Dissertation

Table 2.10: Effect of population aging on household behavior and factor prices under different values of leisure share of total time endowment.

(a) Effect of population aging with l_W = 0.575.

Baseline Case 1 Case 2 Case 3 Case 4 Capital stock 59.96 - 74.17 - 74.67 Retirement age (actual) 64.72 - - 64.96 67.52
Labor supply 14.71 - 16.38 - 17.08
Rate of return 0.066 - 0.0567 - 0.0597
Wage rate 1.06 - 1.1 - 1.09

(b) Effect of population aging with l_W = 0.6458.

Baseline Case 1 Case 2 Case 3 Case 4 Capital stock 50 - 61.61 - 62.09 Retirement age (actual) 64.2 - - 64.44 66.96 Labor supply 12.17 - 13.53 - 14.12 Rate of return 0.0653 - 0.0563 - 0.0593 Wage rate 1.07 - 1.1 - 1.09

25

the household-level responses and the aggregate factor price adjustments to population aging

are not sensitive to the underlying l_W -value used in the simulations. Households respond

to population aging by increasing their private saving (and therefore aggregate capital and

the wage rate) and also by delaying retirement, which leads to an increase in the tax base

of the social security program under both l_W = 0.575 and 0.6458. Moreover, similar to

the experiments with different values of capital’s share in total income, the social security

tax rate required to restore projected retirement benefits to their respective baseline levels

under Case 4 is roughly 13.8% for both l_W = 0.575 and 0.6458.

The coefficients of the age-dependent household efficiency profile (e(s)) are also treated

as observable in the initial baseline calibration. Given that it is difficult to observe effi-

ciency, the coefficients in (2.28) were estimated from the normalized average cross-sectional

hourly wages data from the 2001 CPS. However, the age-dependent component of household

efficiency used in several other studies on social security and population aging (De Nardi

et al., 1999; Conesa and Garriga, 2008a,b) are estimated from Hansen (1993). Therefore,

the next step is to verify the sensitivity of the simulation results using the age-dependent

household efficiency data from Hansen (1993). The efficiency units in Hansen (1993) are

constructed by taking a weighted sum of the hours worked by each age-sex subgroup using

annual data from 1979 to 1987, where the weights reflect the relative productivity of that

subgroup. To use this data, I first calculate the average of male and female weights for each

age group, and then use piecewise linear interpolation to obtain the weights for all ages

between 25 and 65. To control for the sample selection effects beyond age 65, I assume that

age 65 onwards, efficiency declines at the same rate as it decline before age 65. Finally, I

fit the a quartic polynomial to the interpolated data, which gives

ln e(s) = 0.00271799 + (0.01490187) s −

−

where s is household age. The age-dependent efficiency profiles estimated from the inter-

1.6

1.4

1.2

1

0.8

0.6

0.2

0.4

2001 CPS Hansen (1993)

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25 40 55 70 85 100

Age