Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {2,3,4} | {}
{1} ⊥ {3,4} | {2}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₄σ₂₃λ₂₃-σ₁₃σ₂₄λ₂₃-σ₁₄σ₃₃+σ₁₃σ₃₄

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃λ₃₄-σ₁₄

Instrumental Variable:

1 | {}
1 | {2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

-σ₁₄σ₂₃²+σ₁₃σ₂₃σ₂₄+σ₁₄σ₂₂σ₃₃-σ₁₃σ₂₂σ₃₄+σ₁₄σ₂₃ω₂₃-σ₁₃σ₂₄ω₂₃

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₃-σ₁₃σ₂₄+σ₁₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²σ₁₄²σ₂₃²-2σ₁₃³σ₁₄σ₂₃σ₂₄+σ₁₃⁴σ₂₄²+σ₁₁σ₁₄²σ₂₃²σ₃₃-σ₁₁σ₁₃²σ₂₄²σ₃₃-σ₁₁σ₁₄²σ₂₂σ₃₃²-2σ₁₁σ₁₃σ₁₄σ₂₃²σ₃₄+2σ₁₁σ₁₃²σ₂₃σ₂₄σ₃₄+2σ₁₁σ₁₃σ₁₄σ₂₂σ₃₃σ₃₄-σ₁₁σ₁₃²σ₂₂σ₃₄²+σ₁₁σ₁₄²σ₂₃²ω₃₃-2σ₁₁σ₁₃σ₁₄σ₂₃σ₂₄ω₃₃+σ₁₁σ₁₃²σ₂₄²ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₃₃+2σ₁₃σ₁₄σ₃₄-σ₁₃²σ₄₄+σ₁₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}
{1} ⊥ {3,4} | {2}

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₁₂

All constraints are determinantal

Trek-separation:

{1} ⊥ {2} | ({},{})