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The problem with U-U

About 50% of unemployed workers this month will be categorized as unemployed in the next month as well. Let’s call this concept of unemployment persistence the U-U rate and calculate this way: Take the number of workers observed as unemployed in two consecutive months and divide that by the number of workers unemployed as of the first month. The U-U rate is a potentially powerful tool for understanding unemployment dynamics, but we should test how accurately it predicts unemployment duration.

Here, the U-U rate is the “persistence” and 1 minus the U-U rate is the probability of exiting unemployment. We also apply properties of the exponential distribution to calculate its implied mean and median.*

Spoiler alert: The U-U rate poorly predicts unemployment duration. The graphs plot the implied mean and median durations using the U-U rate compared with self-reported unemployment duration. For both the mean and median, the implied duration from U-U is far from the corresponding statistic of self-reported unemployment duration. Why?

  1. The U-U rate we measure here isn’t really the persistence of unemployment, nor is 1 minus the U-U rate the rate of exiting unemployment. The Current Population Survey (CPS) provides these data by following workers for only four months at a time. So, the number of unemployed from one month to the next can’t include those who exited the survey in the fourth month. Hence, the number staying unemployed for 2 months is 1/4 lower, but the total unemployed in 1 month isn’t.
  2. A deeper problem is the way the CPS counts “unemployed” workers. To be counted as unemployed, a worker must be actively searching for a job. Very often, though, a worker won’t search for a month, despite still wanting a job. For example, a job seeker could have applied for appealing jobs last month but, since she’s waiting to hear back, hasn’t applied for any jobs this month. She could also be waiting for new postings or have gotten a job with a delayed start date. To further complicate things, a job seeker may find a temporary job that doesn’t feel like it truly interrupted her unemployment spell when she reports her duration of unemployment, but reporting it would break the U-U pattern.
  3. One feature of unemployment is called “duration dependence”: As workers are unemployed for longer, their individual probability to remain in unemployment tends to increase. This extends their duration further than would be expected using the average unemployment persistence. Even if we could accurately measure the persistence of unemployment, some exit unemployment much more slowly. These job seekers pull out the mean of unemployment duration more than they push up the average persistence.

*We treat the implied exit rate from unemployment as constant across individuals, so the exponential is the proper distribution for the number of people who exit unemployment at different times. The mean is (exit rate)-1 and median is log(2)*(exit rate)-1.

How these graphs were created: The top graph uses mean unemployment, and the bottom graph uses median unemployment duration and a slightly different formula for the implied median. Search for “flow from unemployed to unemployed workers 16+” and add that series to the graph. (FYI: We use the seasonally adjusted series.) In the “Edit Graph” section, add a line to this series: unemployment level. Divide the flow by the number of unemployed by using the formula a/b. Compute the implied mean duration by using the formula 1/(1-a/b). To add the reported mean duration, use the “Add line” option, search for mean unemployment duration, and then convert it to a monthly statistic (since it’s reported in weeks): Divide by 52 and multiply by 12 with the formula a/52*12. For the bottom graph, use the median versions and be sure to use the formulas as noted in the graph labels.

Suggested by David Wiczer.

View on FRED, series used in this post: LNS17500000, UEMPMEAN, UEMPMED, UNEMPLOY

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