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.

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Megan McArdle is a columnist at Bloomberg View and a former senior editor at The Atlantic. Her new book is The Up Side of Down.

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