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# re: Re: st: growth rate

 From Christopher Baum To "statalist@hsphsun2.harvard.edu" Subject re: Re: st: growth rate Date Wed, 10 Oct 2012 14:18:07 +0000

```<>
One can do better than any of the suggestions posed when the growth rate is non-infinitesimal, as it may well be over a multi-year span:

clear
input gdp year
100 1995
. 1997
. 2002
. 2007
end

// compute GDP to grow steadily at 5% p.a.
replace gdp = gdp[_n-1] * 1.05^(year - year[_n-1]) in 2/l
g lgdp = log(gdp)

// Nick's suggestion

gen growthN = (lgdp - lgdp[_n-1]) / (year - year[_n-1])

// Kit's suggestion, taking compounding into account,
// avoiding the approximation that ln(1+x) ~ x for small x

g growthK = exp((lgdp - lgdp[_n-1]) / (year - year[_n-1])) - 1
l

. l

+--------------------------------------------------+
|      gdp   year       lgdp    growthN    growthK |
|--------------------------------------------------|
1. |      100   1995    4.60517          .          . |
2. |   110.25   1997   4.702751   .0487902   .0500001 |
3. |   140.71   2002   4.946702   .0487902        .05 |
4. | 179.5856   2007   5.190652   .0487902        .05 |
+--------------------------------------------------+

Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html

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```