Opt Out or Top Up? Voluntary Health Care Insurance and the Public vs. Private Substitution

Published date01 February 2016
AuthorChiara Monfardini,Daniele Fabbri
Date01 February 2016
DOIhttp://doi.org/10.1111/obes.12107
75
©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 78, 1 (2016) 0305–9049
doi: 10.1111/obes.12107
Opt Out or Top Up? Voluntary Health Care Insurance
and the Public vs. Private Substitution*
Daniele Fabbri and Chiara Monfardini
Dipartimento di Scienze Economiche, Universit`a di Bologna, Bologna, Italy (e-mail:
d.fabbri@unibo.it; chiara.monfardini@unibo.it)
Abstract
We investigate whether in a mixed insurance system, people enrolled into voluntary health
care insurance (VHI) substitute public consumption with private (opt out) or just enlarge
their private consumption without reducing reliance upon public provisions (top up). We
specify a joint model for public and private specialist visits counts, allowing for different
degrees of endogenous supplementary insurance coverage.We find evidence of opting out:
richer and wealthier individuals consume more private services and concomitantly reduce
those services publicly provided through selection into for-profitVHI. Accounting for VHI
endogeneity in the joint model of the two counts is crucial to this conclusion.
I. Introduction
It has been noticed that when there are limits to redistribution policy, instruments that help
to sort income classes become useful. In this line of reasoning, Besley and Coate (1991)
argue that the public provision of health care can work as a redistributive device whenever
low-income citizens choose the publicly provided good while high-income citizens, who
contribute to subsidizing the public supply through income taxes, opt out to the private sec-
tor. Voluntary Healthcare Insurance (VHI) might strengthen the redistributive role played
by Statutory Healthcare Insurance plan (SHI), as far as richer individuals are also more
inclined to buy supplementary health insurance, thus, being less cost conscious when they
consume private health care supplements. That being the case, relaxing regulations on ac-
cess to VHI and introducing tax deductions and incentives to buy supplementary coverage
might ease the process.
We investigate this issue in Italy, where a prominent share of the health care supply
is publicly provided by the National Health Service (NHS) and about 10% is enrolled in
not-for-profit (NFP) VHI whileabout 11% of the population subscribes more complete and
expensive for profit (FP) VHI plans. Our research question is whether people enrolled into
the two different VHI plans substitute public consumption with private (i.e. opt out) or,
JEL Classification numbers: C35, H44, I11
*Weare grateful to Francesca Barigozzi, Partha Deb, Simona Grassi, Astrid Kiil,Thomas Lifkin, Owen O’Donnell,
Pravin Trivedi and par ticipants of seminars in Lausanne, Darmstadt and Ithaca (ASHE-2010) for useful comments
and suggestions. Usual disclaimers apply.
76 Bulletin
TABLE 1
Specialists visits & insurance status in our case study
Average# of visits % of positives
Insurance status Public Private Total Public Private Total
NO VHI 0.079 0.057 0.136 5.8% 4.3% 9.6%
NFP VHI only 0.067 0.066 0.132 5.3% 5.2% 9.9%
FP VHI 0.054 0.083 0.137 4.0% 6.2% 9.5%
ALL 0.075 0.061 0.136 5.5% 4.6% 9.6%
Semi-elasticity
NFP VHI only 17.4* 14.1 3.09.0 17.6* 3.7
FP VHI 38.2*** 37.6*** 0.7 36.7*** 36.9*** 0.5
Notes: ***, **, * denotes significance levels at 1, 5 and 10% respectively.
†Percentagechange in expected consumption for being covered by each class ofVHI estimated with no controls
and under exogeneity.
Source: Elaborations on our sample from ‘Indagine Statistica Multiscopo sulle Famiglie: condizioni di salute
e ricorso ai servizi Sanitari 1999–2000’.
alternatively, they just enlarge their private consumption without reducing reliance upon
public provisions, (i.e. top up).Table 1 describes the relationship between insurance status
and health care consumption as measured by specialists visits in Italy. While the overall
consumption is homogenous across insurance status, we observe a different public vs.
private composition: the larger is coverage, the lower is reliance upon public provision and
concomitantly larger is the use of privately supplied visits.
Despite its relevance for normative and positive models of the public provision of
health care (recently surveyed by Pita Barros and Siciliani, 2012), empirical evidence
about the impact of health care insurance status on the public vs. private health care service
substitution is underprovided in the literature. A notable example is the contribution by
opez Nicol´asand Vera-Hern´andez (2008) exploring the self-financing nature of subsidies
for VHI plans in Spain (see Cheng, 2014, for a recent exploration on the same issue
in Australia). They estimate simultaneous discrete choice models for the polychotomous
decision to rely upon alternative combinations of public and private health care services
and for the binary decision to hold a private insurance. According to this contribution,
the doubly insured do rely more upon private GPs and specialists while access to public
alternatives is unaffected, thus being supportive of the top up explanation.
Motivated by the evidence from the Italian case study and by its key institutional fea-
tures, we develop here a general model for the joint determination of counts for public and
private health care visits that also accounts for the endogeneity of health insurance status
and considers different degrees of supplementary insurance coverage. The resulting mod-
elling framework is a simultaneous equation system with trinomial endogenous treatment.
This represents a contribution to the literature on count data models which has either devel-
oped methods to address the endogeneity of a multinomial treatment in a single equation
approach (see Deb and Trivedi, 2006, for a simulation based classical estimation approach;
Munkin and Trivedi, 2008, for a Bayesian analysis) or has jointly specified multiple equa-
tions sharing a common binary endogenous variable (see Zimmer and Trivedi, 2006, for a
Copula based estimation; Cheng and Vahid, 2010, for a simulation-based classical estima-
tion approach; Shen, 2013, for a semiparametric analysis). Our generalization to multiple
©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd

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