Consider the population model with a valid instrument matrix where E[z] E[z22] inverse are given by...

  

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Consider the population model with a valid instrument matrix where E[z] E[z₁2¹2] inverse are given by - Yil Yi2 22= = = Z= - (On on) 021 022 Xi13₁ + Uil Xi23₂ + Ui2 Z1 0 0 Z2 = 0. The variance-covariance matrix of u = 2-1 oll ·(₁ 021 012 022 (² (b) Calculate E[Z-¹u₂] under the assumption that is diagonal. -1 (c) Calculate E[Z¹u₂] under the assumption that z₁ = Z2. U2 and its (a) Calculate E[ZM ¹u;] and show that it may not equal zero. What does this tell you about the consistency of 3 when applying an FGLS method using different instruments for different equations? Consider the population model with a valid instrument matrix where E[z] E[z₁2¹2] inverse are given by - Yil Yi2 22= = = Z= - (On on) 021 022 Xi13₁ + Uil Xi23₂ + Ui2 Z1 0 0 Z2 = 0. The variance-covariance matrix of u = 2-1 oll ·(₁ 021 012 022 (² (b) Calculate E[Z-¹u₂] under the assumption that is diagonal. -1 (c) Calculate E[Z¹u₂] under the assumption that z₁ = Z2. U2 and its (a) Calculate E[ZM ¹u;] and show that it may not equal zero. What does this tell you about the consistency of 3 when applying an FGLS method using different instruments for different equations?

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a To calculate EZu we need to multiply Z by the inverse of the variancecovariance matr... View the full answer