# The Not-So-Simple Finance of Social Security Privatization

Brad DeLong’s The Simple Arithmetic of Social Security Privatization suggests how Bush’s “reform” might work for someone nearing the age of 50.

The word is that the Bush administration will shortly propose the diversion of 2% of the taxable Social Security payroll to private Social Security accounts… Since benefits for the next generation or so are not going to be touched, that means that benefits for those of us half a generation or more from retirement–say, in their early 50s, or younger–must be cut by proportionately more: 40 percent or so. In return, as compensation, those of us in our early 50s or younger will get our private Social Security accounts. Will this be a good deal? It could be, if – [t]he large premium return on equities really is a market failure that private accounts can profit from, rather than merely compensation for risk.

If I understand what Brad is saying, this would represent a massive transfer of income away from those of us in our mid-40s and the large premium required to leave us whole would strain all crediblity. Let me pose this in terms of a hypothetical professor named Jill who started working in 1985 and plans to work until 2025. In our example, Jill’s contribution to the Trust Fund over her lifetime have been \$6000 in inflation-adjusted dollars per year and Jill has also put in another \$6000 per year in a private account (the importance of this comes later). Let’s calculate the amount that would be hers – assuming a defined contributions analogy – in terms of the value as of 2025. If the real return to accumulated funds is 3%, the value as of 2025 would be \$452,408.

Taking away 40% of this value reduces her Social Security benefits by \$180,963 in terms of present value as of 2025. For this, Jill gets about \$1000 per year for the last 20 years of her life to invest as she pleases but none of her prior contributions. Now if Jill decides to invest these funds conservatively in government bonds, the accumulated value as of 2025 would be only \$26,870. My math would suggest that Jill would have to get a 19.7% real return on her private Social Security account to make up the difference.

But would Jill get any extra expected return? Let’s go back to our asusmption that half of her retirement savings was done by the Trust Fund placing \$6000 per year into an account paying safe but modest 3% real return and the other half was placed in her private account, which will shall assume is invested in some S&P 500 account paying an expected return of 7% with risk equal to S. Jill invested her funds this way because her optimal return-risk trade-off was to have expected return = 5% with risk = S/2. So under the Bush partial privatization plan, Jill has \$5000 per year placed into the Trust Funds government bonds and has \$7000 per year to invest anyway she chooses. Assuming this perfect capitals market world with the defined contributions analogy and rational Jill, which is what the Bush crowd assumes, Jill would take the \$1000 she is getting back from partial privatization into 3% bonds and not some incredibly high risk, high expected return portfolio. So I fail to understand how this could ever be a good deal for hypothetical Jill – or for that matter for me or for Brad. Even though Brad has been arguing for a somewhat different way of modeling this issue, I’m not sure how his model would work out to be a good deal in the context of the interesting problem he poses.