Calculating the Relative Cost of Budget Items

The Center on Budget and Policy Priorities has responded to my critique of their graph:

First of all, the $700-billion figure that McArdle cites isn't the full 10-year cost of the high-income tax cuts. It's only the revenues that President Obama's upper-income tax proposal would generate. The President's proposal, however, also would reduce the tax rate on dividends from 39.6 percent under current law to 20 percent for high-income taxpayers. In addition, it would extend the 28-percent income tax bracket up to $200,000 for individuals and $250,000 for couples. Adding these two items, the total cost of the upper-income tax cuts is $837 billion over the 2011-2020 period and $120 billion in 2020 alone, based on estimates from the Joint Committee on Taxation and the Department of the Treasury. That's about 0.5 percent of gross domestic product (GDP) in 2020.

Income taxes tend to grow as a share of income each year because rising real incomes push people into higher tax brackets, and we project that the high-income tax cuts will cost about 0.7 percent of GDP over the next 75 years. Social Security's trustees estimate that Social Security's shortfall over the next 75 years also equals 0.7 percent of GDP, so the cost of the upper-income tax cuts and the amount of the Social Security shortfall are about the same. McArdle correctly notes that the Social Security shortfall 75 years from now is higher than the 75-year average, but so is the cost of the upper-income tax cuts.

Despite what McArdle implies, the Center has not suggested that "you could 'pay for' the Social Security shortfall by rescinding the Bush tax cuts on the rich." We have made quite clear that President Obama and Congress should let the upper-income tax cuts expire and devote the proceeds to deficit reduction. At the same time, as Kathy and I wrote, we have consistently argued that Congress should enact revenue and benefit changes that would place Social Security on a sound long-term financial footing.

In comparing the high-income tax cuts to the Social Security shortfall, we wanted to illustrate the hypocrisy of Members of Congress who argue that the tax cuts are affordable but Social Security is not, even though their cost is about the same.

My thoughts, at rather unfortunate length, below the fold:

1)  $837 billion is still not 0.7% of GDP over the forecast period.  It's 0.44% of GDP--about the size of the gap in 2020, which then rapidly grows beyond it.

2)  You could argue that it grows towards the out years.  But so does the Social Security shortfall.  Their figure for Social Security is a very low percentage of GDP, compared to the 1.2-1.4% forecast for the overwhelming majority of the forecast period.  The reason it's so low is that they've used the present value of the Social Security obligations.   That is to say, they've applied an annual discount rate to future cash flows.

I won't go into the rather tedious math, but remember the exercises in grade school you did with compound interest, where you start with $100 in year one, leave it at 5% interest for thirty years, and end up with over $400?  (Which is to say, all the money in the whole world?)

Present value works sort of like compounding, in reverse. With present value, in order to derive the total value of all of our expected future cash flows, we estimate those cash flows, and then discount the ones that come later relative to the ones that come sooner, in order to account for the time value of money--the fact that a dollar today is worth more to you than a dollar tomorrow.  Other things may factor into your discount rate--the risk of not getting the money after all, the opportunity cost of the money, inflation, or what have you.  These are the sorts of calculations done by the folks who offer you CASH NOW for your structured settlement on late night television--and also, many more reputable financial analysts.

The important thing for my purposes is that when you apply this discounting--especially over very long time horizons, like the 75 years that the CBPP chose--it is most strongly influenced by relatively early cash flows

Remember the compound interest exercises?  Remember that they'd sort of toddle along boringly for years and years, and then really start growing more than halfway through the exercise?  Present value works exactly the opposite.  Depending on what discount rate you use, the overwhelming majority of the cash flows in your present value tend to come from the first 10-to-20 years of the forecast period; the very heavily discounted cash flows a long time off almost might as well not even be there, unless they're growing very rapidly.

This is not quite true of Social Security, because the gap grows so much bigger by 2030.  But it is still true that the next ten years--when the gap is smallest--are very heavily overweighted compared to the last 60 years, when the gap will range between 1-1.4% of GDP.

3)  Onto the tax cuts:  they essentially argue that bracket creep will increase the value of the tax cut by almost 50% over time.  Maybe so.  But relying on bracket creep over a 75 year time horizon does not seem like a very realistic forecast technique.  $250,000 may be about the cost of a pack of Dentyne Ice in 2085, at which point I assume that Congress is probably going to step in and readjust the brackets to keep our nation's poor from paying almost half their income to Uncle Sam.  And at that point, saying the tax cuts apply "exclusive to high earners"--which is how they labeled their graph--makes no sense.

For that matter, the odds that extending or repealing the Bush tax cuts will be the last change to the tax code we make over the next 75 years--sort of implied by their choice of a forecast period--do not seem all that high.

4)  I don't understand how they're discounting the tax cuts--which you have to do, because it's moronic to compare an undiscounted cash flow to a discounted one.  Since the folks at the CBPP are not morons, I assume they are discounting the projected cash flows.  But I don't understand how they're doing it.

For a tax that generates something like 0.2% of GDP next year and 0.5% of GDP in 2020 to have a present value of 0.7% of GDP over 75 years, the growth rate of the bracket creep must be very high, or the discount rate must be very low, in order to overcome that early-year bias. 

Just to show you how big a difference discounting makes, if you used a present value of extending the Bush tax cuts for the wealthy, as calculated by the CBO, the cost would be $500 billion instead of $700 billion just over the next ten years.  If I compare that to discounted GDP--which is what they do for Social Security--then I get the tax cuts costing only 0.3% of GDP, rather than 0.35%. 

Why?  Because there's a zero in 2010, and an abnormally low take (due to the recession) in 2011.  These have a much bigger effect than the 0.5% in year 2020--even though I used a pretty conservative discount rate of 5%.

A similar thing happens with Social Security--the surpluses/small deficits now count much more heavily than the large deficits later. 

The only way you can end up with very late (30+) years making a big contribution to the total, is if the growth rate of the cash flows is bigger than the discount rate--say, your business is growing by 10% a year, but you're discounting by 5%.  The higher the discount rate you use, the faster the cash flows have to be growing to overcome this effect.

Do we think that the percentage of GDP the government could earn through bracket creep is going to be growing steadily, year on year, faster than any reasonable discount rate?

Well, the CBO doesn't.  In its forecast, the revenue (cost of cuts) projected for these taxes is growing around 3% a year.  Even with a very low discount rate, this should not be having much effect on the comparison.  So don't understand how we get to 0.7% of GDP without some really unrealistic assumptions about the future course of tax revenues.  Even adding interest costs doesn't get me there, because the US borrows at such cheap rates, and because inflation and GDP growth tend to erode the cost of old debt.  That's how real net interest costs fell under Bush, even though the deficit and the debt both grew.

5)  Overall, I find this an extraordinarily muddy way to make the comparison.  One doesn't usually present cash flows as a bar graph with a single bar.

To me, you want to compare tax revenues and expenditures year-to-year, because the government is not very good at saving extra cash.  When we compare the yearly inflow we expect from repealing the Bush tax cuts, to the extra money we'll have to find in order to cover the shortfall, we do not see anything that looks like what is implied by this bar graph.  We see this graph from the Social Security Trustees.

SS Chart.png

Instead, we see tax cuts which are costly now, and stay at roughly the same cost--and a social security deficit which starts small, grows to roughly the same size as the tax cuts in 2020, and then rapidly blows beyond them.  We see a shortfall that is not going to be covered by any tax raising less than 1% of GDP.

6)  To round up: the purpose of comparing two present values of different cash flows is, at least in a case like this, to see whether you could use one to pay for the other.  Is there any way that, by simply repealing the tax cuts now, we could generate a hunk of cash capable of paying for Social Security benefits over the next 75 years?  I don't see how that's possible unless you assume very rapid bracket creep, and that the US will be paying extraordinarily high rates on its debt in the near future--high enough that the compound interest will, in later years, equal something close 1% of GDP. 

.The best you can say about presenting the numbers this way is that they represent an iffy sort of time arbitrage; the relative sums only match up because the coming tax increases generate relatively steady revenues, while the social security deficits don't start until 2017 and don't reach their full height until 2030.  It is not true that at any given point in time, you can generate enough money with the one, to pay for the other--or rather, it is true for a time so brief as to be meaningless in the context of the 75-year forecast period that they chose.

7)  The CBPP says it's not actually making that last claim--it's just trying to make a point about extending the tax cut versus "fixing" social security--about Republican hypocrisy.  Well, I've already seen at least one blogger, and more commenters, take it to mean that the tax cuts could be used to pay for the shortfall.  However they intended it, it's clearly misleading some people.  Which is not surprising to me, given how its labeled.  If you release a graph indicating that the social security shortfall is the same size as the Bush tax cuts, people are going to assume that we could therefore use the one to pay for the other.

Republicans are indeed being very silly and hypocritical about the tax cuts (just as many on the left are being very silly and hypocritical on the spending side.  I believe I may have mentioned that almost nobody really cares about the deficit).  But this graph does not seem like a good way to make that point.