Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₃λ₁₂-σ₂₃,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,4} | {}
{1} ⊥ {2} | {3}

Instrumental Variable:

3 | {}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂λ₂₄-σ₁₄,
-σ₁₃σ₁₄+σ₁₁σ₂₃λ₂₄

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₃σ₂₂+σ₁₂σ₂₃+σ₁₃ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₂-σ₁₂σ₂₄+σ₁₂ω₂₄,
σ₁₃σ₁₄σ₂₂-σ₁₁σ₂₃σ₂₄+σ₁₁σ₂₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

σ₁₄σ₂₃-σ₁₂σ₃₄+σ₁₂ω₃₄,
σ₁₃σ₁₄-σ₁₁σ₃₄+σ₁₁ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₂₂+2σ₁₂σ₁₄σ₂₄-σ₁₂²σ₄₄+σ₁₂²ω₄₄,
-σ₁₃σ₁₄²σ₂₂+2σ₁₁σ₁₄σ₂₃σ₂₄-σ₁₁σ₁₂σ₂₃σ₄₄+σ₁₁σ₁₂σ₂₃ω₄₄,
-σ₁₃²σ₁₄²σ₂₂+2σ₁₁σ₁₃σ₁₄σ₂₃σ₂₄-σ₁₁²σ₂₃²σ₄₄+σ₁₁²σ₂₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,4} | {}

Vanishing Ideal

Constraint Set:

σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {1,3} | ({1},{})