Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₄λ₁₂-σ₂₄,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

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

Instrumental Variable:

3 | {4}
4 | {}
4 | {3}

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₂λ₁₄-σ₂₄,
σ₁₁λ₁₄-σ₁₄

Single Door Criterion:

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

Instrumental Variable:

2 | {}
2 | {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: ω₂₂ Identified

Algebraic Equations:

-σ₁₄σ₂₂+σ₁₂σ₂₄+σ₁₄ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄σ₂₄σ₃₃+σ₁₂σ₃₄²-σ₁₂σ₃₃σ₄₄+σ₁₂σ₃₃ω₄₄,
σ₁₄²σ₃₃+σ₁₁σ₃₄²-σ₁₁σ₃₃σ₄₄+σ₁₁σ₃₃ω₄₄

Vanishing Ideal

Constraint Set:

σ₂₃,
σ₁₃,
σ₁₂σ₁₄-σ₁₁σ₂₄

All constraints are determinantal

Trek-separation:

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