Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₁λ₁₄-σ₁₄

Single Door Criterion:

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

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₄λ₂₃-σ₃₄,
σ₂₂λ₂₃-σ₂₃

Single Door Criterion:

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

Instrumental Variable:

1 | {4}
4 | {}
4 | {1}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₃λ₂₄-σ₃₄,
σ₂₂λ₂₄-σ₂₄

Single Door Criterion:

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

Instrumental Variable:

3 | {}
3 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₂₄σ₃₃+σ₂₃σ₃₄+σ₂₄ω₃₃,
σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄²σ₂₃+σ₁₁σ₂₄σ₃₄-σ₁₁σ₂₃σ₄₄+σ₁₁σ₂₃ω₄₄,
σ₁₄²σ₂₂+σ₁₁σ₂₄²-σ₁₁σ₂₂σ₄₄+σ₁₁σ₂₂ω₄₄

Vanishing Ideal

Constraint Set:

σ₁₃,
σ₁₂,
σ₂₃σ₂₄-σ₂₂σ₃₄

All constraints are determinantal

Trek-separation:

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