Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3,4} | {}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₂₃λ₃₄-σ₂₄,
σ₁₃λ₃₄-σ₁₄

Instrumental Variable:

1 | {}
1 | {2}
2 | {}
2 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₂σ₁₃-σ₁₁σ₂₃+σ₁₁ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

σ₂₄σ₃₃-σ₂₃σ₃₄+σ₂₃ω₃₄,
σ₁₄σ₃₃-σ₁₃σ₃₄+σ₁₃ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₂₄²σ₃₃+2σ₂₃σ₂₄σ₃₄-σ₂₃²σ₄₄+σ₂₃²ω₄₄,
-σ₁₄σ₂₄σ₃₃+2σ₁₃σ₂₄σ₃₄-σ₁₃σ₂₃σ₄₄+σ₁₃σ₂₃ω₄₄,
-σ₁₄²σ₃₃+2σ₁₃σ₁₄σ₃₄-σ₁₃²σ₄₄+σ₁₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}

Vanishing Ideal

Constraint Set:

σ₁₄σ₂₃-σ₁₃σ₂₄

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {3,4} | ({},{3})