admissions for the

i -th individual. Suppose conditional on the exogenous covariates Xi1 and Xi2, the endoge-

nous variable di, and random unobserved heterogeneity terms ε1 and ε2, myi and mov

i have

independent Poisson distributions, with mean parameters µyi and µovi

f(myi |Xi1, di, εi1) = Po[µyi ] (4)

f(movi |Xi2, di, εi2) = Po[µovi ] (5)

µyi = exp(X ′i1β1 + λ1di + σ1εi1) (6)

µovi = exp(X ′i2β2 + λ2di + σ2εi2) (7)

where ε1 and ε2 are standardised and distributed standard normal, that is ε1, ε2 ∼ 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 di is in turn related to d∗i by a dichotomous rule.

These are written as

d∗i = X ′i3β3 + εi3 (8)

di = 1[d∗i > 0] (9)

where ε3 ∼ N(0, 1). The RHS insurance variables di in (6) and (7) are allowed to be endogenous

by assuming that ε1 and ε2 are correlated with ε3. A mixed bivariate Poisson lognormal model

is adopted to gain efficiency, in which the unobserved heterogeneity terms ε1 and ε2 are allowed

9

to be correlated. More specifically, it is assumed that the unobserved variables, ε1, ε2 and ε3,

are distributed trivariate normal with zero means, unit variances, and correlation parameters

ρεjεk, ∀ 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 qy∗ and d∗ respectively where

qy∗i = Z ′i1α1 + δdi + vi1; qyi = 1[qy∗i > 0] (10)

d∗i = Z ′i2α2 + vi2; di = 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 di in (10) is allowed to be endogenous

by assuming that vi1 and vi2 are distributed bivariate normal with zero means, unit variances

and correlation parameter ρv. The insurance outcome d is observed for all individuals, whereas

qy 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 sti denote the duration of hospital stay and qovi 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 di as above. Suppose conditional on Wi, qi, di, and the unobserved

heterogeneity ξi1, sti follows a Poisson distribution with truncation at zero, with mean parameter

µi.

10

f(sti|Wi1, di, qi, ξi1) =exp−µi µmi

i

mi! (1− exp−µ)(12)

µi = exp(W ′i1γ1 + ψ1di + ψ2q

ovi + σ3ξi1) (13)

where ξi1 is N(0, 1). The decision rules to seek private hospital care and to purchase insurance

are given by the continuous latent variables qov∗i and d∗i and are related to the observed outcomes

by the respective decision rules

qov∗i =W ′i2γ2 + ψ3di + ξi2; qovi = 1[qov∗i > 0] (14)

d∗i =W ′i3γ3 + ξi3; di = 1[d∗i > 0] (15)

The RHS variables qovi and di in (13) and di in (14) are allowed to be endogenous by

assuming that ξi1, ξi2 and ξi3 are distributed trivariate normal with zero means, unit variances

and correlation parameters ρξjξk∀ j = k; j, k = 1, 2, 3. It is emphasised that the outcome

variablesmi, qovi , di are observed only for individuals who have been hospitalised for an overnight

admission, and for non-hospitalised individuals only di is observed. The likelihood function

accommodates this feature of the data, and is shown in equation (A.3).

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 ex-

pression. 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 (Gourieroux and Monfort 1996). 2000 simula-

11

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 longi-

tudinal 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 17209 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, individ-

uals 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

3The following are the variables (top five by frequency) and the corresponding the number of observations (inbrackets) dropped due to missing or incomplete information: Private insurance and policy type (335); whetherhospitalised for day (418) or overnight (59) admission; self assessed health (1026); daily alcohol consumption(353).

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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 2003-04 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

4In the original data set, 6.9 percent (N=428) of the 6183 respondents who indicated that they have PHI haveancillary-only policies.

5Household expenditure data on premiums for PHI are obtained from Wave 5 (2005) of the HILDA survey andadjusted to account for the average growth in premiums of 7.6 percent between 2004 and 2005 (Private HealthInsurance Administrative Council 2005).

6Children under the 21 years of age and full-time students below 25 years may be covered under their parents’policy without additional cost.

13

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 insur-

ance, 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 ac-

count 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

with combined hospital and ancillary cover pay a larger premium, and receive expected bene-

fits 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 straight-

forward 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 Garcıa 2003). For this paper, premiums

for uninsured individuals are estimated using the predictions from a regression of premium ex-

penditure 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 ac-

cruing to each household.7 Expected benefits are calculated using statistics published by the

Private Health Insurance Administrative Council for the 2004–05 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

7The approach adopted in a number of studies estimating the price elasticity of private health insurance isto 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 variablesaccount for the expected benefits of insurance, although in a non-specific way. Hence the definition of theinsurance price adopted in this paper provides a more structured interpretation in that these characteristics affectinsurance choice by influencing individuals’ assessment on the expected benefits from insurance. The impliedprice elasticity estimates from both approaches are quite similar. These results are available upon request fromthe author.

15

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 con-

sidered, 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 ben-

efits, and these will be subsumed into the unobservables in the insurance equation. Endogeneity

arises if these unobservables correlate with the unobserved characteristics that influence admis-

sion 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 ob-

served 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 esti-

mates 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

8The price of insurance would potentially be mismeasured if individuals with higher utilisation switch intoplans with more generous coverage. This is a possibility given that data on premium expenditure is collectedin 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 towhich plan switching takes place in the Australian context is unclear. Models of risk selection under communityrating predict adverse selection while more recent research (e.g. Doiron et al. 2008) suggest advantageousselection. Hence whether the institutional context supports adverse or advantageous selection, and whether thesefactors drive plan-switching, remain open research questions. I am grateful to a referee for raising this issue.

9Aggregate data on plan characteristics indicate that 96 percent of insurance contracts in-force at the endof 2004 have no exclusion conditions, and 59 percent have a front-end deductible. (Private Health InsuranceAdministrative Council 2004)

10The results of the simulation analysis based on predicted premiums are presented as a sensitivity check inthe paper, but not the regression estimates. These are available upon request.

16

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 loga-

rithm of annual premium expenditure observed from individuals with private hospital insur-

ance. 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

11Data on the supply-side variables are obtained from a variety of sources: information on policies with excessand the number of health insurance contracts based on 2004–05 data published by the PHI AdministrativeCouncil; information on the number of individuals employed in the insurance industry and characteristics of

17

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 Australiabased 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-reporteddata also from the MABEL data.

12The possibility of selectivity bias is investigated by estimating a regression of observed premiums using aHeckman selection model. The results obtained were counter-intuitive: predicted premiums were higher forinsured individuals compare with those without insurance.

13It is expected that these individuals would purchase private hospital insurance given they would be financiallybetter off, although it is observed that a small percentage (4.9 percent) are not privately insured. This may be

18

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 (S2y) is larger than its mean

(y). 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 fol-

lowing 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 vari-

ables 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 intermedi-

explained by a variety of factors, including the presence of measurement error in household income. For theseuninsured 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

ate local area of the survey respondents’ residential location. This variable is derived using

information on industry and location of employment based on data from the 2001 Australian

Census of Population and Housing.14 The second variable is the distance to the nearest private

hospital from the survey respondents’ location of residence. This is defined as the euclidian

distance between the centroids of the postal area of survey respondents’ and the postal area of

the nearest private hospital.15 Distance is calculated using data on the coordinates (longitude

and latitude) of centroids via the haversine formula.

The descriptive statistics for the explanatory variables are presented in Table 4. The average

age of the sample is 49.9 years, with a range of 25 to 99 years. Females make up roughly 54

percent of the sample. The average annual household income is $60,120. Approximately 47

percent of individuals have no postschool qualification (Year 12 and below). By occupations,

40 percent of individuals are not in the labour force, while the largest group is Professionals

(24 percent). Measures of individuals’ health status include indicators of self-assessed health

status collected in wave 3 and a set of binary variables that indicate the presence of chronic

conditions that affect physical and social functioning. For the self-assessed health status, 45

percent of individuals reported to be in excellent or very good health in the wave 3 survey,

with 36 percent indicating that their health is good and 19 percent fair and poor. Indicators

of health risk factors include whether individuals consume alcohol daily (9.7 percent) and are

regular smokers (19 percent). Geographical information include state/territory indicators as

well as remoteness categories. Approximately 58 percent of individuals reside in major cities in

Australia. The average number of individuals employed in the general and health insurance in

a statistical subdivision is 800 and the mean distance to the nearest private hospital is 30.3 km.

In the regression analysis, the entire set of covariates described above is included in the

intensity of hospital use, and the choice of admission types and insurance equations except

for the age, gender and income unit types (presence of dependent children, couple vs. single)

variables which are excluded from the insurance equation.16 The effects of these covariates on the

14The industry category is Industry Code 742 (Other Insurance), which includes 7421 (Health Insurance) and7422 (General Insurance) based on the Australian and New Zealand Standard Industrial Classification (ANZSIC)in 1993. The unit of reference for defining the location of employment is the Statistical Subdivision (SSD), aspatial unit of intermediate size. In the 2001 Australian Standard Geographical Classification, there were a total207 SSDs, with each SSD containing an average of 22 postal areas. The postal codes of respondents in the HILDAsurvey are linked to the SSD using the 2001 Australian Bureau of Statistics (ABS) “Statistical Subdivision andPostal Area Concordance” data that is available by request from the ABS.

15Data on the centroids of postal areas are obtained from the Australian Bureau of Statistics (2006).16A case may be made to include the supply-side variables that are used to predict premiums into the insurance

20

propensity to insure have been factored into the insurance price variable, through the calculation

of the expected benefits from insurance. The implicit assumption here is that age, gender and

household composition are not expected to have an independent effect on the propensity to

insure after controlling for the price of insurance. It is emphasised that these exclusions are

justified on theoretical grounds, and are not required for the identification of the econometric

models. The identification strategy is discussed next.

4.6 Identification and exclusion restrictions

Formally, the econometric model described in Section 3 is identified by the nonlinearity of the

functional form and error distributions. However, the reliance on such a strategy is unappeal-

ing and hence exclusion restrictions are imposed to strengthen the identification. The model in

Section 3.1 constitutes a mixed bivariate Poisson lognormal model with a single common en-

dogenous binary insurance variable while that in Section 3.2 is a probit model for the admission

type (day hospitalisation) equation with one endogenous binary variable. The model in Sec-

tion 3.3 consists of a Poisson lognormal model with endogenous insurance and admission type

binary variables, as well as a probit model for the admission type (overnight hospitalisation)

equation with one endogenous insurance variable. Imposing exclusion restrictions for the model

in Section 3.1 requires that there is at least one variable in X3 that is excluded from X1 and

X2, and for the model in Section 3.2 one variable in Z2 that is excluded from Z1. For the model

in Section 3.3, this requires that there is one variable in W3 that is excluded from W1 and W2

, and one variable that is in W2 that is excluded in W1.

To satisfy the above exclusion restrictions, the number of individuals employed in the general

and health insurance industry is included in the insurance equation (X3, Z2,W3) but not in the

admission type choice (Z1,W2), frequency of admissions (X1, X2) and length of stay equations

(W1). This variable performs the role as a proxy for the accessibility to insurance services which

influences the ease with which individuals can acquire information on health insurance products.

This is likely to influence whether individuals choose to purchase private hospital insurance but

not the choice between public and private hospital care and the intensity of hospital care use.

In addition, the distance to the nearest private hospital is included in the admission type for

equation. This would be justified if individuals residing in states where specialist fees are higher are more likelyto purchase insurance to afford these high fees. Including the supply-side variables as additional regressors in theinsurance equation produced estimates that are virtually identical.

21

overnight hospitalisation equation but excluded from the length of stay equation. Data on

distance to hospitals have frequently been employed as instruments to address selection bias in

studies on treatment outcomes and hospital quality (e.g. McClellan et al. 1994; Gowrisankaran

and Town 1999). For our purpose, individuals’ choice to seek private or public hospital care is

based on a variety of factors which include the types and severity of illness, the availability of

private hospital insurance, as well as the proximity of private hospitals. The distance to private

hospitals is very likely to be uncorrelated with the unobserved type and severity of individuals’

medical conditions and for this reason would justify as an excluded variable in the length of

stay equation.

5 Results

The simultaneous equation models are estimated, along with their corresponding single equation

variants, to assess the relative merits of the different models. For the single equation models, the

number of hospital admissions and length of stay are estimated using a Poisson lognormal model,

while the admission type and insurance equations are estimated using simple probit regressions.

An underlying assumption of these single equation models is that the insurance and admission

type regressors, d and q, may be treated as exogenous. For the bivariate Poisson lognormal

model in Section 3.1, the likelihood ratio test overwhelmingly rejects the single equation model

in favour of the simultaneous model. The likelihood ratio test statistic is 1553.18, which rejects

the null hypothesis that the correlation parameters ρϵjϵk are jointly equal to zero. For the

models in Sections 3.2 and 3.3, the likelihood tests cannot reject the null hypothesis that the

correlation parameters are zero.

It is noted that the correlation parameters (see bottom of Tables B.1 and B.2) are indi-

vidually statistically significant in some instances. For the model of the number of hospital

admissions (Table B.1), there is significant positive correlation (ρϵ1ϵ2) between the unobserved

determinants of day and overnight hospital admissions. This result is expected as individuals’

treatment regimen may involve overnight hospitalisations for more intensive investigations and

interventions and further day admissions for follow-up procedures. For the model of length of

hospital stay and admission type for overnight hospitalisation (Table B.2), the estimate of the

correlation parameter between the unobservables in the conditional mean equation for length

22

of stay with the insurance equation (ρϵ1ϵ3) is statistically significant from zero suggesting that

there is evidence of endogeneity in the decision to purchase insurance and the length of overnight

stay. The positive signs of these correlation parameters indicate that the unobserved factors

that positively influence the propensity to purchase private insurance have a positive effect on

the intensity of overnight stay.

Goodness of fit measures for the simultaneous and single equation models are shown in Table

5. The measures, which include the correctly classified ratio (CCR), root mean squared predic-

tion error (RMSPE), and the mean absolute prediction error (MAPE), quantify the deviations

between observed outcomes and their predictions. Both models performed almost identically

on how well the predictions fit the observed data for most outcome variables except for hospital

nights. For the binary outcomes, the percentage of correctly classified predictions range from

71.6 percent for private health insurance status, to 87.1 percent for the proportion of day admis-

sion patients who sought private hospital care. For the count data measures, the frequencies of

day and overnight hospital admissions are considerably better predicted compared with hospital

nights. This may be because the distribution of hospital nights has a long upper tail that is not

satisfactorily accommodated by conventional models for overdispersed data such as the Poisson

lognormal and negative binomial. An alternative is to use more flexible approaches such as the

semi-parametric finite mixtures and flexible count models based on series expansions (Cameron

and Trivedi 2013). These however are not attempted as they are computationally complex, even

without considering the presence of endogenous regressors.

Below, the results on the determinants of the intensity of hospital care use and the choice

to receive public or private care is discussed. The estimates of the marginal effects of private

insurance is discussed, followed by a brief overview of the coefficient estimates for the remaining

explanatory variables. These results are based on the estimates from the simultaneous equation

models. For the discussion on the marginal effects, the results obtained under the single equation

models are included for comparison.

Before proceeding, a note on interpreting the marginal effects. For the count data outcome

measures, the marginal effects for binary variables (e.g. insurance) is expressed as a proportional

change in the expected outcome E(m|X) from changing xj from 0 to 1, which is calculated as

E(m |xj = 1, X)/E(m |xj = 0, X) = eβj+∑

i=j βixi/e∑

i=j βixi = eβj . For the binary outcomes

23

measures, the marginal effects are calculated in the usual way with the remaining covariates

at their mean values. All standard errors for the marginal effects are calculated via the delta

method.

5.1 Marginal effects of insurance

Table 6 presents the marginal effects of PHI on the intensity and type of hospital care use. The

results from the simultaneous equation models are presented in column (1). Those from the

single equation modelling are shown in column (2) for comparison.

The first two sets of estimates are the marginal effects of private insurance on the number

of day and overnight admissions. The estimates from the simultaneous models are 1.32 and

1.09 for day and overnight admissions respectively, and are not statistically significant from

unity. These results indicate that privately insured individuals do not have significantly higher

intensity of hospital admissions compared to those without private insurance. The results from

the single equation estimation on the other hand indicate that privately insured individuals

utilise both day and overnight hospital care at a higher intensity.

A priori, it is not clear whether individuals with double insurance coverage, through both

PHI and the public health insurance system, are expected to have higher or lower use of hospital

care compared with individuals insured only under the public system. This is because the

measures of hospital admission observed in the data reflect total (i.e. public and private)

admissions. On one hand, privately insured individuals face a lower effective price for private

hospital care, and may therefore have higher use of private hospital services. On the other

hand, these individuals may concurrently reduce their use of public hospital services. The net

effect depends on whether individuals with private insurance substitute private for public health

care, or expand their use of private health care without reducing their reliance on the public

system.17 The relative efficiency of the public and private sectors is another important factor

(Vera-Hernandez 1999). It may be the case that private hospitals are more efficient, hence the

treatment of a given medical condition would require less visits in private hospitals compared

with public ones.

The interpretation of the marginal effect of insurance on the duration of private overnight

17Fabbri and Monfardini (2011) find evidence that individuals with voluntary health insurance consume moreprivate specialist visits, and at the same time demand less public specialist visits in the Italian National HealthService.

24

hospital stay is slightly more straightforward. Given that privately insured individuals face a

lower effective price for private care, one would expect that the length of private overnight stay

is on average higher among those with PHI. The point estimate from the simultaneous model

is 1.62 but is not statistically significant from unity. This result suggests that privately insured

individuals do not have longer duration of private hospital stays compared to those without

private insurance. In contrast, the estimate from the single equation modelling suggests that

privately insured individuals have a significantly higher duration of hospital stay.

The last two estimates are the marginal effects of private insurance on the probability

that an individual chooses to obtain day and overnight hospital care as private patients. The

choice variables are binary and hence the marginal effect is interpreted as the difference in the

expected probability of choosing private care by individuals with or without private insurance.

The estimates from the simultaneous model indicate that privately insured individuals are 78

percent and 56 percent more likely to choose private care for day and overnight admissions

respectively. An interesting observation can be seen by comparing the estimates from the two

different modelling approaches. For day admissions, the marginal effect from the simultaneous

model is larger compared with the single equation model whereas for overnight admissions the

relative magnitude is reversed. These results suggest that the direction of the endogeneity

effects are different for day and overnight admissions.

5.2 Coefficient estimates

Before proceeding to the policy simulations which is the key focus of the paper, the coefficient

estimates from the regressions are briefly discussed. These are presented in Tables B.1 and B.2 in

Appendix B.18 The coefficient estimates have the expected signs, and indicate that demographic

and socioeconomic characteristics such as age, sex, household income and employment status

are important determinants of the demand for hospital care, the choice to seek private care, and

the decision to purchase private insurance. Health status plays an important role in influencing

the intensity of hospital admissions and propensity to be privately insured. The headcount and

18The estimates in columns (1)–(3) of Table B.1 correspond to the model of hospital admissions and insurance(c.f Section 3.1), and those presented in columns (4)–(5) refer to the model of the choice of private care for dayhospital admission (c.f Section 3.2). The estimates in Table B.2 refer to the model of private care and length ofstay for overnight admission (c.f Section 3.3). To interpret the coefficient estimates on binary variables for thecount data measures, eβj ≈ 1 + βj when βj is small so the coefficient approximates the proportional increase inE(m|X) as xj changes from 0 to 1. For a continuous explanatory variable xk, the coefficient βk is a semi-elasticity.Hence an increase in xk by 0.01 changes the expected length of stay E(m|X) by βk percent.

25

distance variables, which serve as exclusion restrictions, are mostly statistically significant.19

Finally, the positive and statistically significant estimates on the standard deviations of the

heterogeneity terms strongly suggest the presence of overdispersion in the data, which justifies

the use of the Poisson lognormal model.20

6 Policy simulations

The estimates from the econometric models are used in a simulation analysis to investigate

the impact of reducing subsidies for PHI on the use of public and private hospital care. A

representative sample is first constructed by taking 10,000 random draws from the analysis

sample, using information on the age-sex distribution of the Australian population in 2005.

To allow for uncertainty in the projections, distributions of the simulated outcomes (e.g.

proportion of individuals with PHI, number of day admissions) are obtained by repeatedly

drawing from the estimated sampling distribution of the parameters (Creedy and Kalb 2006).

Random draws are taken from a multivariate normal distribution with the means and covari-

ances given by the point estimates and the estimated variance-covariance matrix. For each

draw, model calibration is performed for binary outcomes by taking random draws of error

terms via Cholesky transformation using the vector of correlation parameters. A total of 200

sets of draws are taken, and the simulated mean outcomes from each set of draws are used in

the construction of confidence intervals. For the count data measures, the conditional mean

E[mi|Xi] is calculated as µi exp(σ2/2).

For the simulation, private hospital insurance rebates are reduced by a multiple of 5, from

a minimum of 5 percent to a maximum of 25 percent. The outcomes of interest are (i) the

change in the proportion of individuals with PHI; (ii) changes in the proportions of individuals

obtaining day and overnight hospital care as private patients; and (iii) changes in the frequency

of day and overnight hospitalisations, and the number of hospital nights. In the simulations,

the predicted PHI choice for every observation in the sample is first determined. Thereafter,

19The sensitivity of the regression estimates were assessed in relation to the instrument set. The results obtainedare largely similar in sign, magnitude, and statistical significance compared with the benchmark specification.Convergence problems were encountered when the headcount variable was excluded from the variable set plausiblydue to weak model identification in the absence of this instrument. These results are available on request fromthe author.

20For Poisson lognormal model, the conditional variance V [mi |Xi] is given by E[mi |Xi, ξi]{1+τE[mi |Xi, ξi]}where τ = [exp(σ2)−1] (See equations 2.2-23 and 2.2-26 in Greene (2005)). Overdispersion is present in the dataif V [mi |Xi] > E[mi |Xi, ξi] which occurs if σ > 0.

26

these predicted insurance choices are used to compute the predicted admission types choices

and the expected intensity of day and overnight hospital use in a fashion that is consistent with

the recursive structure of the econometric models.

The expected impact on public and private hospital use, based on the estimates obtained

from the simultaneous equation models, is presented in Table 7. In the sample of 10000 obser-

vations, the number of individuals hospitalised for day and overnight care are 1144 and 1276

respectively. To illustrate the results, consider the scenario where rebates are reduced by 10

percent (see column (2) in Table 7). As shown in Panel A, the reduction in the premium subsidy

is expected to reduce the proportion of individuals with PHI from a baseline of 52.37 percent

to 51.61 percent. This translates to a decrease of 0.76 percentage points.

The point estimates of the percentage change in the number of day and overnight admissions

are -0.27 percent and -0.06 percent respectively. However these estimates are not statistically

significant from zero given that the 95 percent confidence intervals contain the null value of

zero. Hence, the decrease in the proportion of privately insured individuals is not expected to

have any effect on the frequency of hospital admissions. This result is not surprising given that

the estimates of the marginal effect of insurance on the number of day and overnight hospital

admissions (cf. Table 6) are not statistically significant.

The decrease in the number of individuals with private insurance is expected to reduce

the proportion of individuals seeking hospital care as private patients. As shown in Panel

B of column (2), the fraction of individuals choosing to be private patients for day hospital

admissions is predicted to decrease from a baseline of 59.81 percent to 59.22 percent, or 0.59

percentage points. This is also the case for overnight hospital admissions (Panel C), which is

predicted to drop by 0.45 percentage points, from 46.94 percent to 46.49 percent. As with the

number of hospital admissions, the change in the proportion of individuals with PHI has no

predicted effect on the number of hospital nights. This is because the mean predicted changes

in hospital nights are small in magnitude, and are not statistically significant from zero.

The implied arc price elasticity for private health insurance can be calculated using the

estimates in Table 7. This is calculated as the percentage change in the proportion of individuals

with private insurance divided by the percentage change in the price of insurance. For the latter,

each reduction of premium rebates by 5 percent corresponds approximately to a 2.14 percent

27

increase in the insurance price. Consider the scenario where premium rebates are reduced

by 10 percent (column (2) of Panel A), which corresponds to a 4.29 percent increase in the

insurance price. The price elasticity is calculated as -1.45/4.29 = -0.34. Overall, the implied

price elasticities across the different simulated scenarios fall in the range of -0.32 to -0.35.

The simulation results based on the single equation econometrics models (Table B.3) are

broadly similar with the results from the simultaneous equation models. The notable difference

is that the estimate of the change in the proportion seeking private overnight hospital care

from the single equation model is not statistically significant from zero (Panel C in Table B.3).

This is probably because the corresponding coefficient estimate from this model is less precisely

estimated.

6.1 Predicted impact on public expenditure for hospital care

The estimates from the simulation analysis are combined with published statistics on hospital

activity and expenditure to assess the effects of reducing premium subsidies on public expendi-

ture for hospital care. The predicted number of day and overnight public hospital admissions

are first calculated by applying the simulation estimates in Table 7 to public hospital discharges

in 2004–05 (Australian Institute of Health and Welfare 2006). These are then multiplied by

the expenditure per unit discharge from public hospitals to calculate the changes to the total

expenditure on public hospitals. Published data on the total recurrent expenditure on public

hospitals ($21,758 million Australian dollars in 2004–05) are used to calculate the former. Both

the data on activity and expenditure are adjusted using the public patient day proportion, and

where applicable, the admitted patient cost proportion.21 For the activity data, the average

public cost weights for day and overnight discharges are applied to adjust for differences in the

resource use across the two types of hospital care.

Table 8 summarises the expected impact on public sector expenditure. These projections

are based on the simulation estimates from the simultaneous equation models (cf Table 7). As

an illustration, consider the effects of reducing premium rebates by 10 percent (column (2) in

Table 8). A 10 percent reduction in rebates is expected to increase public hospital expenditure

from $12,794 million to $12,902 million, corresponding to an increase of $108.76 million or 0.85

21The admitted patient cost proportion and the public patient day proportion are 0.70 and 0.84 respectively.See Table 4.1 in Australian Institute of Health and Welfare (2006)

28

percent. The estimated increase in expenditure is however not statistically significant given

that its confidence interval contains the null of zero. Concurrently, the reduction of premium

rebates by 10 percent is expected to decrease government expenditure on the subsidy by $298.5

million given that total public spending on these subsidies was $2,985 million in 2004-05. Based

on the point estimates, the reduction in premium rebates is expected to generate net savings

of $189.74 million to the public budget, as the reduced spending on premiums rebates is larger

than the increase in spending on public hospitals.

The cost projections presented in Table 8 are imprecisely estimated given that a number of

the simulated outcomes have large confidence intervals. These include changes in the frequency

of day and overnight hospital admissions and changes in hospital nights (cf Table 7). An

alternative modelling strategy is to incorporate only statistically significant outcomes into the

cost projections. This approach effectively assumes that changing the proportion of privately

insured individuals does not have any effect on the number of hospital admissions and hospital

nights. These projections are shown in Table 9. For a 10 percent reduction in premiums, the

expected increase in public expenditure is $124.82 million, and the corresponding projected net

savings is $173.68. Not surprisingly, the confidence intervals are narrower and indicate that the

cost increase is statistically significant.

7 Robustness checks

To assess the robustness of the results, a set of sensitivity analyses is conducted. The analyses

consider the simulation scenario where rebates are reduced by 10 percent. These results are

shown in Table 10. As with the cost projections presented in Table (9), the sensitivity analyses

use only simulated outcomes that are statistically significant in the cost projections. In the

discussion herein, the reference case refers to the results from the simultaneous equation model

(column (1)).

7.1 Endogeneity

The first two sets of robustness checks assess the sensitivity of the results when different esti-

mation strategies are used to address the potential problem that the insurance and patient type

binary variables are endogeneous. Column (2) of Table 10 shows the cost estimates and the

29

implied price elasticity when each equation in the econometric model is estimated separately

rather than simultaneously. This estimation approach assumes that there is no endogeneity

problem. The point estimate of the net effect on public expenditure is $38.61 million, and

considerably smaller compared to the reference case. This is because the number of overnight

hospital admissions is expected to remain unchanged, hence the cost increase is driven solely

by changes in day admissions.

The second robustness check involves modelling endogeneity using two-stage residual inclu-

sion estimation (column (3)). The projected increase in public cost is $36.24 million, and is also

considerably smaller than the reference case. As with the projections from the single equation

model, the expected increase in cost results only from changes in day admissions. The two

alternative estimation strategies produced price elasticity estimates that are very similar to the

simultaneous equation model.

7.2 Predicted premiums

As discussed in Section 4.2, the price of insurance is formulated using the observed premium

expenditure data for individuals who have private health insurance, and predicted premiums

for those who are not privately insured. As a robustness check, predicted premiums are used

for all observations in the sample to compute the insurance price. Using predicted premiums

(column (4)), public expenditure is projected to increase by $83.64 million. The expected cost

increase is lower because this model predicts that a smaller shift from private to public care for

both day and overnight admissions.

The implied price elasticity lie within the range -0.36 – -0.41 and is similar to that of the

reference case. In Section 4.2, it was suggested that the price elasticity estimates may be biased if

the price of insurance variable, formulated using observed premiums, omits plan characteristics

that are unobserved. It is worth emphasising that since the implied price elasticities from using

either observed or predicted premiums are similar, there is no indication of a significant bias.

7.3 Lifetime Health Cover

The last set of sensitivity check uses the approach adopted by Ellis and Savage (2008) to analyse

the impact of the Lifetime Health Cover policy. As shown in column (5), this approach produces

30

estimates of the price elasticities, and projections of cost increase that are very similar to the

reference case.

8 Discussion and conclusions

Policy incentives such as premium or tax rebates for duplicate private health insurance are often

justified based on the argument that private financing can relieve cost and capacity pressures on

the public system. This paper investigates the question of whether cost savings that are achieved

from reducing subsidies for private health insurance outweigh the potential increase in public

expenditure on hospital care in the context of the Australian health care system. The study

develops a microeconometric framework to analyse the effect of policy incentives on the decision

to buy private health insurance, and the effect of private insurance on the decisions of whether

to obtain hospital care from the public or private sector, and how much care to consume. The

econometric estimates are used in a simulation analysis to assess whether reducing premium

rebates on private health insurance in Australia is likely to generate net cost savings to the

public budget.

The econometric results indicate 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 estimates of the elasticity of demand for private insur-

ance are in the range of -0.32 to -0.35. The simulation projections show that reducing premium

subsidies is expected to generate net cost savings to the public budget. This result is obtained

in all 5 different simulation scenarios that are considered, and is robust to different methods

used to account for uncertainty in the projections. To illustrate, a 10 percent reduction in

rebates for instance is projected to lead to an increase in public expenditure that is either not

statistically different from zero, or substantially smaller than the cost savings achieved through

lower spending on premium subsidies.

The estimates of the price elasticity and the simulation results are mostly robust to different

approaches used to formulate the insurance price. For example, using predicted premiums in

placed of observed premiums, and accounting for entry-age rating through the Lifetime Health

Cover policy produce elasticity estimates that are very similar. Although the cost projections

31

from the simulation analysis vary slightly by the estimation strategies used to address potential

endogeneity problems, the conclusion that reducing subsidies generate cost savings remains

unchanged.

A question that naturally arises is whether the simulation results are driven primarily by

the inelastic demand for private insurance, or whether it is due to the differential rates of

hospital care use by the insured and uninsured groups. The simulation projections indicate

that the frequency of hospital admissions and the number of hospital nights remain unchanged

when the proportion of privately insured individuals decreases. This suggests that differences in

utilisation across the insured and uninsured groups are not the reason why cost savings occur.

It is also not the case that individuals continue to use private hospital services despite dropping

private health insurance cover. The inelastic demand is the main reason for the cost savings,

as only a small fraction of individuals are likely to respond to the higher prices for insurance

by dropping private health coverage. This conclusion is consistent with previous studies by

Emmerson et al. (2001) and Frech and Hopkins (2004), who both show that the price elasticity

needs to be substantially higher for private health insurance subsidies to be self-financing.

The estimates of the demand elasticity for private insurance obtained in this study is broadly

comparable with those from previous Australian studies. Butler (1999) for instance uses a

similar definition of the insurance price and obtained a price elasticity estimate of -0.44 for

hospital cover. This study is based on data that predates the policy reform when financial

incentives were introduced. It is conceivable that consumers are more responsive to price changes

back then, in the absence of the tax levy that penalises high income individuals without private

insurance. Frech III et al. (2003) use time series data and model the spike in private health

insurance coverage in the Australia population following the introduction of the 30 percent

rebate and obtained a price elasticity estimate of -0.37, which is very similar to those in this

study. In a recent study, Ellis and Savage (2008) use survey data from the post-reform period and

obtained elasticity estimates with respect to premiums of -0.6 for singles and -0.4 for families. In

this paper, using the method by Ellis and Savage (2008) to incorporate entry-age rating produces

elasticity estimates in the range of -0.33 to -0.36, which are quite similar to their estimate for

families. This is interesting to note that the estimates of the price elasticities for duplicate and

supplementary PHI are broadly comparable internationally (e.g. -0.5 in UK and Spain (King

32

and Mossialos 2005; Lopez Nicolas and Vera-Hernandez 2008), -0.4 to -0.49 in Canada (Stabile

2001, Finkelstein 2002)). Obviously, differences in definitions and empirical methods may limit

comparability. Notwithstanding, the slightly smaller elasticity estimates obtained in this paper

are likely due to the tax levy and the entry-age rating policy in Australia. What follows is that

individuals, particularly those with high incomes, would have considerable financial incentives

to take up or maintain private insurance cover even in the face of premium increases.

It is important to highlight that the results in this paper may not be generalisable, and do

not necessarily imply that reducing subsidies on private health insurance would generate cost

savings in other countries. This is because the Australian context is unique in that a series of

three different policy incentives exists to encourage individuals to buy private health insurance.

Reducing the premium subsidy may have little effect given that individuals would still have

considerable financial incentives to buy private health insurance because of the tax levy and

entry-age premium adjustments.

With further cost pressures on public health care budgets, interest in a greater role of

private financing is only likely to increase. Two follow-on questions that are open for further

research arise from this study. First, what are the alternative measures that are available to

policy makers seeking to expand the role of private financing? Second, how do these measures

compare in terms of their costs and effectiveness in achieving the stated health policy goals?

These are some important questions that would inform the debate surrounding the appropriate

roles and relative sizes of the public and private sectors for health care.

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36

010

0020

0030

0040

0050

00$

0 20−24 45−49 70−74 95+Age in years

NSW−M VIC−M QLD−M SA−M WA−MNSW−F VIC−F QLD−F SA−F WA−F

Figure 1: Expected annual hospital benefits by age, sex & states

37

Table 1: Private hospital insurance status and premiums by coverage and income unit types

Lone person Lone parent Couple only Couple family TotalInsurance statusNo hospital cover 789 (60.9%) 264 (71.9%) 1086 (43.7%) 1085 (44.9%) 3224 (49.1%)With hospital cover 507 (39.1%) 103 (28.1%) 1397 (56.3%) 1330 (55.9%) 3337 (50.9%)% Hospital only 22.7 17.5 23.2 17.1 20.5% Hospital & Ancillary 77.3 82.5 76.8 82.9 79.5

Premiums ($)Ancillary onlya 410.45 670.76 712.03 683.75Hospital only 751.95 894.39 1,261.79 1,345.17Hospital & Ancillary 1,095.72 1,549.65 1,766.07 1,939.09

Total 957.20 1,326.58 1,602.96 1,761.21

HES (2003-04)b 982.90 1,367.55 1,694.08 1,740.29a Individuals with ancillary only policies are not included in the analysis but shown here for comparison.b Source: Confidentialised Unit Record Files (CURF) from the Household Expenditure Survey (HES)2003-04. Derived from weekly household expenditure on ‘hospital, medical and dental insurance’.

Table 2: OLS regression of log annual expenditure on premiums

Variables Coeff Std Err.

Hospital & ancillary cover 0.310*** 0.025Family policy 0.575*** 0.023Couple-only policy 0.543*** 0.030Sole parent policy 0.198 0.184% of policy with excess 4.778*** 1.822% over 65 years 9.127*** 1.990Avg specialist fees (’00) 0.0045*** 0.00086Specialist density -0.923*** 0.253(Specialist density)2 0.0045** 0.0012Policy to employees ratio -0.035*** 0.013Constant 51.186*** 12.367

Number of obs. 3533Adjusted R-squared 0.201

38

Table 3: Summary statistics: hospital care utilisation measures

Frequency Day Overnight Hospital Private: Private:admissions admissions nights Day Overnight

Pr(y=0) 0.874 0.866 0.414 0.531Pr(y=1) 0.098 0.098 0.310 0.586 0.469Pr(y=2) 0.018 0.022 0.132Pr(y=3) 0.005 0.006 0.124Pr(y=4) 0.001 0.004 0.081Pr(y=5)a 0.001 0.002 0.104

Range 0-12 0-12 1-135 0-1 0-1Mean (y) 0.177 0.194 5.058Variance (S2

y) 0.406 0.372 65.930

S2y/y 2.283 1.919 13.035

N 6594 6594 881 800 881aFor brevity, only frequencies up to Pr(y=5) are presented for the count utilisation measure.

See ‘Range’ for information on all realisations.

39

Table 4: Descriptive statistics: explanatory variables (N=6594)

Variable Description Mean Std devInsurance price Log of insurance price -0.40 0.83Age Age 49.91 15.45Female Female (0/1) 0.54 0.50Couple Couple income unit (1/0) 0.75 0.43Depchild Have dependent children (1/0) 0.42 0.49Country of birth:Australia (Ref ) Person is born in Australia (0/1) 0.77 0.42Main English Person is born in main English speaking countries (0/1) 0.12 0.32Other Person is born in other countries (0/1) 0.11 0.31HH Income Annual household income ($ ‘000) 60.12 40.63Education Qualification (qual.):School (Ref ) Person’s highest qual. is Year 12 or below (0/1) 0.47 0.50Certificate Person’s highest qual. is a Certificate (0/1) 0.23 0.42Dipl/Adv Dipl Person’s highest qual. is a (Advanced) Diploma (0/1) 0.097 0.30Bach. and postgrad Person’s highest qual. is a degree or above(0/1) 0.21 0.41Occupation category:Unemploy (Ref) Not in employment (0/1) 0.40 0.49Manager/Admin Managers and Administrators (0/1) 0.063 0.24Professional Professionals (0/1) 0.24 0.43Clerical/Service Clerical and Service workers (0/1) 0.15 0.36Trades/Transport Trades, Production, Transport, Labourers (0/1) 0.15 0.36Self assessed health (SAH):Very Good/Excellent (Ref ) Person’s SAH in t-1 is excellent or very good (0/1) 0.45 0.50Good Person’s SAH in t-1 is good (0/1) 0.36 0.48Fair/Poor Person’s SAH in t-1 is fair or poor (0/1) 0.19 0.39Chronic health conditions (conds.):Work Limiting Conds. limit amount and type of work (0/1) 0.39 0.67Self Care Conds. causes difficulties with self care (0/1) 0.041 0.20Mobility Conds. causes difficulties with mobility activities (0/1) 0.086 0.28Communication Conds. causes difficulties with communication (0/1) 0.0080 0.089Alcohol daily Person drinks alcohol daily (0/1) 0.097 0.30Regular smoker Person is a regular smoker (0/1) 0.19 0.39State:NSW (Ref ) Person lives in New South Wales (0/1) 0.29 0.45VIC Person lives in Victoria (0/1) 0.25 0.43QLD Person lives in Queensland (0/1) 0.21 0.41SA Person lives in South Australia (0/1) 0.091 0.29WA Person lives in Western Australia (0/1) 0.10 0.30TAS/NT Person lives in Tasmania or Northern Territory (0/1) 0.039 0.19ACT Person lives in the Australian Capital Territory (0/1) 0.017 0.13Remoteness:Major cities (Ref ) Person resides in major cities (0/1) 0.58 0.49Inner region Person resides in inner regional areas (0/1) 0.28 0.45Other Person resides in outer regional and (very) remote (0/1) 0.15 0.35Headcount Number (’000) of persons working in the health and general 0.80 1.89

insurance industry (respondents’ residential local area)Distance Euclidian distance (in km) to the nearest private hospital 30.30 90.18

40

Table 5: Goodness of fit statistics

Variables Day Overnight Hospital Private patient: Private patient: Private healthadmissions admissions nights Day Overnight insurance

– Simultaneous Equation –CCR 76.69% 75.45% 11.0% 87.13% 86.04% 71.57%RMSPE 0.75 0.74 7.99MAPE 0.29 0.32 3.70

– Single Equation –CCR 76.58% 75.28% 12.83% 84.40% 87.06% 71.58%RMSPE 0.74 0.74 7.80MAPE 0.29 0.31 3.52Note: CCR: Correct classification ratio.

RMSPE : Root mean square prediction error.MAPE : Mean absolute prediction error.

Table 6: Marginal effect of private insurance on hospital use and public/private choice.

(1) (2)Variables Simultaneous Single

Equation Equation

Day admissions 1.317 1.270**(0.640) (0.115)

Overnight admissions 1.094 1.210**(0.357) (0.101)

Hospital nights: private patients a 1.616 2.422**(0.578) (0.558)

Private patient: Day admissionb 0.779*** 0.732***(0.132) (0.031)

Private patient: Overnight admissionb 0.555*** 0.746***(0.171) (0.027)

*** p < 0.01, ** p < 0.05, * p < 0.1. Standard errors in parenthesis.

Note: For count outcomes, test for statistical significance from the null hypothesis that the

marginal effect, which is interpreted as a proportional change in the expected outcome,

is equal to 1. For binary outcomes, marginal effect is the change in the expected probability

of the event occurring.

aLength of overnight stay for private patients in the last admission episode.bAdmitted as private patient in the last day/overnight admission.

41

Tab

le7:

Sim

ulatingreductionsin

premium

rebates

onhospital

use

(Sim

ultan

eousEquation).

N=

1000

0%

△in

premium

rebate

(1)

(2)

(3)

(4)

(5)

Baseline

-5%

-10%

-15%

-20%

-25%

Pan

elA:Number

ofday

andovernightad

mission

s%

withprivate

hospital

insurance

52.37

51.99

51.61

51.26

50.90

50.56

%chan

ge-0.73%

-1.45%

-2.13%

-2.80%

-3.46%

[-1.03

,-0.52

][-1.85

,-1.09

][-2.64

,-1.70

][-3.42

,-2.28

][-4.18

,-2.81]

%chan

gein

day

admission

s0.18

-0.13%

-0.27%

-0.39%

-0.52%

-0.64%

[-8.75

,11.87

][-8.82

,12.17

][-8.88

,12.48

][-8.94

,12.84

][-8.99

,13.07]

%chan

gein

overnightad

mission

s0.21

-0.03%

-0.06%

-0.09%

-0.12%

-0.15%

[-7.54

,9.01]

[-7.64

,8.96]

[-7.67

,9.07]

[-7.71

,9.16]

[-7.74

,9.11]

Pan

elB:Public-private

choice:day

admission

N(D

ayad

mission

)=

1144

%withprivate

hospital

insurance

52.37

51.99

51.61

51.26

50.91

50.57

%chan

ge-0.73%

-1.44%

-2.13%

-2.79%

-3.43%

[-1.00

,-0.52

][-1.85

,-1.13

][-2.60

,-1.72

][-3.42

,-2.31

][-4.11

,-2.85]

%private

patient:

day

admission

59.81

59.50

59.22

58.90

58.60

58.32

%chan

ge-0.52%

-0.97%

-1.53%

-2.02%

-2.49%

[-1.21

,-0.04

][-1.79

,-0.18

][-2.67

,-0.62

][-3.25

,-0.91

][-3.83

,-1.35]

Pan

elC:Public-private

choice

&lengthof

stay

:Overnightad

mission

N(O

vernightad

mission

)=

1276

%withprivate

hospital

insurance

52.37

51.98

51.61

51.24

50.89

50.53

%chan

ge-0.75%

-1.46%

-2.16%

-2.84%

-3.50%

[-1.03

,-0.52

][-1.87

,-1.09

][-2.75

,-1.72

][-3.55

,-2.26

][-4.32

,-2.85]

%private

patient:

overnightad

mission

46.94

46.70

46.49

46.26

46.04

45.85

%chan

ge-0.50%

-0.97%

-1.46%

-1.92%

-2.33%

[-1.17

,-0.00

2][-2.17

,-0.17

][-2.67

,-0.17

][-3.67

,-0.34

][-4.34

,-0.34]

%chan

gein

hospital

nights:publicpatient

5.97

0.01

%0.04

%0.06

%0.09

%0.10

%[-20

.80,26

.88]

[-20

.79,27

.17]

[-20

.79,27

.35]

[-20

.81,27

.45]

[-20

.98,27

.31]

%chan

gein

hospital

nights:private

patient

4.09

-0.06%

-0.12%

-0.20%

-0.26%

-0.32%

[-17

.09,18

.62]

[-17

.06,18

.72]

[-17

.21,18

.08]

[-17

.36,18

.02]

[-17

.42,17

.34

Note:95%

confiden

ceintervals

inparenth

esis

basedon2.5

and97.5

percentilesofth

edistribution.

42

Tab

le8:

Predictedim

pacton

publichospital

use

andexpen

diture.

(1)

(2)

(3)

(4)

(5)

Percentage

chan

gein

premium

rebates

Baseline

-5%

-10%

-15%

-20%

-25%

(A)

Expenditure

onpublichospitals($

mil.)

12,794

a12

,851

12,902

12,959

13,012

13,058

[11,95

7,13

,717

][12,00

2,13

,763

][12,06

4,13

,858

][12,14

1,13

,928

][12,192,139655]

(A1)

Chan

gein

expenditure

($mil.)

56.84

108.76

165.55

218.15

264.83

[-83

6.62

,92

3.01

][-79

1.31

,96

9.55

][-72

9.47

,1,06

4.66

][-65

2.61

,11

34.71]

[-601.54,1,171.56]

(A2)

Percentage

chan

ge0.44

%0.85

%1.29

%1.71

%2.07%

[-6.54

,7.21

][-6.19

,7.58

][-5.70

,8.32

][-5.10

,8.87

][-4.70,9.16]

(B)

Chan

gein

publicexpenditure

149.25

298.50

447.75

597.00

746.25

onrebates

($mil.)

(C)

Net

effecton

publicexpenditure

($mil.)

-92.41

-189

.74

-282

.20

-378

.85

-481.42

[(C)=

(A1)

-(B

)]

Note:95%

confiden

ceintervals

inparenth

esis.

aThebaselineestimate

ofth

etotalrecu

rren

tex

pen

diture

onpublicinpatien

tca

reis

calculatedbymultiplyingth

etotalrecu

rren

tex

pen

diture

onpublichosp

itals

byth

eadmittedpatien

tco

standpublicpatien

tdayproportions($21,758milX

0.7

X0.84=

$12,794mil).

43

Tab

le9:

Predictedim

pacton

publichospital

utilisation

andexpen

diture

(excludingstatisticallyinsign

ificantsimulatedou

tcom

es).

(1)

(2)

(3)

(4)

(5)

Percentage

chan

gein

premium

rebates

Baseline

-5%

-10%

-15%

-20%

-25%

(A)

Expenditure

onpublichospitals($

mil.)

12,794

a12

,859

12,919

12,983

13,043

13,098

[12,80

1,12

,924

][12,82

8,13

,033

][12,85

7,13

,118

][12,88

6,13

,194

][12,907,13,265]

(A1)

Chan

gein

expenditure

($mil.)

64.90

124.82

189.49

249.83

304.23

[7.47,

130.77

][33.83

,23

8.97

][63.01

,32

4.16

][92.47

,40

0.64

][113

.00,471.16]

(A2)

Percentage

chan

ge0.51

%0.98

%1.48

%1.95

%2.38%

[0.06,

1.02

][0.26,

1.87

][0.49,

2.53

][0.72,

3.13

][0.88,3.68]

(B)

Chan

gein

publicexpenditure

149.25

298.50

447.75

597.00

746.25

onrebates

($mil.)

(C)

Net

effecton

publicexpenditure

($mil.)

-84.35

-173

.68

-258

.26

-347

.17

-442.02

[(C)=

(A1)

-(B

)]

Note:95%

confiden

ceintervals

inparenth

esis.

aThebaselineestimate

ofth

etotalrecu

rren

tex

pen

diture

onpublicinpatien

tca

reis

calculatedbymultiplyingth

etotalrecu

rren

tex

pen

diture

onpublichosp

itals

byth

eadmittedpatien

tco

standpublicpatien

tdayproportions($21,758milX

0.7

X0.84=

$12,794mil).

44

Tab

le10:Rob

ustnesscheck-expectedcost

andprice

elasticity

from

a10

percentreductionin

premium

rebates

($mil.)

Specification

sa(1)

(2)

(3)

(4)

(5)

Sim

ultan

eous

Single

2SRI

Predicted

LHC

Equation

Equation

Premiums

Loa

ding

Chan

gein

expenditure

(%)

124.82

(0.98)

38.61(0.30)

36.24(0.28)

83.64(0.65)

126.29

(0.99)

[33.83

,23

8.97

][11.14

,71

.81]

[5.52,

76.63]

[11.50

,17

5.81

][54.06

,23

1.34

]

Implied

insurance

elasticity

(–)

0.32

–0.35

0.31

–0.34

0.32

–0.35

0.36

–0.41

0.33

–0.36

Note:Theabovesetofco

stpro

jectionsusesonly

simulatedoutcomes

thatare

statisticallysignifica

nt.

aThesp

ecifica

tionsco

nsidered

are

asfollows:

(1)Sim

ulatedeff

ects

from

simultaneo

useq

uationmodel

(cf.

Table

9).

(2)Single

equation(cf.

Table

B.3)

(3)Usingtw

o-stageresidualinclusion(2SRI)

approach

toaccountforen

dogen

eity

ininsu

rance

andadmissiontypebinary

variables.

(4)Usingpredictedpremiumsto

constru

ctinsu

rance

price.

(5)Premium

loadingunder

Lifetim

eHea

lthCover

inaccord

ance

withEllis

andSavage(2008).

45

A Likelihood functions

Demand for day and overnight hospital admissions (cf Section 3.1)

ℓi1(Θ1) =

∫ +∞

−∞

∫ +∞

−∞f(my

i |Xi1, di, εi1) · f(movi |Xi2, di, ρε1ε2, εi1, ζi)

·

[diΦ

(X ′i3β3 + θ1θ2

)+ (1− di)

(1− Φ

(X ′i3β3 + θ1θ2

))]ϕ(ζi)ϕ(εi1)dζidεi1

(A.1)

where

θ1 =ρ13εi1 +(ρε2ε3 − ρε1ε2ρε1ε3√

1− ρ2ε1ε2

)ζi

θ2 =

√(1− ρ2ε1ε3)−

(ρε2ε3 − ρε1ε2ρε1ε3)2

1− ρ2ε1ε2

and Θ1 is the set of parameters to be estimated.

Admission type choice for day hospital admission (cf Section 3.2)

ℓi2(Θ2) = Hdi · Φ2

[yi1(Z

′i1α1 + δdi), yi2(Z

′i2α2), yi1yi2ρv

]+ (1−Hdi) · Φ

[y2i(Z

′i2α2)

](A.2)

where Hdi = 1 if the i -th individual has been hospitalised for a day admission and 0 otherwise;

Θ2 is the set of parameters to be estimated; Φ and Φ2 denote the univariate and bivariate

normal cumulative density functions respectively.

Admission type choice and length of hospital stay for overnight admission (cf

Section 3.3)

ℓi3(Θ3) = Hoi ·∫ +∞

−∞f(sti |Wi1, qi, di, ξi1) · Φ2[y1iθ3, y2iθ4, ρ

∗]ϕ(ξi1)dξi1 + (1−Hoi) · Φ[y2i(W3iγ)]

(A.3)

46

with

θ3 =Wi2γ2 + ψ3di + ρξ1ξ2ξi1

(1− ρ2ξ1ξ2)1/2

θ4 =Wi3γ3 + ρξ1ξ3ξi

(1− ρ2ξ1ξ3)1/2

ρ∗ =y1i · y2i ·(ρξ2ξ3 − ρξ1ξ2ρξ1ξ3)√1− ρ2ξ1ξ2

√1− ρ2ξ1ξ3

where Hoi = 1 if the i-th individual has been hospitalised overnight and 0 otherwise; Θ3 is the

set of all unknown parameters to be estimated; and y1i = 2qovi − 1 and y2i = 2di − 1.

47

B Coefficient estimates & Sensitivity Analysis

Table B.1: Model estimates: demand for hospital admissions and choice of private care for dayadmissions

Hospital admissions Private day admission(1) (2) (3) (4) (5)

Variable Day Overnight Private health Private patient: Private healthadmission admission insurance Day insurance

Insurance Price -0.476*** -0.478***(0.035) (0.034)

Insurance 0.276 0.090 2.474***(0.486) (0.242) (0.703)

Age 0.0035 -0.111*** -0.023(0.018) (0.015) (0.026)

(Age)2 4.92e-06 0.0010*** 0.00025(0.00016) (0.00014) (0.00024)

Female 0.264*** 0.206** -0.236*(0.084) (0.081) (0.134)

Couple 0.102 0.074 -0.082(0.100) (0.097) (0.153)

Depchild -0.199** 0.074 -0.182(0.099) 0.097) (0.161)

Country of birth:Main English 0.104 0.139 -0.300*** -0.178 -0.305***

(0.137) (0.113) (0.060) (0.198) (0.060)

Other -0.162 -0.079 -0.240*** -0.184 -0.241***(0.135) (0.124) (0.064) (0.198) (0.064)

Education:Certificate 0.097 0.040 0.051 0.012 0.057

(0.096) (0.101) (0.043) (0.180) (0.042)

Dipl/Adv Dipl. 0.149 -0.062 0.250*** 0.553*** 0.253***(0.139) (0.137) (0.060) (0.225) (0.060)

Bach. and postgrad. 0.131 0.102 0.300*** -0.048 0.301***(0.124) (0.116) (0.056) (0.192) (0.056)

HH Income 0.0048 0.0014 0.014*** 0.0052 0.013***(0.0039) (0.0032) (0.0016) (0.0065) (0.0015)

(HH Income)2 -1.33e-05 1.71e-05 -4.46e-05*** -1.54e-05 -4.38e-05***(1.47e-05) (1.22e-05) (8.32e-06) (2.80e-05) (7.87e-06)

Occupation:Manager/Admin -0.366* -0.664*** 0.598*** -0.027 0.595***

(0.204) (0.202) (0.090) (0.335) (0.090)

Professional -0.535*** -0.568*** 0.319*** 0.281 0.318***(0.130) (0.126) (0.057) (0.206) (0.057)

Clerical/Service -0.299** -0.662*** 0.207*** -0.025 0.207***(0.130) (0.138) (0.059) (0.203) (0.059)

Trades/Transport -0.554*** -0.762*** -0.130** -0.104 -0.134**(0.151) (0.162) (0.058) (0.244) (0.058)

Continued on next page

48

Table B.1– continued from previous page(1) (2) (3) (4) (5)

Variable Day Overnight Private health Private patient: Private healthadmission admission insurance Day insurance

Self assessed health:Good 0.212** 0.285*** 0.044 -0.148 0.045

(0.089) (0.091) (0.040) (0.141) (0.040)

Fair/Poor 0.642*** 0.793*** -0.151*** -0.229 -0.150***(0.117) (0.112) (0.055) (0.171) (0.055)

Health conditions:Work Limiting 0.292*** 0.379*** 0.0142 0.129 0.014

(0.054) (0.053) (0.028) (0.093) (0.028)

Self Care 0.436** 0.383** -0.093 -0.156 -0.099(0.181) (0.150) (0.098) (0.247) (0.082)

Mobility Activities -0.011 0.257** -0.091 0.043 -0.082(0.149) (0.127) (0.071) (0.214) (0.072)

Communication Diff. -0.124 0.077 -0.211 -1.332** -0.222(0.414) (0.295) (0.198) (0.592) (0.198)

Alcohol daily 0.169 -0.023 0.149** 0.487** 0.154***(0.128) (0.134) (0.062) (0.210) (0.062)

Regular smoker -0.155 -0.0045 -0.482*** 0.089 -0.485***(0.134) (0.111) (0.050) (0.206) (0.050)

State:VIC 0.386*** 0.153 0.123** -0.063 0.125**

(0.105) (0.103) (0.058) (0.2+2) (0.058)

QLD 0.217* 0.150 -0.075 0.337* -0.069(0.112) (0.110) (0.063) (0.179) (0.064)

SA 0.321** 0.303** 0.252*** 0.209 0.264***(0.143) (0.140) (0.080) (0.241) (0.081)

WA 0.097 0.186 0.231*** 0.279 0.233***(0.147) (0.134) (0.076) (0.262) (0.076)

TAS/NT 0.451** -0.413* -0.049 0.578** -0.040(0.188) (0.213) (0.117) (0.267) (0.117)

ACT 0.397 0.420 0.114 -0.422 0.111(0.285) (0.291) (0.189) (0.391) (0.189)

Remoteness:Inner regional 0.0080 0.305*** -0.038 -0.368** -0.041

(0.093) (0.090) (0.057) (0.160) (0.057)

Other0.127 0.242* -0.038 -0.327 -0.044(0.117) (0.115) (0.096) (0.247) (0.096)

Headcount 0.138*** 0.139***(0.038) (0.038)

(Headcount)2 -0.016*** -0.016***(0.0038) (0.0038)

Distance -0.157* -0.090 -0.153*(0.085) (0.230) (0.086)

(Distance)2 0.015 0.014 0.014(0.011) (0.027) (0.011)

Constant -3.737*** -0.409 -0.844*** -0.602 -0.847***Continued on next page

49

Table B.1– continued from previous page(1) (2) (3) (4) (5)

Variable Day Overnight Private health Private patient: Private healthadmission admission insurance Day insurance(0.521) (0.445) (0.082) (0.742) (0.081)

σ 1.291*** 1.247***(0.046) (0.049)

Correlationρε1ε2 0.440***

(0.073)

ρε1ε3 -0.012(0.236)

ρε2ε3 0.059(0.121)

ρv -0.153(0.498)

Loglikelihood -9111.45 -4004.52

Number of observations 6594 6594*** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors in parenthesis, clustered at household level.

50

Table B.2: Model estimates: demand for hospital stay, choice of private patient and privateinsurance

Overnight hospital stay(1) (2) (3)

Variable Hospital Private patient: Private healthnights Overnight insurance

Insurance Price -0.479***(0.034)

Insurance -0.462 1.538***(0.339) (0.587)

Private Pat. -0.855**(0.369)

Insurance X Private Pat. 0.942***(0.287)

Age -0.043** -0.0099(0.018) (0.025)

(Age)2 0.00051*** 0.00023(0.00018) (0.00022)

Female 0.073 -0.027(0.094) (0.118)

Couple 0.0049 -0.140(0.110) (0.132)

Depchild 0.393*** -0.248(0.139) (0.174)

Country of birth:Main English 0.070 -0.280* -0.303***

(0.131) (0.167) (0.060)

Other 0.194 -0.515*** -0.240***(0.134) (0.180) (0.064)

Education:Certificate 0.133 -0.018 0.052

(0.107) (0.152) (0.042)

Dipl/Adv Dipl. 0.155 0.152 0.252***(0.156) (0.215) (0.060)

Bach. and postgrad. 0.059 -0.052 0.299***(0.131) (0.179) (0.055)

HH Income -0.0015 0.011* 0.013***(0.0033) (0.0056) (0.0015)

(HH Income)2 1.63e-05 -1.02e-05 -4.39e-05***(1.34e-05) (2.96e-05) (7.83e-06)

Occupation:Manager/Admin -0.419* 0.107 0.600***

(0.1235 (0.286) (0.090)

Professional -0.278** 0.597*** 0.321***(0.139) (0.177) (0.057)

Clerical/Service -0.202 0.077 0.209***(0.153) (0.208) (0.059)

Trades/Transport 0.013 0.038 -0.127**(0.190) (0.289) (0.058)

Continued on next page

51

Table B.2– continued from previous page(1) (2) (3)

Variable Hospital Private patient: Private healthnights Overnight insurance

Self assessed health:Good -0.033 0.021 0.044

(0.112) (0.145) (0.040)

Fair/Poor 0.179 -0.164 -0.155***(0.126) (0.168) (0.055)

Health conditions:Work Limiting 0.102 0.157* 0.016

(0.062) (0.086) (0.028)

Self Care 0.203* -0.0099 -0.096(0.150) (0.224) (0.098)

Mobility Activities -0.086 0.069 -0.095(0.120) (0.175) (0.072)

Communication Diff. -0.134 -0.602 -0.259(0.202) (0.455) (0.194)

Alcohol daily 0.117 0.050 0.147**(0.128) (0.194) (0.062)

Regular smoker -0.224* -0.466*** -0.486***(0.120) (0.163) (0.050)

State:VIC -0.063 -0.074 0.122**

(0.112) (0.157) (0.058)

QLD -0.176 0.042 -0.075(0.122) (0.160) (0.063)

SA -0.148 0.192 0.252***(0.140) (0.184) (0.080)

WA -0.085 0.198 0.230***(0.156) (0.213) (0.076)

TAS/NT 0.120 -0.135 -0.056(0.183) (0.295) (0.116)

ACT -1.047*** -0.221 0.113(0.375) (0.318) (0.189)

Remoteness:Inner regional 0.067 -0.270* -0.040

(0.093) (0.142) (0.057)

Other 0.052 -0.681*** -0.045(0.120) (0.258) (0.095)

Headcount 0.135***(0.037)

(Headcount)2 -0.015***(0.0038)

Distance 0.542** -0.149*(0.241) (0.085)

(Distance)2 -0.075** 0.015(0.031) (0.011)

Constant 1.620*** -1.445** -0.849***(0.520) (0.736) (0.080)

Continued on next page

52

Table B.2– continued from previous page(1) (2) (3)

Variable Hospital Private patient: Private healthnights Overnight insurance

σ 0.989***(0.044)

ρξ1ξ2 0.167(0.151)

ρξ1ξ3 0.328***(0.137)

ρξ2ξ3 0.475(0.347)

Loglikelihood -6114.97

Number of observations 6594*** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors in parenthesis,

clustered at household level.

53

Tab

leB.3:Sim

ulatingreductionsin

premium

rebates

onhospital

use

(SingleEquation).

N=

1000

0%

△in

premium

rebate

(1)

(2)

(3)

(4)

(5)

Baseline

5%10

%15

%20

%25

%Pan

elA:Number

ofday

andovernightad

mission

s%

withprivate

hospital

insurance

52.80

52.42

52.05

51.69

51.33

51.00

%chan

ge-0.72%

-1.41%

-2.10%

-2.77%

-3.41%

[-0.97

,-0.49

][-1.81

,-1.08

][-2.52

,-1.67

][-3.31

,-2.27

][-4.05

,-2.80]

%chan

gein

day

admission

s0.18

-0.09%

-0.18%

-0.27%

-0.36%

-0.45%

[-8.97

,10.51

][-9.07

,10.39

][-9.16

,10.21

][-9.23

,10.07

][-9.33

,9.96]

%chan

gein

overnightad

mission

s0.22

-0.07%

-0.13%

-0.20%

-0.26%

-0.32%

[-8.10

,7.92]

[-8.16

,7.82]

[-8.21

,7.79]

[-8.26

,7.75]

[-8.32

,7.73]

Pan

elB:Public-private

choice:day

admission

N(D

ayad

mission

)=

1144

%withprivate

hospital

insurance

52.80

52.42

52.05

51.69

51.33

51.00

%chan

ge-0.73%

-1.43%

-2.11%

-2.78%

-3.41%

[-1.01

,-0.49

][-1.78

,-1.06

][-2.58

,-1.69

][-3.30

,-2.27

][-3.96

,-2.79]

%private

patient:

day

admission

59.84

59.54

59.26

58.97

58.70

58.45

%chan

ge-0.49%

-0.97%

-1.45%

-1.90%

-2.32%

[-1.10

,-0.00

][-1.79

,-0.28

][-2.21

,-0.56

][-2.90

,-0.83

][-3.46

,-1.11]

Pan

elC:Public-private

choice

&lengthof

stay

:Overnightad

mission

N(O

vernightad

mission

)=

1276

%withprivate

hospital

insurance

52.80

52.49

52.13

51.79

51.44

51.12

%chan

ge-0.72%

-1.41%

-2.06%

-2.71%

-3.33%

[-2.66

,1.10]

[-3.34

,0.44]

[-4.04

,-0.28

][-4.64

,-0.98

][-5.40

,-1.60]

%private

patient:

overnightad

mission

45.98

45.74

45.51

45.27

45.06

44.85

%chan

ge-0.53%

-1.02%

-1.55%

-2.00%

-2.46%

[-5.78

,5.64]

[-6.25

,5.16]

[-6.57

,4.52]

[-7.19

,3.89]

[-7.51

,3.26]

%chan

gein

hospital

nights:publicpatient

4.92

-0.05%

-0.10%

-0.15%

-0.19%

-0.23%

[-11

.77,13

.80]

[-11

.89,13

.80]

[-11

.87,13

.56]

[-11

.89,13

.54]

[-11

.76,13

.38]

%chan

gein

hospital

nights:private

patient

4.81

-0.13%

-0.25%

-0.40%

-0.53%

-0.66%

[-11

.79,13

.76]

[-11

.81,13

.58]

[-11

.99,13

.41]

[-12

.13,13

.26]

[-12

.32,13

.01

Note:95%

confiden

ceintervals

inparenth

esis

basedon2.5

and97.5

percentilesofth

edistribution.

54