Parameter: λ₁₂

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₂λ₁₃-σ₂₃,
σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3} | {}
{1} ⊥ {3} | {2}

Instrumental Variable:

2 | {}

Parameter: λ₁₄

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₃σ₂₂λ₂₄-σ₁₂σ₂₃λ₂₄+σ₁₄σ₂₃-σ₁₃σ₂₄,
σ₁₂²λ₂₄-σ₁₂σ₁₄-σ₁₁σ₂₂λ₂₄+σ₁₁σ₂₄

Single Door Criterion:

{2} ⊥ {3,4} | {1}
{2} ⊥ {4} | {1,3}

Parameter: λ₃₄

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃,
σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₃₄

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₃λ₃₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄

Path-specific Effect of X₁ on X₄: λ₁₃λ₃₄

Vanishing Ideal

Constraint Set:

σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {1,3} | ({},{1})