Dissertation

Table 3.9: Baseline equilibria under different values of capital’s share in total income.

(a) Unobservable parameter values.
α = 0.3 α = 0.35 α = 0.4

Discount rate (ρ) 0.001 -0.0015 -0.0025 IEIS (σ) 1.8 1.9 1.7 Share of consumption in period utility (η) 0.177 0.176 0.175 Efficiency heterogeneity parameter (ω) 0.16 0.2 0.2 Benefit redistribution parameter (ζ(ω)) 0.38 0.46 0.48


0.202 0.205 0.208
(b) Model performance.
α = 0.3 α = 0.35 α = 0.4

Capital-output ratio 2.92 3.37 3.86 Avg. fraction of work time between ages

25-55

Replacement rate for the poorest house- holds
0.93 0.896 0.9

Social security tax rate 0.102 0.107 0.106


0.25

1

2

3

0.2
0.15
0.1

0
0.05
4

5

25 40 55 70 85 100

Age

Consumption

Figure 3.6: Baseline cross-sectional age-consumption profiles under α = 0.3.

50

45

40

35

30

25

20

15

10

0

5


1

2

3

4

5


62

25 40 55 70 85 100

Age

Figure 3.7: Baseline cross-sectional age-labor hour profiles under α = 0.3.

0.3

1

2

0.25
0.2




0.15
0.1

0
0.05
3

4

5

Student Version of MATLAB

25 40 55 70 85 100

Age

Consumption

Labor hours per week
Figure 3.8: Baseline cross-sectional age-consumption profiles under α = 0.4.

50

45

40

35

30

25

20

15

10

0

5


1

2

3

4

5


63

25 40 55 70 85 100

Age

Figure 3.9: Baseline cross-sectional age-labor hour profiles under α = 0.4.

Student Version of MATLAB

Labor hours per week
household IRR distributions for the two α values: {0.0501, 0.0322, 0.0256, 0.0221, 0.0199}

and {0.0489, 0.0327, 0.0256, 0.0215, 0.0189}, respectively. Comparing these IRR distribu-

tions with the rates of return from capital stock shows that only the bottom two quintiles

of the model population experience welfare gains from participating in the social security

program. Therefore, the welfare implications of social security in this model are not sen-

sitive to the α values used in the simulations. The gross benefit replacement rates in the

baseline model under the different α values are compared to the ones implied by the U.S.

PIA benefits formula in Figures 3.10 and 3.11.

The baseline optimal retirement age distributions under the different values of capital’s

share in total income are compared in Table 3.10. Also, note that in the table, 1 corresponds

to the lowest efficiency level and 5 corresponds to the highest. The table demonstrates that

even with different values of capital’s share in total income, households with lower efficiency

continue to exit the labor force earlier than those with higher efficiency.

The next step is to conduct experiments 1, 2 and 3 on the calibrated model with different

1

0.9

0.8

0.7

0.6

0.5

0.4

Model U.S.

64

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Multiple of average earnings