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: ω₁₄ Identified

Algebraic Equations:

-σ₁₄σ₂₃²+σ₁₃σ₂₃σ₂₄+σ₁₄σ₂₂σ₃₃-σ₁₂σ₂₃σ₃₄+σ₂₃²ω₁₄-σ₂₂σ₃₃ω₁₄,
-σ₁₃σ₁₄σ₂₃+σ₁₃²σ₂₄+σ₁₂σ₁₄σ₃₃-σ₁₂σ₁₃σ₃₄+σ₁₃σ₂₃ω₁₄-σ₁₂σ₃₃ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₂₂σ₂₄σ₃₃-σ₂₂σ₂₃σ₃₄+σ₂₃²ω₂₄-σ₂₂σ₃₃ω₂₄,
σ₁₂σ₂₄σ₃₃-σ₁₂σ₂₃σ₃₄+σ₁₃σ₂₃ω₂₄-σ₁₂σ₃₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₂₃²σ₂₄²σ₃₃+2σ₂₃³σ₂₄σ₃₄-2σ₂₂σ₂₃²σ₃₄²+σ₂₂²σ₃₃σ₃₄²-σ₂₃⁴σ₄₄+2σ₂₂σ₂₃²σ₃₃σ₄₄-σ₂₂²σ₃₃²σ₄₄+σ₂₃⁴ω₄₄-2σ₂₂σ₂₃²σ₃₃ω₄₄+σ₂₂²σ₃₃²ω₄₄,
-σ₁₃σ₂₃σ₂₄²σ₃₃+2σ₁₃σ₂₃²σ₂₄σ₃₄-2σ₁₂σ₂₃²σ₃₄²+σ₁₂σ₂₂σ₃₃σ₃₄²-σ₁₃σ₂₃³σ₄₄+2σ₁₂σ₂₃²σ₃₃σ₄₄-σ₁₂σ₂₂σ₃₃²σ₄₄+σ₁₃σ₂₃³ω₄₄-2σ₁₂σ₂₃²σ₃₃ω₄₄+σ₁₂σ₂₂σ₃₃²ω₄₄,
-σ₁₃²σ₂₄²σ₃₃+2σ₁₃²σ₂₃σ₂₄σ₃₄-2σ₁₂σ₁₃σ₂₃σ₃₄²+σ₁₂²σ₃₃σ₃₄²-σ₁₃²σ₂₃²σ₄₄+2σ₁₂σ₁₃σ₂₃σ₃₃σ₄₄-σ₁₂²σ₃₃²σ₄₄+σ₁₃²σ₂₃²ω₄₄-2σ₁₂σ₁₃σ₂₃σ₃₃ω₄₄+σ₁₂²σ₃₃²ω₄₄

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})