Last week I said

It would be great to measure how much reported GDP volatility would fall if we calculated the whole thing the same way we calculate the government part of GDP.
Since the government doesn’t report profits, and since profits are an extremely volatile category of GDP it’s almost tautological that if you measured the whole economy the same way you measure the contribution of government workers–that is, on a wage basis–you’d wind up with a more stable-looking economy.  [I’ll leave the consideration of exceptions and oddities to others.]
So today I’m making a first attempt at measuring the volatility of a wage-only GDP measure, I hope to spur others. I can’t just compare the volatility of “total wages and salaries” to the volatility of overall GDP since GDP includes a lot of fake, artificially smooth data–the most important of which is the rent you save by living in your own house.  Instead, I’m proxying for total Gross Domestic Income (GDI) by adding wages and salaries together with pretax corporate profits, proprietor’s income, and rental income.  After all, GDP=GDI=Wages + Profit.  I also directly pulled down GDI data on wages and net operating surplus and got about the same result.
I know that I’m leaving some stuff out (indirect taxes, anyone?) but consider this a first look.  I’m using year-over-year growth rates.
Standard deviation of real wage growth: 2.7%
Standard deviation of real profit growth: 7.9%
And now, the GDP proxy:
Standard deviation of (real wage plus profit) growth: 3.4%

[Note: Standard deviation is a measure of volatility; if you randomly chose two data points from a sample and compared the distance between them, and did that again and again, calculating the average distance between each pair of data points, that final average would be the “standard deviation” between them.]

Results looked the same when I pulled out a long-run trend (via HP filtering) rather than just year over year, and when I used nominal instead of real growth.  Wage growth is about 20% more stable than overall economic growth, so any sector of the economy–like, say, the K-12 education sector–made up disproportionately of wage payments is probably going to look quite stable.

An illustration: Some sectors of the economy slow way down in a recession, creating a lot less GDI.  Housing comes to mind.  But government bureaucracies closely tied to the housing sector probably don’t suffer nearly as a large a decline in GDI–building inspectors, property tax assessors, recorder’s offices.  But the government side of the housing sector becomes less productive on average during recessions: Fewer inspections per inspector mean longer lunches. But the GDI created by the inspector stays the same–that’s the magic of drawing a government paycheck.
Just imagine: If governments privatized those inspector/assessor/recorder jobs, official GDI/GDP would ride the same wave as the housing sector, growing in booms and crashing during busts.  The decision to privatize would boost (measured) GDP volatility.
The more workers we shift from the profit-earning private sector (including government contractors) over to the profit-free government payroll, the more stable GDP will become. Government hiring is (almost) an axiomatic stabilizer.