## Sunday, April 5, 2015

### Mendacity at FRED, a tangent

Since 21 March I have been mostly looking at the inflation-adjustment of debt. The effect of inflation can be calculated, and it can then be removed from the debt numbers. But the calculation is less straightforward for debt than, say, for GDP.

GDP is a "flow" variable, where each year's number represents only that year's activity. Debt, on the other hand, is a "stock" variable. Any one year's debt number includes all the outstanding debt from prior years in addition to the new debt accumulated during the year under consideration.

The accumulation of "many years" in each debt number means that to remove the effects of inflation, each year's accumulated debt number must be split up into separate amounts for each year debt was added to the accumulation, so that each year's inflation can be removed from that year's piece of the debt. After that, the adjusted numbers can be totaled up to get an accurate measure of accumulated debt with the effects of inflation stripped away.

If that all sounds a little confusing... Well, it is. Perhaps that's why we often see people inflation-adjust debt the same way they inflation-adjust GDP. But it is certainly wrong to do that. The inflation-adjustment is incorrect, and it leads to incorrect conclusions about our economic problems. This is no small matter.

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To strip inflation out of any one year's GDP, you just divide that GDP number by the price number for the same year.

Here's how dividing works: If you have a lot of company and you divide a pie into 10 pieces, all the pieces are small. But if you only have a few people over and you divide the pie into 4 pieces, all the pieces are big! When you divide by a big number, the result is small. And when you divide by a small number the result is big.

Since prices were going up let's say continuously from World War Two until the 2009 recession, old price numbers are smaller than new ones. So dividing by an old price number is like dividing by a small number. And dividing by new price number is like dividing by a big number.

If you have a series of numbers (like GDP numbers, say) and you divide each year's GDP number by that year's price number, the older numbers come out bigger and the newer numbers come out smaller. That's why when you see a graph that shows actual GDP (with prices going up) and "real" GDP (with the price changes stripped away), the old real numbers are higher and the new real numbers are lower. Red is real:

 Graph #1: GDP in Recent Years, at Actual Prices (blue) and with Inflation Stripped Away (red)
For the years before 2009, the red line is higher than the blue line. For the years after 2009, the red line is lower than the blue line. The old real numbers are higher and the new real numbers are lower than the numbers we started with.

That remains true even when you look at all the years in the data set:

 Graph #2: GDP since 1947, at Actual Prices (blue) and with Inflation Stripped Away (red)
The blue line goes up faster than the red line, because the blue line shows prices going up and the red line does not. And the lines cross in 2009 because 2009 is the "base" year.

Again, the red line is calculated by dividing the price increases out of the blue line. For the next graph I got rid of the red "Real Gross Domestic Product" series and in its place I show the blue line again (now in red) divided by the price numbers. So you can see the calculation:

 Graph #3: GDP at Actual Prices (blue) and with Inflation removed by Calculation (red)
Graph #3 looks just the same as Graph #2, when you look at the red and blue lines. But comparing the titles (across the top of the two graphs), you can see the calculation that gives you "Real Gross Domestic Product". The change is also evident in the left-border labels.

Of course, the same calculation has been used for things other than Gross Domestic Product. Here's Disposable Personal Income:

 Graph #4: Disposable Personal Income (blue) and the Inflation-Adjusted version (red)
Looks almost the same as Graph #3, doesn't it?

We can do the same thing with Median Household Income, too:

 Graph #5: Median Household Income (blue) and the Inflation-Adjusted version (red)
Now this one looks a little different! There are a few reasons. It only goes back to the mid-1980s, for one thing. So you don't see as much up-slope as on the previous graphs. And then, there just isn't as much up-slope. And this time the lines cross at 2013 rather than 2009. That's a big difference. But it is only because the red line is shown in "2013 dollars". Prices were higher in 2013 than any prior year, so it took more dollars that year than it took in, say, 2009 to buy the same stuff. And since the red line is shown in 2013 dollars (when it took the most dollars of any year, to buy stuff), all the years seem to show a lot of dollars. That's why the red line is so high.

Come to think of it, using "2013 dollars" was a pretty slick trick because it makes Median Household Income look high. You weren't fooled by that, were you?

It's easy enough to change it. I can divide all the red line's numbers by the red value for 2009, and multiply by the blue value for 2009. That will shift the red line down so the two lines cross in 2009 -- same as the first four graphs today.

The graph at FRED shows a value of 54,059 dollars for the red line in 2009. It shows a value of 49,777 for the blue line in 2009. I'll use those numbers, and you will be able to see them in the title text across the top of the graph:

 Graph #6: Median Household Income (blue) and Inflation-Adjusted to 2009 base (red)
Now, you see, the two lines cross in 2009. But heck, we can push the red line down even more. I'll redo it now using the FRED values from 1991:

We can make that sucker look flat!

But remember, we didn't flatten the red line. It was already flat. We just moved it down some. Now we can see it. Now we can see something other than how high FRED has it.