## Monday, August 5, 2013

### Spoiler Alert

In yesterday's post we considered three possible causes of inflation and looked at the evidence in each case. The first cause was the cost of labor; the evidence was a graph of Unit Labor Cost (ULC). The second was the quantity of money, and the evidence was a "money relative to output" (MRTO) graph. The third possible cause, the ringer I made up for yesterday's post, was the cost of economic growth. The evidence for it was a graph of nominal GDP relative to output.

The three graphs use similar calculations to derive their evidence. We have considered this calculation model before, for ULC and MRTO:

Both follow the same pattern:

1. Divide GDP by a price index to get a fraction called "real" GDP.
2. Use this fraction as the denominator of another fraction.
3. Compare the result to inflation, and find similarity.

Using the MRTO as an example, I showed it is Step 1 on that list -- dividing by the price index -- that creates the appearance of similarity to inflation.

Yesterday's Graph #3 shows far greater similarity to inflation than either of the other graphs in the post. The reason is plain: The choice of a numerator, which is held to be the cause of inflation in the calculation model, is better in my graph than in the others.

But my graph does not show that anything is the cause of inflation. The calculation my graph uses for comparison to the price level is the standard equation that relates the price level to real and nominal GDP. As used on my graph, the calculation *must* produce a graph that looks just like the price trend, because I used a calculation that produces the price numbers. I faked it.

That is the reason I chose nominal GDP for the numerator. Not because it is "the most legitimate, well-respected data we could use" -- that's just silly -- but because it relies on the relation between nominal GDP, real GDP, and the price level. (That relation is reviewed in the two "related posts" provided yesterday.)

This doesn't mean my graph is better evidence. My graph isn't evidence at all. Neither are the other graphs. That was the point of yesterday's post: I was pretending to use the graph as evidence, to show that the ULC and MRTO are not evidence, either.

My graph provides a perfect match to inflation, not because growth is the cause of inflation, but because I use the well-defined relation between prices and real and nominal GDP. That's why I chose nominal GDP for the numerator. I knew what the outcome would be before I started, because using nominal GDP gave me the standard equation that produces the price trend.

If you take the standard equation, change the numerator, and make a graph, your graph may be quite similar to the price trend, but it will not be as good a match as you get from the standard equation. That is what we see in the ULC and MRTO graphs.

Those graphs provide pretty good matches to inflation, not because the evidence is solid, but because they use an equation similar to the standard equation. But they plug in labor costs or the quantity of money in place of nominal GDP. And that makes them less similar.

Labor costs and the quantity of money are both numbers that increase along with GDP and most everything else in the economy. It all moves up faster together, or slower together, or maybe even goes down together. So you can substitute labor cost or the quantity of money or some other variable in place of nominal GDP, and you will still get a reasonably good match to the path of inflation as long as the denominator still has inflation stripped away. This is all that Milton Friedman showed with his MRTO graphs, and this is what we see in the ULC graph.

None of yesterday's graphs show any cause of inflation. The similarity to inflation is manufactured by the calculation model they use.