Between the stock market nosedive and the S&P downgrade (based on a $2 trillion math error), last week wasn't a great one for the U.S. economic outlook. There was, however, one glimmer of hope: U.S. employers reported they added an above-expected 117,000 jobs in July, as the unemployment rate fell from 9.2 percent to 9.1 percent.

Unfortunately, there to throw cold water on that hope was NYU professor Nouriel Roubini — best known as the man who predicted the housing bubble — who promptly tweeted:

 Lousy job report: payrolls gotta rise by >150k to prevent unemp rate from rising: it fell to 9.1% only because 200K folks left labor force

The translation, in more than 140 characters: The unemployment rate is determined by dividing the number of people looking for work but unable to find it by the number of people in the total workforce. ("Looking for work" here is defined as telling interviewers they're actively seeking work; they don't have to be receiving unemployment insurance.) Because the U.S. adult population is continually rising (thanks to both immigration and kids' persistence in growing up), the economy normally needs to add 150,000 jobs a year just to keep up. But if one month 200,000 people throw up their hands and say, "There are no jobs, I'm going to crawl under the covers and watch TV," then the numerator goes down by enough that the unemployment rate falls — even though the number of adults without jobs has continued to rise.

What does this mean for New York City, where the unemployment rate has actually dipped below the national rate in recent months, and where Mayor Bloomberg has boasted of the city creating jobs "at nearly twice the national rate"?

The image above shows what the city labor force, jobs, and unemployment rate numbers look like for the past four-and-a-half years (all figures from the New York State Department of Labor). New York City's unemployment rate has indeed fallen, from its high of 10.4 percent in January 2010 to as low as 8.3 percent in April. Very little of this, though, is the result of local employers hiring more people: The city has only added 22,000 jobs since the start of last year, nowhere near the pace that would be need to gain back the jobs lost in the 2008-09 crash. Rather, what's happened is that blue line (the black line on top of it is a moving average, intended to smooth out seasonal blips like Christmas season) has stopped the slow rise it was on until mid-2009 and reversed direction, with the city labor force now shrinking by almost 3,000 people per month. As a result, the space between the blue and red lines — that's the number of unemployed — has fallen, and with it the unemployment rate.

In other words, the main force at work here isn't the resilience of the New York City economy — though compared to some other parts of the country we could be doing worse — but rather that either people are moving out of New York City, or those who are here have given up looking for work. Or, less likely, our kids have stopped growing up.