Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁σ₁₄σ₂₃λ₁₃-σ₁₃σ₁₄σ₂₃-σ₁₁σ₁₃σ₂₄λ₁₃+σ₁₃²σ₂₄+σ₁₂σ₁₄σ₃₃-σ₁₂σ₁₃σ₃₄

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₄σ₂₃λ₂₃-σ₁₃σ₂₄λ₂₃-σ₁₄σ₃₃+σ₁₃σ₃₄

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃λ₃₄-σ₁₄

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₂σ₁₃σ₁₄σ₂₃-σ₁₁σ₁₄σ₂₃²-σ₁₂σ₁₃²σ₂₄+σ₁₁σ₁₃σ₂₃σ₂₄-σ₁₂²σ₁₄σ₃₃+σ₁₁σ₁₄σ₂₂σ₃₃+σ₁₂²σ₁₃σ₃₄-σ₁₁σ₁₃σ₂₂σ₃₄+σ₁₁σ₁₄σ₂₃ω₂₃-σ₁₁σ₁₃σ₂₄ω₂₃

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₃-σ₁₃σ₂₄+σ₁₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²σ₁₄²σ₂₃²-2σ₁₃³σ₁₄σ₂₃σ₂₄+σ₁₃⁴σ₂₄²-2σ₁₂σ₁₃σ₁₄²σ₂₃σ₃₃+σ₁₁σ₁₄²σ₂₃²σ₃₃+2σ₁₂σ₁₃²σ₁₄σ₂₄σ₃₃-σ₁₁σ₁₃²σ₂₄²σ₃₃+σ₁₂²σ₁₄²σ₃₃²-σ₁₁σ₁₄²σ₂₂σ₃₃²+2σ₁₂σ₁₃²σ₁₄σ₂₃σ₃₄-2σ₁₁σ₁₃σ₁₄σ₂₃²σ₃₄-2σ₁₂σ₁₃³σ₂₄σ₃₄+2σ₁₁σ₁₃²σ₂₃σ₂₄σ₃₄-2σ₁₂²σ₁₃σ₁₄σ₃₃σ₃₄+2σ₁₁σ₁₃σ₁₄σ₂₂σ₃₃σ₃₄+σ₁₂²σ₁₃²σ₃₄²-σ₁₁σ₁₃²σ₂₂σ₃₄²+σ₁₁σ₁₄²σ₂₃²ω₃₃-2σ₁₁σ₁₃σ₁₄σ₂₃σ₂₄ω₃₃+σ₁₁σ₁₃²σ₂₄²ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₃₃+2σ₁₃σ₁₄σ₃₄-σ₁₃²σ₄₄+σ₁₃²ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃+λ₁₃ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}

Total Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄+λ₁₃λ₃₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Zero Vanishing Ideal