In a comment on a recent post, and in more detail on The Dead Parrot Society, Victor tries to answer this request:
Matthew Yglesias asks, "The first thing that would be nice to calculate if someone can figure out how to do it is the exact average productivity growth over the next 75 years that we need to make sure that the Trust Fund is never exhausted."
In his search for an answer, and as a critique of a rough answer at Brad DeLong's blog, he finds the sensitivity analysis in the 2004 Trustees Report (Table VI.D4):
A far superior approach would be to do what the Social Security Trustees did: let the real-wage differential vary, keep all the other assumptions constant, and see how the results changed. They found that a 0.5%-points increase in the real-wage differential, improved actuarial balance by .54%-points of taxable payroll, from a 1.89% deficit to 1.35% deficit. Assuming the SSA truly held all other factors constant, this would be equivalent to increasing productivity from their baseline of 1.6% to 2.1%. That's a whopping increase in productivity, and a pretty good improvement in the actuarial balance, but you are still far from 75-year solvency. (which, recall, is only one of the issues that many are concerned about)
Victor just stops too early in his calculation. If one were to use the linear approximation in the text of the report, (0.54 percentage point of imbalance per 0.5 percentage point improvement in the real wage differential), then we would need to boost the differential by 1.89/0.54 = 3.5 units of 0.5, or by 1.75 percentage points up to 2.85 percent to go from the intermediate projections to 75-year balance.
If we wanted to be a bit fancier, we would note that the change over the three scenarios is not quite linear. The table gives us three pairs of numbers on {real wage differential, 75-year imbalance}: {0.6, -2.42}, {1.1, -1.89}, {1.6, -1.35}. With three pairs, we can fit a quadratic to do the extrapolation. When we do, we get [omitting the gratuitous algebra] about 2.81 percent for the real wage differential. Let's call it 2.8 percent, or an increase of 1.7 percentage points.
If we maintain the Trustees' other economic assumptions in Table V.B1 (earnings as a percent of compensation, average hours worked, and the wedge between CPI and the GDP price index) and Table V.B2 (total employment growth), this translates into long-term growth rates of 3.3 percent for productivity and 3.5 percent for real GDP. That productivity growth rate strikes me as too high.
However, these rough calculations were made without regard to what happens in the years after the 75-year window. In this case, there may be surpluses in the years near the end of that projection period, and so 2.8 percent for the real wage differential is too high for a longer projection period. We would need the actuaries to run the numbers themselves to be sure.
In addition, the "If we maintain ..." is a very big "if." It is not satisfied, for example, in the Brookings Paper by Robert J. Gordon that Victor cites in an earlier post as the basis of what Kevin Drum has been blogging about. It looks like, yet again, I've got more reading to do before I can make a more definitive statement.
And most importantly, it is hardly sensible to treat the Trustees' assumptions as if they are independent of each other, particularly the ones that work together to go from GDP growth to the real wage differential. If one of them changes, it is likely to be offset by changes in the others. For example, note from the historical series of Tables V.B1 and V.B2 that we have had high productivity growth in the past couple of years, but this has been associated with negative real wage differentials largely because of the decline in average hours worked. Using the last couple of years as evidence that productivity can be much higher than the Trustees have assumed is an incomplete argument. It is not evidence that productivity can be much higher, everything else equal.