Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₄λ₁₂-σ₂₄,
σ₁₃λ₁₂-σ₂₃,
σ₁₁λ₁₂-σ₁₂,
-σ₂₃σ₂₄+σ₁₂σ₃₄λ₁₂

Single Door Criterion:

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

Instrumental Variable:

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

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: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₄+ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₂₃σ₂₄-σ₂₂σ₃₄+σ₃₄ω₂₂,
-σ₁₄σ₂₂+σ₁₂σ₂₄+σ₁₄ω₂₂,
-σ₁₃σ₂₂+σ₁₂σ₂₃+σ₁₃ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

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

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₄₄+ω₄₄

Vanishing Ideal

Constraint Set:

σ₁₃σ₂₄-σ₁₂σ₃₄,
σ₁₄σ₂₃-σ₁₂σ₃₄,
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},{})
{1,3,2} ⊥ {1,3,4} | ({1,3},{})
{1,4,2} ⊥ {1,3,4} | ({1,4},{})
{1,2,3} ⊥ {1,2,4} | ({1,2},{})
{1,4,3} ⊥ {1,2,4} | ({1,4},{})
{1,2,3} ⊥ {3,1,4} | ({1},{3})
{1,2,3} ⊥ {2,1,4} | ({1},{2})