Dissertation

Table 3.17: Baseline equilibria with efficiency data from 2001 CPS and Hansen (1993).

(a) Unobservable parameter values.
2001 CPS Hansen (1993)

Discount rate (ρ) -0.0015 -0.004 IEIS (σ) 1.9 1.8
Share of consumption in period utility (η) 0.176 0.175 Efficiency heterogeneity parameter (ω) 0.2 0.18 Benefit redistribution parameter (ζ(ω)) 0.46 0.4

(b) Model performance.

2001 CPS Hansen (1993) Capital-output ratio 3.38 3.39
Avg. fraction of work time between ages 25-55 0.205 0.203 Replacement rate for the poorest households 0.896 0.924 Social security tax rate 0.107 0.104
baseline calibration in Table 3.17. It is clear from the table that the values for the unknown

preference parameters which calibrate the model to data under the efficiency profile esti-

mated from Hansen (1993) are very similar to those under the efficiency profile estimated

from 2001 CPS. The baseline cross-sectional age-consumption and age-labor hour profiles

are plotted in Figures 3.13 and 3.14, where in the figures 1 corresponds to the lowest effi-

ciency level, and 5 corresponds to the highest. Note that the baseline labor hours under the

efficiency profile estimated from Hansen (1993) are not hump-shaped, which is inconsistent

with empirical evidence.

The baseline households’ IRR distribution with the efficiency profile from Hansen (1993)

is as follows: {0.0485, 0.0321, 0.0256, 0.0221, 0.0198}. As in the initial baseline, the bottom

two quintiles of the model population experience a welfare gain from participating in the

social security program, as their IRRs are higher than the rate of return on capital stock.

The gross benefit replacement rates in the baseline model with the efficiency profile from

Hansen (1993) are compared to the ones implied by the U.S. PIA benefits formula in Figure

3.15.

Baseline household retirement behavior under the two different age-dependent efficiency

0.3
0.25
0.2




0.15
0.1

0
0.05


1

2

3

4

5


73

25 40 55 70 85 100

Age