Parameter: λ₁₂

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₂λ₂₄-σ₂₄,
σ₁₂λ₂₄-σ₁₄

Single Door Criterion:

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

Instrumental Variable:

1 | {}
1 | {3}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

-σ₃₄+ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₂₄²-σ₂₂σ₄₄+σ₂₂ω₄₄,
σ₁₄σ₂₄-σ₁₂σ₄₄+σ₁₂ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₂₃,
σ₁₃,
σ₁₄σ₂₂-σ₁₂σ₂₄

All constraints are determinantal

Trek-separation:

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