Parameter: λ₁₂

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₂λ₁₄-σ₂₄,
σ₁₁λ₁₄-σ₁₄

Single Door Criterion:

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

Instrumental Variable:

2 | {}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₂λ₂₃-σ₁₃,
-σ₁₃σ₁₄+σ₁₁σ₂₄λ₂₃

Single Door Criterion:

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

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃,
σ₁₃σ₁₄σ₂₃-σ₁₁σ₂₄σ₃₃+σ₁₁σ₂₄ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

σ₂₃σ₂₄-σ₂₂σ₃₄+σ₂₂ω₃₄,
σ₁₃σ₂₄-σ₁₂σ₃₄+σ₁₂ω₃₄,
σ₁₃σ₁₄-σ₁₁σ₃₄+σ₁₁ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄σ₂₄-σ₁₂σ₄₄+σ₁₂ω₄₄,
σ₁₄²-σ₁₁σ₄₄+σ₁₁ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃

Vanishing Ideal

Constraint Set:

σ₁₃σ₂₂-σ₁₂σ₂₃,
σ₁₂σ₁₄-σ₁₁σ₂₄

All constraints are determinantal

Trek-separation:

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