# Short-term economic fluctuations

Problem 2. Duration of expansions and contractions.

Data on the dates and duration of expansions ("booms") and contractions ("recessions") are available from the
National Bureau of Economic Research .

Although the NBER is a private organization, it is a very prestigious one, and its dating system for recessions and expansions is authoritative. A full explanation of that system is available here. Careful readers will note that the NBER dates depend on considering several factors, including employment, industrial production and overall income -- not just GDP.

Problem 3. Output gap calculation.
The Congressional Budget Office has the most widely accepted calculation of potential output . A description of their methodology is available here .

Figures for actual and potential output and the output gap follow, note that since

Output Gap = Y* - Y = Potential GDP - Actual GDP

a positive output gap is a recession , and a negative output gap is an expansion .

Year Actual GDP Potential GDP Output gap Percent gap
1988 5844 5788 -56 -0.97
1989 6056 5943 -113 -1.90
1990 6172 6102 -70 -1.15
1991 6075 6265 190 3.03
1992 6214 6432 218 3.39
1993 6360 6604 244 3.69

On the basis of the above table, the years 1988, 1989 and 1990 were years of prosperity, and the years 1991, 1992 and 1993 were years of recession. Note that the NBER does not count 1993 as a year of recession, since it dates a boom from the trough of the business cycle -- and output was recovering, although not yet up to potential.

Problem 4 -- Unemployment rates by age and the "Natural Rate of Unemployment"
Go to Bureau of Labor Statistics to fill in the following table:

1960
1970
1980
1990
2000
2002 15.6 5.0 5.0

(See the powerpoint slides for the percentage of each group in the work force)

Problem 5 -- Okun's law
Arthur Okun found the relation between output gap and unemployment rate to be:

(Y* - Y) / Y* = 2 (u - u*)

Use that relationship to complete the following table: (completions are in bold
Note that:

• NAIRU = "Non-Accelerating Inflation Rate of Unemployment " or the Natural Rate
• UNRATE = Actual Unemployment rate

Year Actual GDP Potential GDP Output Gap % gap NAIRU UNRATE
2001 7,840 8,000 160 2.0 5.0 6.0
2002 8,100 8,100 0 0 5.0 5.0
2003 9,020 8,200 -820 -1.0 4.5 4.0
2004 8,415 8,250 -165 -2.0 5.0 4.0

The first and last rows go naturally together:

• 2001: Since Potential GDP is 8,000 and actual GDP is 7,840, the
output gap = Y* - Y = 8,000 - 7,840 = 160 . The economy is in recession .
In percentage terms, the output gap is therefore 160 / 8,000 = .02 or 2 percent.

Okun's law is that (Y* - Y) / Y* = 2 (U - U*) ,
-- and in this case we have 2 = 2 (U - U*) so that U - U* = 1
The actual unemployment rate is above the NAIRU by 1 percent;
Since the actual rate is given as 6.0, the NAIRU had to be 5.0

• 2004: Since Potential GDP is 8,250 and actual GDP is 8,415, the
output gap = Y* - Y = 8,250 - 8,415 = -165 . The economy is in enjoying prosperity .
In percentage terms, the output gap is therefore -165 / 8,250 = - 0.02 or 2 percent.

Okun's law is that (Y* - Y) / Y* = 2 (U - U*) ,
-- and in this case we have -2 = 2 (U - U*) so that U - U* = -1
The actual unemployment rate is below the NAIRU by 1 percent;
Since the NAIRU is given as 5.0, the actual rate had to be 4.0

The middle two rows also go naturally together: we can calculate
the percentage output gap as 2(U - U*) and then find the value of Y and Y*.

• 2002: The actual unemployment rate is equal to the NAIRU.
The output gap is therefore zero which in turn means that Y = Y*

• 2003: The acutal unempoyment rate is 1/2 percent below the NAIRU.
Hence the output gap will be minus one percent , or

(Y* - Y) / Y* = - .01. Multiplying through by Y*, we have
(Y* - Y) = - .01 Y*; so using the fact that Y* = 8,200, we have
8,200 - Y = - 82, and rearranging terms:
Y = 8,200 + 82 = 8,282