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My model has been given as: $$\ln (H_ed) = 18.08 - 0.53\ln Pop -2.01 \ln Distance + 0.47\ln RGD $$

Where (Hed) is higher education, pop is population, and RGD = Real GDP per capita.

I have been asked to find the "income elasticity of the demand for higher education".

As there are no income variables in this model, I am unsure of where to look for the income elasticity.

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    $\begingroup$ This strikes me as more a question of economic theory than statistics. This belongs on the Economics SE site, not here. $\endgroup$ – gung May 21 '16 at 9:52
  • $\begingroup$ Can you say more about the sample? the period? Can you define what is Distance here? $\endgroup$ – emeryville May 21 '16 at 17:14
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    $\begingroup$ A hint: as far as I understand this is a cross-country regression where GDP per capita gives you some information about income. Then, you have some information about the population effect... $\endgroup$ – emeryville May 21 '16 at 17:23
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Real GDP is a variable for aggregate income. You might think of your model very loosely as an "aggregate demand function". Then, as the elasticity of a function $\varepsilon=\frac{\partial f}{\partial x}\frac{f(x)}{x}$ can be expressed in terms of logarithms $\varepsilon=\frac{\partial \ln f}{\partial \ln x}$, in your estimation it would amount to say that, ceteris paribus, the elasticity of (assuming average) higher education to real income per capita is $0.47$.
This implies that the "demand" for higher education is inelastic ($\varepsilon \in (0,1)$), which kind of makes some sense.


Within that framework (aggregate average, not consistent with demand theory), I think a better model would come from adding ${(\ln RGD)}^2$ to your model, to let the "income elasticity" describe some nonlinearities as it would sound really strange that if RGDP would go up 1000x average education would go up 470x, as this would mean people would be living some centuries before completing their education...

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  • $\begingroup$ I am pretty sure that countries that have a 1:1000 GDP ratio would also have a ridiculously large education ratio. But if you take a closer look, RGDP increasing a 1000 fold would only increase education approximately 26 fold as the relationship is between their logarithms. $\endgroup$ – Giskard May 21 '16 at 17:25
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    $\begingroup$ I thought we were not supposed to fully answer to homework questions, but I am wondering if the income per capita elasticity is the "asked" elasticity? $\endgroup$ – emeryville May 21 '16 at 17:29
  • $\begingroup$ @desnesp I can't see it. Can you detail? For $\varepsilon$ would give the $\Delta \%$ in both. As we have here a constant income elasticity, I assumed I could just $\Delta \% y \times \varepsilon = \Delta \% x$. $\endgroup$ – user_newbie10 May 21 '16 at 17:29
  • $\begingroup$ @emeryville I don't understand to which degree are we supposed to answer. It seemed it could be an essay instead of hw. About the elasticity looked for, if you have ln of average education as a depvar, if would assume the elasticity would relate avg educ with avg income $\endgroup$ – user_newbie10 May 21 '16 at 17:34
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    $\begingroup$ @dugo note that the LHS is higher education not avg education. Anyway, it would be important that the OP gives more details about the variables and the sample. $\endgroup$ – emeryville May 21 '16 at 20:06

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