Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3} | {}

Parameter: λ₁₄

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂σ₁₃λ₂₄-σ₁₃σ₁₄-σ₁₁σ₂₃λ₂₄+σ₁₁σ₃₄

Instrumental Variable:

3 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₂σ₁₃-σ₁₁σ₂₃+σ₁₁ω₂₃

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₃σ₁₄σ₂₂-σ₁₂σ₁₄σ₂₃-σ₁₂σ₁₃σ₂₄+σ₁₁σ₂₃σ₂₄+σ₁₂²σ₃₄-σ₁₁σ₂₂σ₃₄+σ₁₂σ₁₃ω₂₄-σ₁₁σ₂₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Algebraic Equations:

σ₁₁σ₁₂σ₁₃λ₁₂λ₂₄-σ₁₂σ₁₃σ₁₄-σ₁₁²σ₂₃λ₁₂λ₂₄+σ₁₁σ₁₂σ₃₄

Vanishing Ideal

Zero Vanishing Ideal