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Table 2.1: The impact of population aging on the projected retirement benefits.
Decline from the baseline Case 1 32.48%
Case 2 22.23%
Case 3 24.64%
Case 4 19.87%
Table 2.2: Effect of population aging on household behavior and factor prices.
Baseline Case 1 Case 2 Case 3 Case 4 Capital stock 42.69 - 52.44 - 52.84 Retirement age (actual) 64.4 - - 64.6 67.12 Labor supply 10.46 - 11.64 - 12.14 Rate of return 0.0659 - 0.0571 - 0.0601 Wage rate 1.06 - 1.1 - 1.09
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fixed at the baseline (Case 3) causes the projected benefits to decline by about 25%. 6
What is the intuition behind the smallest decline in the projected retirement benefits
under Case 4? Table 2.2 shows that when the private annuity markets are incomplete,
households respond to a higher life expectancy by saving more, which leads to a higher
aggregate capital stock, and also by delaying retirement by almost three years, which in-
creases the effective labor supply (Case 4). However, a larger-than-proportional increase in
the capital stock leads to a lower rate of return and a higher wage rate than the baseline,
which along with the delayed retirement implies a strictly larger level of aggregate taxable
income. This increase in the tax base of the social security program is behind the smallest decline in the projected retirement benefits under Case 4.7 Experimenting with different so-
cial security tax rates also shows that given this decline, increasing the tax rate from 10.6%
to 13.8% restores the projected retirement benefits to their baseline level. This increase is
significantly smaller than Feldstein’s (2005) projection of 15.7%.
2.6 Sensitivity analysis
Given that the extent of the social security crisis identified in the current model is
conditional on the set of parameter values used in the baseline calibration, it is important 6With a future demographic projection that generates a roughly 25% decline in the baseline benefits
holding retirement and the factor prices fixed (Case 1), the respective declines under cases 2, 3 and 4 are 16%, 17% and 15%. Therefore, in this case, the crisis would be overestimated by as much as 67% (25/15 = 1.67).
7Note from Table 2.2 that when household retirement is held fixed at the baseline but the consumption-
saving and the factor price adjustment mechanisms are allowed (Case 2), the increase in the labor supply documented in the third row is purely due to a higher life expectancy. Also, holding the factor prices fixed at the baseline but allowing for the household retirement mechanism (Case 3) leads to a slight delay in retirement that is documented in the second row of Table 2.2.
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to verify whether the quantitative predictions of the model are sensitive to them or not. To
do this, in this section I estimate the impact of population aging on the projected retirement
benefits under different values of some key model parameters.
Three parameters that are treated as observable in the baseline calibration of the model
are capital’s share in total income (α), leisure share of total time endowment (lW ) and
the age-dependent household efficiency endowment (e(s)). The value of capital’s share in
total income is set to α = 0.35 in the initial baseline calibration, but the macroeconomic
estimates historically observed in the U.S. range between 30 − 40%. Therefore, to verify
the sensitivity of the simulation results with respect to α, I first compute new calibrated
baseline equilibria of the model under α = 0 .3 and α = 0 .4, and then study the impact of
population aging on the projected retirement benefits. The unknown preference parameters
and target values for the baseline calibrations with α = 0 .3, 0.35 and 0.4 are reported in
Table 2.3. It is clear from the table that calibrated baseline equilibria of the model under
α = 0 .3 and α = 0 .4 provide reasonable fits to the data targets, with the values for the
unknown parameters falling conveniently in the range used in the larger macro-calibration
literature.
Once the baseline equilibria under the different α-values have been identified, the next
step is to determine the values of the parameters γ and µ, which control the extent by which
the baseline retirement benefits decline in response to population aging. As in the initial
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