Household survey vs payroll survey

As everyone knows under Bush employment has shrunk shockingly according to the payroll survey and grown (slowly) according to the household survey. I just learned from Brad Delong that there was an even larger shift in the difference between the two measures during the late 1990s. The difference went from 5% of working age population to 3 % and has since widened back to 4%. What is going on ?

Since the household survey counts the self employed, a natural guess is that changes in the gap are due to changes in the number of self employed. In the household survey people are asked if they are self employed. Subtracting such people from household survey employment explains a small part of each of the changes in the gap (less than a third of it).

In comments to Brad I thought about the underground economy

Then I had a crazy idea. The idea is that the widening really is due to increase in the number of self employed but they don't report themselves as self employed. In the household survey, one member of the household answers for all leading to fairly high error rates. In particular, I thought about outsourcing services but not to Bangalore to self employed contractors. What if employees are being replaced by cheaper contractors (or laid off and turned into contractors). Would such people who ahve only the disadvantages of self employment call themselves self employed ? Would their spouses consider them self employed ? Hmmmm.

Then there is a reasonable argument made in another comment by Barry Ritholtz
who cites a study by the Fed. The point is that th e payroll survey counts jobs not workers so, if someone has two jobs, they are counted twice. This means that the change in the gap could be do to changes in the number of moonlighters. This certainly fits the cyclical pattern.

Finally, of course, there is the Fed's current view that population growth has been over estimated. This would mean that the payroll survey gives an accurate estimate of the decline of employment and the household survey gives an accurate estimate of the decline in the ratio of employment to the working age population.