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INVESTING RETIREMENT WEALTH: A LIFE-CYCLE MODEL – Welfare Analysis 3

The last panel of Table 7 reports results for a household headed by a self-employed college graduate. This household has risky labor income that is unusually correlated with the stock market, so its desired stock holdings are smaller than those of the benchmark household; it actually loses slightly from investment of retirement wealth in equities with a fixed tax rate. On the other hand, this household also has a particularly pronounced hump shape in labor income so it is particularly anxious to smooth consumption over the life cycle. The household gains 3.8% from a risky retirement system with a lower payroll tax rate, comparable to the results for the benchmark household.
All the results in Table 7 can be criticized on the grounds that they are derived from a model in which there is no role for a Social Security system. Since households save and invest their liquid wealth optimally, the mandatory saving and rigid asset allocation of the retirement system can only reduce their welfare. In this setting, any reform that effectively reduces the scale of Social Security will increase welfare.
As a partial response to this concern, in Table 8 we report a “paternalistic” welfare analysis in which the government uses different utility parameters than those of the household itself. In the first panel, the household is impatient, with B = 0.8; left to its own devices it will do very little saving for retirement, as illustrated in Table 6. The government, however, discounts utility using B = 0.96 as in our benchmark case. Here there is a modest welfare gain of 2.0% from a shift of retirement wealth towards equities with a fixed tax rate, but a small welfare loss of -0.6% if the payroll tax rate is reduced. The reason, of course, is that from the government’s point of view people make poor use of their tax cuts, spending them early in life and failing to save enough for retirement.
The second panel of Table 8 reports results when the household is highly risk-averse, with 7 = 10, but the government is risk-tolerant, with 7 = 2. In this case a shift of retirement wealth towards equities forces households to take on more risk, which improves their welfare from the government’s point of view. Welfare rises by 1.7% and 2.4%, respectively, in the cases with fixed and reduced payroll tax rates.
All the results we have reported so far assume that the riskless real interest rate is fixed at 2% and the equity premium at 4%. As a final exercise, in Table 9 we consider variations in these parameters. This is a valuable check on the robustness of our basic results; it also enables us to consider what might happen to welfare if the investment of retirement wealth in risky assets reduced the equilibrium equity premium.

Table 8: Paternalistic Welfare Analysis.

B Too Low Tax Rate Welfare Age 20 Welfare Age 65 Gain Age 20 Gain Age 65
Mean Std. Mean Std. Mean Std. Mean Std.
0/100 10.00% 18.13 1.64 17.26 1.31
50/50* 10.00% 18.50 1.77 25.33 8.05 2.04% 7.93% 46.76% 514.50%
50/50 6.00% 18.03 1.62 17.03 1.20 -0.55% -1.22% -1.33% -8.40%
7 Too High Tax Rate Welfare Age 20 Welfare Age 65 Gain Age 20 Gain Age 65
Mean Std. Mean Std. Mean Std. Mean Std.
0/100 10.00% 20.67 1.09 20.26 2.75
50/50 10.00% 21.02 1.22 30.59 7.34 1.69% 12.12% 50.96% 166.82%
50/50 6.00% 21.17 1.21 27.39 6.24 2.42% 11.01% 35.19% 126.91%

Table 9: Welfare Analysis with Alternative Mean Asset Returns.

Baseline Case Tax Rate Welfare Age 20 Welfare Age 65 Gain Age 20 Gain Age 65
> = 4%, RP = 1.02 Mean Std. Mean Std. Mean Std. Mean Std.
0/100 10.00% 18.67 1.75 22.69 3.42
50/50 10.00% 18.76 1.80 27.30 7.41 0.48% 2.86% 20.32% 116.67%
50/50 6.00% 19.36 1.81 24.46 6.22 3.70% 3.43% 7.80% 81.87%
Alternative 1 Tax Rate Welfare Age 20 Welfare Age 65 Gain Age 20 Gain Age 65
> = 3%, rf = 1.02 Mean Std. Mean Std. Mean Std. Mean Std.
0/100 10.00% 18.57 1.70 22.15 3.53
50/50 10.00% 18.63 1.78 25.13 6.64 0.33% 4.43% 13.48% 87.89%
** 0.22% 1.73% 10.75% 94.05%
50/50 7.25% 19.20 1.82 25.49 6.74 3.38% 6.69% 15.11% 90.74%
** 2.82% 3.93% 12.35% 97.00%
Alternative 2 Tax Rate Welfare Age 20 Welfare Age 65 Gain Age 20 Gain Age 65
> = 3%, RF = 1.03 Mean Std. Mean Std. Mean Std. Mean Std.
0/100 7.00% 19.30 1.79 24.20 4.16
50/50 7.00% 19.32 1.84 26.76 6.88 0.12% 2.81% 10.60% 65.38%
** 3.50% 5.16% 17.96% 101.16%
50/50 4.75% 19.61 1.83 25.07 6.11 1.61% 2.23% 3.60% 46.88%
** 5.03% 4.57% 10.49% 78.65%