Real GDP Over the Business Cycle: Amplitude

[Silvia Haertl]

Dear all,

I would like to investigate business cycle features of my dataset.
Therefore, I used the Bry and Boschan algorithm (from Bry, Gerhard and Charlotte Boschan (1971). Cyclical Analysis of Time Series: Selected Procedures
and Computer Programs. NBER), which generates dates of peaks and troughs in economic activity for each country in my sample seperately.

The command therefore was

//Bry and Boschan Algorithm
sbbq rgdpmad, w(1) p(1) c(1)

Using real GDP per Capita (variable: rgdpmad), a peak corresponds to a local maximum whereas a trough corresponds to a local minimum.
The algorithm created two dummy variables: 1 for a business cycle peak, -1 for a business cycle trough.

To differ between expansion and recession times, I also created the variable rgdpmad_p2
1 refers to an expansion
- 1 refers to an recession

//to differ between expansion and recession times
gen rgdpmad_p2 = rgdpmad_point
bysort id (year): replace rgdpmad_p2 = rgdpmad_p2[_n-1] if rgdpmad_p2 == 0 & _n>1

my variables look like the following:

year country rgdpmad_point _spell _seq _end length rgdpmad_p2
1870 Australia 0 0 0 0 0
1871 Australia 0 0 0 0 0
1872 Australia 0 0 0 0 0
1873 Australia 0 0 0 0 0
1874 Australia 0 0 0 0 0
1875 Australia 1 1 1 1 1 1
1876 Australia -1 2 1 0 2 -1
1877 Australia 0 2 2 1 2 -1
1878 Australia 1 3 1 1 1 1
1879 Australia -1 4 1 0 2 -1
1880 Australia 0 4 2 1 2 -1
1881 Australia 1 5 1 1 1 1
1882 Australia -1 6 1 1 1 -1
1883 Australia 1 7 1 1 1 1
1884 Australia -1 8 1 1 1 -1
1885 Australia 1 9 1 1 1 1
1886 Australia -1 10 1 1 1 -1
1887 Australia 1 11 1 1 1 1
1888 Australia -1 12 1 1 1 -1
1889 Australia 1 13 1 1 1 1
1890 Australia -1 14 1 1 1 -1
1891 Australia 1 15 1 0 2 1
1892 Australia 0 15 2 1 2 1
1893 Australia -1 16 1 1 1 -1
1894 Australia 1 17 1 1 1 1
1895 Australia -1 18 1 1 1 -1



What I know would like to calculate is the amplitude, which denotes the average change of real GDP per Capita between turning points.
In the paper, I am working with, they say, that amplitude is the absolute log difference between peak and trough levels.
Which means I have to log my variable rgdpmad

gen lrgdp = log(rgdpmad)

But then I really don´t find a way to get the amplitude.
Maybe someone can help?
Thank you very much in advance

[Silvia Haertl]

I found a solution which works perfectly in this case

//Therefore I need the log-value
gen lrgdp = log(rgdpmad)

//amplitude
bysort country _spell (year): gen diff1 = lrgdp[_N] - lrgdp[1] if _spell

gen diff = diff1*100 if rgdpmad_point[_n+1]==-1 | rgdpmad_point[_n+1]==1

Thank you