Parameter: λ₁₂

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3} | {}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₃λ₂₄-σ₃₄,
σ₁₂λ₂₄-σ₁₄

Instrumental Variable:

1 | {}
1 | {3}
3 | {}
3 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₂σ₁₃-σ₁₁σ₂₃+σ₁₁ω₂₃

Parameter: ω₂₄ Identified

Algebraic Equations:

-σ₂₃σ₂₄+σ₂₂σ₃₄+σ₂₃ω₂₄,
σ₁₄σ₂₂-σ₁₂σ₂₄+σ₁₂ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

2σ₂₃σ₂₄σ₃₄-σ₂₂σ₃₄²-σ₂₃²σ₄₄+σ₂₃²ω₄₄,
-σ₁₄σ₂₂σ₃₄+2σ₁₂σ₂₄σ₃₄-σ₁₂σ₂₃σ₄₄+σ₁₂σ₂₃ω₄₄,
-σ₁₄²σ₂₂+2σ₁₂σ₁₄σ₂₄-σ₁₂²σ₄₄+σ₁₂²ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₁₄σ₂₃-σ₁₂σ₃₄

All constraints are determinantal

Trek-separation:

{1,3} ⊥ {2,4} | ({},{2})