Command to turn Economic growth averaged in 5 year periods

[Guest]

Hello,

I have a panel dataset that consists of 67 countries and I want to compute economic growth averaged in 5 year periods. I have data from 1989-2012 and through averaging I aim to get 5 observations per country such as 1989-1993 (1 obs), 1994-1998 (1 obs) ... and the last one consists only of 2009-2012.

So far I have tried manually to get the economic growth for 5 year periods as follows:
1) take logs of real GDP per capita
2) ln(1993)-ln(1989) divided with 4; ln(1998)-ln(1993) divided with 5 , ln(2003)-ln(1998) divided with 5... and for the last ln(2012) - ln(2008) divided with 4.

I have two questions:
1) Is this the correct way to compute growth averaged in 5 year periods?
2) what is the state command/commands that can give me the averaged data for economic growth?

Thank you!

[Andrew Musau]

You should average first before taking logs. Otherwise, you will have a geometric average. Either the -ceil()- or -floor()- function can be used for this. The growth rate can be approximated by the difference of logarithms.

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte id float(year gdp)
1 1989 3.92
1 1990 3.21
1 1991 3.74
1 1992 3.88
1 1993 3.14
1 1994 3.01
1 1995 3.55
1 1996 3.32
1 1997 3.98
1 1998 3.08
1 1999 3.32
1 2000 3.75
1 2001 4.15
1 2002 4.02
1 2003 4.23
1 2004 4.76
1 2005 4.29
1 2006 4.67
1 2007 4.04
2 1989  3.3
2 1990 3.97
2 1991 3.98
2 1992 3.65
2 1993 3.02
2 1994  3.4
2 1995  3.6
2 1996 3.57
2 1997 3.69
2 1998 3.19
2 1999 3.10
2 2000 3.73
2 2001 3.35
2 2002 3.95
2 2003 3.27
2 2004 3.48
2 2005 3.84
2 2006 3.38
2 2007 3.06
3 1989 2.14
3 1990 2.13
3 1991  2.4
3 1992 2.76
3 1993  2.6
3 1994 2.17
3 1995 2.928
3 1996 2.63
3 1997 2.62
3 1998 2.11
3 1999 2.48
3 2000    2.1
3 2001 2.55
3 2002 2.93
3 2003 2.16
3 2004 2.27
3 2005 2.2
3 2006 2.76
4 1989 2.27
4 1990 2.29
4 1991 2.63
4 1992 2.07
4 1993 2.62
4 1994 2.13
4 1995 2.19
4 1996 2.37
4 1997 2.95
4 1998 2.76
4 1999 2.18
4 2000 2.79
4 2001   2.4
4 2002 2.86
4 2003 2.12
end


bys id (year): gen time=_n
gen period= ceil(time/5)
collapse gdp, by(id period)
gen lngdp= ln(gdp)
bys id (period): gen g1= (gdp/gdp[_n-1])-1
xtset id period
gen g2= lngdp-l.lngdp

Res.:

. sort id period

. l, sepby(id)

     +---------------------------------------------------------+
     | id   period      gdp      lngdp          g1          g2 |
     |---------------------------------------------------------|
  1. |  1        1    3.578   1.274804           .           . |
  2. |  1        2    3.388    1.22024   -.0531023   -.0545642 |
  3. |  1        3    3.894   1.359437    .1493507    .1391971 |
  4. |  1        4     4.44   1.490654    .1402157    .1312175 |
     |---------------------------------------------------------|
  5. |  2        1    3.584   1.276479           .           . |
  6. |  2        2     3.49   1.249902   -.0262277   -.0265777 |
  7. |  2        3     3.48   1.247032   -.0028653   -.0028695 |
  8. |  2        4     3.44   1.235471   -.0114942   -.0115608 |
     |---------------------------------------------------------|
  9. |  3        1    2.406   .8779657           .           . |
 10. |  3        2   2.4916   .9129251    .0355777    .0349594 |
 11. |  3        3    2.444    .893636   -.0191042    -.019289 |
 12. |  3        4     2.41   .8796268   -.0139116   -.0140092 |
     |---------------------------------------------------------|
 13. |  4        1    2.376   .8654184           .           . |
 14. |  4        2     2.48   .9082586    .0437711    .0428402 |
 15. |  4        3     2.47   .9042181   -.0040323   -.0040404 |
     +---------------------------------------------------------+

.

[Guest]

Thank you very much! Can you please explain what is g1 exactly?

bys id (period): gen g1= (gdp/gdp[_n-1])-1 I did not entirely understand the purpose of this command.

[Andrew Musau]

You define the growth rate of GDP as the percentage change in GDP, year on year. Maybe you are more accustomed to seeing this as:

$$g_{GDP} = \frac{GDP_{t}- GDP_{t-1}}{GDP_{t-1}} \;\; \text{(Eq. 1)}$$

With a common denominator, we can write the right hand side of Eq. 1 as

$$g_{GDP} = \frac{GDP_{t}}{GDP_{t-1}} - \frac{GDP_{t-1}}{GDP_{t-1}} = \frac{GDP_{t}}{GDP_{t-1}} - 1 \;\; \text{(Eq. 2)}$$

So the code is Eq. 2's representation of the growth rate of GDP.