Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₂λ₁₃-σ₂₃,
σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3,4} | {}
{1} ⊥ {3} | {2}

Instrumental Variable:

2 | {}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃λ₃₄-σ₁₄,
-σ₁₂σ₁₄+σ₁₁σ₂₃λ₃₄

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂ Identified

Algebraic Equations:

-σ₁₂+ω₁₂

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₃-σ₁₃σ₂₄+σ₁₃ω₂₄,
σ₁₂σ₁₄-σ₁₁σ₂₄+σ₁₁ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃,
σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

σ₁₄σ₃₃-σ₁₃σ₃₄+σ₁₃ω₃₄,
σ₁₂σ₁₄σ₃₃-σ₁₁σ₂₃σ₃₄+σ₁₁σ₂₃ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₃₃+2σ₁₃σ₁₄σ₃₄-σ₁₃²σ₄₄+σ₁₃²ω₄₄,
-σ₁₂σ₁₄²σ₃₃+2σ₁₁σ₁₄σ₂₃σ₃₄-σ₁₁σ₁₃σ₂₃σ₄₄+σ₁₁σ₁₃σ₂₃ω₄₄,
-σ₁₂²σ₁₄²σ₃₃+2σ₁₁σ₁₂σ₁₄σ₂₃σ₃₄-σ₁₁²σ₂₃²σ₄₄+σ₁₁²σ₂₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {3,4} | {}

Vanishing Ideal

Constraint Set:

σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {1,3} | ({},{1})