According to the Bureau of Labor Statistics unemployment report for December, released on Friday, the US unemployment rate has dropped to 9.4%.  Good news, right?  Not so much, says James Hamilton, writing at Econbrowser:

Unfortunately, the household numbers look much less rosy when you look at them a little more closely. For one thing, the impressive December gain comes right after an estimated loss according to the household survey of 175,000 jobs in November and a whopping loss of 294,000 in October. How can the household survey be signaling a falling unemployment rate over the last 3 months if its measure of the number of people working has actually gone down?

Hamilton goes on to provide an answer to that question, and his approach is very instructive:

Let me use an average over the last two months to smooth out some of the wild volatility in the household employment numbers and highlight what's changed in terms of people's employment status. In November and December, the civilian noninstitutional population over age 16 increased by 180,000 per month. The figure below illustrates what would have happened if these new people had entered into the respective employment categories at the same rate as the existing population. For example, if 58% of those 180,000 new potential workers found jobs, the number of employed individuals would have increased by 105,000 each month. If in December the number of employed had increased by 105,000, the number of unemployed increased by 11,000, and the number not in the labor force by 64,000, then measures such as the unemployment rate and the labor force participation rate would have been unchanged.

Average additions (in thousands of people per month) that would have kept the unemployment rate, employment rate, and labor force participation rate unchanged between October and December.

But we know that in reality, the unemployment rate was not unchanged, but fell from 9.7% in October to 9.4% in December. The figure below shows that this is attributable mathematically to the fact that almost 200,000 fewer workers were counted as being unemployed in December compared with October.

Actual average monthly changes in November and December in the number of people in different employment categories, with the actual change minus the change predicted in the previous figure indicated in parentheses.

Read Interpreting the employment numbers here.