Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂,
σ₁₄σ₂₃λ₁₂-σ₂₃σ₂₄-σ₁₂σ₃₄λ₁₂+σ₂₂σ₃₄

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₃λ₂₄-σ₃₄,
σ₁₂²λ₂₄-σ₁₂σ₁₄-σ₁₁σ₂₂λ₂₄+σ₁₁σ₂₄

Single Door Criterion:

{2} ⊥ {4} | {1}

Instrumental Variable:

3 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₄σ₂₃+σ₁₂σ₃₄+σ₂₃ω₁₄,
σ₁₁σ₁₄σ₂₂-σ₁₁σ₁₂σ₂₄+σ₁₂²ω₁₄-σ₁₁σ₂₂ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂,
-σ₁₄σ₂₂σ₂₃+σ₁₂σ₂₃σ₂₄+σ₁₄σ₂₃ω₂₂-σ₁₂σ₃₄ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₂σ₁₃-σ₁₁σ₂₃+σ₁₁ω₂₃,
-σ₁₄σ₂₃²+σ₁₃σ₂₃σ₂₄-σ₁₃σ₂₂σ₃₄+σ₁₂σ₂₃σ₃₄+σ₁₄σ₂₃ω₂₃-σ₁₂σ₃₄ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

2σ₂₃σ₂₄σ₃₄-σ₂₂σ₃₄²-σ₂₃²σ₄₄+σ₂₃²ω₄₄,
-σ₁₂σ₁₄σ₂₂σ₃₄+2σ₁₂²σ₂₄σ₃₄-σ₁₁σ₂₂σ₂₄σ₃₄-σ₁₂²σ₂₃σ₄₄+σ₁₁σ₂₂σ₂₃σ₄₄+σ₁₂²σ₂₃ω₄₄-σ₁₁σ₂₂σ₂₃ω₄₄,
σ₁₂σ₁₄²σ₂₂σ₃₄-2σ₁₂²σ₁₄σ₂₄σ₃₄+σ₁₁σ₁₄σ₂₂σ₂₄σ₃₄-σ₁₁σ₁₄σ₂₂σ₂₃σ₄₄+σ₁₁σ₁₂σ₂₃σ₂₄σ₄₄+σ₁₂³σ₃₄σ₄₄-σ₁₁σ₁₂σ₂₂σ₃₄σ₄₄+σ₁₁σ₁₄σ₂₂σ₂₃ω₄₄-σ₁₁σ₁₂σ₂₃σ₂₄ω₄₄-σ₁₂³σ₃₄ω₄₄+σ₁₁σ₁₂σ₂₂σ₃₄ω₄₄,
-σ₁₂²σ₁₄²σ₂₂+2σ₁₂³σ₁₄σ₂₄-2σ₁₁σ₁₂²σ₂₄²+σ₁₁²σ₂₂σ₂₄²-σ₁₂⁴σ₄₄+2σ₁₁σ₁₂²σ₂₂σ₄₄-σ₁₁²σ₂₂²σ₄₄+σ₁₂⁴ω₄₄-2σ₁₁σ₁₂²σ₂₂ω₄₄+σ₁₁²σ₂₂²ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₁₂σ₁₄σ₂₃-σ₁₁σ₂₃σ₂₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄

Non-determinantal constraints:

list non_determinantal = 1;

Trek-separation: