Tuesday, August 4, 2015

Better Measure

To figure the "real" (inflation-adjusted) values for a data series like GDP is a two-step process:

1. Divide the series by a price series like the GDP Deflator to remove the inflation; and
2. Multiply by 100 to express the numbers as dollars from the year 2009.

Graph #1: The GDP Deflator (Base Year 2009)
If we multiply by 12.886 instead of by 100, we can express the numbers as dollars from the year 1947.


Inflation makes prices go up.

If we use a price series with a base year of 2009 and prices go up, a graph of the years after 2009 will show that inflating prices are higher than stable prices. Sure, we knew that already. (But at least the graph will show something that makes sense.)

If there was inflation in the years before the base year, the graph will show the inflating prices lower than stable prices. I know that's true. But it bothers me, because inflation makes prices go up. You have to think about it like you're going backward in time, to watch inflation push prices down in the years before 2009. It's more like science fiction than economics.


The simplest way I can think of, to eliminate the conundrum of inflation pushing prices down in the years before the base year, is to move the base year back in time. I did it the other day with 1958. I'm going to do it now with 1947, the first year on the graph that I'll be showing you. So there won't be any years before the base year, and when there is inflation it will make prices go up. Just like in the real world.

On Graph #2, the blue line shows GDP, replete with inflation. The red line shows GDP at stable 2009 prices. The green line shows GDP at stable 1947 prices. The calculations are as described above.

Graph #2: Nominal GDP (blue) and Real GDP, 2009 base (red) and 1947 base (green)

The red and blue is how economists like to show inflation. The green and blue is a more honest picture.


I keep going back to Noah Smith's claim that government deficits "exploded" in the early 1980s. Exploded, meaning they suddenly increased a lot. Noah didn't investigate the claim. He just repeated it, then tried to explain why it happened.

But it didn't happen. That's my claim. And I propose to prove my point once again, here and now. Let me begin with the opening of Noah's post:

The U.S. federal deficit, which had been decreasing since the end of WW2, began to trend upward beginning around 1980:

You can see on Noah's graph, the blue line comes down slowly until 1980 or '81, then takes off uphill at a rapid clip. Just as Noah says.

Unfortunately, the blue line does not represent the U.S. Federal deficit. It represents the Federal debt -- the accumulation of deficits -- relative to GDP. You cannot just glance at the graph and see evidence of deficits exploding after 1981. The graph does not show deficits.

"Relative to GDP" is a reasonable context. That's what Noah used for his graph, and I have no problem with that. But GDP was severely affected by inflation between 1965 and the early 1980s. After that, the Great Inflation suddenly became disinflation. GDP growth, nominal GDP growth, underwent a sudden slowdown.

Graph #4: Inflation fell precipitously in the early 1980s
Inflation fell precipitously in the early 1980s. So the increase of GDP was suddenly much slower than it had been since the mid-1960s. Anything that did not slow precipitously in the early 1980s -- the Federal deficits, perhaps -- would appear to show an "explosive" increase when compared to GDP. That increase, at least in part, is an illusion.

I'm not saying the Federal deficits didn't increase. I'm not saying they didn't increase a lot. I am saying they didn't increase as much as you might think, and the increase didn't start when you might think.

I'm just asking you to reserve judgement till I've made my case.


Let me take the Federal debt numbers, as Noah does, and look at them a little more carefully than he does. I want to look at the year-to-year change in the Federal debt. I want to look at each year's increase. That's like looking at the deficits, just as Noah wanted.

I want to remove the inflation from each year's deficit, and then add up all the deficits to see the inflation-adjusted debt. This is a necessary step, as Noah's "explosion" occurs just as the Great Inflation is coming to an end. How can we know whether the explosion Noah sees was the result of policy or an accident of inflationary numbers?

We have to look.

Graph #5: Noah's Numbers (blue) and My Numbers (red)
The blue line on Graph #5 shows a sudden increase beginning in the early 1980s, just as Noah Smith showed. The red line shows the increase beginning around 1974, after a decline that ends around 1966. Does it matter? It might. It wouldn't be right to say the U.S. federal deficit "began to trend upward beginning around 1980".

"Real" numbers provide the better measure of growth. If you are looking at the growth of deficits, "explosive" or otherwise, you want to use the red line. Not the blue line.


Most people will tell you that the red line should be identical to the blue line because a ratio of reals comes out the same as a ratio of nominals.

It depends how you do the math. Here's how I did the math:

1. Take the annual change in Gross Federal Debt (FRED's FYGFD) as a measure of Federal deficits.
2. Convert these deficit numbers to "real" deficits: Divide each year's deficit by that same year's GDP Deflator, and multiply the result by the Deflator value for 1947.
3. Calculate the "real" Federal debt: Start with the FYGFD value for 1947 and add to it the "real" deficit numbers for 1948-2013 as calculated in Step 2.
4. Calculate "real" GDP for Base Year 1947 by following the same method I used to calculate real deficits.
5. Plot real debt as a percent of real GDP, and nominal debt as a percent of nominal GDP.

The trick is to figure each year's inflation for that year's deficit.

You can download the Excel file fredgraph(1yWX) from Google Drive.

My source data is from this FRED graph.

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