## Thursday, August 25, 2016

### The math behind analyzing delays in business cycle announcements

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 Jun-09 Trough 20-Sep-10 Dec-07 Peak 1-Dec-08 Nov-01 Trough 17-Jul-03 Mar-01 Peak 26-Nov-01 Mar-91 Trough 22-Dec-92 Jul-90 Peak 25-Apr-91 Nov-82 Trough 8-Jul-83 Jul-81 Peak 6-Jan-82 Jul-80 Trough 8-Jul-81 Jan-80 Peak 3-Jun-80

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 Jun-09 Trough 20-Sep-10 15 Dec-07 Peak 1-Dec-08 12 Nov-01 Trough 17-Jul-03 20 Mar-01 Peak 26-Nov-01 8 Mar-91 Trough 22-Dec-92 21 Jul-90 Peak 25-Apr-91 9 Nov-82 Trough 8-Jul-83 8 Jul-81 Peak 6-Jan-82 6 Jul-80 Trough 8-Jul-81 12 Jan-80 Peak 3-Jun-80 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.

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 e-mail at Bernstein.book1958@gmail.com so we can discuss publishing your blog post on this topic.