Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₄λ₁₂-σ₂₄,
σ₁₃λ₁₂-σ₂₃,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

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

Instrumental Variable:

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

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₃₃λ₃₄-σ₃₄,
σ₂₃λ₃₄-σ₂₄,
σ₁₃λ₃₄-σ₁₄

Single Door Criterion:

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

Instrumental Variable:

1 | {}
1 | {2}
2 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

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

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₃₄²-σ₃₃σ₄₄+σ₃₃ω₄₄,
σ₂₄σ₃₄-σ₂₃σ₄₄+σ₂₃ω₄₄,
σ₁₄σ₃₄-σ₁₃σ₄₄+σ₁₃ω₄₄

Vanishing Ideal

Constraint Set:

σ₂₄σ₃₃-σ₂₃σ₃₄,
σ₁₄σ₃₃-σ₁₃σ₃₄,
σ₁₄σ₂₃-σ₁₃σ₂₄,
σ₁₂σ₁₄-σ₁₁σ₂₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

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