Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₄λ₁₂-σ₂₄,
σ₁₃λ₁₂-σ₂₃,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

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

Instrumental Variable:

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

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃λ₁₄-σ₃₄,
σ₁₁σ₂₃λ₁₄-σ₁₂σ₃₄

Instrumental Variable:

3 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₃σ₂₄+σ₁₂σ₃₄+σ₂₃ω₁₄,
-σ₁₃σ₁₄+σ₁₁σ₃₄+σ₁₃ω₁₄

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:

2σ₁₃σ₂₄σ₃₄-σ₁₂σ₃₄²-σ₁₃σ₂₃σ₄₄+σ₁₃σ₂₃ω₄₄,
2σ₁₃σ₁₄σ₃₄-σ₁₁σ₃₄²-σ₁₃²σ₄₄+σ₁₃²ω₄₄,
2σ₁₁σ₂₃σ₂₄σ₃₄-σ₁₂²σ₃₄²-σ₁₁σ₂₃²σ₄₄+σ₁₁σ₂₃²ω₄₄

Vanishing Ideal

Constraint Set:

σ₁₄σ₂₃-σ₁₃σ₂₄,
σ₁₂σ₁₄-σ₁₁σ₂₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

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