Unemployment spell and long-term unemployment. According to the data presented in this chapter, about 47% of unemployed workers leave unemployment each month.
a- What is the probability that an employed worker will still be unemployed after one month? two months? Six months?
Now consider the composition of the unemployment pool. We will use a simple experiment to determine the proportion of the unemployed who have been unemployed for six months or more. Suppose the number of unemployed workers is constant and equal to x (where x is some constant). Each month, 47% of the unemployed find jobs, and an equivalent number of previously employed workers become unemployed.
b- Consider the group of x workers who are unemployed this month. After a month, what percentage of this group will still be unemployed? (Hint: if 47% of unemployed workers find a job every month, what percentage of the original x unemployed workers did not find jobs in the first month?).
c- After a second month, what percentage of the original x unemployed workers has been unemployed for at least two months? (Hint: given your answer to part (b), what percentage of those unemployed for at least one month do not find jobs in the second month?), after the sixth month, what percentage of the original x unemployed workers has been unemployed for at least six months?