Suppose we have a simultaneous equation system of G equation: Yi = Xi + . where...

 

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Suppose we have a simultaneous equation system of G equation: Yi = Xiß + €₁. where Yi Yli 3 X₂ = diag (₁,...,Gi), B = 3₁ Ei Eli YG₁ BG with X, being the potentially endogenous variable matrix. Further suppose that we have a matrix of IVs: Z₁ = diag (Z₁i..... ZGi), which satisfies the relevance and exogeneity assumptions for instruments. Please demonstrate that if Σ, the covariance matrix of e, is diagonal, then the system 2SLS and 3SLS are numerically identical regardless of the model being just or over identified. Suppose we have a simultaneous equation system of G equation: Yi = Xiß + €₁. where Yi Yli 3 X₂ = diag (₁,...,Gi), B = 3₁ Ei Eli YG₁ BG with X, being the potentially endogenous variable matrix. Further suppose that we have a matrix of IVs: Z₁ = diag (Z₁i..... ZGi), which satisfies the relevance and exogeneity assumptions for instruments. Please demonstrate that if Σ, the covariance matrix of e, is diagonal, then the system 2SLS and 3SLS are numerically identical regardless of the model being just or over identified.