Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {2} | {3}

Parameter: λ₁₄

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₃λ₂₄-σ₃₄

Instrumental Variable:

3 | {}
3 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

-σ₂₃+ω₂₃

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₂σ₁₄σ₂₃-σ₁₁σ₂₃σ₂₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄+σ₁₁σ₂₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Algebraic Equations:

σ₁₁σ₂₃λ₁₂λ₂₄-σ₁₂σ₃₄

Vanishing Ideal

Constraint Set:

σ₁₃

All constraints are determinantal

Trek-separation:

{1} ⊥ {3} | ({},{})