Dissertation

Table 3.3: The demographic experiments.

Experiment n(%) γ µ Life expectancy Low-cost (1) 0.16 1 × 10⁻⁴ 1.5577 80.55
Intermediate (2) 0.09 6 × 10⁻⁵ 1.9077 83.95 High-cost (3) 0.01 4 × 10⁻⁵ 2.1298 87.55

survival probabilities with an age-specific increment of the form

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d Q(s) = γs^µ (3.64)
where γ and µ are positive constants to be parameterized, and s represents household age.

Therefore, the projected survival probabilities are given by

Q_p(s) = Q(s) + γs^µ (3.65)
Note that these age-specific increments are consistent with the fact that old-age survivorship

in the U.S. has increased at a faster rate in the later half of the twentieth century, making the

population survival curve more rectangular (Arias, 2004) (see Figure 3.5). Then, I choose

values for γ and µ such that the model life expectancies under the augmented survival

probabilities match the projections described above. I report the specific demographic experiments in Table 3.3.^10,11 I incorporate these population projections into the baseline

model, and then compute a new SCE with an optimal OASI tax rate under each experiment.

I report the corresponding values of the social security tax rate and some other relevant

variables in Table 3.4.

The results of the three experiments can be summarized as follows. First, the optimal

or welfare-maximizing social security tax rate increases from the baseline level by 1.8 per-

centage points under the low-cost projection, 3.2 percentage points under the intermediate

¹⁰I hold the maximum lifespan unchanged at T^¯ = 75 under all the three experiments.
¹¹Note that in the current model, both the baseline life expectancy and the increases under population

aging are symmetric across the different income groups. However, there is evidence that both life expectancy (Attanasio and Emmerson, 2003; De Nardi et al., 2006) and its rate of improvement (Waldron, 2007) are strongly correlated with income.

1

0.9

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0.3

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0

0.1

Baseline Low−cost Intermediate High−cost

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25 40 55 70 85 100

Age