Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₄σ₂₃λ₂₃-σ₁₃σ₂₄λ₂₃-σ₁₄σ₃₃+σ₁₃σ₃₄

Single Door Criterion:

{2} ⊥ {1,3} | {}
{2} ⊥ {3} | {1}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃λ₃₄-σ₁₄,
σ₂₃²λ₃₄-σ₂₃σ₂₄-σ₂₂σ₃₃λ₃₄+σ₂₂σ₃₄

Single Door Criterion:

{3} ⊥ {4} | {2}
{3} ⊥ {4} | {1,2}

Instrumental Variable:

1 | {}
1 | {2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₃-σ₁₃σ₂₄+σ₁₃ω₂₄,
σ₂₂σ₂₄σ₃₃-σ₂₂σ₂₃σ₃₄+σ₂₃²ω₂₄-σ₂₂σ₃₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₄σ₃₃-σ₁₃σ₂₃σ₃₄+σ₁₄σ₂₃ω₃₃-σ₁₃σ₂₄ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₃₃+2σ₁₃σ₁₄σ₃₄-σ₁₃²σ₄₄+σ₁₃²ω₄₄,
-σ₁₄σ₂₃σ₂₄σ₃₃+2σ₁₃σ₂₃σ₂₄σ₃₄+σ₁₄σ₂₂σ₃₃σ₃₄-2σ₁₃σ₂₂σ₃₄²-σ₁₃σ₂₃²σ₄₄+σ₁₃σ₂₂σ₃₃σ₄₄+σ₁₃σ₂₃²ω₄₄-σ₁₃σ₂₂σ₃₃ω₄₄,
-σ₂₃²σ₂₄²σ₃₃+2σ₂₃³σ₂₄σ₃₄-2σ₂₂σ₂₃²σ₃₄²+σ₂₂²σ₃₃σ₃₄²-σ₂₃⁴σ₄₄+2σ₂₂σ₂₃²σ₃₃σ₄₄-σ₂₂²σ₃₃²σ₄₄+σ₂₃⁴ω₄₄-2σ₂₂σ₂₃²σ₃₃ω₄₄+σ₂₂²σ₃₃²ω₄₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₁₂,
σ₁₄σ₂₃²-σ₁₃σ₂₃σ₂₄-σ₁₄σ₂₂σ₃₃+σ₁₃σ₂₂σ₃₄

All constraints are determinantal

Trek-separation:

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