Interpreting simple statistics isn't always as simple as they are

Current unemployment rate is something like 9.2%. I've either read or heard somewhere that almost half of the currently unemployed have been out of a job for six months or longer. (Because whether or not that rate is accurate does not matter for this post, let's assume it's exactly 50%.) That sounds simple enough. But what does it actually mean? Does it mean that half of the unemployed are chronically unemployed? Well, in a way it does. But in another way it does not.

Suppose you've just been laid off and you want to know the crudest and easiest-to-obtain measure of the probability that you'll still be unemployed in six months. Is it 50%? No, it's less than that, and the reason is that a point-in-time measure overestimates the ratio of long-term unemployed to all unemployed, by definition: some of those who have been unemployed for a short period of time are no longer unemployed and so aren't counted. To have a better estimate of your probability of being unemployed for a long time you'd need to look at the ratio of long-term to all unemployed not on a given day, but over some period of time, say the past six months. This is called the "cohort method." You take a representative sample of all those who've lost their job, say, during the week of January 15th, 2010, and then follow them for the next six months, recording how many of them managed to get a new job during your period of study. From such data you can get an estimate that gets closer to the intuitive notion of "the ratio of chronically unemployed to all unemployed." Point-in-time statistics overestimate the number of long-termers, but also tend to underestimate the overall number of people who have experienced the measured phenomenon. For example, the rate of unemployed to labor force is now 9.2%, but if we were to measure the rate of all those who have experienced an unemployment spell last year to labor force, it would almost certainly be higher than that.

I recently quoted a piece arguing that one of the myths about homelessness is that most homeless people are chronically homeless. Perhaps one of the reasons why it's so pervasive is because whenever homeless shelters publish statistics about what percentage of their clients are long-term stayers, it's always point-in-time numbers. Cohort studies of shelter stay duration usually paint quite a different picture.