Age and Choice in Health Insurance:
Evidence from Switzerland
Karolin Becker und Peter Zweifel
Socioeconomic Institute, University of Zurich
[email protected]
ARIA Annual Meeting
Washington DC, 6-9 August, 2006
Motivation
• Rising health care expenditure due to more ample
coverage in compulsory health insurance  higher
premiums for health insurance
• Expansion of benefits in1996  increasing welfare
loss due to uniformity in the presence of preference
heterogeneity (Cutler and Zeckhauser, 1997)
• Political debate focuses on the cost side.
• Here, issues relate to the benefit side:
...what is the compensation asked by Swiss
consumers for accepting more stingy contracts?
... Will such new options not be rejected by the
elderly in particular?
Socioeconomic Institute
University of Zürich
Age and Choice Behavior
3 Hypotheses
H1: increased variance in asset "health" caused by
health problems  demand for comprehensive
coverage increases with age (Arrow, 1973)
H2: demand for health insurance follows the value of life
over the life cycle  demand for coverage
decreases beyond the age of ca. 40 (Shepard and
Zeckhauser, 1984)
H3: transition to retirement causes transitory reduction in
variance of "health" and in value of life  demand
for coverage decreases
Socioeconomic Institute
University of Zürich
Discrete Choice Experiments (1)
• Allows individuals to express preferences for nonmarketed goods
• Is based on the Random Utility Model (Luce, 1959;
Manski and Lerman 1977; McFadden, 1973 and 2001)
– individuals choose alternative with the highest
utility (hypothetical choice)
– choices are deterministic, but the researcher
cannot observe all determinants of utility
Socioeconomic Institute
University of Zürich
Discrete Choice Experiments (2)
• Comparison of utility values determined by indirect
utility function (i=individual, j=product alternative)
Vij  v j ( p j , b j ; y i , si , ij )
• choice between alternatives j and 
Pij  Pr{ v j [ p j , b j , y i , s i ,  ij ]  v l [ pl , bl , y i , s i ,  il ] }
• decomposition into a stochastic and a deterministic part
Pij  Pr { il   ij  w j [ p j , b j , y i , s i ]  w l [ pl , bl , y i , s i ]}
Socioeconomic Institute
University of Zürich
Setup of the Study (1)
• Sample of 1000 Swiss residents (older than 24)
• Telephone survey (two contacts)
– questions on utilization of the health system and
socioeconomic variables
– DCE: 10 choices per individual
(status quo vs hypothetical alternative)
• Attributes considered:
–
–
–
–
–
–
annual deductible (deduct)
copayment rate (copay)
alternative treatment methods (altmed)
list of medications (generics)
restricted access to innovations (innovation)
monthly premium per capita (premium)
Socioeconomic Institute
University of Zürich
Setup of the Study (2)
example of a choice card
status quo insurance contract
alternative contract
deductible: CHF 230 ($177)
deductible: CHF 1500 ($1155)
copayment: 10%
copayment: 10%
alternative medicine (status quo)
fewer treatments are covered
generics (status quo)
status quo
innovation (status quo)
access to innovative treatments
with delay of 2 years
premium: CHF 290/month
premium reduction - CHF 50
Which of these contracts would you choose?
My current contract •
Socioeconomic Institute
University of Zürich
This alternative contract •
Estimation strategy
• Random-effects Probit specification
• Model 1: Serves to check for the relevance of
attributes
simple model, only product attributes included
• Model
2: Designed
to relevant
capture socioeconomic
age-specific effects
controlling
for all
variables (interaction terms)
Socioeconomic Institute
University of Zürich
Results
• Derive marginal willingness-to-pay (WTP) for Model 1
MWTP : 
v i /b j
v i /premium j
marginal WTP
(in CHF)
deductible
standard errors
(bootstrapped)
-0.03205
0.01099
copayment
-18.91
3.30448
alt.med.
(+coverage)
12.36
3.01507
generics
-13.77
3.14571
innovation
-38.39
3.36486
Socioeconomic Institute
University of Zürich
Table 1a: Random-effects Probit estimation results (selected interactions)
coefficient
s.e.
zvalue
deduct
-0.00085
0.00012
-6.87
deduct2
1.12e-07
3.17e-08
3.53
copay
-0.33744
0.18329
-1.87
alt.med.
0.28399
0.18338
1.55
generics
-0.07629
0.17453
-0.44
innovation
-0.00488
0.21739
-0.02
premium
-0.01508
0.00273
-5.53
constant
-0.87395
0.23906
-3.66
 =0.91*, = 0.45*
Log likelihood: -2964
n=9,334
Socioeconomic Institute
University of Zürich
Table 1b: Random-effects Probit estimation results (selected interactions)
coefficient
s.e.
zvalue
deduct*sexm
0.00015
0.00006
2.34
deduct*a63+
0.00020
0.00010
1.93
deduct*rich
0.00028
0.00009
3.07
deduct*poor
-0.00027
0.00011
-2.54
-1.63e-08
7.51e-09
-2.16
copay*a63+
0.26306
0.13380
1.97
copay*notreat
0.29779
0.09277
3.21
altmed*sexm
-0.16156
0.08891
-1.82
innov*a2539
-0.23113
0.11262
-2.05
innov*french
0.24711
0.11308
2.19
deduct2*hhsize
Socioeconomic Institute
University of Zürich
Table 1c: Random-effects Probit estimation results (selected interactions)
coefficient
s.e.
zvalue
-0.00322
0.00141
-2.29
prem*a63+
0.00543
0.00183
2.97
prem*french
0.00215
0.00141
1.53
-0.05830
0.13744
-0.42
0.13103
0.13352
0.98
a63+
-0.46353
0.17655
-2.63
rich
-0.10998
0.13653
-0.81
poor
0.05966
0.20956
0.28
hhsize
0.00957
0.05781
0.17
notreat
-0.18403
0.12322
-1.49
prem*a2539
sex
a2539
Socioeconomic Institute
University of Zürich
WTP for age groups (all interaction terms)
- evaluated at the median individual of each subgroup
marg. WTP 25-39
deduct
copay
alt.med(+)
generics
marg. WTP 40-62
-0.06 deduct
-0.05 deduct
-0.03
(0.04)
(0.02)
(0.01)
-16.64 copay
-30.36 copay
-8.24
(16.00)
(12.31)
(6.96)
67.51 alt.med(+)
19.95 alt.med(+)
0.77
(44.88)
(10.60)
(6.38)
-31.77 generics
-13.81 generics
-8.91
(22.00)
Innov.
marg. WTP 63+
(9.57)
-54.12 innov.
-25.50 innov.
(35.41)
(11.57)
Socioeconomic Institute
University of Zürich
(6.90)
-14.10
(8.34)
Age-specific results
Compensation demanded for a 20%
copayment
(status quo 10%)
Socioeconomic Institute
University of Zürich
Compensation demanded for delayed
access to innovations (3 yrs)
Conclusion (1)
3 Hypotheses with respect to age
H1:
H2:
H3:
increased asset variance  demand for
coverage increases with age
demand follows the value of life  demand for
coverage decreases with age
transition to retirement  demand for coverage
temporarily decreases with age
• H1 cannot be confirmed (contrary to popular belief)
• H2 and H3 tend to be confirmed for the median
individual
Socioeconomic Institute
University of Zürich
Conclusion (2)
• Estimation results for socioeconomic groups indicate
preference heterogeneity
Uniform insurance contracts cause a welfare loss
• Contracts with certain restrictions and lower
premiums might be attractive also for the elderly,
affording them a utility gain
Socioeconomic Institute
University of Zürich
Links
• SOI-Working Paper:
http://www.soi.unizh.ch/research/wp/wp0410.pdf
• Study Report (German):
http://www.soi.unizh.ch/staff/becker/beckerzweifel_summary.pdf
Socioeconomic Institute
University of Zürich
References (1)
• Arrow, K. (1971), Alternative approaches to the theory of choice
in risk-taking situations, in: Arrow, K., Essays in the Theory of
Risk-bearing, Amsterdam: North-Holland, 1-44.
• Ben-Akiva, M. and S.R. Lerman (1985), Discrete Choice
Analysis, Cambridge: The MIT Press.
• Felder, S. (1997), Costs of dying: alternatives to rationing,
Health Policy, 39: 167-176.
• Louvière, J.L., Hensher, D.A. and J.D. Swait (2000), Stated
Choice Methods. Analysis and Applications, Cambridge:
University Press.
• Luce, D. R. (1959), Individual Choice Behaviour, New York:
Wiley and Sons.
• Manski, C. and S.R. Lerman(1977), The estimation of choice
probabilities from choice based samples, Econometrica, 45(8):
1977-88.
Socioeconomic Institute
University of Zürich
References (2)
• McFadden (2000), Economic Choices, AER, 91(3): 351-378.
• Ryan, M. and K. Gerard (2003), Using discrete choices
experiments to value health care programmes: current practice
and future reflections, Applied Health Economics and Health
Policy, 2(1): 55-64.
• Samuelson, W. and R.J. Zeckhauser (1988), Status quo bias in
decision making, Journal of Risk and Uncertainty, 1: 7-59.
• Shepard, D.S. and R.J. Zeckhauser (1984), Survival and
consumption, Management Science, 30(4): 423-439.
• Telser H. et al. (2004), Was leistet unser Gesundheitswesen?,
Schlussbericht, Bern.
Socioeconomic Institute
University of Zürich