Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂,
σ₁₄σ₃₃λ₁₂-σ₂₄σ₃₃+σ₂₃σ₃₄

Single Door Criterion:

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

Instrumental Variable:

4 | {3}

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₁λ₁₄-σ₁₄,
σ₁₂σ₃₃λ₁₄-σ₂₄σ₃₃+σ₂₃σ₃₄

Single Door Criterion:

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

Instrumental Variable:

2 | {3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₃₃λ₃₄-σ₃₄,
σ₁₂σ₁₄+σ₁₁σ₂₃λ₃₄-σ₁₁σ₂₄

Single Door Criterion:

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

Instrumental Variable:

2 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂,
-σ₁₄σ₂₂σ₃₃+σ₁₂σ₂₄σ₃₃-σ₁₂σ₂₃σ₃₄+σ₁₄σ₃₃ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

-σ₂₃+ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄σ₂₄σ₃₃-σ₁₄σ₂₃σ₃₄+σ₁₂σ₃₄²-σ₁₂σ₃₃σ₄₄+σ₁₂σ₃₃ω₄₄,
σ₁₄²σ₃₃+σ₁₁σ₃₄²-σ₁₁σ₃₃σ₄₄+σ₁₁σ₃₃ω₄₄,
σ₁₄²σ₂₃-σ₁₂σ₁₄σ₃₄+σ₁₁σ₂₄σ₃₄-σ₁₁σ₂₃σ₄₄+σ₁₁σ₂₃ω₄₄

Vanishing Ideal

Constraint Set:

σ₁₃,
σ₁₂σ₁₄σ₃₃-σ₁₁σ₂₄σ₃₃+σ₁₁σ₂₃σ₃₄

All constraints are determinantal

Trek-separation:

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