st: How to identify patterns of cyclicality using STATA?

[Natasha Xingyuan Che <ilovewordsworth@gmail.com>]

Dear All,

I'm trying to identify business cycle peaks, troughs, and phases of
recession and recovery in a panel data set of countries's quarterly
output series.  I identified peaks and troughs, but am having trouble
marking the periods in between (i.e., recessions and recoveries).  I
would really appreciate it if any of you have suggestions about how to
do this.

The specific definitions of the variables are the following --

A peak occurs at Quarter t of a time series of Y_t if:
(Y_t - Y_t-1) > 0 and (Y_t - Y_t-2) > 0 and (Y_t - Y_t+1) > 0 and (Y_t
- Y_t+2) > 0

A trough occurs at Quarter t if:
(Y_t - Y_t-1) < 0 and (Y_t - Y_t-2) < 0 and (Y_t - Y_t+1) < 0 and (Y_t
- Y_t+2) < 0

A "recession" is a phase from peak to the next trough.  A "recovery"
is a phase from trough to the quarter when Y reaches the level of the
previous peak.

I generated two 0/1 variables, peak and trough, as the following --

tsset country time
gen peak=(lny>l.lny&lny>l2.lny&lny>f.lny&lny>f2.lny)
gen trough=(lny<l.lny&lny<l2.lny&lny<f.lny&lny<f2.lny)

Now I want to generate two variables marking the quarters when the
economy is in recession and in recovery and calculate the respective
duration of the two.  But I'm not sure how to proceed.  Again, all
your inputs are very much appreciated.  Thank you so much for your
help!

Best,
Natasha
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