Friday GDP arithmetic

We have new GDP numbers from the Department of Commerce’s Bureau of Economic Analysis.

  • U.S. real Gross Domestic Product grew at an annual 1.6% rate in the second quarter of this year.
  • This is the second estimate for Q2 GDP. The first, released at the end of July, was +2.4%. This is therefore a downward revision, but we’re still growing, albeit slowly.
  • The economy is growing more slowly than it did in Q1, when it was growing at a 3.7% annual rate.

As a rule of thumb, when the economy is operating near full employment, the U.S. can sustain a long-term real GDP growth rate of between 3 and 3.5 percent. When we’re operating way below capacity, as we are now, in a strong recovery you would expect and hope that we’d grow much faster than that. This is not yet a strong recovery.

I want to use this as an opportunity to explain an arithmetic point about GDP growth rates and stimulus. The conclusion sounds simple but when they see it in the numbers a lot of people get confused: When stimulus ends, the GDP growth rate goes down.

Let’s imagine we have an economy that this year will produce 100. Also imagine that we have a magic crystal ball that lets us see that, if we do nothing, GDP will grow by 1 for each of the next three years. We call this our baseline.

year 1 year 2 year 3 year 4
baseline GDP 100 101 102 103

Now suppose we want GDP to grow faster, and suppose we have a magic wand which will do that. The magic wand could be monetary stimulus, it could be fiscal stimulus, or it could just be magic. Maybe it cuts interest rates, maybe it cuts taxes, or maybe it increases government spending. I’ll let other people argue about how effective those various magic wands are. For this exercise, please grant that the magic wand will increase GDP by however much we want, and for whatever limited duration we want. My point here has nothing to do with economics, or about whether a particular type of stimulus works. It’s just arithmetic.

Suppose we set our magic wand so it will add 2 to GDP for two years, beginning in year 2, and then stop.

year 1 year 2 year 3 year 4
baseline GDP 100 101 102 103
stimulus / magic wand 0 +2 +2 0
GDP + stimulus 100 103 104 103

What makes this a bit funky is that GDP is rarely reported in raw numbers, but instead as growth rates. In the real world this is done on a quarterly basis, but I’m keeping everything simple here by just using years instead. Let’s compare the annual growth rates of GDP, with and without our magic wand stimulus.

year 1 year 2 year 3 year 4
baseline GDP 100 101 102 103
growth rate +1% +1% +1%
GDP + stimulus 100 103 104 103
growth rate +3% +1% -1%

Economists of different stripes will argue that various stimulus magic wands have beneficial effects that last beyond the direct stimulus, and that their preferred type of stimulus will create a virtuous cycle that will permanently increase the level of the economy. Even if they’re right, you’ll still see a decline in the growth rate as the direct stimulus is withdrawn, especially if it was big in the first place. So maybe we end up at 104 in year 4 rather than 103. Even so, the growth rate would still decline to 0. My point is simply that, when the annual +2 ends, the measured annual growth rate will decline. This is mathematically trivial but politically significant.

Remember that in the real world we don’t know baseline GDP, and the raw (GDP + stimulus) numbers are rarely reported in the press. All we see are the growth rates that actually occurred, post-stimulus:

year 1 year 2 year 3 year 4
growth rate +3% +1% -1%

I have constructed this example to be as simple as possible, and in doing so the GDP growth rate actually went negative after the stimulus ended. This does not have to be the case. When stimulus ends, the GDP growth rate will go down, but that doesn’t mean it has to go down so far as to dip below zero.

Now let’s put on our political hats. Year 2 is a good year politically, with GDP growing 3%. We brag about the success of our stimulus policy.

In year 3 the economy is 2 bigger than it would be without stimulus, but since we pretty much look only at growth rates, we don’t get political credit for it. This is particularly difficult, because everybody knows it was a two-year magic wand, and here we are in the second year of the stimulus and growth is slowing down.

After the stimulus ends, our measured metric declines even further. It might even go negative. As a matter of simple math this is entirely predictable. As a political matter it’s super hard to explain. If the stimulus worked, why is the economy shrinking/slowing down?

Imagine you have a triple espresso at 1 PM. At 4 PM you “crash” as the caffeine leaves your system. Maybe your energy is where it would have been at 4 PM had you never had that drink. Maybe it’s even a little higher than it would otherwise have been, because even though the caffeine is gone, your frenetic pace over the past few hours has tapped some hidden reserve of energy that continues. Either way, it will feel like a crash as the temporary stimulus is removed.

(photo credit: hz536n)

By | 2017-05-23T19:06:22+00:00 Friday, 27 August 2010|