In the debt ceiling treatments DC , public debt is restricted to cents by default. Hence, proposals that imply a public debt level above the debt ceiling are not allowed and technically cannot be submitted. At the beginning of each period, however, the debt ceiling can be removed by majority vote. If the absolute debt ceiling is removed, accumulated public debt can be increased to any level. The debt ceiling can be reinstalled in the following period. In order to analyze optimal values for the public debt level and public good size, we use optimal control theory as introduced by [ 24 ].
We use optimal control theory because it is currently the only approach that enables us to derive theoretical predictions in our rather complicated multi-period, multi-player, overlapping generations game. With our approach we can derive predictions on optimal dynamic choices in our specific framework, but cannot provide a fully fledged game-theoretic analysis of the dynamic game.
We will leave these analyses to future research because they go well beyond the scope of this paper. We assume that the participants want to maximize their expected payoff. Over-indebtedness and individual lifetime in OLG are stochastic variables. We restrict the choices to the points in the action space that lead to critical debt levels, i.
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It is evident that increasing debt up to the next critical debt level i. Hence, it is sufficient to analyze the dynamic decision at only the critical debt levels. Since we assume zero debt in the a priori situation, i. We determine the optimal policy for each treatment and present detailed explanations in S2 Appendix. Figs 1 — 3 show the optimal new debt policy in our treatments.
Note that the displayed optimal new debt can only be implemented in those periods in which the individuals have a choice, but not in a forced debt reduction phase following over-indebtedness. But note also that even after a forced debt reduction phase, the individuals continue with the presented optimal new debt policy of the corresponding period.
The optimal new debt policy in our single-gen treatments Fig 1 is characterized by a long phase without deficit spending periods 1—6 in the single-gen 10 treatment and periods 1—26 in the single-gen 30 treatment. Four periods before the termination, public debt is increased. There are three periods with a single step increase, followed by one last period with a double step increase.
The optimal new debt policy in the last two periods 9 and 10 or 29 and 30 can only be implemented if forced debt reduction measures are not in place. Hence, the cumulative debt development path is stochastic even if all individuals use the optimal choice policy.
Fig 2 shows the optimal new debt policy in the multi-gen treatments. The solution for the multi-gen treatments is similar to that in single-gen. However, it is expanded by the possibility of different starting points regarding the public debt level. If the starting debt amounts to 0, optimal debt policy is identical to the optimal debt policy in the single-gen 10 treatment. If there is public debt beyond the safe threshold , the debt is paid back until it reaches the safe threshold.
The only difference between situations with a starting debt and those without is that in the former case the safe part of the debt up to the safe threshold is acquired in and retained from the generation before. Fig 3 shows the optimal new debt policy in the OLG treatments. As before, inherited public debt above the safe threshold is paid back in the early rounds. Hence, stochastic life duration has a time discount effect on choices.
It is important to note that in the OLG treatments the three individuals in each economy are typically at different in-game ages. According to our calculations, each individual will vote for the optimal new debt policy that corresponds to her own in-game age. Hence, given our median voter paradigm, the debt policy in each OLG economy is determined by the median aged individual in that economy.
This should lead to age-related political cycles in which economies with a young median age vote to acquire less debt than economies with an old median age. Note that the optimal new debt policy for the treatments with a debt ceiling are identical to those without a debt ceiling because debt ceilings can always be adapted to fit perfectly to the optimal new debt policy.
Written informed consent was obtained by all subjects. Before the experiment started, the subjects were asked to complete a comprehension test to check that they had understood the rules of the game and the math regarding the payoffs. After all the participants successfully finished the comprehension test, they participated in practice runs to familiarize themselves with the game situation. The first practice run consisted of 10 periods of the game with an initial public debt of zero. The second practice run consisted of 5 periods of the game with an initial public debt of In the multi-gen treatments, each generation of subjects was invited to the lab at the same time, with a generous time lag between generations.
Subjects were randomly assigned to individual cubicles. After receiving instructions see S1 File , completing the comprehension test, and participating in the practice runs, the subjects proceeded with the actual experiment. The only difference between the different generations was the size of the public debt at the outset of their in-game lifetime, i.
To allow for a smooth transition between our in-game generations in the OLG treatments, we used two separate laboratories located directly next to each other. The subjects for all the generations were invited to one of the two labs at the same time. Each subject was assigned to an individual cubicle. After receiving instructions, completing the comprehension test, and participating in the practice runs, the subjects were randomly assigned to the generations. The first generation subjects were picked up individually and transferred to separate cubicles in the second lab.
There they proceeded with the actual experiment. The subjects awaiting their in-game birth remained in the first lab, waiting silently in their cubicles until the lifetime of their in-game predecessor ended.
Sustainability And Optimality Of Public Debt (Contributions To Economics) -
The waiting subjects were allowed to read offline, but all forms of communication were prohibited, including e-mailing or texting on mobile phones. First, we examine the effect of the generational configuration on the accumulated public debt and on the level of public good provision. Table 3 shows the overall average values of public good provision, of new public debt, and of accumulated public debt in the baseline treatments. The average values for the new public debt exclude the forced debt reduction measure due to over-indebtedness.
Fig 4 shows the development of the average values over time. In both single-gen treatments, we observe a moderate increase of public debt over time.
Until period 9 in single-gen 10 and period 29 in single-gen 30, respectively, the accumulated public debt on average does not exceed the safe threshold of In these treatments, average public debt rises above only in the last period, in which no risk of over-indebtedness exists. We do not observe over-indebtedness in any of the economies in the single-gen treatments.
In contrast to the high degree of prudence that we observe in the economies of our single-gen treatments, all the economies in our multi-gen baseline and OLG baseline treatments quickly accumulate substantial amounts of public debt. While the level of public debt level starts and fluctuates at high levels in both multiple generations treatments, the pattern of debt accumulation and reduction varies over time.
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In the multi-gen baseline treatment, we observe a strong increase of debt just before and in the periods 10 and 20, i. In the OLG baseline treatment, debt is quickly accumulated from the beginning and is greater than in the multi-gen baseline treatment, except for the periods 9 to 11 and 19 to We find no significant difference between the single-gen 10 and the multi-gen baseline treatments. If we compare the public debt levels at the end of an economy, we observe almost the same levels in the single-gen 10, single-gen 30, and multi-gen baseline treatments 22pprox.
All in all, it is remarkable that the behavior in the multi-gen treatment is rather close to the theoretical benchmark. We find signs of intergenerational concern when comparing the end of lifetime periods 10 and 20 debt levels in the multi-gen baseline to the end-of-lifetime debt levels in the single-gen 10 and 30 treatments. We find the end-of-lifetime debt levels of the first and second generations in the multi-gen treatment are lower than all the end-of-lifetime debt levels of the final generations.
This seems to indicate that the non-final generations exhibit some debt restraint when compared to the final generations i. On the aggregated level, we therefore observe only small effects of intergenerational concerns. With respect to public good provision, we find that in both single-gen treatments the size of the public good remains almost constant over time except in the two final periods.
Public debt sustainability:Methodologies and debates in European institutions
In contrast, the extent of public good provision varies greatly in the multi-gen baseline and in the OLG baseline treatments. The systematic difference between the single-gen treatments and the multi-gen and OLG treatments is the lack of prudence in the latter. Hence, the economies in the treatments with multiple or overlapping generations are repeatedly over-indebted and are forced to pay imposed taxes.
This reduces their overall capability to provide public goods, making them inferior to the single generation economies. Table 4 confirms the findings so far on a period-by-period basis. Note, however, that individuals with a similar life expectancy i. They differ, however, in the share of balanced budget, voluntary surplus, and imposed austerity rounds. The individuals in the single-gen 10 treatment very rarely accumulate savings and never face imposed austerity measures. But, the voluntary debt reduction effort exhibited in these treatments is neither frequent nor sizable enough to offset the accumulated debt.
To address the problem of multiple hypothesis testing, we adjusted our reported p-values in accordance with [ 28 ] as a robustness test see also [ 29 ]. In particular, we used the number of comparisons in the respective analysis part e. The adjusted p-value is then compared to the conventional significance level.
The only exemption refers to the observed weak sign of intergenerational fairness concerns.
The identified statistical significance when comparing the end-of-lifetime debt level in period 20 of the multi-gen treatment with the end-of-lifetime debt level in period 10 of single-gen 10 vanishes. Thus, if the Bonferroni correction procedure is applied, we do not find statistical support for a sign of intergenerational fairness concerns at the aggregated level. The Tobit regressions presented in Table 5 provide further evidence for the treatment differences discussed above robust standard errors clustered at the group level are shown in the parentheses under each coefficient. In all the models 1—10 dependent variable: public debt , only the first 10 periods are considered and the single-gen 10 treatment serves as the reference group.
In the b-models, we extend the a-models by adding interaction terms for the treatment dummies and the period. We observe no significant effect of the treatment dummy for the multi-gen baseline treatment in any of the models with 10 periods. In contrast, we find a significantly positive effect of the treatment dummy on public debt accumulation for the OLG baseline treatment.
Model b, however, shows that over time debt accumulation in the OLG treatment declines when compared to the single-gen 10 treatment. This is plausible since subjects push their debt accumulation to the end of their lifetime, i. In the OLG treatment, however, debt is accumulated early on and remains on a high level throughout. In models 1—30, all 30 periods of the respective treatments are considered and the single-gen 30 treatment serves as the reference group.
We find a significantly positive overall effect of the treatment dummies for the multi-gen baseline and the OLG baseline treatments on public debt accumulation. While we observe a significantly positive effect of the period, we do not observe any treatment and period interaction effects on public debt. We run similar Tobit regressions with the public good provision as the dependent variable.