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Last week, I argued that this Center on Budget and Policy Priorities graph comparing the cost of the Bush tax cuts to the cost of fixing Social Security is more confusing than helpful, because it compares two numbers that don't really match up very well if you look at how they evolve over time. 


They replied with a lengthier explanation of their methodology, and  I responded with a longer analysis of exactly why, which relied on some hamfisted attempts to replicate their figures, using only a copy of excel and my damson-pure motives.  As far as I could tell, the only reason the numbers looked even remotely the same size was that they were using a present value, rather than comparing the future tax flows; I was also unable to make the tax figures match their social security data.

I emailed to ask them for clarification on how they derived their tax figures, and they assured me in multiple that they would get back to me.  Unfortunately, I assumed that meant they would email me, while apparently they assumed that this meant they would put up a blog post on Thursday evening, which passed unnoticed in the Labor-day maelstrom.

Since I didn't know it was there, I did not dig into their methodology; now that I have, I still find it problematic.  However, the Committee for a Responsible Federal Budget did notice, and wrote the blog post that I would have liked to write, except much better than I would have written it.  A long excerpt, below the fold.
Present value calculations are an important way to measure our fiscal obligations. But cash flow matters too. Here is a graph comparing CBPP's projections of the upper-income tax cuts to Social Security's shortfalls as measured by the Trustees:


As you can see, the Social Security shortfall begins to exceed the value of the upper-income tax cuts at the very beginning of next decade, and is projected to be significantly larger over the course of the following quarter century.

So why do the cash-flow numbers make Social Security's shortfall look so much larger? Well, there are two major reasons. First, by their very natures, present value estimates favor the near-term over the far term. This is logical, since a dollar today is worth more to us than a dollar tomorrow. But it also means that the first decade of relatively modest deficits (and brief surpluses) in Social Security weigh heavily on the calculation.

Secondly, these calculations include the value of the $2.6 trillion Social Security trust fund - and weight those heavily since we are holding that money today. If we were looking at the present value of Social Security's future shortfalls, as opposed to accounting for its past surpluses (which have accumulated in the trust fund), the program's unfunded costs would be closer to 0.9 or 1 percent of a GDP, rather than 0.7 percent. (That 0.7 percent isn't irrelevant, since most reform plans would rely on the trust fund, at least for a while. But looking out to the end of the 75-year window, the gap will reach 1.4 percent of GDP.)

Aside from these cash-flow issues, we also have some concerns about CBPP's methodology for projecting forward the value of the tax cuts - which appears to be highly sensitive to a few uncertain assumptions.

Essentially, CBPP assumes that the growth rates in revenue loss from 2017 through 2020 will continue forever. Over time, the compounding effects of these growth rates are significant -- increasing the value of the cuts to about 1.1 percent of GDP by 2080. Yet tiny changes in some of the numbers they use can drastically alter this number.

For example, they estimate that the tax cuts will cost $99 billion in 2017 and $120 billion in 2020 based off of a combination of Treasury and TPC estimates. We used some TPC tables to estimates these numbers at $102 billion in 2017 and the same $120 billion in 2020. When we tried to roughly apply their methodology using our $102 billion instead of their $99 billion (in other words, a nominal growth rate of about 5.6% instead of 6%) we found that the shortfall only reaches about 0.65 percent of GDP rather than 1.1 percent.

This is not to say that our $102 billion is right and their $99 billion is wrong - both are plausible and surely both will be wrong. The point is that tiny changes in these numbers cause wild swings in the ultimate cash flow results. (Though the magnitude of the present value cost wouldn't swing nearly as much - under the scenario we presented, the present value of the upper-income cuts would be between 0.5 and 0.6 percent of GDP rather than 0.7 percent).

We also tried projecting forward two other ways: assuming that the upper income tax cuts remained a fixed proportion of total revenue under CBO's extended baseline scenario and assuming bracket creep for the upper-income cuts in line with the total bracket creep we estimate in our CRFB baseline.
Here are the results:

To sum up: as I said in my follow-up post, the only reason the two numbers look even remotely similar is that they're using a present value calculation and a very long time frame. The present value calculation weights very near-term revenues and expenditures much more heavily than later ones; as a result, even though the expenditures on Social Security over the next 75 years are much larger than those on the Bush tax cuts for the wealthy in almost every time period, the early small surplus/small deficit of social security, and the fairly steady size of the Bush tax cuts, makes the present value much closer than the cash flows.

This might arguably be a good way to do the calculation for a corporation--though no corporation would forecast anything over such a long time frame. But since the government doesn't really have any mechanism to save, it's not very helpful to compare present values, because current cash flows can't actually be stored up to use in the future. The present value of social security's liabilities is perhaps a good way for us to understand the magnitude of the obligations we're undertaking, but it is not a good way to think about paying for the program.

However, it seems that I was wrong about the way that they calculated the Social Security flows. I derived a discount rate on the order of 7% by trying to work back from known social security numbers to the numbers they gave. Unfortunately, it seems that they included the social security trust fund, which--as the CFRB notes--again biases the social security numbers heavily downward, because the trust fund is treated as "cash in hand". Which it is, for the Social Security Administration. But which it is not, for the government as a whole.

I don't think it makes sense to include the trust fund in a comparison of the cost of the Bush tax cuts to the cost of the Social Security shortfall. The unified budget does not have a trust fund; it has assets (the bonds in the trust fund) and liabilities (the bonds in the trust fund) which exactly cancel each other out.

The Social Security Administration has a trust fund. But a comparison of the cost of the Bush tax cuts only makes sense in the context of the unified budget. The Bush tax cuts aren't going to cost the Social Security Administration anything. They are going to cost the Federal government as a whole some hundreds of billions of dollars (if they happen).

As, of course, is the widening gap between the taxes collected to pay for Social Security, and the benefits owed to seniors. And the cost to the Federal government as a whole is going to be whatever the difference is between payroll taxes taken in, and benefits paid out; from the viewpoint of the unified budget, the bill for Social Security will not be reduced even a single dollar by the changing accounting entries in the trust fund.

So if you are going to compare these two cost streams, you need to be looking at the actual cash flows, not the trust fund. And without the trust fund, the present values aren't close to each other. That's why I wondered if they had discounted the tax revenues; it turns out they had, but they'd added in the value of the trust fund on the other side, which I don't think makes sense in this context.

A few other thoughts:

1) This goes to show how careful we need to be with long range projections; they're simply extraordinarily sensitive to initial projections. The social security projections are probably the most reliable ones they have, because the system is roughly indexed for both wage growth and inflation, and its funding mechanism is a flat tax which hits the most inelastic bit of personal income. That means that we're largely forecasting the interplay of relatively predictable demographic changes with broad economic trends . . .

. . . And nonetheless, the numbers jump around tremendously from year to year. Forecasting tax revenue seventy five years in the future from a tax that isn't flat, and will be substantially changed by Congress if it hits too many people, seems basically pointless to me.

2) I agree with the CBPP and the CFRB that the Bush tax cuts should be allowed to lapse, and the money used to cover the coming gaping holes in the deficit. But I just don't think that the original graph was a good way to make that point. It required a lot of questionable assumptions to make the two numbers the same size--and comparing them in that way encouraged more than one blogger to mistake the graph's message as "we could fix Social Security by repealing the Bush tax cuts on the wealthy".

And this simply isn't true. Imagine that we somehow magically made the whole rest of the budget balance, including the Bush tax cuts. Then imagine that we were simply deciding how to pay for our remaining Social Security deficit, and someone said, "Hey, I know! Let's repeal the Bush tax cuts on high earners, as outlined in this CBPP graph!" Would the budget balance?

Not even if the US government used every dollar from the tax increases to retire its debt; not as long as Treasuries yield less than 4% a year. Even in a best case scenario, our interest savings would be less than $30 billion a year, far less than the difference between the extra tax revenue in their scenario (1.1% of GDP) and the Social Security deficit (1.4% of GDP). And, of course if you use less optimistic forecasts of tax revenue, those numbers are even farther apart.

Given that fact, I don't see how it can be meaningful to call the two cash flows equivalent.

I don't mean to say that the CBPP was deliberately misleading. But I think it's clear that their graph did mislead some people, and also, that their result is heavily sensitive to their starting assumptions, the inclusion of the trust fund in a unified budget comparison, and their decision to compare present value rather than cash flows.

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