Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₁₄-2σ₁₂σ₁₃σ₂₃λ₁₄+σ₁₁σ₂₃²λ₁₄-σ₁₄σ₂₃²+σ₁₃σ₂₃σ₂₄+σ₁₂²σ₃₃λ₁₄-σ₁₁σ₂₂σ₃₃λ₁₄+σ₁₄σ₂₂σ₃₃-σ₁₂σ₂₄σ₃₃-σ₁₃σ₂₂σ₃₄+σ₁₂σ₂₃σ₃₄

Single Door Criterion:

{1} ⊥ {4} | {2,3}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₂₄-2σ₁₂σ₁₃σ₂₃λ₂₄+σ₁₃σ₁₄σ₂₃+σ₁₁σ₂₃²λ₂₄-σ₁₃²σ₂₄+σ₁₂²σ₃₃λ₂₄-σ₁₂σ₁₄σ₃₃-σ₁₁σ₂₂σ₃₃λ₂₄+σ₁₁σ₂₄σ₃₃+σ₁₂σ₁₃σ₃₄-σ₁₁σ₂₃σ₃₄

Single Door Criterion:

{2} ⊥ {4} | {1,3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₃₄-σ₁₃σ₁₄σ₂₂-2σ₁₂σ₁₃σ₂₃λ₃₄+σ₁₂σ₁₄σ₂₃+σ₁₁σ₂₃²λ₃₄+σ₁₂σ₁₃σ₂₄-σ₁₁σ₂₃σ₂₄+σ₁₂²σ₃₃λ₃₄-σ₁₁σ₂₂σ₃₃λ₃₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄

Single Door Criterion:

{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₂σ₁₃-σ₁₁σ₂₃+σ₁₁ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄²σ₂₃²-2σ₁₃σ₁₄σ₂₃σ₂₄+σ₁₃²σ₂₄²-σ₁₄²σ₂₂σ₃₃+2σ₁₂σ₁₄σ₂₄σ₃₃-σ₁₁σ₂₄²σ₃₃+2σ₁₃σ₁₄σ₂₂σ₃₄-2σ₁₂σ₁₄σ₂₃σ₃₄-2σ₁₂σ₁₃σ₂₄σ₃₄+2σ₁₁σ₂₃σ₂₄σ₃₄+σ₁₂²σ₃₄²-σ₁₁σ₂₂σ₃₄²-σ₁₃²σ₂₂σ₄₄+2σ₁₂σ₁₃σ₂₃σ₄₄-σ₁₁σ₂₃²σ₄₄-σ₁₂²σ₃₃σ₄₄+σ₁₁σ₂₂σ₃₃σ₄₄+σ₁₃²σ₂₂ω₄₄-2σ₁₂σ₁₃σ₂₃ω₄₄+σ₁₁σ₂₃²ω₄₄+σ₁₂²σ₃₃ω₄₄-σ₁₁σ₂₂σ₃₃ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄ Identified

Each Parameter Identified

Vanishing Ideal

Zero Vanishing Ideal