Last Friday’s unemployment report was met with cheers and skepticism, and all because of the annual pre-announced and well-telegraphed statistical adjustments made by the Bureau of Labor Statistics were both large and confusing.

Like most statistical pronouncements, the first reports are not as reliable as the revisions made later as the data relies less on estimates and more on actual reports.

The most reliable part of the unemployment report is the rise in payroll jobs. The exact words of the press release from the BLS are “Total nonfarm payroll employment rose by 243,000 in January, and the unemployment rate decreased to 8.3 percent…” And that’s the problem.

I’ve explained before that the BLS has two surveys, the establishment survey and the household survey. The payroll employment number comes from the establishment survey, and is mainly based on Social Security tax filings where every employee for who those taxes have been withheld and also paid by employers is counted. This is a very reliable number. The main reason it is subject to revision from month to month is because large businesses submit their payments weekly, and small businesses submit their payments less often. Generally, the revision numbers are reflections of new data coming from small and mid-size businesses.

The second part of the BLS statement, “… and the unemployment rate decreased to 8.3 percent…” comes from the household survey. This is one of the best-run research surveys in the world, actually, and it is the survey used to calculate the unemployment rate. One of the problems with the BLS releases is that they report the changes in payrolls and the unemployment rate together, leading most people to believe that they are derived from exactly the same data. They are not.

The household survey data are critical, because they include self-employment by proprietors, partners, and freelance workers. This is a broader universe than the payroll employment data, by definition, and a better indicator of economic conditions, especially in this age where workers can be anywhere and they can offer their services well beyond the areas where they reside.

So what happened? It was really clear in the BLS release, and as mentioned, everyone knew this was going to happen, but no one knew what the final extent of things would be. Their release stated: “…household survey data for January 2012 reflect updated population estimates…” Later in the release, it explains that those population estimates were based on new data from the 2010 Census that identified an undercount of about 1.5 million people compared to the Census of 2000. That is, the Census Bureau had been underestimating population by about 150,000 people per year for each of the last ten years.

So, just to use round numbers, let’s say the US population is 300 million today (it’s higher than that), and then say that the undercount is 1.5 million (it’s slightly higher). How “bad” has the Census estimate been? Over ten years, the Census miscounted by 0.5%. Half a percentage point… the problem is they supplied the adjustment all at once, and in a political year.

The biggest political problem with the data was that of the 1.5 million people, 1.2 million people were considered as not being in the labor force.

The first thing that happened statistically was that this added 300,000 more workers to the household survey, which reduced the unemployment rate more than would have occurred “naturally.” Second, it reduced the labor participation rate from 64% to 63.7%.

This meant that all along the BLS was undercounting both the number of jobs holders and undercounting the number of people not working at the same time. (But it was the Census Bureau’s fault, if you count being off by 0.5% as being a statistical felony, and the BLS is as pure as the driven snow; besides that, they warned us).

The conspiracy theorists went crazy, about how the unemployment rate was being manipulated downward for political purposes. If the economy was strong, this would have passed with only mild acknowledgment that the normal annual revisions made every January were in place. Some of the more cited conspiracy-based comments were at ZeroHedge, but then they became more introspective and thoughtful, and more analytical. A voice of reason was cited at Barry Ritholz’ widely-followed Big Picture blog.

The entire process is a reminder that statistical precision is often elusive, the application of statistical concepts is more art than science, and that data series like the unemployment data are best viewed over time, not as a single event.

There’s a few things to keep in mind. The monthly payroll number has a statistical range of about plus or minus 130,000. So we know that payrolls definitely increased. It is still not in a direction to return to full employment (between 4% and 6%) at any time soon. We also know that there is no sign of an economic boom, just some positive economic activity that is barely above muddling by.

The updated macroeconomic indicators include the new productivity data that show productivity as still greater than GDP, indicating that employment growth will be slow. When GDP is greater than productivity is the time when employment booms occur. 

The recovery indicators were very good for a second consecutive month. Though the economic recovery has been slow, it does appear to be solidifying, finally. 

The NASDAQ rebounded, and is above 2900, with a very strong January for stocks. It is more than 9% ahead of where it was at the start of the recession. More importantly, it is now ahead of the inflation-adjusted level 2860.

The ISM reports for both manufacturing and non-manufacturing were good throughout. Each ISM index is comprised of separate components for orders, prices, employment, and others. In both industry segments, the individual components in the report were almost all uniformly good.

Proprietors’ income, a measure of the health of small business, was up +0.2% on an annualized basis compared to the third quarter, and is +2.4% higher than the start of the recession. Unfortunately, inflation has eroded those gains, and then some. Proprietors’ income is below the December 2007 level on an inflation-adjusted basis by -4.7%.