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Checking if Z and u are correlated?

This is a homework question that I have for econometrics. I have the two functions:

Yi=B0+B1(Xi)+ui Y_i = B_0 + B_1(X_i) + u_i

And:

Zi=G0+G1(Yi)+vi Z_i = G_0 + G_1(Y_i) + v_i

The question is: Are Zi Z_i and ui u_i correlated? Explain your answer.

I know that the correlation formula is

Correl(X,Y)=Cov(X,Y)/oxoy Correl(X, Y) = Cov(X, Y) / o_x o_y

Zi=G0+G1(B0+B1Xi+ui)+vi Z_i = G_0 + G_1(B_0 + B_1X_i + u_i) + v_i

But I'm not sure how to proceed?
Reply 1
Anyone? :frown:
Since you have Yi Y_i as a linear function, this means perfect multicollinearity.
Reply 3
Original post by JulietheCat
Since you have Yi Y_i as a linear function, this means perfect multicollinearity.


That's one step closer - thank you :smile:

But how would I show that Zi Z_i is correlated with the error term ui u_i formally?

Edit: Is it really perfect multicollinearity or just imperfect multicollinearity?
(edited 10 years ago)
Original post by SecretDuck
That's one step closer - thank you :smile:

But how would I show that Zi Z_i is correlated with the error term ui u_i formally?

Edit: Is it really perfect multicollinearity or just imperfect multicollinearity?


You cannot - you just need to look at the fact that one of the regressors is a linear function of other regressors to see that Zi Z_i is correlated, not just with ui u_i but with Xi X_i as well.

My bad - perfect multicollinearity is accidental, imperfect multicollinearity is just a feature of the sample. Saying it's perfect will lose you marks so best to say that there is evidence of multicollinearity because one of the regressors has a linear function of other regressors.

Hope this helps :smile:
Reply 5
Original post by JulietheCat
You cannot - you just need to look at the fact that one of the regressors is a linear function of other regressors to see that Zi Z_i is correlated, not just with ui u_i but with Xi X_i as well.

My bad - perfect multicollinearity is accidental, imperfect multicollinearity is just a feature of the sample. Saying it's perfect will lose you marks so best to say that there is evidence of multicollinearity because one of the regressors has a linear function of other regressors.

Hope this helps :smile:


Thank you - I get it now :smile:

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