Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₃λ₁₂-σ₂₃

Instrumental Variable:

3 | {}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₃λ₂₄-σ₃₄,
σ₂₂λ₂₄-σ₂₄,
σ₁₂λ₂₄-σ₁₄

Single Door Criterion:

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

Instrumental Variable:

1 | {}
1 | {3}
3 | {}
3 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂ Identified

Algebraic Equations:

-σ₁₂σ₁₃+σ₁₁σ₂₃+σ₁₃ω₁₂

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₃²σ₂₂+2σ₁₂σ₁₃σ₂₃-σ₁₁σ₂₃²+σ₁₃²ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₂₄σ₃₄-σ₂₃σ₄₄+σ₂₃ω₄₄,
σ₂₄²-σ₂₂σ₄₄+σ₂₂ω₄₄,
σ₁₄σ₂₄-σ₁₂σ₄₄+σ₁₂ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₂₃σ₂₄-σ₂₂σ₃₄,
σ₁₄σ₂₃-σ₁₂σ₃₄,
σ₁₄σ₂₂-σ₁₂σ₂₄

All constraints are determinantal

Trek-separation:

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