Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃σ₂₃λ₁₄+σ₂₄σ₃₃-σ₂₃σ₃₄

Instrumental Variable:

2 | {3}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃

Single Door Criterion:

{2} ⊥ {1,3,4} | {}
{2} ⊥ {3,4} | {1}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₂₃λ₃₄-σ₂₄

Instrumental Variable:

2 | {}
2 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₃σ₁₄σ₂₃+σ₁₃²σ₂₄-σ₁₁σ₂₄σ₃₃+σ₁₁σ₂₃σ₃₄+σ₁₃σ₂₃ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-2σ₁₃σ₁₄σ₂₃σ₂₄σ₃₃+σ₁₃²σ₂₄²σ₃₃-σ₁₁σ₂₄²σ₃₃²+2σ₁₃σ₁₄σ₂₃²σ₃₄+2σ₁₁σ₂₃σ₂₄σ₃₃σ₃₄-σ₁₁σ₂₃²σ₃₄²-σ₁₃²σ₂₃²σ₄₄+σ₁₃²σ₂₃²ω₄₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Back Door Criterion:


{2} ⊥ {1,3,4} | {}
{2} ⊥ {3,4} | {1}

Vanishing Ideal

Constraint Set:

σ₁₂

All constraints are determinantal

Trek-separation:

{1} ⊥ {2} | ({},{})