Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₁σ₂₃²λ₁₄-σ₁₄σ₂₃²+σ₁₃σ₂₃σ₂₄-σ₁₁σ₂₂σ₃₃λ₁₄+σ₁₄σ₂₂σ₃₃-σ₁₂σ₂₃σ₃₄,
σ₁₁σ₁₃σ₂₃λ₁₄-σ₁₃σ₁₄σ₂₃+σ₁₃²σ₂₄-σ₁₁σ₁₂σ₃₃λ₁₄+σ₁₂σ₁₄σ₃₃-σ₁₂σ₁₃σ₃₄

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₂λ₂₃-σ₁₃

Single Door Criterion:

{2} ⊥ {3} | {}
{2} ⊥ {3} | {1}

Instrumental Variable:

1 | {}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₂₃²λ₃₄-σ₂₃σ₂₄-σ₂₂σ₃₃λ₃₄+σ₂₂σ₃₄,
σ₁₃σ₂₃λ₃₄-σ₁₃σ₂₄-σ₁₂σ₃₃λ₃₄+σ₁₂σ₃₄

Single Door Criterion:

{3} ⊥ {1,4} | {2}
{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂ Identified

Algebraic Equations:

-σ₁₂+ω₁₂

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₂σ₁₄σ₂₃²-σ₁₂σ₁₃σ₂₃σ₂₄-σ₁₂σ₁₄σ₂₂σ₃₃+σ₁₁σ₂₂σ₂₄σ₃₃+σ₁₂²σ₂₃σ₃₄-σ₁₁σ₂₂σ₂₃σ₃₄+σ₁₁σ₂₃²ω₂₄-σ₁₁σ₂₂σ₃₃ω₂₄,
σ₁₂σ₁₃σ₁₄σ₂₃-σ₁₂σ₁₃²σ₂₄-σ₁₂²σ₁₄σ₃₃+σ₁₁σ₁₂σ₂₄σ₃₃+σ₁₂²σ₁₃σ₃₄-σ₁₁σ₁₂σ₂₃σ₃₄+σ₁₁σ₁₃σ₂₃ω₂₄-σ₁₁σ₁₂σ₃₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄²σ₂₃⁴-2σ₁₃σ₁₄σ₂₃³σ₂₄+σ₁₃²σ₂₃²σ₂₄²-2σ₁₄²σ₂₂σ₂₃²σ₃₃+2σ₁₂σ₁₄σ₂₃²σ₂₄σ₃₃-σ₁₁σ₂₃²σ₂₄²σ₃₃+σ₁₄²σ₂₂²σ₃₃²+2σ₁₂σ₁₄σ₂₃³σ₃₄-2σ₁₂σ₁₃σ₂₃²σ₂₄σ₃₄+2σ₁₁σ₂₃³σ₂₄σ₃₄-2σ₁₂σ₁₄σ₂₂σ₂₃σ₃₃σ₃₄+σ₁₂²σ₂₃²σ₃₄²-2σ₁₁σ₂₂σ₂₃²σ₃₄²+σ₁₁σ₂₂²σ₃₃σ₃₄²-σ₁₁σ₂₃⁴σ₄₄+2σ₁₁σ₂₂σ₂₃²σ₃₃σ₄₄-σ₁₁σ₂₂²σ₃₃²σ₄₄+σ₁₁σ₂₃⁴ω₄₄-2σ₁₁σ₂₂σ₂₃²σ₃₃ω₄₄+σ₁₁σ₂₂²σ₃₃²ω₄₄,
σ₁₃σ₁₄²σ₂₃³-2σ₁₃²σ₁₄σ₂₃²σ₂₄+σ₁₃³σ₂₃σ₂₄²-2σ₁₂σ₁₄²σ₂₃²σ₃₃+2σ₁₂σ₁₃σ₁₄σ₂₃σ₂₄σ₃₃-σ₁₁σ₁₃σ₂₃σ₂₄²σ₃₃+σ₁₂σ₁₄²σ₂₂σ₃₃²+2σ₁₂σ₁₃σ₁₄σ₂₃²σ₃₄-2σ₁₂σ₁₃²σ₂₃σ₂₄σ₃₄+2σ₁₁σ₁₃σ₂₃²σ₂₄σ₃₄-2σ₁₂²σ₁₄σ₂₃σ₃₃σ₃₄+σ₁₂²σ₁₃σ₂₃σ₃₄²-2σ₁₁σ₁₂σ₂₃²σ₃₄²+σ₁₁σ₁₂σ₂₂σ₃₃σ₃₄²-σ₁₁σ₁₃σ₂₃³σ₄₄+2σ₁₁σ₁₂σ₂₃²σ₃₃σ₄₄-σ₁₁σ₁₂σ₂₂σ₃₃²σ₄₄+σ₁₁σ₁₃σ₂₃³ω₄₄-2σ₁₁σ₁₂σ₂₃²σ₃₃ω₄₄+σ₁₁σ₁₂σ₂₂σ₃₃²ω₄₄,
σ₁₃²σ₁₄²σ₂₃²-2σ₁₃³σ₁₄σ₂₃σ₂₄+σ₁₃⁴σ₂₄²-2σ₁₂σ₁₃σ₁₄²σ₂₃σ₃₃+2σ₁₂σ₁₃²σ₁₄σ₂₄σ₃₃-σ₁₁σ₁₃²σ₂₄²σ₃₃+σ₁₂²σ₁₄²σ₃₃²+2σ₁₂σ₁₃²σ₁₄σ₂₃σ₃₄-2σ₁₂σ₁₃³σ₂₄σ₃₄+2σ₁₁σ₁₃²σ₂₃σ₂₄σ₃₄-2σ₁₂²σ₁₃σ₁₄σ₃₃σ₃₄+σ₁₂²σ₁₃²σ₃₄²-2σ₁₁σ₁₂σ₁₃σ₂₃σ₃₄²+σ₁₁σ₁₂²σ₃₃σ₃₄²-σ₁₁σ₁₃²σ₂₃²σ₄₄+2σ₁₁σ₁₂σ₁₃σ₂₃σ₃₃σ₄₄-σ₁₁σ₁₂²σ₃₃²σ₄₄+σ₁₁σ₁₃²σ₂₃²ω₄₄-2σ₁₁σ₁₂σ₁₃σ₂₃σ₃₃ω₄₄+σ₁₁σ₁₂²σ₃₃²ω₄₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₁₃σ₂₂-σ₁₂σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {2,3} | ({},{2})