Dissertation

Figure 2.2: Baseline and the projected survival probabilities.

Student Version of MATLAB

Survival probability
It is also useful to note that with the above demographic projection, holding household

behavior and factor prices fixed at the baseline, a payroll tax rate of θ = 15.7% restores

the projected retirement benefits to their baseline level. This value is consistent with what

Feldstein (2005) reports to be necessary to prevent a decline in projected retirement benefits

in the year 2075.

The next step of the analysis is to compute the implied decline in the projected re-

tirement benefits when the household-level and macroeconomic adjustments to population

aging have been accounted for. To do this, I incorporate the constructed demographic pro-

jection in the baseline model and then compute a new stationary competitive equilibrium

in which both household consumption-saving and retirement, as well as the factor prices

respond to the demographic change. Also, to understand the relative importance of the

household retirement and the factor price adjustment mechanisms, I compute projected

retirement benefits under two situations: holding retirement fixed at the baseline level, but

allowing the consumption-saving and factor price adjustment mechanisms to respond to

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population aging, and holding the factor prices fixed at the baseline level, but allowing the

household retirement mechanism to respond to population aging. I label the four cases as

follows:

• Case 1: exogenous retirement, exogenous factor prices,

• Case 2: exogenous retirement, endogenous factor prices,

• Case 3: endogenous retirement, exogenous factor prices, and

• Case 4: endogenous retirement, endogenous factor prices.

The percentage decline in the projected retirement benefit at actual age 70 from the baseline

level for all the four cases are reported in Table 2.1. The following facts are clear from the

table. First, the impact of population aging on the projected retirement benefits is smallest

when both the household-level consumption-saving and retirement responses, as well as the

aggregate factor price adjustments are fully accounted for (Case 4). The percentage decline

in the projected benefits from the baseline level in this case is roughly 20%, which implies

that ignoring these adjustments could lead to an overestimation of the crisis by about 65%

(33/20 = 1.65). The two intermediate cases also provide some interesting insights into

how ignoring either of the two mechanisms leads to an overestimation of the decline in the

projected retirement benefits. On the one hand, holding retirement fixed at the baseline

level but allowing for the consumption-saving and factor price adjustment mechanisms (Case

2), population aging leads to a roughly 22% decline in the projected benefits. On the other

hand, allowing for the household-level retirement response but holding the factor prices