Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₃λ₁₂-σ₂₃,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}
{1} ⊥ {2} | {3}

Instrumental Variable:

3 | {}

Parameter: λ₁₄

Parameter: λ₂₄

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₄σ₂₃+σ₁₂σ₃₄+σ₂₃ω₁₄,
-σ₁₃σ₁₄+σ₁₁σ₃₄+σ₁₃ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₃σ₂₂+σ₁₂σ₂₃+σ₁₃ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄ Identified

Algebraic Equations:

σ₁₃λ₁₂λ₂₄+σ₁₃λ₁₄-σ₃₄,
σ₁₁σ₂₃λ₁₂λ₂₄+σ₁₁σ₂₃λ₁₄-σ₁₂σ₃₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {1,3} | ({1},{})