The math behind
analyzing delays in business cycle announcements
A recent post at my blog www.EconomicMemos.com found that NBER
announcement dates of the beginning and end of recessions often lagged the
event by a considerable amount.
The findings in the post have important ramifications for
monetary and fiscal policy. Policy
makers can’t successfully put in place policies that prevent recessions or
inflation unless they can accurately track the economy in a timely fashion
This math post describes the calculation in the business
cycle post. I also include a question
for my readers with good Excel skills.
Question: Consider the data on NBER business cycle
events presented in the table below.
How does one calculate the following items?
The gap in announcement date and turning point in months
The average and median gap between turning point and
announcement dates
The average and median gap between turning point and
announcement dates for peaks and troughs separately
The identification of instances where the announcement of a
recession occurred after the actual recession ended.
Gap Between NBER Business
Cycle Event and Announcement


Turning Point Date

Peak or Trough

Announcement Date with
Link

Jun09

Trough

20Sep10

Dec07

Peak

1Dec08

Nov01

Trough

17Jul03

Mar01

Peak

26Nov01

Mar91

Trough

22Dec92

Jul90

Peak

25Apr91

Nov82

Trough

8Jul83

Jul81

Peak

6Jan82

Jul80

Trough

8Jul81

Jan80

Peak

3Jun80

Analysis:
The calculation of the difference between the announcement
date of a business cycle event and the actual date of the event relies on the
year and month functions in Excel
I use the following formula:
=12*(year(announce_date) year(event_date)) +
(month(announce_date)month(event_date))
This is what I get:
Gap Between NBER Business
Cycle Event and Announcement


Turning Point Date

Peak or Trough

Announcement Date with
Link

Gap Between Event and
Announcement Date

Jun09

Trough

20Sep10

15

Dec07

Peak

1Dec08

12

Nov01

Trough

17Jul03

20

Mar01

Peak

26Nov01

8

Mar91

Trough

22Dec92

21

Jul90

Peak

25Apr91

9

Nov82

Trough

8Jul83

8

Jul81

Peak

6Jan82

6

Jul80

Trough

8Jul81

12

Jan80

Peak

3Jun80

5

To take the average and the median over all events use the
average and median functions in Excel.
This is straightforward.
To get the average for trough or peak used the
averageif statement. The syntax of this function is fairly clear.
AVG_IF=Averageif(range,
criteria,average_range)
The range is the second column Peak or trough data.
The criteria is “Trough” or “Peak”
The average_range is the data in the fourth column.
The median for trough or peak separately is harder.
The Excel help pages on the web indicate that this can be
accomplished with the combination of an if or median statements. Other pages indicate this could be done with
an And plus a Median statement. I
couldn’t figure out how to do this either way.
I ended up sorting the data by data in column two. I then took median of all peak gap values and
median of all trough gap values.
This is how I would accomplish the task in SAS or
STATA. Just run a procedure on a by
variable.
The issue of the identification of whether a recession
announcement date occurs after the actual recession ends involves the use of an
if statement comparing peak announcements to actual troughs. If the peak announcement date is larger than
(later than) the actual trough date the existence of a recession was announced
after the recession actually ended.
The NBER is not providing a useful service if it can’t
identify the existence of a recession
until after the recession ends.
Question for Readers:
I have a question for readers with good Excel skill. I would be interested in publishing a post
that calculates the trough and peak median in gap between announcement dates
and actual event. I want the calculation
to be conducted with logical statements and to be accomplished without sorting
the database. I would like to present
more than one solution and I want the cell locations rows and columns to be
clearly identified so that people can replicate the result.
Please communicate with me via email at Bernstein.book1958@gmail.com so
we can discuss publishing your blog post on this topic.
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