E(ui-E(ui I X1i, X2i) I X1i,X2i) = E(ui I X1i, X2i)- E(ui I X1i, X2i) = 0 i cant

Question

E(ui-E(ui I X1i, X2i) I X1i,X2i) = E(ui I X1i, X2i)- E(ui I X1i, X2i) = 0

i cant really do the conditional-on line thats suppose to be here properly, i hope that makes sense, the question is regarding conditional mean independence. As a second question i need to learn the rules that are in play regarding conditional expectations, i cant seem to find them collected anywhere. How to manuever them and what you allowed to do. do you have any recommendations of book or link where i could find this?

Explanation / Answer

Given X1i,X2i, E(ui I X1i, X2i) is a constant.

Let it be denoted by a.

a = E(ui I X1i, X2i) , given X1i, X2i

So,

E(ui-E(ui I X1i, X2i) I X1i,X2i) = E(ui-a I X1i,X2i)

You can simply take 'a' outside of the expectation as it is a constant..

= E(ui I X1i,X2i) - a

= E(ui I X1i, X2i)- E(ui I X1i, X2i) = 0

You might consider reading about conditional probability from the book of W. Hines (Wiley publications)

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