Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3,4} | {}
{1} ⊥ {2,4} | {3}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂λ₂₄-σ₁₄

Instrumental Variable:

1 | {}
1 | {3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₄σ₂₂+σ₁₂σ₂₃λ₃₄-σ₁₂σ₂₄

Instrumental Variable:

1 | {2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

-σ₂₃+ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

σ₁₄σ₂₃²-σ₁₄σ₂₂σ₃₃+σ₁₂σ₂₄σ₃₃-σ₁₂σ₂₃σ₃₄+σ₁₂σ₂₃ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄²σ₂₂σ₂₃²-σ₁₄²σ₂₂²σ₃₃+2σ₁₂σ₁₄σ₂₂σ₂₄σ₃₃-σ₁₂²σ₂₄²σ₃₃-2σ₁₂σ₁₄σ₂₂σ₂₃σ₃₄+2σ₁₂²σ₂₃σ₂₄σ₃₄-σ₁₂²σ₂₃²σ₄₄+σ₁₂²σ₂₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}
{1} ⊥ {2,4} | {3}

Vanishing Ideal

Constraint Set:

σ₁₃

All constraints are determinantal

Trek-separation:

{1} ⊥ {3} | ({},{})