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: (i)If losses fully covered by aggregate contributions, each victim gets full compensation and any surplus is burnt; (ii)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?

5. 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.

6. Notations: Players: N=100 Victims: S =4 Individual endowment: Y = 100 Individual contribution: : loss suffered by k, i.i.d. (with d=Y=100) : total losses in the group Probability of a loss: Individual payoff:

7. Uniform taxation Uniform (compulsory) tax if a deficit occurs unexpectedly = 1/N (deficit) + quadratic adjustment cost α, β>0 g i =0 is a Nash equilibrium if αL<N-1

8. Individualized taxation The tax is tailored to the first-stage contribution g i In addition, taxation involves a quadratic adjustment cost if a deficit occurs unexpectedly Nash equilibrium = social optimum or near-optimum

9. Uniform rationing In case of deficit, compensation is partial => payoff becomes uncertain. All victims receive a uniform compensation g i =0 is the unique Nash equilibrium

10. Individualized rationing A victim’s 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 c i (0<c i <1) is the rate of coverage with

11. s.t. The Nash equilibrium is positive but below the optimum

12. 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 g i >0

13. 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 €)

14. Experimental results Optimum

15. Null contribution Relative frequency of contributions corresponding to

16. 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.

17. 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.

18. 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) - Gambler’s 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)

19. Heterogeneity of individual strategies Cluster analysis identifies distinct homogeneous groups based on 3 criteria: - Frequency of positive contributions Mean contributions Standard 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

20. 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.