Why is the functional form of the 1st stage in 2SLS not important?

In a presentation today the speaker made the above claim. He said that even if the first stage is mis-specified, the coefficient estimates of the second stage will still be valid. As a lowly graduate student I could not ask for an explanation, so now I begged for your help!

Answer

Because OLS is unbiased at the mean. Unless it is dramatically incorrect (biased) it really shouldn’t matter much what the functional form is.

However, a poor functional form might to cause inaccuracies (slower convergence).

Poor choice of functional form cannot lead to omitted variable bias. Only the omission of a variable.

Using g(x) instead of f(x) is poor functional form. Using g(x) instead of g(x,y) is an omitted variable.

Attribution
Source : Link , Question Author : Heisenberg , Answer Author : RegressForward

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