Question

Suppose a cohort of 25,000 people become unemployed. You are told that the job finding rate for this group depends on the elapsed duration of the unemployment spell as follows: Job Finding Rate Spell Duration (months) 1 2 3 4 5 0. 60 0. 20 0. 20 0. 20 0. 20 0. 10 6

a) Explain in economic terms why the job finding rate might decline with spell duration. B) Calculate how many unemployment months this cohort will experience in total. C) Compute the fraction of (out of 25,000) who will be "long-term" unemployed, here defined as having unemployment spells of 5 months or longer. D) What fraction of unemployment months do this long-term unemployed group account for? e) For this cohort, does the "unemployment problem" seem to be too many job losses or too many long spells?

Answer 1

a) The job finding rate might decline with spell duration because as time goes on, the pool of available jobs may become smaller, as some jobs may have been filled by other job seekers or may have been eliminated. Additionally, employers may be more hesitant to hire someone who has been unemployed for a longer period of time, as they may perceive them as less motivated or less skilled than someone who has been employed more recently.

b) To calculate the total number of unemployment months this cohort will experience, we need to multiply the number of people in the cohort by the job finding rate for each spell duration, and sum across all spell durations. Using the information given, we can calculate:
- For spell duration 0: 25,000 x 0.60 = 15,000 employed, 10,000 unemployed
- For spell duration 1: 10,000 x 0.20 = 2,000 employed, 8,000 unemployed
- For spell duration 2: 8,000 x 0.20 = 1,600 employed, 6,400 unemployed
- For spell duration 3: 6,400 x 0.20 = 1,280 employed, 5,120 unemployed
- For spell duration 4: 5,120 x 0.20 = 1,024 employed, 4,096 unemployed
- For spell duration 5: 4,096 x 0.10 = 410 employed, 3,686 unemployed
- For spell duration 6: 3,686 x 0 = 0 employed, 3,686 unemployed

Therefore, the total number of unemployment months this cohort will experience is:
10,000 + 8,000 + 6,400 + 5,120 + 4,096 + 3,686 + 3,686 = 41,988

c) To compute the fraction of the cohort who will be "long-term" unemployed, we need to add up the number of people who have been unemployed for 5 months or longer. Using the information given, we can calculate:
- For spell duration 5: 4,096 x 0.10 = 410 employed, 3,686 unemployed
- For spell duration 6: 3,686 x 1.00 = 0 employed, 3,686 unemployed

Therefore, the fraction of the cohort who will be "long-term" unemployed is:
(3,686 + 0) / 25,000 = 0.1474 or approximately 14.74%

d) To calculate the fraction of unemployment months that the long-term unemployed group accounts for, we need to divide the total number of unemployment months for the long-term unemployed group by the total number of unemployment months for the entire cohort. Using the information given, we can calculate:
- For spell duration 5: 3,686 unemployment months
- For spell duration 6: 3,686 unemployment months

Therefore, the total number of unemployment months for the long-term unemployed group is:
3,686 + 3,686 = 7,372

The fraction of unemployment months that the long-term unemployed group accounts for is:
7,372 / 41,988 = 0.1753 or approximately 17.53%

e) For this cohort, the "unemployment problem" seems to be too many long spells, as the majority of the unemployment months are accounted for by those who have been unemployed for 5 months or longer. This suggests that policies aimed at addressing long-term unemployment, such as job training programs, wage subsidies, and targeted job search assistance, may be particularly effective in reducing unemployment in this cohort.