I am trying to show that the Sargan statistics of a classical linear 2SLS estimation can be expressed as the form nR^2, assuming homoscedasticity.

I start with the original form of Sargan statistics:

S=N x (e’Pz e)/(e’e)

Where n is the sample size, Pz= Z(Z’Z)^-1Z’ and Z is the nxL matrix of instruments.

I tried to rewrite R^2 to the matrix form = 1 - (e’e/Y’Y), Y is the demeaned y

I could come up with something like 1- (y’Mzy)/Y’Y but i cannot proceed any further.

Can anyone show me how do i get from e’Pze/e’e to R^2?