Parameter: λ₁₂

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3} | {}

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₂σ₁₃λ₁₄-σ₁₁σ₂₃λ₁₄+σ₁₄σ₂₃-σ₁₃σ₂₄

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₂σ₁₃λ₃₄-σ₁₂σ₁₄-σ₁₁σ₂₃λ₃₄+σ₁₁σ₂₄

Instrumental Variable:

2 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₂σ₁₃-σ₁₁σ₂₃+σ₁₁ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

-σ₁₃σ₁₄σ₂₃+σ₁₃²σ₂₄+σ₁₂σ₁₄σ₃₃-σ₁₁σ₂₄σ₃₃-σ₁₂σ₁₃σ₃₄+σ₁₁σ₂₃σ₃₄+σ₁₂σ₁₃ω₃₄-σ₁₁σ₂₃ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₁σ₁₄²σ₂₃²-2σ₁₁σ₁₃σ₁₄σ₂₃σ₂₄+σ₁₁σ₁₃²σ₂₄²-σ₁₂²σ₁₄²σ₃₃+2σ₁₁σ₁₂σ₁₄σ₂₄σ₃₃-σ₁₁²σ₂₄²σ₃₃+2σ₁₂²σ₁₃σ₁₄σ₃₄-2σ₁₁σ₁₂σ₁₄σ₂₃σ₃₄-2σ₁₁σ₁₂σ₁₃σ₂₄σ₃₄+2σ₁₁²σ₂₃σ₂₄σ₃₄-σ₁₂²σ₁₃²σ₄₄+2σ₁₁σ₁₂σ₁₃σ₂₃σ₄₄-σ₁₁²σ₂₃²σ₄₄+σ₁₂²σ₁₃²ω₄₄-2σ₁₁σ₁₂σ₁₃σ₂₃ω₄₄+σ₁₁²σ₂₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄+λ₁₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {3,4} | {}

Vanishing Ideal

Zero Vanishing Ideal