From scanning blogs and news stories, it's clear that a number of people believe the Social Security Trustees projections are overly pessimistic. They might be. (They also might be overly optimistic -- there's a great deal of uncertainty involved here.)

Leaving aside the question of whether the Trustees projections are reasonable -- I believe they are -- it's important to understand how differences in those projections might change outcomes for the system. In other words, if the Trustees ARE pessimistic, how much better will Social Security's finances be?

It's possible to estimate this using the Sensitivity Analysis contained in each year's Social Security Trustees Report. It reports high and low estimates for each demographic variable and how a high or low value for any given variable would by itself affect system financing. If all the variables are set to their high or low cost value, we get the overall high or low cost scenarios for the system.

To make this process easier, I created a simple spreadsheet that estimates how different values for a few of the major economic/ demographic variables affect Social Security's annual cash flows and trust fund ratio (the ratio of trust fund assets to benefit costs in a given year). I used the Policy Simulation Group's SSASIM model to estimate cash flows for the high/low cost values of four different variables: the total fertility rate (children per woman); net immigration; improvements in mortality; and real wage growth. These are the biggies in affecting annual cash flows. Other factors have smaller effects, and changes to interest rates affect only the trust fund ratio.

Using the SSASIM output, I calculated a simple linear function for each variable, which allowed me to estimate the change in annual cash flows for each variable. I then net these out so a number of changes can be combined to estimate the effects on the total system.

Please note: this simple model is designed for illustrative, educational purposes, to give a ballpark estimate of how different demographic/economic assumptions affect Social Security's financings. So it's a crude tool.

But it's also a useful tool. Consider that many people argue that the Trustees' economic assumptions are overly pessimistic. Well, the principal economic assumption is real wage growth; that's how productivity filters through to the program. What if we increase real wage growth from 1.1 percent, which is about its average over the past 40 years, to 1.7 percent?

The chart below shows the change in cash flows. The red line is the Trustees' intermediate projections, while the blue line is adjusted for higher wage growth. The difference is significant -- deficits are delayed for a few years past 2017 and are always smaller than under the lower-growth assumption. However, is higher wage growth -- 50% higher than projected or seen over the past four decades -- enough to fix the system, such that we don't need to bother with reform? No. By the 75th year the deficit is around 3.75% of payroll rather than 5.3%. In other words, economic growth -- while certainly helpful -- won't plausibly be high enough that we can safely ignore the problem.

You can play with other variables as well. Fertility is a big factor: if we can increase our fertility rate significantly then Social Security's problems really do become a lot easier. But if fertility falls to European levels, we're in big trouble. I hope this little tool is interesting. You can download the spreadsheet here.

## Thursday, February 28, 2008

### Gadgets: How will Social Security fare under different economic or demographic assumptions?

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## 7 comments:

In your simple model changes in fertility, immigration, and productivity have no impact on taxable payroll. Can you explain why you modeled it that way?

That's a good question. One answer is just that it's a 'simple model'. But the real answer is that the simple model is based on the sensitivity analysis in the Trustees Report and using the SSASIM model, which DO account for changes in taxable payroll. In other words, it doesn't calculate changes in dollar terms and then apply them to an unchanging payroll base; it calculates changes directly as a percentage of payroll, based on what the TR and SSASIM report. So the results for any single variable (say, wage growth) will be correct, or very nearly so.

Where things can get funny is interactions between different variables, say if you change both wage growth and life spans. I don't expect the errors would be very large, but for a very important task I would model it directly rather than using a tool like this.

But to get a general idea of how things play out, this tool will be close enough for most purposes. Thanks.

As a follow-up, it was basically for this reason that the model doesn't calculate the actuarial balance (which is equal to the PV cash deficit minus the current TF balance, over the PV of total payroll). It might be possible to get around that limitation, but I'm not sure. But you can judge 75-year solvency if the TF ratio remains above 100% at the 75th year, and sustainable solvency if the ratio is stable or rising as of the 75th year.

Well I would point out that the Trustees' Low Cost alternative does show you can get a 100% solution with a combination of 2.0% productivity, 1.6% real wage growth, 2.8% Real GDP, even with ultimate immigration numbers at rates slightly lower than 2001. None of those numbers seem out of line with performance over at least the last ten years.

And an examination of the results of Low Cost in Figure II.D7 in the 2007 Report shows a TF ratio that stabilizes around 2055 and starts rising pretty sharply after 2070, indeed since 1997 Low Cost has operationally equated to sustainable solvency. (Which raises questions of its own.)

So we have a model that does the job and I have not seen a convincing argument that suggests Low Cost is out of reach. The best they can do it point to the fertility figure while ignoring the offsetting pessimistic immigration figure.

We don't look to be hitting Low Cost numbers near term but over the medium to long term they seem pretty reasonable.

The Low Cost "scenario" gets to sustainable solvency, but the low cost value for real wage growth (i.e., 1.6% rather than 1.1%) doesn't. The scenario combines higher wage growth with better values for all the other variables as well (immigration, life expectancies, etc.). If I added interest rates to the gadget you could probably replicate the low cost scenario pretty accurately. For now, though, what it shows is that higher wage growth alone is very unlikely to get you there.

In the base case, the gadget has the trust fund becoming insolvent in 2041 (vs. 2040 in the TR). Raise real wage growth to 1.6% and the trust fund stays solvent til 2049. Raise it to 2.1% (a very high number by historical figures) and you get to 2071. This shows how hard it is for economic growth alone to fix the problem.

Well as you said SS is not assured in the long term, but you do a great job showing that it's far from insolvent. If we are even having this debate, then it means only minor changes in the SS rules would fix the problem long-term.

Well, it depends on what time period you're interested in solvency over. 20 years? There's probably a 75 percent chance of solvency. 30 years? Around a 50 percent chance. 50 years? Much less than 50 percent.

I suspect that for a number of people, raising these questions regarding assumptions is a way of implying that any changes needed will be small. But remember a) both non-partisan groups that look at the finances (SSA actuaries and CBO) agree that there's a very good chance of a very significant shortfall; and b) if they're wrong, they're as likely to be so on the optimistic as the pessimistic side. In other words, errors won't always be in our favor.

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