Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃,
σ₁₄σ₂₃λ₁₃-σ₁₃σ₂₄λ₁₃+σ₂₄σ₃₃-σ₂₃σ₃₄

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {3} | {2}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₂₃λ₃₄-σ₂₄,
σ₁₃²λ₃₄-σ₁₃σ₁₄-σ₁₁σ₃₃λ₃₄+σ₁₁σ₃₄

Single Door Criterion:

{3} ⊥ {4} | {1}
{3} ⊥ {4} | {1,2}

Instrumental Variable:

2 | {}
2 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₄σ₂₃+σ₁₃σ₂₄+σ₂₃ω₁₄,
σ₁₁σ₁₄σ₃₃-σ₁₁σ₁₃σ₃₄+σ₁₃²ω₁₄-σ₁₁σ₃₃ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

-σ₂₃+ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃,
-σ₁₄σ₂₃σ₃₃+σ₁₃σ₂₃σ₃₄+σ₁₄σ₂₃ω₃₃-σ₁₃σ₂₄ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₂₄²σ₃₃+2σ₂₃σ₂₄σ₃₄-σ₂₃²σ₄₄+σ₂₃²ω₄₄,
-σ₁₃σ₁₄σ₂₄σ₃₃+2σ₁₃²σ₂₄σ₃₄-σ₁₁σ₂₄σ₃₃σ₃₄-σ₁₃²σ₂₃σ₄₄+σ₁₁σ₂₃σ₃₃σ₄₄+σ₁₃²σ₂₃ω₄₄-σ₁₁σ₂₃σ₃₃ω₄₄,
-σ₁₃σ₁₄²σ₂₄σ₃₃+2σ₁₃²σ₁₄σ₂₄σ₃₄-σ₁₁σ₁₄σ₂₄σ₃₃σ₃₄-σ₁₃³σ₂₄σ₄₄+σ₁₁σ₁₄σ₂₃σ₃₃σ₄₄+σ₁₁σ₁₃σ₂₄σ₃₃σ₄₄-σ₁₁σ₁₃σ₂₃σ₃₄σ₄₄+σ₁₃³σ₂₄ω₄₄-σ₁₁σ₁₄σ₂₃σ₃₃ω₄₄-σ₁₁σ₁₃σ₂₄σ₃₃ω₄₄+σ₁₁σ₁₃σ₂₃σ₃₄ω₄₄,
-σ₁₃²σ₁₄²σ₃₃+2σ₁₃³σ₁₄σ₃₄-2σ₁₁σ₁₃²σ₃₄²+σ₁₁²σ₃₃σ₃₄²-σ₁₃⁴σ₄₄+2σ₁₁σ₁₃²σ₃₃σ₄₄-σ₁₁²σ₃₃²σ₄₄+σ₁₃⁴ω₄₄-2σ₁₁σ₁₃²σ₃₃ω₄₄+σ₁₁²σ₃₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₁₂,
σ₁₃σ₁₄σ₂₃-σ₁₃²σ₂₄+σ₁₁σ₂₄σ₃₃-σ₁₁σ₂₃σ₃₄

All constraints are determinantal

Trek-separation:

{1} ⊥ {2} | ({},{})
{1,2,3} ⊥ {3,1,4} | ({1},{3})