Macroeconomics 5th Edition by Olivier Blanchard

Exercise 3

Unemployment spells and long-term unemployment According to the data presented in this chapter, about 45% of unemployed workers leave unemployment each month.
a. What is the probability that an unemployed 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 pro-portion of the unemployed who have been unemployed six months or more. Suppose the number of unemployed workers is constant and equal to x (where x is some constant). Each month, 45% 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 45% of unemployed workers find jobs 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 ,v 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 This percentage applies to the economy at any time (remember that we started with an arbitrary month). Under our assumptions, the percentage of the unemployed who have been unemployed six months or more is constant.
d. Using Table 13-44 of the Economic Report of the President (www.access.gpo.govieop/), compute the proportion of unemployed who have been unemployed six months or more (27 weeks or more) for each year between 1996 and 2003. How do these numbers compare with the answer you obtained in part (c) Can you guess what may account for the difference between the actual numbers and the answer you obtained in this problem (Hint: Suppose that the probability of exiting unemployment goes down the longer you are unemployed.)