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How to choose best model specification for time serie data ?

I am trying to build a regression on the impact of private universities on social inequalities in europe. I have a panel data for the 28 european countries from 2008 to 2018. I will compare inequalities of wealth, income and access to higher education

Independent variables are Gini index, p80/p20, %of 20-24 years old in tiertiary education.Can I use fixed effect model to compare social inequalities between countries with free (or almost free public universities fees ) with countries with high fees?
(edited 4 years ago)
I don't see why you can't use fixed effects but I am not quite sure of your regression. If you want to see the impact of private universities on inequality, then wouldn't your dependent variable be the Gini Index and you would regress on this a dummy variable indicating whether the particular country has free or private education, controlling for %of people in tertiary education:

Inequality = a + b(Free Educ dummy) + c(% of people in Tertiary education) + e

Is this what you were thinking of?
The only reason you would want to use FE is if you think there is an omitted variable (contained in e) which is correlated with both inequality and free education. This is probably a reasonable assumption.

However, if you want to estimate b then I think you will be need some countries which have moved from private to free education (or vice versa) in order to get enough variation for estimation.

Best,
Rhys

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