What is going on here?
The unemployment rate is calculated from a survey of households querying how many adults there are in the household, how many are employed or seeking work, etc. The unemployment rate is the ratio of the number of unemployed individuals seeking work divided by the total size of the labor force (people working or seeking work). Based on this survey, in September estimated total employment rose by a huge number, 873,000. The number of individuals in the labor force also grew by a large number 468,000 – so the unemployment rate went down despite the fact that the labor force itself grew. The civilian labor force participation rate (fraction of adult population working or seeking work) did not change much - increasing from 63.5% to 63.6%.
The statistic that I am fond of as being among the most reliable, the employment-population ratio (fraction of adults who are working), also ticked up substantially from 58.3% in August to 58.7% in September. This ratio had been above 63% before the onset of the recession in 2007 and has been stubbornly stuck around 58% ever since. I am fond of the employment-population ratio as a measure because it does not depend on the subjective state of mind of unemployed individuals being surveyed – whether they are looking for work or not – which does affect the calculation of the unemployment rate.
In contrast to the household survey, the non-farm payroll employment is calculated from the Establishment survey – a survey of the payrolls of 141,000 businesses and government agencies. Obviously there is a huge discrepancy in the increase in employment as estimated from the Establishment survey (116,000 for non-farm payroll) versus the household survey (873,000). Talking heads on television have suggested that the estimates may be volatile, there may be methodological/technical issues in the collection of the data, etc. Also, the Bureau of Labor statistics notes that there are some types of workers that are included in one survey and not the other (e.g. agricultural workers, underage workers, domestic workers, etc). However, I doubt that these factors can account for the huge discrepancy.
I would like to hypothesize another explanation. There is a change in the nature of work. More and more people are working outside of established businesses and government agencies. In the age of internet, more and more people may be self-employed working at home on their computers. An increasing number of people may be working as individual consultants or contractors or in small businesses not included in the Establishment survey. These individuals do not show up in the Establishment survey of the Bureau of Labor Statistics but do show up in the Household survey.
The bottom line is that, at least for September, the employment situation appears to be brightening - and the nature of work may be changing.