0

Suppose I want to calculate the average annual growth in GDP per capita from year 1980 to 1988. I suppose this is done by ln(gdp per capita 1998) - ln(gdp per capita 1990) ? So for example:

ln(900)-ln(100) / 8 = 0.2747 , so 27.47%.

But if I take the start value times the growth increase i get:

100 x 1.2747^8 = 697

But if I use the geometric growth average (compound annual growth) to calculate growth I get:

8^√(900/100) = 1.316 , so 31.6%.

and taking the start value times growth increase i get:

100 x 1.316^8 = 899.6 , so almost exact 900.

Does the log difference method underestimate the growth increase? Why? Which is best to use?

And if I have calculated the growth rate with the geometric approach and regress it against another percentage change in say increase of cars (growth of cars bought), would such a relationship be an elasticity between average growth in gdp per capita and average growth of cars?

Crazzzy12
  • 15
  • 1
  • 4

1 Answers1

3

I think you are mixing up different things a little bit. This is exactly what you need, even the example is with GDP.

Relative change can be computed with two differnt ways. Discrete or with log, both have advantages and disadvantages.

For average growth rates you should take the geometric mean.

If you take the arithmetic mean and compute the mean of this you will get wrong results, there are a lot of examples, especially if you have negative changes in between, where you can clearly see, that the geometric mean is correct and the average of the simple averages is wrong.

And for the second part of your question see the related/linked posts, especially this one: Elasticity of log-log regression and this one: Interpretation of log transformed predictor or maybe also this one: How to interpret regression coefficients in a log-log model

Community
  • 1
Stat Tistician
  • 2,113
  • 4
  • 29
  • 54