Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {2} | {3}

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₁σ₂₃λ₁₄-σ₁₄σ₂₃+σ₁₂σ₃₄

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₃λ₂₄-σ₃₄

Instrumental Variable:

3 | {}
3 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

-σ₂₃+ω₂₃

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₂σ₁₄σ₂₃-σ₁₁σ₂₃σ₂₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄+σ₁₁σ₂₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄²σ₂₃²-2σ₁₂σ₁₄σ₂₃σ₃₄+2σ₁₁σ₂₃σ₂₄σ₃₄+σ₁₂²σ₃₄²-σ₁₁σ₂₂σ₃₄²-σ₁₁σ₂₃²σ₄₄+σ₁₁σ₂₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄ 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} | ({},{})