Wednesday, September 23, 2015

Random correlation of the day

I noticed a random correlation today:

The employment-population ratio and Federal tax (and tariff, etc) receipts to NGDP. With the exception of the structural shift in the emp-pop ratio due to women breaking into the workforce, this is pretty remarkable. There are plenty of logical explanations (e.g. taxes proportional to employed, GDP proportional to population), but is there really a good reason for the relative size of the government to be the same over the course of 60 years? There were lots of Democrats on the front half end and lots of Republicans on the back half. Neither had any impact; bupkis.

Also, the emp-pop ratio is considered by the information transfer model to be effectively constant. With the Federal revenues being even more stable (it lacks the structural shift), a fortiori, the relative size of the government sector is constant. It joins the ratio of nominal wages to nominal GDP as some of the most constant things in macroeconomics.

That is to say if you can't explain the price level over the past 60 years, what hope does your theory have for something that changes by an order of magnitude less!

PS The unemployment rate is only slightly less stable:


  1. Jason,

    This doesn't suggest that the size of government has been stable over the past 60 years. What it does show is that tax revenue has been stable. This is known as Hauser's law.

    In fact, as shown in the attached graph, the size of government has not been stable. It has been rising as a proportion of the economy, while recently reversing course.

    1. Hi eli,

      That graph is also stable in the sense of the graphs above. It changes inside a narrow window between 15 and 25 percent. If you zoom out so that the graph shows zero to 100 percent, it moves only slightly.

    2. A range of 10 percentage points, doesn't seem stable to me. Perhaps it's just a semantics issue.

      Regardless, here is what it would look like looking back to 1930.

      Do you consider this stable?

    3. Interestingly, back in the proto-information transfer economics days I looked at that graph as a phase transition from a low gov't state to a high gov't state.

      I wasn't saying it was remarkably stable for all time, just for a long time.

      And given that it can suddenly change from a few percent to 20% makes the more recent stability even more remarkable. Why haven't there been changes back to a few percent or up to 50 percent? Changes of that scale occurred in the past.

    4. IMO, neither taxation nor government expenditure is as good a measure of the size of government as the number of government employees.

  2. i don't find it surprising that it has gravitated between 15 and 25% in the past 60 years. Though i wouldn't call this stable.There are rigidities or limiting factors that contribute to these bounds. The limits can change but they are very slow to change. For instance, cost of financing deficits serves as an upper bound that can probably only be exceeded during war times. Additionally, the preferences of the populace which to some extent allows, consents, or at least doesn't interfere with the spending decisions of governments, can serve as a lower bound (or upper) are very very slow to change. They perhaps move with generations. Once in 60 years or so.
    I could easily imagine the ratio exploding upwards for a short period in the event of a geopolitical conflict escalating. Downwards is more difficult. You'd need a massive and coordinated change in voter preferences and these are much more sticky.

  3. The title of this post sounds like something Brad DeLong might post on a quasi-regular basis (about as frequently as his smack downs say).

    This was always one of my favorite "random correlation" plots. Which I first saw here.