Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃σ₂₂λ₁₄-σ₁₂σ₂₃λ₁₄+σ₂₃σ₂₄-σ₂₂σ₃₄,
σ₁₂σ₁₃λ₁₄-σ₁₁σ₂₃λ₁₄+σ₁₄σ₂₃-σ₁₂σ₃₄,
σ₁₂²λ₁₄-σ₁₁σ₂₂λ₁₄+σ₁₄σ₂₂-σ₁₂σ₂₄

Single Door Criterion:

{1} ⊥ {4} | {2}
{1} ⊥ {4} | {2,3}

Instrumental Variable:

3 | {2}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₂σ₁₄σ₂₃λ₂₃-σ₁₃σ₁₄σ₂₃+σ₁₂σ₁₃σ₂₄λ₂₃-σ₁₁σ₂₃σ₂₄λ₂₃-σ₁₂²σ₃₄λ₂₃+σ₁₁σ₂₂σ₃₄λ₂₃

Single Door Criterion:

{2} ⊥ {3} | {}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₃σ₂₂λ₂₄-σ₁₂σ₂₃λ₂₄-σ₁₃σ₂₄+σ₁₂σ₃₄,
σ₁₂σ₁₃λ₂₄-σ₁₃σ₁₄-σ₁₁σ₂₃λ₂₄+σ₁₁σ₃₄,
σ₁₂²λ₂₄-σ₁₂σ₁₄-σ₁₁σ₂₂λ₂₄+σ₁₁σ₂₄

Single Door Criterion:

{2} ⊥ {4} | {1}
{2} ⊥ {4} | {1,3}

Instrumental Variable:

3 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂ Identified

Algebraic Equations:

-σ₁₂+ω₁₂

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃σ₂₂+σ₁₂σ₂₃+σ₂₂ω₁₃,
-σ₁₂σ₁₃²σ₂₄+σ₁₁σ₁₃σ₂₃σ₂₄+σ₁₂²σ₁₃σ₃₄-σ₁₁σ₁₃σ₂₂σ₃₄+σ₁₂σ₁₄σ₂₃ω₁₃+σ₁₂σ₁₃σ₂₄ω₁₃-σ₁₁σ₂₃σ₂₄ω₁₃-σ₁₂²σ₃₄ω₁₃+σ₁₁σ₂₂σ₃₄ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₁₄σ₂₃²-σ₁₂σ₁₄σ₂₃σ₃₃-σ₁₂σ₁₃σ₂₄σ₃₃+σ₁₁σ₂₃σ₂₄σ₃₃+σ₁₂²σ₃₃σ₃₄-σ₁₁σ₂₂σ₃₃σ₃₄+σ₁₂σ₁₄σ₂₃ω₃₃+σ₁₂σ₁₃σ₂₄ω₃₃-σ₁₁σ₂₃σ₂₄ω₃₃-σ₁₂²σ₃₄ω₃₃+σ₁₁σ₂₂σ₃₄ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄σ₂₃σ₂₄+σ₁₃σ₂₄²+σ₁₄σ₂₂σ₃₄-σ₁₂σ₂₄σ₃₄-σ₁₃σ₂₂σ₄₄+σ₁₂σ₂₃σ₄₄+σ₁₃σ₂₂ω₄₄-σ₁₂σ₂₃ω₄₄,
-σ₁₄²σ₂₃+σ₁₃σ₁₄σ₂₄+σ₁₂σ₁₄σ₃₄-σ₁₁σ₂₄σ₃₄-σ₁₂σ₁₃σ₄₄+σ₁₁σ₂₃σ₄₄+σ₁₂σ₁₃ω₄₄-σ₁₁σ₂₃ω₄₄,
-σ₁₄²σ₂₂+2σ₁₂σ₁₄σ₂₄-σ₁₁σ₂₄²-σ₁₂²σ₄₄+σ₁₁σ₂₂σ₄₄+σ₁₂²ω₄₄-σ₁₁σ₂₂ω₄₄

Vanishing Ideal

Constraint Set:

σ₁₃σ₁₄σ₂₂-σ₁₂σ₁₄σ₂₃-σ₁₂σ₁₃σ₂₄+σ₁₁σ₂₃σ₂₄+σ₁₂²σ₃₄-σ₁₁σ₂₂σ₃₄

All constraints are determinantal

Trek-separation:

{1,2,3} ⊥ {1,2,4} | ({},{1,2})