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Do residuals from an IV regression sum to 0? i.e Let e = y- Xb* where e is the residual and b* is the IV estimator using Z as an instrument for X. (Assume that dimension of Z = dimension of X and both X and Z include intercepts). Will the residuals sum to 0?

What will happen if there are more instruments than regressors? In this case my intuition is that residuals will not sum to 0 but I am not sure how to prove it.

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