Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₄λ₁₂-σ₂₄,
σ₁₃λ₁₂-σ₂₃,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

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

Instrumental Variable:

3 | {}
3 | {4}
4 | {}
4 | {3}

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₄λ₁₃-σ₃₄,
σ₁₃σ₂₄λ₁₃-σ₂₃σ₃₄,
σ₁₁σ₂₄λ₁₃-σ₁₂σ₃₄

Instrumental Variable:

4 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃σ₂₄+σ₁₂σ₃₄+σ₂₄ω₁₃,
-σ₁₃σ₁₄+σ₁₁σ₃₄+σ₁₄ω₁₃

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₄+ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₄σ₂₂+σ₁₂σ₂₄+σ₁₄ω₂₂,
-σ₁₃σ₂₂+σ₁₂σ₂₃+σ₁₃ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₁₄σ₂₄σ₃₃+2σ₁₃σ₂₄σ₃₄-σ₁₂σ₃₄²+σ₁₄σ₂₄ω₃₃,
-σ₁₄²σ₃₃+2σ₁₃σ₁₄σ₃₄-σ₁₁σ₃₄²+σ₁₄²ω₃₃,
-σ₁₃σ₂₄²σ₃₃+2σ₁₃σ₂₃σ₂₄σ₃₄-σ₁₂σ₂₃σ₃₄²+σ₁₃σ₂₄²ω₃₃,
-σ₁₁σ₂₄²σ₃₃+2σ₁₁σ₂₃σ₂₄σ₃₄-σ₁₂²σ₃₄²+σ₁₁σ₂₄²ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₄₄+ω₄₄

Vanishing Ideal

Constraint Set:

σ₁₄σ₂₃-σ₁₃σ₂₄,
σ₁₂σ₁₄-σ₁₁σ₂₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

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