Our new co-blogger, Luigi Zingales, in his first post, has done an excellent job of dispelling the conspiracy theory that political operatives in the Obama administration “got to” the professionals in the Bureau of Labor Statistics who gather and report unemployment data. By the way, welcome, Luigi.

One disagreement, though. I do think that Luigi exaggerated somewhat with his rhetorical question: “How many millions of dollars would a newspaper pay to the first employee of the Bureau of Labor Statistics to blow the whistle?” The actual answer would be zero. In a later post I will tell my own experience in the Reagan Labor Department when, in 1982, I approached a Chicago Tribune reporter with a scandal story about unemployment data regarding the governor of Illinois. She wouldn’t do a thing about it. It wasn’t because of her political views. Her views were close to mine. But I couldn’t give her the whole story and she didn’t want to make the effort of digging.

With that taken care of, it’s important to look at the latest employment data themselves.

And rather than do that from scratch, I’ll refer to two excellent posts that dig into the data. The first is Greg Mankiw’s.

The big thing that caught many people by surprise was the divergence between establishment data that measure employment from the employers’ viewpoint and the household data that measure employment from the individuals’ viewpoint. The establishment data show a net increase in nonfarm payroll employment in September by 114,000. The household data show a whopping 873,000 increase in employment.

Which is right? The one thing we can be sure of is that neither is right. These are estimates. Here’s Mankiw’s exposition:

One might expect these two measures of employment to be identical, but that is not the case. Although they are positively correlated, the two measures can diverge, especially over short periods of time. A particularly large divergence occurred in the early 2000s, as the economy recovered from the recession of 2001. From November 2001 to August 2003, the establishment survey showed a decline in employment of 1.0 million, while the household survey showed an increase of 1.4 million. Some commentators said the economy was experiencing a “jobless recovery,” but this description applied only to the establishment data, not to the household data.

Why might these two measures of employment diverge? Part of the explanation is that the surveys measure different things. For example, a person who runs his or her own business is self-employed. The household survey counts that person as working, whereas the establishment survey does not because that person does not show up on any firm’s payroll. As another example, a person who holds two jobs is counted as one employed person in the household survey but is counted twice in the establishment survey because that person would show up on the payroll of two firms.

Another part of the explanation for the divergence is that surveys are imperfect. For example, when new firms start up, it may take some time before those firms are included in the establishment survey. The BLS tries to estimate employment at start-ups, but the model it uses to produce these estimates is one possible source of error. A different problem arises from how the household survey extrapolates employment among the surveyed households to the entire population. If the BLS uses incorrect estimates of the size of the population, these errors will be reflected in its estimates of household employment. One possible source of incorrect population estimates is changes in the rate of immigration, both legal and illegal.

Paul Krugman digs into the data further and finds some plausible grounds for hope about the recovery. He starts by pointing out that instead of measuring unemployment, which, as economists know, doesn’t capture the people who quit looking for work and leave the labor force, it makes sense to measure the employment to population ratio. That has been falling until recently and that looks bad. But, notes Krugman, the population has been changing. In particular, the leading edge of the baby boomers (typically defined as people born between 1946 and 1964) are retiring. So the raw employment to population ratio is not ideal either.

What to do? Here’s what Krugman does:

So here’s an arguably better measure: constant-demography employment, which shows what would have happened to the employment-population ratio if the age structure of the population had stayed constant.

For my calculation, I’ve divided the population into three age groups, 16-24, 25-54, and 55 plus, for which employment-population ratios are available in the BLS databases. (Scroll down and use the one-screen data search). I’ve then taken a weighted average of these ratios, where the weights are the 2007 shares of each group in the civilian noninstitutional population.

Then he shows a graph that has the constant-demography employment to population ratio improving and sums it up:

So there is real if modest improvement over the past year. Also, the September numbers looks not like an aberration but like a return to trend from what looks like noise in the data over the previous couple of months.

There is one element of the household employment data, though, that shows the 873,000 increase to be less good than it appears. Of those new jobs, about two thirds are part-time jobs for what the Bureau of Labor Statistics calls “economic” reasons: because the workers’ hours had been cut back or because they were unable to find a full-time job.