Consider the following two-equation model: y 1 = 1 y 2 + 11 x 1

Consider the following two-equation model:
y₁ = γ₁y₂ + β₁₁x₁ + β₂₁x₂ + β₃₁x₃ + ε₁,
y₂ = γ₂y₁ + β₁₂x₁ + β₂₂x₂ + β₃₂x₃ + ε₂.

a. Verify that, as stated, neither equation is identified.

b. Establish whether or not the following restrictions are sufficient to identify (or partially identify) the model:
(1) β₂₁ = β₃₂ = 0,
(2) β₁₂ = β₂₂ = 0,
(3) γ₁ = 0,
(4) γ₁ = γ₂ and β₃₂ = 0,
(5) σ₁₂ = 0 and β₃₁ = 0,
(6) γ₁ = 0 and σ₁₂ = 0,
(7) β₂₁ + β₂₂ = 1,
(8) σ₁₂ = 0, β₂₁ = β₂₂ = β₃₁ = β₃₂ = 0,
(9) σ₁₂ = 0, β₁₁ = β₂₁ = β₂₂ = β₃₁ = β₃₂ = 0.