Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₃λ₁₂-σ₂₃,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

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

Instrumental Variable:

3 | {}

Parameter: λ₁₃

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₃₃λ₃₄-σ₃₄,
σ₁₃λ₃₄-σ₁₄,
-σ₁₂σ₁₄+σ₁₁σ₂₃λ₃₄

Single Door Criterion:

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

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₃σ₂₂+σ₁₂σ₂₃+σ₁₃ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

-σ₂₄σ₃₃+σ₂₃σ₃₄+σ₃₃ω₂₄,
σ₁₄σ₂₃-σ₁₃σ₂₄+σ₁₃ω₂₄,
σ₁₂σ₁₄-σ₁₁σ₂₄+σ₁₁ω₂₄

Parameter: ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₃₄²-σ₃₃σ₄₄+σ₃₃ω₄₄,
σ₁₄σ₃₄-σ₁₃σ₄₄+σ₁₃ω₄₄,
σ₁₂σ₁₄σ₃₄-σ₁₁σ₂₃σ₄₄+σ₁₁σ₂₃ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄

Vanishing Ideal

Constraint Set:

σ₁₄σ₃₃-σ₁₃σ₃₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

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