Thursday, November 10, 2011

Idiotic Political Calculations

UPDATE: This clown is now spouting his graphically verbose nonsense all over Seeking Alpha. Somehow I thought they were a serious site...

TLDR: Ironman from Political Calculations posts visually stimulating but utterly meaningless crap. In this example, I show how his "GDP per Capita" graph is really "GDP per Capita per Capita", which is like measuring the MPG per gallon of a car and concluding that filling the tank half full doubles the fuel economy.

I wouldn't normally care that a blog called Political Calculations has published the following visually pleasing but ridiculous graph that overstates the U.S. debt burden in 1831 relative to 2010 by a factor of 23:

EXCEPT that this blog has been picked up up by two publications that I respect, namely Reason Magazine and Townhall. In this time of unprecedented fiscal irresponsibility and risk, the last thing that we need to do is to understate the debt problem so severely.

So how did this happen? Quite simply Political Calculation takes the standard measure of debt burden, the ratio of debt to income (aka debt/GDP or debt/GNP), and divides it by the population. But the ratio of debt/income is already adjusted for the size of the population automatically.

[Debt / population] / [Income / population] = Debt / Income. Political calculation is effectively dividing [Debt per capita squared] by [Income per capita].

This makes about as much sense as calculating fuel efficiency as miles per gallon per gallon and then concluding that we can double a car's gas mileage by only filling the tank half full.

Debt / income is already scaled to population size. If I make $100,000 and my debt is $80,000 then my debt / income is 80%. If there are 10 people on my block exactly like me, our total debt / income is still 80% ($800,000 / $1,000,000). Using the formula from Political Calculations, my 10 person block would only have 1/10th of the debt burden that I have. Quite simply it's idiotic, worse than worthless.

Now we all make mistakes and I like to give people the benefit of the doubt. I initially mailed a quick note to "Ironman" at Political Calculations, thinking that he would see this problem and fix it. I was wrong. Apparently Ironman/Political Calculations has been making this particular mistake since 2005 and from private email correspondence, other people have pointed out this error, apparently to no effect.

That tells me that despite the pretty graphs, Political Calculations is run by an numerically-challenged individual who shouldn't really be trusted by anyone let alone publications that aspire to report factual information. If the numbers are wrong, does it really matter how pretty the charts are?

Here is a visual depiction of how debt burden should and shouldn't be calculated. Let's start with a straight graph of the debt in nominal dollars:

This isn't useful for describing the debt burden because it mixes in three other variables that have all been increasing: inflation, population and income. To make a consistent comparison we need to adjust for all three.

First we adjust for inflation:

Next we divide the inflation-adjusted debt by the population:

Finally, we divide [debt/population] by [GDP/population] to get the debt to income ratio that is generally used for historical and international comparisons. Note that the population number cancels out so that (debt/population) / (GDP/population) becomes debt/GDP:

THIS is the graph that shows the standard representation of the U.S. public debt burden over time, scaled to inflation, the size of the population and the size of the economy. If we want to deceptively make the current numbers seem worse, then we could use one of the orange graphs above and if we want to deceptively make it seem better, then we could use debt / GOVERNMENT income although that would make the trend over the last few years actually look even worse.  The ratio debt / govt income makes sense for some analyses, but it's not the best measure for historical comparisons of the public debt burden since tax levels can be changed more easily than income levels especially when government spending per GDP is low as it was in the past and ultimately the debt burden is held by the people.

But in NO case is it meaningful to do what Political Calculation did and divide the RATIO by the population:

You can see the illogic behind this particular example of innumeracy proudly on display for the last 6 years at the Political Calculations blog. Apparently he thinks he's adjusting for the size of the population. Well, not exactly. He's DOUBLE adjusting the debt for the size of the population.

If it makes sense to adjust debt for population size twice, then why not TRIPLE adjust debt by the size of the population?

By this measure the debt in 2010 is trivial compared to 1831.

I booked-marked the blog a while ago because of the chart porn, but I find it unforgivable that this guy has persisted for 6 years in drastically misstating something as simple and fundamental as debt / GDP. My advice to my fellow consumers of chart porn? Don't trust anything he posts. If he'll get this wrong, he'll get other things wrong as well.


JS said...

Thank you for demonstrating why I don't trust statistics from wing-nuts like yourself.

Matthew Holbrook said...

You don't seem to understand the calculation. He is not squaring the debt amount.

First, the debt-to-income ratio is defined as:

DTI = Debt / GDP

which is the same as dividing per capita debt by per capita income

DTI = (Debt/Population) / (GDP/Population)

Divide both sides of this equation by Population and you get:

DTI/Population = (Debt/Population) / GDP

which is the same as:

(Debt/GDP)/Population = (Debt/Population) / GDP

So the equation is supposed to show the relationship among debt, GDP, AND population together, whereas per capita debt, per capita GDP, and debt-to-GDP each show a relationship between 2 variables.

I haven't quite gotten my arms around what this equation tells us, but I don't think it is idiotic. Based on my historical knowledge of the Jacksonian period, there was a major effort by Old Hickory to bring down the national debt, which he did quite thoroughly. Political Calculation's equation and graph shows the steep decline quite clearly.

Mercy Vetsel said...

Right, because we value truth over ideological fealty.

Matthew Holbrook:
> I haven't quite gotten my arms
> around what this equation tells
> us

Well I think I have, sadly, gotten my arms around it. It scales DTI to the size of the population a second time since DTI is already scaled to the population.

I think my post explains in way too much detail why this is meaningless, but consider another example:

Why not average weight PER CAPITA?

So in 1900: 130 lbs / 100 m = 1.3

in 2010: 180 lbs / 300 m = 0.6

So relative to the total population, we've actually gotten smaller in size!

I'd call that technically true, but idiotic.