Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {2,3,4} | {}
{1} ⊥ {3,4} | {2}

Parameter: λ₂₃

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

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₃-σ₁₃σ₂₄+σ₁₃ω₂₄

Parameter: ω₃₃

Parameter: ω₃₄

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

Vanishing Ideal

Constraint Set:

σ₁₂

All constraints are determinantal

Trek-separation:

{1} ⊥ {2} | ({},{})