Parameter: λ₁₂

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂λ₂₄-σ₁₄,
σ₂₃²λ₂₄-σ₂₂σ₃₃λ₂₄+σ₂₄σ₃₃-σ₂₃σ₃₄

Single Door Criterion:

{2} ⊥ {4} | {3}
{2} ⊥ {4} | {1,3}

Instrumental Variable:

1 | {}
1 | {3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₄σ₂₃+σ₁₂σ₃₃λ₃₄-σ₁₂σ₃₄,
σ₂₃²λ₃₄-σ₂₃σ₂₄-σ₂₂σ₃₃λ₃₄+σ₂₂σ₃₄,
σ₁₄σ₂₂+σ₁₂σ₂₃λ₃₄-σ₁₂σ₂₄

Single Door Criterion:

{3} ⊥ {4} | {2}
{3} ⊥ {4} | {1,2}

Instrumental Variable:

1 | {2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

-σ₂₃+ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄σ₂₄σ₃₃-σ₁₄σ₂₃σ₃₄+σ₁₂σ₃₄²-σ₁₂σ₃₃σ₄₄+σ₁₂σ₃₃ω₄₄,
-σ₂₄²σ₃₃+2σ₂₃σ₂₄σ₃₄-σ₂₂σ₃₄²-σ₂₃²σ₄₄+σ₂₂σ₃₃σ₄₄+σ₂₃²ω₄₄-σ₂₂σ₃₃ω₄₄,
σ₁₄σ₂₃σ₂₄-σ₁₄σ₂₂σ₃₄+σ₁₂σ₂₄σ₃₄-σ₁₂σ₂₃σ₄₄+σ₁₂σ₂₃ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₁₃,
σ₁₄σ₂₃²-σ₁₄σ₂₂σ₃₃+σ₁₂σ₂₄σ₃₃-σ₁₂σ₂₃σ₃₄

All constraints are determinantal

Trek-separation:

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