Parameter: λ₁₂

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₂λ₁₃-σ₂₃,
σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3} | {}
{1} ⊥ {3,4} | {2}
{1} ⊥ {3} | {2,4}

Instrumental Variable:

2 | {}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₂λ₂₄-σ₂₄,
σ₁₂λ₂₄-σ₁₄,
-σ₁₃σ₁₄+σ₁₁σ₂₃λ₂₄

Single Door Criterion:

{2} ⊥ {4} | {}
{2} ⊥ {3,4} | {1}
{2} ⊥ {4} | {1,3}

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃,
σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

σ₂₃σ₂₄-σ₂₂σ₃₄+σ₂₂ω₃₄,
σ₁₄σ₂₃-σ₁₂σ₃₄+σ₁₂ω₃₄,
σ₁₃σ₁₄-σ₁₁σ₃₄+σ₁₁ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₂₄²-σ₂₂σ₄₄+σ₂₂ω₄₄,
σ₁₄σ₂₄-σ₁₂σ₄₄+σ₁₂ω₄₄,
σ₁₃σ₁₄σ₂₄-σ₁₁σ₂₃σ₄₄+σ₁₁σ₂₃ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₁₄σ₂₂-σ₁₂σ₂₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {2,4} | ({},{2})
{1,2} ⊥ {1,3} | ({},{1})