Confusion in 4 sources of employment data

There are four sources of employment data: ADP provides a snapshot of how many jobs it thinks have been added or lost in the U.S. economy based on their managing roughly 1/6 of all non-government payroll jobs. Last Thursday ADP reported an increase of 40,000 jobs in May. So far, good strength in the labor market.

The U.S. Labor Department reports once a month on jobs based on their "household survey" and their "payroll survey". The "household survey" reports gained or lost jobs by calling families (some 70,000). This picks up people who have jobs but are not in the payroll system (they pay estimated taxes - or they're tax cheats) and is responsible for the unemployment rate which increased for May from 5% to 5.5% Score one for a weak job market. But why didn't these people who lost their jobs apply for unemployment insurance (more about that below)?

The Labor Department "payroll survey" reported a loss of 60,000 jobs during May. The Labor Department calls the biggest 300,000 companies for their survey. How could their survey and the ADP survey both be correct at the same time? But, again, why didn't these people who lost their jobs apply for unemployment.

How do I know that most of them didn't apply for unemployment insurance? Because the Labor Department also produces a weekly report of new unemployment claims. According to these reports, new unemployment claims have fallen for 3 out of the last 4 weeks. In the most recent report new claims were 357,000 from a revised 375,000 the previous week. If lots of folks were losing their jobs I think most of them (except for those who aren't in the payroll system) would end up collecting unemployment checks.

Adding all of this up: the evidence points to a moderately strong labor market. I think we have to discount the "household survey" because it is known to be volatile at this time of year due to an influx of college kids into the job market. As to the "payroll survey" - the only way this loss of jobs makes sense in accordance with no increase in unemployment claims (and ADP's report of an increase in jobs) is if the people who lost jobs were able to get new ones in companies that were not part of the government's survey. ADP must have a much wider cross section of the U.S. economy.