# What are the advantages of using log GDP per capita versus simple GDP per capita when analyzing economic growth? [duplicate]

I have quite a lot to learn regarding analysis and economics, one thing I have noticed is that when analyzing growth, log is used quite often, why is this so?

## 1 Answer

The GDP is growing exponentially.

Start with a GDP at 1, the first year it grows by 1%: $$1\times(1+0.01)$$ Second year it grows by 2 percent: $$1\times(1+0.01)\times(1+0.02)$$

It is not easy to see how GDP2 depends on GDP1 and GDP0.

if you take the log: \begin{align} lGPD_0 &= 0 \\ lGDP_1 &= lGDP_0 + \log(1+0.01) &=& \log(1+0.01) \\ lGDP_2 &= \log(1+0.1) + \log(1+0.02) &=& lGDP_1 + \log(1+0.02) \end{align} So the difference between the log GDP is clearer.

Plus if you add constant rate of growth (for comparison for example) you would obtain a straight line and not an exponential shaped curve.

• Does GDP always grow exponentially? Certainly when it does, your effect would hold, but I wonder if you meant something slightly different that what you said. – gung - Reinstate Monica Oct 8 '14 at 23:47
• Simply, it's a better approximation that GDP changes multiplicatively than that it changes additively, so analysis on logarithmic scale is helpful. Exponential growth at constant rate is just the simplest mathematical caricature to start thinking about; newspapers and television remind us repeatedly that growth rates vary over time, including periods of recession. The meta-question here is quite what kind and level of explanation is being asked for. Analysis per capita factors out population size and its growth but that's taken as read in the question. – Nick Cox Oct 8 '14 at 23:53