Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₄λ₁₂-σ₂₄,
-σ₂₃σ₂₄+σ₁₂σ₃₄λ₁₂,
-σ₁₃σ₂₄+σ₁₁σ₃₄λ₁₂

Instrumental Variable:

4 | {}

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: ω₁₂ Identified

Algebraic Equations:

σ₁₃σ₂₄-σ₁₂σ₃₄+σ₃₄ω₁₂,
-σ₁₂σ₁₄+σ₁₁σ₂₄+σ₁₄ω₁₂

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₄+ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₃σ₂₄²-σ₁₄σ₂₂σ₃₄+2σ₁₂σ₂₄σ₃₄+σ₁₄σ₃₄ω₂₂,
-σ₁₄²σ₂₂+2σ₁₂σ₁₄σ₂₄-σ₁₁σ₂₄²+σ₁₄²ω₂₂,
-σ₁₃σ₂₃σ₂₄²+2σ₁₂σ₂₃σ₂₄σ₃₄-σ₁₂σ₂₂σ₃₄²+σ₁₂σ₃₄²ω₂₂,
-σ₁₃²σ₂₄²+2σ₁₁σ₂₃σ₂₄σ₃₄-σ₁₁σ₂₂σ₃₄²+σ₁₁σ₃₄²ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

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

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₄₄+ω₄₄

Vanishing Ideal

Constraint Set:

σ₁₄σ₂₃-σ₁₂σ₃₄,
σ₁₃σ₁₄-σ₁₁σ₃₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

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