Dissertation

Figure 2.1: Efficiency data from the 2001 CPS along with the fitted quartic polynomial.

a steady state capital-output ratio of K/Y = 2.495, an optimal (actual) retirement age of

64.4, and a consumption to income ratio of C/Y = 75.1%. The equilibrium rate of return

from the capital stock is r = 0.0659, and the accidental bequest is B = 0.01.

2.5 The impact of population aging

Student Version of MATLAB

Efficiency endowment
To understand the quantitative importance of accounting for the household-level and

macroeconomic adjustments to population aging, the first step is to construct a future de-

mographic projection that generates a decline in the projected retirement benefits that is

consistent with the commonly reported estimates of the social security crisis. More specifi-

cally, I construct a demographic scenario such that the decline in model benefits (without

the household-level and the macroeconomic adjustments) matches the upper-bound esti-

mate of a 33% decline in benefits in the real world. To accomplish this, I first set the

population growth rate to n = 0.47%, and then I change the survival probability distri-

bution of the model such that holding household behavior, factor prices, and the social

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security tax rate constant at the baseline level, the model predicts a 33% decline in the projected retirement benefits.⁵ Specifically, I augment the model survival probabilities with

an age-specific increment of the form

d Q(s) = γs^µ (2.29)
where γ and µ are positive constants to be parameterized, and s represents household age.

Therefore, the projected survival probabilities are given by

Q_p(s) = Q(s) + γs^µ (2.30)
Note that these age-specific increments are consistent with the fact that old-age survivorship

in the U.S. has increased at a faster rate than young-age survivorship in the later half of the

twentieth century, making the population survival curve more rectangular (Arias, 2004).

With household behavior, factor prices, and the social security tax rate held fixed at

the baseline level, parameter values of γ = 0.0001 and µ = 1.553 lead to a 32.48% decline

in the projected retirement benefits. With these values, the model life expectancy increases

from 51.31 in the baseline calibration to 53.7 under the future projections, which implies

an increase in the actual life expectancy from age 76.31 to age 78.7. It is worth noting

that these values are very close to the average life expectancies for the years 2001 and 2075

respectively reported in the 2009 OASDI Trustees Report. The baseline and the projected

survival probabilities are plotted together in Figure 2.2.

⁵_{Note that studies published by the SSA identify smaller declines required in the projected retirement}

benefits. For example, Goss (2006) reports that with no change in the current social security laws, about 70% of currently scheduled OASI benefits would be payable in 2080 (implying a decline of 30%). In the 2009 Social Security Trustees Report, the long-range actuarial estimates predict that tax revenues under the current laws are sufficient to support expenditures at a level of 74% of scheduled benefits in 2083 (implying a decline of 26%). My results (accounting for the household-level and macroeconomic adjustments to population aging) continue to be quantitatively important when I consider an alternative demographic projection under which the baseline decline in model benefits (without the household-level and macroeconomic adjustments) matches the lower-bound estimate of a 25% decline. This suggests that constructing future demographic projections that are consistent with smaller alternative estimates of the social security crisis simply amounts to a re-scaling of the problem. Therefore, for the remaining part of the discussion I simply focus on the quantitative results generated assuming a baseline decline of 33% in model benefits.

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Age