Dissertation

Table 2.3: Calibrated baseline equilibria under different values of capital’s share in total income.

α = 0.3 α = 0.35 α = 0.4 Discount rate (ρ) -0.003 0.016 0.032 IEIS (σ) 3.4 3.2 3.1 Share of consumption in period utility (η) 0.308 0.332 0.357 Optimal (actual) retirement age 64.2 64.4 64.36 Capital-output ratio 2.508 2.495 2.499 Consumption-income ratio 0.749 0.751 0.75 Rate of return 0.0452 0.0659 0.0857 Accidental bequest 0.0066 0.016 0.014

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Table 2.4: Values of the population aging parameters under different values of capital’s share in total income.

α = 0.3 α = 0.4 γ 0.0001 0.0001 µ 1.554 1.553 Actual life expectancy 78.72 78.7 Decline in projected benefits 32.51% 32.51%

baseline, I augment the model survival probabilities by choosing γ and µ such that holding

household behavior, factor prices and the social security tax rate fixed, the model predicts

a 33% decline in the projected retirement benefits. In Table 2.4, I report the values of

these two parameters under α = 0.3 and 0.4, and I also report the actual life expectancies associated with them.⁸ It is worth noting from the table that with the reported γ- and

µ-values, the actual life expectancies of the model households are very close to the SSA’s

projections for the year 2075. Also, as in the initial baseline, holding household behavior

and factor prices fixed, a social security tax rate of θ = 15.7% restores the post-population

aging retirement benefits to the respective baseline levels.

To identify the quantitative importance of the household-level and macroeconomic ad-

justments to population aging under different values of capital’s share in total income, I

compute new stationary competitive equilibria in which both household consumption-saving

and retirement, as well as the factor prices respond to the demographic change (Case 4).

I also compute the two intermediate cases: holding retirement fixed at the baseline but

allowing the consumption-saving and the factor price mechanisms to respond (Case 2), and

holding the factor prices fixed at the baseline level but allowing the household retirement

mechanism to respond (Case 3). I report the percentage declines in the projected retirement

benefits from the respective baselines in Table 2.5. The table reveals a pattern very similar

to the one observed under α = 0.35: the smallest decline in the projected benefits occurs

under Case 4, when all the household-level and macroeconomic adjustments to population

aging are accounted for. Moreover, the magnitude of the decline in the projected benefits

⁸As in the initial baseline, I set the population growth rate to n = 0.47% under both α = 0.3 and 0.4.

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