# Income Elasticity of Demand for Higher Education

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.

• This strikes me as more a question of economic theory than statistics. This belongs on the Economics SE site, not here. – gung May 21 '16 at 9:52
• Can you say more about the sample? the period? Can you define what is Distance here? – emeryville May 21 '16 at 17:14
• 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... – emeryville May 21 '16 at 17:23

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...
• @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 $\Delta \% y \times \varepsilon = \Delta \% x$. – user_newbie10 May 21 '16 at 17:29