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Can anyone suss out the interpretation of beta here:

D.log(gdp) = alpha + beta(log(military expenditure %)

Where D.log(gdp) = growth of GDP (first difference of log(GDP)

Would it be:

A 1% point increase in military expenditure is associated with a beta% point change in the growth of GDP?

OR

A 1% increase in military expenditure is associated with a beta % change in the growth of GDP?

OR neither?

N.B. Also what implication does the underlying variable military expenditure have being a %, wouldn't that make the interpretation a percentage point?

Thanks Labib

  • Is this a homework problem? – Matthew Gunn Apr 05 '18 at 14:31
  • See https://stats.stackexchange.com/search?q=regression+interpret+log+answers%3A1 for more answers. – whuber Apr 05 '18 at 14:35
  • @MatthewGunn no its for a paper trying to measure the effect that corruption has indirectly via military spending, however i have recently changed specification of the model from where the independent variables were first differenced to simple logs, as such i have confused myself. Any help would be appreciated.. – Stat-metrics Apr 05 '18 at 15:55
  • @whuber i have looked and havent been able to find something which interprets a dlog-log regression coefficient – Stat-metrics Apr 05 '18 at 16:23
  • If I'm reading what you wrote correctly, a military expenditure increase as a share of GDP of 1% (eg. from 10% of the budget to 10.1%) is associated with a $\beta$ * 1% increase in the GDP growth rate. (You almost certainly don't want to give this a causal interpretation.) – Matthew Gunn Apr 05 '18 at 17:16
  • @MatthewGunn just to clarify - when you say a 1% increase in ((military expenditure share of GDP) 10.1%, is as the 0.1% increase is 1% of 10%? correct? Sorry for that confusing interpretation. Also just for my future understanding why is it not percentage point/ when would it be? Thanks again! – Stat-metrics Apr 05 '18 at 17:31
  • @MatthewGunn also why would you not give this causal interpretation? – Stat-metrics Apr 05 '18 at 17:32
  • $\log(.101)−\log(.1)\approx.01$. You would not give this a causal (right side causes left side) interpretation because you've got reverse causation, confounding, etc.... Clearly GDP growth affects the budget. When I spend a larger percentage of my income on diamonds, my income grows faster? That's quite possible, but buying diamonds almost certainly doesn't raise my income. – Matthew Gunn Apr 05 '18 at 17:44
  • @MatthewGunn ah i see, reverse causality - i am trying to account for that using a system gmm estimator. Thank you Matthew. – Stat-metrics Apr 05 '18 at 17:46

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