Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₁λ₁₄-σ₁₄,
σ₁₃σ₂₂λ₁₄+σ₂₃σ₂₄-σ₂₂σ₃₄

Single Door Criterion:

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

Instrumental Variable:

3 | {2}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₃σ₁₄+σ₁₁σ₂₄λ₂₃-σ₁₁σ₃₄

Single Door Criterion:

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

Instrumental Variable:

4 | {1}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₂λ₂₄-σ₂₄,
σ₁₃σ₁₄+σ₁₁σ₂₃λ₂₄-σ₁₁σ₃₄

Single Door Criterion:

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

Instrumental Variable:

3 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
-σ₁₃σ₁₄σ₂₃-σ₁₁σ₂₄σ₃₃+σ₁₁σ₂₃σ₃₄+σ₁₁σ₂₄ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄²σ₂₃-σ₁₃σ₁₄σ₂₄+σ₁₁σ₂₄σ₃₄-σ₁₁σ₂₃σ₄₄+σ₁₁σ₂₃ω₄₄,
-σ₁₄σ₂₃σ₂₄+σ₁₃σ₂₄²+σ₁₄σ₂₂σ₃₄-σ₁₃σ₂₂σ₄₄+σ₁₃σ₂₂ω₄₄,
σ₁₄²σ₂₂+σ₁₁σ₂₄²-σ₁₁σ₂₂σ₄₄+σ₁₁σ₂₂ω₄₄

Vanishing Ideal

Constraint Set:

σ₁₂,
σ₁₃σ₁₄σ₂₂+σ₁₁σ₂₃σ₂₄-σ₁₁σ₂₂σ₃₄

All constraints are determinantal

Trek-separation:

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