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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

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marked as duplicate by whuber Apr 5 '18 at 14:36

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  • $\begingroup$ Is this a homework problem? $\endgroup$ – Matthew Gunn Apr 5 '18 at 14:31
  • $\begingroup$ See stats.stackexchange.com/… for more answers. $\endgroup$ – whuber Apr 5 '18 at 14:35
  • $\begingroup$ @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.. $\endgroup$ – Stat-metrics Apr 5 '18 at 15:55
  • $\begingroup$ @whuber i have looked and havent been able to find something which interprets a dlog-log regression coefficient $\endgroup$ – Stat-metrics Apr 5 '18 at 16:23
  • $\begingroup$ 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.) $\endgroup$ – Matthew Gunn Apr 5 '18 at 17:16