Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₃λ₁₂-σ₂₃,
-σ₂₃σ₂₄+σ₁₂σ₃₄λ₁₂,
-σ₁₄σ₂₃+σ₁₁σ₃₄λ₁₂

Instrumental Variable:

3 | {}

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:

σ₁₄σ₂₃-σ₁₂σ₃₄+σ₃₄ω₁₂,
-σ₁₂σ₁₃+σ₁₁σ₂₃+σ₁₃ω₁₂

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₄σ₂₃²-σ₁₃σ₂₂σ₃₄+2σ₁₂σ₂₃σ₃₄+σ₁₃σ₃₄ω₂₂,
-σ₁₃²σ₂₂+2σ₁₂σ₁₃σ₂₃-σ₁₁σ₂₃²+σ₁₃²ω₂₂,
-σ₁₄σ₂₃²σ₂₄+2σ₁₂σ₂₃σ₂₄σ₃₄-σ₁₂σ₂₂σ₃₄²+σ₁₂σ₃₄²ω₂₂,
-σ₁₄²σ₂₃²+2σ₁₁σ₂₃σ₂₄σ₃₄-σ₁₁σ₂₂σ₃₄²+σ₁₁σ₃₄²ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

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

Vanishing Ideal

Constraint Set:

σ₁₃σ₂₄-σ₁₂σ₃₄,
σ₁₃σ₁₄-σ₁₁σ₃₄,
σ₁₂σ₁₄-σ₁₁σ₂₄

All constraints are determinantal

Trek-separation:

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