Multicollinearity and omitted variable bias

[Bernt Evensen]

A model suffer from omitted variable bias if a variable that is correlated with both the dependant variable and the explanatory variable is excluded.

A model suffer from multicollinearity if two explanatory variables are correlated.

So which one is more important?

I have tryed to run a regression with panel data were health care expenditure (HCE) is my dependant variable and GDP.

If average wages is a determinant of HCE and correlated with GDP it is wrong to ommit it.

But if I include it, then mye model haster a high degree of multicollinearity between wages and GDP.

So omitted variable bias and multicollinearity contradict each other?

[Joao Santos Silva]

Dear Bernt,

Please read Chapter 23 of this book. If you have the chance, read the rest as well!

Best wishes,

Joao

[Bernt Evensen]

Thanks, I liked the chapter, but I get scared when I see too much matrix algebra! To sum up all multicollinearity does is to increase the standard error of the estimated coefficents. A variable should be included in the model if it changes the coefficent it is correlated with remarkably. If the variable is not included the model will suffer from OVB. If the new variable only changes the standard error of the coefficent it is correlated with, and not so much the coefficent it should not be included. This link helped me a lot
: https://are.berkeley.edu/courses/EEP...ep118_sp15.pdf
To the question of whether I should include average wages in my regression, I must check tomorrow by how much the standard error and coefficent changes. From an economic perspective I am a bit reluctant to include this variable since I already interpret GDP as income. Increased wages could affect health expenditure in two ways: 1. It raises income and demand. 2. It raises the unit cost of health care (and thus the price). If I include both wages and GDP in my regression, could I say that GDP takes care of the income effect and that wages can solely be interperated as the cost effect of higher wages?