Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₄λ₁₃-σ₃₄,
σ₁₂λ₁₃-σ₂₃,
σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

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

Instrumental Variable:

2 | {}
2 | {4}
4 | {}
4 | {2}

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃λ₁₄-σ₃₄,
σ₁₂λ₁₄-σ₂₄,
σ₁₁λ₁₄-σ₁₄

Single Door Criterion:

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

Instrumental Variable:

2 | {}
2 | {3}
3 | {}
3 | {2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂ Identified

Algebraic Equations:

-σ₁₂+ω₁₂

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₂₄σ₃₃+σ₂₃σ₃₄+σ₂₄ω₃₃,
-σ₁₄σ₃₃+σ₁₃σ₃₄+σ₁₄ω₃₃,
σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃,
σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₂₄σ₃₄-σ₂₃σ₄₄+σ₂₃ω₄₄,
σ₁₄σ₃₄-σ₁₃σ₄₄+σ₁₃ω₄₄,
σ₁₄σ₂₄-σ₁₂σ₄₄+σ₁₂ω₄₄,
σ₁₄²-σ₁₁σ₄₄+σ₁₁ω₄₄

Vanishing Ideal

Constraint Set:

σ₁₃σ₂₄-σ₁₂σ₃₄,
σ₁₄σ₂₃-σ₁₃σ₂₄,
σ₁₃σ₁₄-σ₁₁σ₃₄,
σ₁₂σ₁₄-σ₁₁σ₂₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

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