I looked up "correlation"

One "L" in correlation. Two R's. Merriam-Webster says

a relation existing between phenomena or things or between mathematical or statistical variables which tend to vary, be associated, or occur together in a way not expected on the basis of chance alone.

Tend to vary together in a way not expected on the basis of chance alone.

Following up on Antonio Fatas's defense of debt: On the basis of chance alone, debt would not consistently increase more rapidly than GDP. So maybe the "very strong correlation" that Fatas describes is the simply that debt grows faster than GDP. You think?

Fatas describes a "correlation between GDP per capita and ... the ratio of debt to GDP." Between Real GDP per Capita, and the ratio of debt to nominal GDP. He doesn't specify a measure of debt. Following in the footsteps of Milton Friedman we can, first, assert the economic relation and, second, go looking for a measure of debt that gives a result that pretends to support our assertion.

No matter. Pretty much any measure of debt you pick will be one that grows faster than GDP. Economists generally prefer to use private non-financial (PNF) debt, perhaps because it seems at first blink the most relevant to the production of GDP, and thus the least likely to be questioned by people like me. Fine. PNF debt it is, then.

Fatas sees a relation between debt-to-GDP and real GDP per capita. There's GDP on both sides of that relation. If you take real GDP per capita and multiply by population and prices, you get GDP.

The GDP in debt-to-GDP grows faster than the other one because it includes the growth of population and the rise of prices.

The faster-growing measure of GDP is used in the debt-to-GDP ratio. But still the ratio goes up. That means debt is growing faster than the faster-growing measure of GDP. When you divide debt by the faster-growing measure, Fatas tells us, you get something that has "a very strong correlation" with the slower-growing GDP measure. This is very odd reasoning.

It sounds to me like Fatas, or somebody before Fatas really, was trying to show correlation. And they picked some data that sounded relevant and they did some division, and then brought in other data with different growth rates until they got the two lines to look similar on a graph. And Fatas was impressed, and he repeated it.

But what does the data actually show?

Graph #1: PNF Debt to GDP (red) and Real GDP per Capita (blue)

It shows that debt-to-GDP goes up. And real GDP per Capita goes up. But the red goes up somewhat more slowly than the blue.

Using PNF debt, the ratio runs higher than real GDP per capita from the mid-50s to the mid-70s. Then the two lines run together until the early 1990s.  Then the red runs below the blue until 2009. And after that, the red runs even farther below the blue. The red line not only increases more slowly than the blue, but also seems to do it in steps.

The steps are the most interesting thing about that graph.

Using a different measure of debt, the graph would be different. Graph #2 uses a broad measure of debt:

Graph #2: Like Graph #1 but using a Broad Measure of Debt

Here, the two lines run close together for a decade or so, early on. To me, that looks like a strong correlation. But around 1963 the two lines separate. After that, it almost looks like the red wants to run flat but the blue keeps dragging it upward.

I wouldn't call that correlation. I'd say things are going on, on this graph, that are overlooked when people make announcements about very strong correlations.

This graph is overlooked simply because it uses a broad measure of debt. Economists seem to prefer the PNF debt that gives them graphs that suit their arguments.

Here is another alternative to private non-financial debt -- financial debt:

Graph #3: Again like Graph #1, but this time using Financial Debt

No very strong correlation visible here. No wonder economists like to leave financial debt out of the picture.

Come to think of it, we might see better correlation with financial debt if we change the "real GDP per capita" (blue) to a different measure of GDP:

Graph #4: Like Graph #3, but replacing Real GDP per Capita with Nominal GDP

There ya go: The red and blue follow the same path from the start to the peak. Now that's correlation!

Hmm. Perhaps the growth of financial debt visible in the red line explains the increase of prices embedded in the blue.

Oh, but that line of thought doesn't fit the "defense of debt" argument made by Antonio Fatas. So forget it.

Part 3 of 3