Individual Responsibility and Public Funding of Health Care: An Experiment

1
Individual Responsibility and Public Funding of
Health Care An Experiment

• SABE-IAREP 2008 Conference
• Luiss, Roma
• Louis Lévy-Garboua (Universty of Paris 1, PSE and
  CIRANO)
• Claude Montmarquette (University of Montreal and
  CIRANO)
• Marie-Claire Villeval (GATE-CNRS, University of
  Lyon 2 and IZA)

2
Motivation

• In the face of an increasing financial burden,
  redistributive taxation and rationing are two
  alternatives for financing public health care
  systems. Search for efficient institutions.
• Taxation adjusts aggregate contributions to the
  socially desirable consumption level (ie, full
  coverage of losses to all in the absence of
  loading) at the risk of imposing an adjustment
  cost to taxpayers if a deficit occurs
  unexpectedly.
• Rationing adjusts aggregate consumption to the
  sum of contributions at the risk of providing the
  service at a suboptimal level, at the expense of
  victims.
• Which of these institutions give individuals a
  sense of responsibility by letting them
  spontaneously come close to efficiency?

3
A two-stage public insurance game (1)

• Observe contribution behavior when private needs
  are met collectively and prices are not set on a
  market.
• In the first stage of the game, equally endowed
  subjects choose to contribute to a mutual fund
  compensating for random Bernoulli losses.
• In the second stage, given share of individuals
  hurt
• If losses fully covered by aggregate
  contributions, each victim gets full compensation
  and any surplus is burnt
• If aggregate contributions fall short of losses,
  uniform policies offer equal compensation,
  irrespective of first-stage contributions
  individualized policies favor higher
  contributors.

4
A two-stage public insurance game (2)

• Compare four public health insurance policies
  with a laboratory experiment
• Uniform taxation, Individualized taxation
• Uniform rationing, Individualized rationing.
• These four policies share the same social optimum
  (full coverage equally financed by all)
• but lead to contrasted Nash equilibria
• -no contribution for uniform treatments
• -interior contributions for individualized
  rationing
• -optimal or near-optimal contributions for
  individualized taxation
• Do players perceive the social optimum? Do they
  converge to the Nash equilibria? Which policy is
  the best?

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Public health insurance Theory

• Public health insurance differs both from
• -private insurance it is a game
• -public goods games (i) two-stage game
• (ii) under taxation, returns on
  contribution are non-linear due to an adjustment
  cost in case of an unexpected deficit.
• Hence, multiple equilibria
• (iii) under rationing, private returns on
  contributions are contingent on the private
  occurrence of a health risk.
• Hence, necessity to deal with risk and risk
  aversion in game theory.

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Notations Players N100 Victims S 4
Individual endowment Y 100 Individual
contribution loss
suffered by k, i.i.d. (with dY100)
total losses in the
group Probability of a loss Individual
payoff
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Uniform taxation
Uniform (compulsory) tax if a deficit occurs
unexpectedly 1/N (deficit) quadratic
adjustment cost a, ßgt0 gi0 is a Nash
equilibrium if aLltN-1
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Individualized taxation
The tax is tailored to the first-stage
contribution gi In addition, taxation involves a
quadratic adjustment cost if a deficit occurs
unexpectedly Nash equilibrium social optimum
or near-optimum
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Uniform rationing
In case of deficit, compensation is partial gt
payoff becomes uncertain. All victims receive a
uniform compensation gi0 is the unique Nash
equilibrium
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Individualized rationing
A victims compensation in stage 2 depends on his
individual contribution in stage 1 2
conditions (i) A victim cannot be compensated
for more than his loss (ii) The total amount of
compensations is always covered by the total
amount of contributions
where ci (0ltcilt1) is the rate
of coverage with
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s.t. The Nash equilibrium is positive but below
the optimum
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To sum up

Optimum Equilibrium Uniform
Taxation L/N
0 Individualized Taxation
L/N Almost optimal
contribution

and moderate budget
deficit

with mixture of over and under
contributions Uniform Rationing
L/N
0 Individualized Rationing L/N
gigt0
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Experimental design
Regate software 24 sessions of 12 participants
each (12 in BUL-C3E at CIRANO, Montreal, and 12
at GATE, Lyon) 288 participants from
undergraduate classes in engineering and business
schools 50 repetitions 90 minutes A lottery to
test risk aversion at the end of the session
(Can. 5 or 2 for sure or 50 chance of winning
11 or 5 and 50 chance of winning 0) Average
earnings 35 Can. (23 )
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Experimental results
Optimum
15
Relative frequency of contributions
corresponding to
Optimum
Null contribution
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Aggregate contributions and efficiency (1)

• Voluntary contributions
• Fall short of total losses, except under
  individualized taxation in 13 of periods
  (surplus is burnt).
• Start from a common level close to the social
  optimum (33-34 ECUs) but lower (except for
  uniform rationing).
• Slowly converge to Nash equilibrium go down
  except for individualized taxation.

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Aggregate contributions and efficiency (2)

• Aggregate contribution levels
• determine insurance loading (through adjustment
  costs) under taxation because full insurance is
  guaranteed loading rate as high as 55 with
  uniform taxation vs 14 only with individualized
  taxation.
• determine coverage under rationing as low as 26
  of loss under uniform rationing vs 47 under
  individualized rationing.
• Thus, aggregate contribution levels are a proxy
  measure for efficiency.

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Econometric analysis of individual contributions
A 2-step estimation procedure - Random
effects-Probit model for the decision to
contribute at all - FGLS model corrected for
the selectivity bias for the contribution level
conditional on a positive contribution

• Probability of a positive contribution
• - Conditional cooperation for uniform
  taxation only (contributions positively
  correlate)
• - Gamblers fallacy and hot hand fallacy with
  rationing only (no risk with taxation)
• - With taxation, people stop contributing
  (self-exclude from insurance) under persistent
  bad luck (likely out of strong emotion)
• Contribution level conditional on a positive
  contribution
• - Altruistic cooperation with individualized
  taxation (contributions negatively correlate)

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Heterogeneity of individual strategies Cluster
analysis identifies distinct homogeneous groups
based on 3 criteria - Frequency of
positive contributions Mean contributions Standa
rd deviation of contributions - Application
of the hierarchical Ward method
Cluster 1 cooperative strategy
rather generous contribution behavior
and high SD 55-62 cooperative, but only 43
with individualized taxation (the latter
institution forces people to behave as if they
were cooperative) Cluster 2
non-cooperative strategy
systematic free riding and low SD
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Conclusion

• Experimental results compliant to game theory in
  the long run, even though subjects are initially
  attracted by a social norm (a commonly perceived
  social optimum under incomplete information)

• Individualization improves efficiency both for
  taxation and rationing.
• Individualized taxation is the best institution
  it gives a sense of responsibility by protecting
  high contributors from the exploitation of free
  riders.
• Uniform rationing is the worst institution for
  risk averse individuals (low coverage and high
  variance).
• Policy implications Suggestion of user fees
• Individuals contribute to funding according
  to their needs.