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In our model, privatizing social security contributions just requires setting the model's social

security payroll tax rate to zero; i.e., there is no need to add a formal private pension system to the

model. Since the agents in our model are not liquidity constrained, forcing them to contribute to

private accounts will not affect their net saving or labor supply decisions because they are free to

borrow against their mandated retirement accounts. That said, it is worth noting that in the particular

economies simulated herein, only the poorest 10 percent of agents actually seek to borrow against

social security. So if we added a liquidity constraint to the model (specifically, a constraint against

negative net wealth), it would not materially alter our findings. 

To capture the second feature of privatization, namely giving retirees and workers their full

accrued social security benefits, we phase out social security benefits starting 10 years after the
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privatization reform occurs. The 10-year delay reflects the need to give current retirees the same

benefits they would otherwise have received. In the model, social security benefits are received for

10 years from 45 to 55 (real age 65 to real age 75). Starting in the 11th year of the reform, we phase

out social security benefits by 2.2 percent (of the baseline benefits) per year for 45 years.

We use three alternative taxes to pay for social security benefits during the privatization

transition: proportional payroll taxation using social security's tax base, income taxation with the tax

base reductions noted earlier, and a consumption taxation. These taxes are temporary and go to zero

after the transition is complete.

The transition to a privatized social security system alters the income-tax base. Since we

maintain a constant level of government purchases per effective worker in each transition, we need

to adjust income-tax rates along the transition path even in those simulations in which income taxes

are not used to pay the social security benefits accrued under the old system. 7KH VKDUHV RI

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Macroeconomic Effects

Tables 3 - 7 present the macroeconomic effects of twelve alternative privatization reforms.8

Runs 1 through 6 correspond to forced participation explored in this section and runs 7 through 12

correspond to opting out explored in the next section. The top panels of Figures 3 - 5 graph the
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information corresponding to runs 1, 3, and 5 in which the tax-benefit is perceived.9 Year 1 (1997)

is the first year of the transition path. An agent born (economically) in year -10, for example, is 11

years old (age 31 in real-life).

Consider first Runs 1, 3, and 5 which use payroll taxation, consumption taxation, and income

taxation, respectively, to privatize social security. In each of these runs, agents perceive the taxbenefit linkage they face. These tables and figures show that each of these three runs produces the

same quite striking long-run results. The capital stock rises by 39 percent, labor supply rises by 5

percent, output per person rises by 13 percent, the real wage rises by 7 percent, and the real interest

rate falls by 19 percent.

Although the long-run position of the economy is the same in each of these runs, the time

it takes to get close to the economy’s long-run position, and the size of the short-run economic

response, depends critically on the choice of the tax used to finance transitional social security

benefits. Consider payroll-tax finance. After 25 years, the capital stock is only 5 percent larger,

which is only 13 percent of its ultimate increase. In the case of income-tax finance, the capital stock

is actually 5 percent smaller 25 years after the transition, notwithstanding the fact that it ultimately

ends up 39 percent larger. With consumption-tax finance the transition is much faster, but it’s still

rather slow. After 25 years the capital stock is 13 percent larger which is only one-third of its longrun increase.

One reason why the transitions take time is that social security benefits are reduced gradually

over a 55-year period. A second reason the transitions are slow is that the capital stock is a stock and


even substantial changes in annual saving rates take quite a while to materially alter it. This feature

of neoclassical economies&that policy-induced economic transitions are very slow&was one of the

main messages of Auerbach and Kotlikoff (1987). The third reason the transitions are slow applies

in the case of income-tax finance. Using this tax instrument means that in the short run, there will

be quite high marginal tax rates on labor supply and capital income. This gives households an

incentive to substitute current leisure and consumption for future leisure and consumption. Indeed,

in the case of income-tax finance, the short-term disincentive to work leads to a 5 percent decline

in aggregate labor supply.

With consumption-tax finance, the short-run saving incentives are quite different. The

additional consumption tax starts out at a 10 percent rate and then declines over time to zero. The

temporarily high price of consumption gives agents an incentive to delay their consumption

expenditures and, consequently, save more. Moreover, using the consumption tax rather than an

income or wage tax to finance transitional social security benefits places a larger fiscal burden on

the initial elderly and a lower one on those who are young and middle aged. Since the elderly, who

are closer to the end of their lives, have higher propensities to consume than do the young and

middle aged, redistributing from them to younger cohort leads to less overall consumption and more

national saving. Furthermore most of this redistribution to the young occurs through a efficient onetime tax on existing non-social security wealth.

No Perceived Tax-Benefit Linkage

Runs 2, 4 and 6 repeat each simulation under the assumption of no perceived tax-benefit

linkage. This assumption increases the payroll tax's distortion of labor supply and increases the

efficiency gains from privatizing social security. This translates into growth in capital, labor supply,


and output that is 1 to 2 percentage points larger than with perceived tax-benefit linkage. Notice that

assuming no perceived linkage reverses the sign on the short-run labor supply response to payroll

tax financing from negative to positive. These results suggest therefore that the degree of tax-benefit

linkage can play an important role in determining the gains from privatization.

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Workers will choose to opt out of Social Security if their present value of future Social Security

taxes exceeds the present value of their future benefits. The decision for each worker to opt out,

therefore, depends endogenously vis-a-vis factor prices on whether other workers opt out; i.e., the

program searches for the Nash equilibrium.
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We consider two alternative taxes to supplement social security's revenue: income taxation

with the tax base reductions noted earlier, and consumption taxation. Since all agents eventually

choose to opt out of social security in the final steady state, those taxes are purely transitional. As

a result, all of the opting out experiments converge to the same final steady state&and the same

steady state as the forced participation experiments reported earlier, a fact that facilitates the

comparison of transition paths.

Participation

The solid lines in the top panel of Figure 6 show those generations by income class who

participate in the new privatized system&that is, opt out of social security&for the income tax

finance case.10 All agents younger than 25 years of (real-life) age opt out as do all future agents.

The participation lines therefore are not continued past transitional year 50 for resolution.

The effects of adverse selection can be seen both inter-generationally and intragenerationally. Inter-generationally, many living agents, especially older people, stay with social

security because they have accrued enough benefits and so it is not worth switching. Intragenerationally, a poor agent is less likely to opt out of social security than a richer agent of the same

age. This reflects the progressive nature in which social security benefits are computed.

Macroeconomic and Welfare Effects: A Comparison with Forced Participation

The impact of adverse selection on macroeconomic variables can be seen by comparing each

opting out run with its forced-participation counterpart that uses the same transitional finance tax.
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The macroeconomic responses corresponding to the opting out runs 7 - 12 are reported in Tables 3 -

7 and are graphed in Figures 7 - 10 for the perceived tax-benefit linkage cases. The welfare effects

for each run is shown in Table 8 and, for the cases of perceived tax-benefit linkage, in the bottom

panels of Figures 7 - 10.

Consider income tax financing of benefits. Comparing Run 4 (forced participation) with Run

7 (opting out) shows that opting out leads to a quicker rate of convergence relative to forced

participation. For example, whereas the capital stock is 5 percent smaller after 10 years under the

forced participation scheme, it is only 2.5 percent smaller under opting out. The reason is that the

opting out plan reduces social security wealth for young and middle-age transitional savers by more

than the forced participation plan. Whereas the forced participation plan compensates young and

middle-age savers in proportion to their accrued benefits, many of these same savers are willing to

forfeit their social security wealth under the opting out plan.11 Notice that opting out also does a

slightly better job at protecting the welfare of the initial elderly. The welfare of this age group is

about one half a percentage point higher under opting out than under forced participation. The

reason is that the opting out plan continues to collect some revenue from payroll taxes whereas

forced participation does not. The opting out plan therefore puts more emphasis on wages and

salaries than interest income, the latter of which is the most important source of income for the

elderly. The benefits of quicker convergence and protection of the elderly welfare, however, do not

come for free. Opting out leads to larger welfare losses for middle-age agents across the entire

income distribution. For example, opting out increases the welfare loss for 25-year olds (46 in real


life) in income classes 6 through 9 by almost 1 percentage point relative to forced participation.

Middle-age agents tend to not opt out (Figure 6, top panel) and pay both the existing payroll tax and

higher income taxes.

Now consider consumption tax financing of benefits. The rate of convergence during the

first two decades is now very similar for both forced participation (Run 5) and opting out (Run 9).

Around year twenty, however, the rate of accumulation under the opting out plan actually

accelerates. By year forty, the capital stock is 5 percentage points larger under the opting out plan.

Once again, the opting out plan better protects the welfare of the initial elderly at a cost to middle

age workers. The continued collection of some payroll tax revenue necessitates a smaller hit on the

non-social security wealth of the initial elderly.

Reducing the Payroll Tax Rate

Runs 11 and 12 consider a variation of the opting out plan in which the payroll tax is reduced

to one-half of its present law value. By raising less payroll tax revenue from middle-age workers,

the intention here is to distribute more of the transitional pain to the tails of the age distribution: both

older workers, who pay little or no payroll taxes due to retirement, and younger workers who pay

little or no payroll taxes because they opt out.

Comparing Run 11 with opting out Run 7 for income transition finance shows that middleage workers are now significantly better off when the payroll tax is reduced, by as much as 1.5

percentage points of remaining lifetime utility. Moreover, middle-age agents now fare better than

relative to forced participation, by as much as 1 percentage point. Interestingly, hardly detectable

traces of burden are shifted to the initial elderly. This is because the decrease in the payroll tax rate

causes fewer people to opt out (Figure 6, bottom panel). The payroll tax revenue therefore drops by


only 20 percent in going from Run 7 to Run 11 (about 7 percent of the pre-privatization payroll tax

revenue) instead of 50 percent which could be expected from the outset. Only a small amount of

additional general revenue is therefore needed. Hence, this opting out variation still does a better

job at protecting the welfare of the initial elderly than forced participation. Instead, most of the

burden is shifted to the more plentiful young workers whose welfare decreases, although by less than

one half a percent. Notice, however, that the costs to young workers is only slightly larger than that

corresponding to forced participation (Run 3). For 10-year old workers in income class 6, the

additional loss is only 0.1 percentage points. There is no loss for income class 9 workers and

income class 12 workers are actually better off (0.3 percentage points). Only income class 3 workers

are moderately worse off (0.4 percentage points). Income class 1 workers are worse off by 0.4

percentage points but still have sizeable positive gains (1.2 percentage points). The rate of

convergence of the capital stock is only little slower than straight opting out but still faster than that

corresponding to forced participation. In sum, this variation of the opting out plan moderates the

impact of middle age workers and appears to stack up rather well against forced participation. So

what is the cost of all this good news? Relative to Runs 3 and 7, notice that Run 11 reduces the

gains to generations born during the first decade after privatization. However, everyone of those

agents still faces positive gains and so this burden shifting might be a desirable outcome. Similar

results hold for consumption tax financing (Runs 5, 9 and 12).

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References

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$OWLJ'DYLG$ODQ$XHUEDFK/DUU\.RWOLNRII.HQW6PHWWHUV-DQ:DOOLVHU6LPXODWLQJ86

7D[5HIRUP1%(5:RUNLQJ3DSHU1R

Arrau, Patricio and Klaus Schmidt-Hebbel. "Macroeconomic and Intergenerational Welfare

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Macroeconomics and Growth Division, Washington, D.C.: World Bank, Washington, D.C. 1993.

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Auerbach, Alan J. "Tax Reform, Capital Allocation, Efficiency, and Growth," in: Henry Aaron and

William B. Gale (eds.), Economic Effects of Fundamental Tax Reform, Washington, D.C.: The

Brookings Institution. 1996.

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SDJHV

&&&&&:RXOG3ULYDWL]LQJ6RFLDO6HFXULW\5DLVH(FRQRPLF:HOIDUH"1%(5:RUNLQJ3DSHU

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3DSHU

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1DWLRQDO7D[-RXUQDO0DUFKSDJHV

&&&&&"The Transition Path in Privatizing Social Security," forthcoming in: Martin S. Feldstein

(ed.), Privatizing Social Security, University of Chicago Press, 1997.

Fullerton, Don and Diane Lim Rogers. Who Bears the Lifetime Tax Burden?, Washington, D.C.:

The Brookings Institution. 1993.

Gustman, Alan and Thomas Steinmeier. "Privatizing Social Security: First Round Effects of a

Generic, Voluntary Privatizes U.S. Social Security System." NBER Working Paper No. 5362, 1995.

+XDQJ+H6HORPURKRURyOXDQG7KRPDV6DUJHQW7ZR&RPSXWDWLRQDO([SHULPHQWVWR)XQG

6RFLDO6HFXULW\)RUWKFRPLQJLQ0DFURHFRQRPLF'\QDPLFV


Kotlikoff, Laurence J. "Privatizing Social Security: How It Works and Why It Matters," in: James

M. Poterba (ed.), Tax Policy and the Economy, vol. 10, Cambridge, Mass.: MIT Press, 1996.

Kotlikoff, Laurence J., Kent Smetters, and Jan Walliser. "Privatizing U.S. Social Security % A

Simulation Study," forthcoming in: Klaus Schmidt Hebbel (ed.), Pension Systems: From Crisis to

Reform, Washington, D.C.: The World Bank, 1997.

Menchik, Paul L. and Martin David. "The Incidence of a Lifetime Consumption Tax," National

Tax Journal, vol. XXXV, 1982, pp. 189-203.

Samwick, Andrew. "Discount Rate Heterogeneity and Social Security Reform." Manuscript,

Dartmouth College, November, 1996.

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Table 3

Percentage Change in Capital Stock Relative to Steady State 

Run

Opting

Out?

Finance

of Social

Security

Benefits

TaxBenefit

Linkage

New

Social

Security

Tax Rate

Year of Transition

5 10 25 150

1 No W Yes n/a 0.0 0.1 5.2 39.0

2 No W No n/a 0.5 1.1 6.1 39.8

3 No Y Yes n/a -2.4 -5.0 -4.6 39.0

4 No Y No n/a -2.2 -4.3 -3.5 39.8

5 No C Yes n/a 1.8 4.1 12.8 39.0

6 No C No n/a 2.1 4.7 13.6 39.8

7 Yes Y Yes PL -1.2 -2.5 -3.4 39.0

8 Yes Y No PL -1.4 -3.1 -4.0 39.8

9 Yes C Yes PL 1.5 3.8 14.2 39.0

10 Yes C No PL 1.4 3.4 14.1 39.8

11 Yes Y Yes PL / 2 -1.4 -3.0 -4.5 39.0

12 Yes C Yes PL / 2 1.5 3.5 11.0 39.0

C : Consumption Tax

n/a: non-applicable. For forced privatization, payroll tax is endogenous for payroll tax financing and zero for

income tax and consumption tax financing.

PL: Present Law payroll tax rate

PL / 2: Present Law payroll tax rate divided by 2.

W: Payroll Tax

Y: Income Tax


Table 4

Percentage Change in Labor Supply Relative to Steady State 

Run

Opting

Out?

Finance

of Social

Security

Benefits

BenefitTax

Linkage

New

Social

Security

Tax Rate

Year of Transition

5 10 25 150

1 No W Yes n/a -1.1 -1.1 1.8 5.5

2 No W No n/a 0.3 0.4 3.2 7.0

3 No Y Yes n/a -4.5 -4.7 0.0 5.5

4 No Y No n/a -2.9 -3.1 1.1 7.0

5 No C Yes n/a 0.3 0.4 2.4 5.5

6 No C No n/a 1.8 1.9 3.9 7.0

7 Yes Y Yes PL -3.6 -3.9 -2.1 5.5

8 Yes Y No PL -3.8 -4.0 -0.6 7.0

9 Yes C Yes PL -0.2 0.0 2.4 5.5

10 Yes C No PL -0.2 0.3 3.9 7.0

11 Yes Y Yes PL / 2 -2.6 -3.0 -3.8 5.5

12 Yes C Yes PL / 2 0.8 0.8 0.9 5.5

C : Consumption Tax

n/a: non-applicable. For forced privatization, payroll tax is endogenous for payroll tax financing and zero for

income tax and consumption tax financing.

PL: Present Law payroll tax rate

PL / 2: Present Law payroll tax rate divided by 2.

W: Payroll Tax

Y: Income Tax


Table 5

Percentage Change in Output Relative to Steady State 

Run

Opting

Out?

Finance

of Social

Security

Benefits

BenefitTax

Linkage

New

Social

Security

Tax Rate

Year of Transition

5 10 25 150

1 No W Yes n/a -0.8 -0.7 2.6 13.0

2 No W No n/a 0.4 0.6 3.9 14.4

3 No Y Yes n/a -4.0 -4.8 -1.5 13.0

4 No Y No n/a -2.7 -3.4 0.0 14.4

5 No C Yes n/a 0.6 1.3 4.9 13.0

6 No C No n/a 1.9 2.6 6.3 14.4

7 Yes Y Yes PL -3.0 -3.5 -2.4 13.0

8 Yes Y No PL -3.2 -3.8 -1.4 14.4

9 Yes C Yes PL 0.2 1.0 5.2 13.0

10 Yes C No PL 0.2 1.1 6.4 14.4

11 Yes Y Yes PL / 2 -2.3 -3.0 -4.0 13.0

12 Yes C Yes PL / 2 1.0 1.5 3.3 13.0

C : Consumption Tax

n/a: non-applicable. For forced privatization, payroll tax is endogenous for payroll tax financing and zero for

income tax and consumption tax financing.

PL: Present Law payroll tax rate

PL / 2: Present Law payroll tax rate divided by 2.

W: Payroll Tax

Y: Income Tax


Table 6

Percentage Change in Wages Relative to Steady State 

Run

Opting

Out?

Finance

of Social

Security

Benefits

BenefitTax

Linkage

New

Social

Security

Tax Rate

Year of Transition

5 10 25 150

1 No W Yes n/a 0.4 0.5 0.8 7.1

2 No W No n/a 0.1 0.2 0.7 6.9

3 No Y Yes n/a 0.5 0.0 -1.0 7.1

4 No Y No n/a 0.2 -0.3 -1.2 6.9

5 No C Yes n/a 0.4 0.9 2.4 7.1

6 No C No n/a 0.1 0.6 2.3 6.9

7 Yes Y Yes PL 0.6 0.3 -0.3 7.1

8 Yes Y No PL 0.6 0.2 -0.9 6.9

9 Yes C Yes PL 0.4 0.9 2.8 7.1

10 Yes C No PL 0.4 0.8 2.4 6.9

11 Yes Y Yes PL / 2 0.3 0.0 -0.2 7.1

12 Yes C Yes PL / 2 0.2 0.7 2.4 7.1

C : Consumption Tax

n/a: non-applicable. For forced privatization, payroll tax is endogenous for payroll tax financing and zero for

income tax and consumption tax financing.

PL: Present Law payroll tax rate

PL / 2: Present Law payroll tax rate divided by 2.

W: Payroll Tax

Y: Income Tax


Table 7

Percentage Change in Interest Rates Relative to Steady State 

Run

Opting

Out?

Finance

of Social

Security

Benefits

BenefitTax

Linkage

New

Social

Security

Tax Rate

Year of Transition

5 10 25 150

1 No W Yes n/a -1.0 -1.4 -2.5 -18.6

2 No W No n/a -0.1 -0.7 -2.0 -18.2

3 No Y Yes n/a -1.5 0.0 3.2 -18.6

4 No Y No n/a -0.6 0.9 3.6 -18.2

5 No C Yes n/a -1.1 -2.7 -6.9 -18.6

6 No C No n/a -0.2 -2.0 -6.5 -18.2

7 Yes Y Yes PL -1.8 -1.0 1.1 -18.6

8 Yes Y No PL -1.9 -0.7 2.7 -18.2

9 Yes C Yes PL -1.2 -2.7 -7.8 -18.6

10 Yes C No PL -1.1 -2.3 -6.8 -18.2

11 Yes Y Yes PL / 2 -0.9 0.0 0.5 -18.6

12 Yes C Yes PL / 2 -0.5 -1.9 -6.8 -18.6

C : Consumption Tax

n/a: non-applicable. For forced privatization, payroll tax is endogenous for payroll tax financing and zero for

income tax and consumption tax financing.

PL: Present Law payroll tax rate

PL / 2: Present Law payroll tax rate divided by 2.

W: Payroll Tax

Y: Income Tax


Table 8

Percentage Change in Remaining Lifetime Utility for Selected Income Classes

 

Year of Birth

Run Class -54 -25 -10 1 10 25 150

1 1 0.0 -2.0 -1.3 -0.6 0.1 2.2 6.0

3 -0.1 -1.7 -1.1 -0.4 0.5 3.0 7.4

6 -0.1 -1.4 -0.8 -0.2 0.8 3.3 8.0

9 -0.1 -1.2 -0.7 -0.1 0.9 3.5 8.1

12 -0.1 -0.6 -0.4 -0.1 0.3 1.5 4.4

2 1 -0.2 -1.8 -1.1 -0.5 0.2 2.3 6.0

3 -0.1 -1.4 -0.7 -0.2 0.7 3.2 7.4

6 0.0 -1.1 -0.4 0.1 1.1 3.6 8.0

9 0.0 -0.9 -0.3 0.2 1.2 3.7 8.1

12 0.0 -0.3 -0.1 0.1 0.5 1.8 4.4

3 1 -0.1 -0.2 1.6 3.2 3.1 3.5 6.0

3 -1.4 -1.6 0.0 1.4 1.7 3.3 7.4

6 -1.3 -2.1 -0.7 0.7 1.1 3.2 8.0

9 -1.2 -2.4 -1.0 0.3 0.8 3.1 8.1

12 -1.7 -3.6 -3.6 -3.0 -2.5 -0.2 4.4

4 1 -0.1 0.0 1.9 3.3 3.1 3.6 6.0

3 -1.3 -1.2 0.4 1.7 1.9 3.5 7.4

6 -1.1 -1.8 -0.2 1.0 1.4 3.5 8.0

9 -1.1 -2.1 -0.5 0.6 1.1 3.4 8.1

12 -1.6 -3.2 -3.2 -2.7 -2.1 0.1 4.4

5 1 0.7 -2.1 -0.6 0.5 1.3 3.2 6.0

3 -0.4 -2.0 0.0 1.2 2.1 4.2 7.4

6 -0.9 -1.7 0.3 1.6 2.6 4.8 8.0

9 -1.2 -1.6 0.5 1.7 2.7 4.9 8.1

12 -1.5 -2.5 -1.8 -1.0 -0.1 1.7 4.4


Table 8 Cont.

5XQ &ODVV       

        

       

       

       

       

        

       

       

       

       

        

       

       

       

       

        

       

       

       

       

        

       

       

       

       


Table 8 Cont.

5XQ &ODVV