Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₄λ₁₂-σ₂₄,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {2} | {4}

Instrumental Variable:

4 | {}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₂λ₂₃-σ₁₃,
-σ₁₃σ₁₄+σ₁₁σ₂₄λ₂₃

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₄+ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₄σ₂₂+σ₁₂σ₂₄+σ₁₄ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₃σ₂₂-σ₁₂σ₂₃+σ₁₂ω₂₃,
σ₁₃σ₁₄σ₂₂-σ₁₁σ₂₃σ₂₄+σ₁₁σ₂₄ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₁₃²σ₂₂+2σ₁₂σ₁₃σ₂₃-σ₁₂²σ₃₃+σ₁₂²ω₃₃,
-σ₁₃²σ₁₄σ₂₂+2σ₁₁σ₁₃σ₂₃σ₂₄-σ₁₁σ₁₂σ₂₄σ₃₃+σ₁₁σ₁₂σ₂₄ω₃₃,
-σ₁₃²σ₁₄²σ₂₂+2σ₁₁σ₁₃σ₁₄σ₂₃σ₂₄-σ₁₁²σ₂₄²σ₃₃+σ₁₁²σ₂₄²ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

σ₁₃σ₂₄-σ₁₂σ₃₄+σ₁₂ω₃₄,
σ₁₃σ₁₄-σ₁₁σ₃₄+σ₁₁ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₄₄+ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3} | {}

Vanishing Ideal

Constraint Set:

σ₁₂σ₁₄-σ₁₁σ₂₄

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {1,4} | ({1},{})