Dissertation

Figure 3.10: Gross replacement rates: Model Vs U.S. under α = 0.3.

1

Model U.S.

0.9

0.8

0.7

0.6

0.5

0.4

Student Version of MATLAB

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Multiple of average earnings

Gross replacement rate

Gross replacement rate
Figure 3.11: Gross replacement rates: Model Vs U.S. under α = 0.4.

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Table 3.10: Retirement age distributions under different values of capital’s share in total income.

Capital’s share in income 1 2 3 4 5 0.3 62.75 64.47 64.94 65.15 65.26 0.35 61.48 63.09 63.61 63.86 64.02 0.4 59.52 61.32 61.9 62.18 62.35

Table 3.11: The effect of population aging on the calibrated model.

(a) With capital’s share of α = 0.3.
Experiment Baseline 1 2 3


0.93 0.82 0.79 0.76
Variable
Social security tax rate 0.102 0.127 0.141 0.157 Replacement rate for the poorest

households

Rate of return 0.0285 0.0252 0.0223 0.0195 Wage rate 1.11 1.12 1.14 1.15 Output 6.03 7.25 7.72 8.22 Capital 17.57 21.83 23.97 26.27 Labor 3.81 4.52 4.75 5.0 Capital-output ratio 2.92 3.01 3.1 3.19

(b) With capital’s share of α = 0.4.
Experiment Baseline 1 2 3


0.9 0.73 0.73 0.67
Variable
Social security tax rate 0.106 0.122 0.136 0.151 Replacement rate for the poorest

households

Rate of return 0.0293 0.0249 0.0221 0.0193 Wage rate 1.48 1.52 1.55 1.58 Output 9.69 11.87 12.8 13.81 Capital 37.38 47.84 53.1 58.95 Labor 3.94 4.69 4.96 5.25 Capital-output ratio 3.86 4.03 4.15 4.27

values of capital’s share in total income, and then compute post-population aging SCE

with an optimal OASI tax rate. I report the corresponding values of the tax rate and

some other relevant variables in Table 3.11. It is clear from the table that the general

impact of population aging on the welfare-maximizing social security tax rate and the

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other endogenous variables is fairly robust across different values for capital’s share in total

income. With all realistic α values, the model predicts a 2-5 percentage point increase in the

social security tax rate under the projected future demographics. Population aging reduces

the equilibrium rate of return from capital and increases the equilibrium wage rate, output,

capital stock, labor supply and the capital-output ratio under all realistic α values.

Given that the welfare-maximizing changes in the tax rate predicted by the model are

fairly robust across different values for capital’s share in total income used in the simulation,

it is natural to expect that the factors driving such changes are also robust to the different

α-values. To verify this, I document in Table 3.12 how the households’ IRRs from the

social security program are affected by population aging, holding the social security tax

rate fixed at the corresponding baseline level identified in Table 3.9. The tables reveal a

familiar pattern of the impact of the demographic shocks on the households’ IRRs from

the social security program. Across the baseline and experiment 3, the IRRs of the five

efficiency groups decline by roughly 16, 30, 39, 45 and 51%, respectively, under α = 0.3,

and by roughly 18, 30, 39, 46 and 53%, respectively, under α = 0.4. Therefore, the fact

that population aging imposes a lesser burden on the poorer households who are actually