Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₄σ₂₃λ₂₃-σ₁₃σ₂₄λ₂₃-σ₁₄σ₃₃+σ₁₃σ₃₄

Single Door Criterion:

{2} ⊥ {1,3} | {}
{2} ⊥ {3} | {1}

Parameter: λ₂₄

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃λ₃₄-σ₁₄,
σ₂₃²λ₃₄-σ₂₃σ₂₄-σ₂₂σ₃₃λ₃₄+σ₂₂σ₃₄

Single Door Criterion:

{3} ⊥ {4} | {2}
{3} ⊥ {4} | {1,2}

Instrumental Variable:

1 | {}
1 | {2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₄σ₃₃-σ₁₃σ₂₃σ₃₄+σ₁₄σ₂₃ω₃₃-σ₁₃σ₂₄ω₃₃

Parameter: ω₄₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄

Path-specific Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Algebraic Equations:

σ₁₃σ₂₂λ₂₃λ₃₄-σ₁₄σ₂₃,
σ₂₂σ₂₃²λ₂₃λ₃₄-σ₂₃²σ₂₄-σ₂₂²σ₃₃λ₂₃λ₃₄+σ₂₂σ₂₃σ₃₄,
σ₁₃σ₁₄σ₂₃λ₂₃λ₃₄-σ₁₃²σ₂₄λ₂₃λ₃₄-σ₁₄²σ₃₃+σ₁₃σ₁₄σ₃₄

Vanishing Ideal

Constraint Set:

σ₁₂,
σ₁₄σ₂₃²-σ₁₃σ₂₃σ₂₄-σ₁₄σ₂₂σ₃₃+σ₁₃σ₂₂σ₃₄

All constraints are determinantal

Trek-separation:

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