Econometric Maths Problem - I’m Stuck :(

Clodagh

New member
Joined
Sep 25, 2021
Messages
2
I’m been stuck on this for days. I’ve made up values for X and have done out the equations so many times and I can’t figure out what is wrong. Can anyone please help? The problem is as follows;

The OLS estimator is written as b =(X’X)^-1 X’y
Explain why the following is incorrect;
b = (X’X)^-1 X’y = X^-1(X’)^-1 X’y = X^-1 y

Thank you in advance!
 
I’m been stuck on this for days. I’ve made up values for X and have done out the equations so many times and I can’t figure out what is wrong. Can anyone please help? The problem is as follows;

The OLS estimator is written as b =(X’X)^-1 X’y
Explain why the following is incorrect;
b = (X’X)^-1 X’y = X^-1(X’)^-1 X’y = X^-1 y

Thank you in advance!
I had to look up the context, in order to see how things are defined. That made the problem obvious: X is not a square matrix. Do you see the implication?

Did you use only square matrices for X in your experimentation? For square matrices, the work is perfectly valid, so you didn't need to bother trying things out. You needed to look beyond the formula and see the context.
 
I had to look up the context, in order to see how things are defined. That made the problem obvious: X is not a square matrix. Do you see the implication?

Did you use only square matrices for X in your experimentation? For square matrices, the work is perfectly valid, so you didn't need to bother trying things out. You needed to look beyond the formula and see the context.
Yes! When you point that out, it is so obvious! Thank you! This problem was keeping me up at night! THANK YOU
 
Top