Dissertation

Table 3.27: Parameter values in the baseline calibration with the pollution externality.

σ ρ η ω ζ(ω) κ ν 3 -0.003 0.2449 0.15 0.65 0.25 0.3

Therefore, with the pollution externality, the social planner chooses the tax rate that satisfies

θ = arg max {U_P} = arg max (U − S(0) "^exp □^{(ν(n + g) − ρ)}

T^¯ − 1
_{ν(n + g) − ρ} #) ^(3.73)

With the introduction of the pollution externality, there are two more parameters κ

and ν that must be calibrated. To do this, I choose values for κ and ν such that in

the baseline stationary competitive equilibrium with an optimal social security tax rate,

pollution causes a loss of 15% in steady state life-cycle utility. The values of the parameters

for which the model reasonably matches the targets are reported in Table 3.27. With these

parameter values, the model generates a steady state capital-output ratio of 3.2, an average

retirement age of 62.48, an optimal social security tax rate of 10.51%, and a replacement

rate of 98% for the poorest households. The equilibrium rate of return is r = 0.0293, the

equilibrium stock of the pollution externality is S = 1.08 and it causes a roughly 14% decline

in aggregate utility. The baseline distribution of the households’ IRRs from social security is

{0.0579, 0.0326, 0.0203, 0.0104, 0.0023}, and comparing these with the rate of return shows

that the bottom two efficiency groups experience welfare gains from the social security

program, whereas the top three groups suffer welfare losses. The baseline retirement age

distribution is {62, 62, 62, 62.77, 63.64}, which shows that only the top two efficiency groups in the model continue to supply labor beyond the minimum retirement eligibility age.¹⁴

Once I have identified the baseline calibration of the model with the pollution externality,

I examine the effect of the low-cost, intermediate and the high-cost projections (adjusted

for the absence of mortality risk) on the welfare-maximizing social security tax rate and

some other relevant variables. I report the results in Table 3.28. The table shows that ¹⁴I also assume that household retirement is synchronous with benefits collection, which is another sim- plification. Therefore, I restrict retirement to be ≥ T_min, where T_min = 37 is the minimum eligibility age in

the model (actual age of 62 in the U.S.).

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