# Number Crunching

NUMBER CRUNCHING….Paul Krugman writes today about something that’s already been batted around the blogosphere a fair amount: the rosy projections that Social Security privatizers use when they estimate stock market returns. Typically, they assume long-term returns of 6.5-7%, but returns like that are only feasible if long-term economic growth is also very strong. The problem is that if long-term growth is strong, Social Security isn’t in trouble in the first place:

It really is that stark: any growth projection that would permit the stock returns the privatizers need to make their schemes work would put Social Security solidly in the black.

But is it really that stark? The Social Security trustees ? the same ones who predict insolvency in 2042 ? include their economic assumption in their report. So what happens to the health of Social Security if growth projections are bumped up?

A bunch of math follows. In fact, it’s worse than that: it’s amateur, back-of-the-envelope math. I’m just trying to get an idea of what the answer is, and I hope some real economist will stick these numbers into a model and produce a more rigorous result. Here goes:

• Privatizers assume that stock market returns for the next 75 years will be as high as they have been for the previous 75 years. For that to happen, economic growth for the next 75 years also needs to be roughly as high as it has been for the past 75 years.

• Real GDP growth over the past 75 years has averaged 3.4% per year.

• GDP growth is equal to productivity growth + population growth + growth in average hours worked. The trustees assume long-term labor force growth of .2% per year and no growth in average hours worked. Thus, GDP growth of 3.4% requires productivity growth of 3.2% per year.

Warning: No one believes productivity growth will actually be that high. But given the slowdown in population growth over the next few decades, that’s the assumption we have to make in order to get 3.4% GDP growth.

• In the trustees’ model, real wage growth is closely related to productivity growth. Typically, it’s a few tenths of a percentage point less than productivity growth, which means that productivity growth of 3.2% equates to real wage growth of about 2.9%. This is 1.8 percentage points higher than the intermediate projection for real wage growth of 1.1%.

• Using the sensitivity analysis included in the trustees’ report, an increase of .5% in real wage growth equates to a decrease of .54% in the “actuarial balance” ? a measure of how big the Social Security deficit will be in 75 years. Thus, 1.8 percentage points of additional real wage growth equates to a drop of 1.94 percentage points in the projected Social Security deficit.

• The current intermediate assumption is that the long-term deficit equals 1.89% of taxable payroll. If you subtract 1.94, you get a long-term deficit of -.05%. In other words, you get a surplus of .05% of taxable payroll.

That was fun, wasn’t it? Basically, Krugman is right: if you take the economic assumptions behind stock returns of 6.5-7% and plug them into Social Security’s economic model, the system is solvent as far as the eye can see.

The big caveat here, of course, is that the privatizers are almost certainly wrong. Productivity growth is likely to be higher than the trustees’ estimate of 1.6%, but it’s not going to be 3.2% either. Something in the middle is more likely.

Still, no matter what numbers you use, Krugman’s basic point is sound: if you’re going to compare the current Social Security system to a privatized system, you need to use the same economic assumptions for both. Instead, privatizers like to play a shell game where they use gloomy assumptions for Social Security and rosy assumptions for privatization.

But you can’t have both. You’re free to be as gloomy or rosy as you want, but intellectual honesty requires that you be consistently gloomy or rosy. Unfortunately, there’s been precious little of that in the privatization debate.