Parameter: λ₁₂

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂λ₂₄-σ₁₄

Instrumental Variable:

1 | {}
1 | {3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₃₃λ₃₄-σ₃₄

Single Door Criterion:

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

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₂-σ₁₂σ₂₄+σ₁₂ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₂₂σ₃₃+2σ₁₂σ₁₄σ₂₄σ₃₃+σ₁₂²σ₃₄²-σ₁₂²σ₃₃σ₄₄+σ₁₂²σ₃₃ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₂₃,
σ₁₃

All constraints are determinantal

Trek-separation:

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