ECON 522 - Macroeconomics of the Labor Market Stan Rabinovich UNC Chapel Hill Problem set 8 1. Labor market flows and steady state unemployment In class, we derived the following equation for the steady-state unemployment rate u: u= δ δ+f In the United States, the average monthly job finding probability is approximately 0.45 and the monthly job separation probability is approximately 0.026. (a) Use the above numbers to calculate the implied steady-state rate of unemployment. (b) The historical average of the unemployment rate in the US is about 5.5% (see graph provided by FRED). Is this consistent (at least approximately) with the number you got in (a)? (c) Suppose that, currently, the unemployment rate is 7%. If the job-finding rate and the job separation rate are as given above, would you expect the unemployment rate to rise or fall? 2. Short-term unemployment Let’s define the short-term unemployment rate as the percentage of the labor force who are unemployed but have so far been unemployed for at most one month. (For example, if the unemployment rate is 10% and the short-term unemployment rate is 5%, this would mean that one half of the unemployed workers are workers who just lost their job last month. ) (a) Suppose that, in an economy, the steady-state unemployment rate is 10% and the steady-state short-term unemployment rate is 4.5%. Compute the monthly job-finding rate and the monthly job separation rate. (b) Suppose that two economies, A and B, each have a steady-state unemployment rate of 10%, but economy A has a higher short-term unemployment rate than economy B. Which economy has a higher job finding rate, and which economy has a higher job separation rate? 3. Unemployment duration and unemployment spells The period of time through which a person is continuously unemployed is called an unemployment spell. The length of time that an unemployment spell lasts is called its duration. In the US, we observe that (1) most unemployment spells are short - about 2 months or less; but (2) at any point in time, most unemployed people are people experiencing long unemployment spells. The following exercise helps you reconcile these two seemingly contradictory statements. Suppose that an economy has 500 people in the labor force. At the start of each month, 5 people lose their jobs and remain unemployed for exactly 1 month; at the end of that month, they find new jobs and become employed. In addition, on January 1 of each year, 20 people lose their jobs and remain unemployed for six months (until July 1); on July 1 they find a job. Finally, on July 1 of each year, 20 other people lose their jobs and remain unemployed for six months (until January 1 of next year) before finding new jobs. (a) In a typical month, what is the unemployment rate in this economy? (b) How many unemployment spells are there per year? What fraction of them lasts for one month, and what fraction lasts for six months? (c) What is the average duration of an unemployment spell? (d) On any particular date, how many unemployed people are there? What fraction of the unemployed are suffering a long (six-month) unemployment spell? 1 4. Using FRED data (This is an exercise in using the FRED data. Answers will not be posted, but I am happy to help if you have any questions.) (a) Using the Federal Reserve Economic Database, download these two data series for 1967-latest available: • UNRATE: Civilian Unemployment Rate • UEMPMEAN: Average Weeks Unemployed Display the two series on the same graph. Set the units to “Index” with Scale Value equal to 100 at the start of the 2007 recession. Display the plot of the two series over time. (b) The unemployment rate is one of the most commonly used indicators of economic activity. Does the unemployment duration paint the same picture of the economy as the unemployment rate? Where do they diverge? And why do you think this is? 2
