Parameter: λ₁₂

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂λ₂₄-σ₁₄

Instrumental Variable:

1 | {}
1 | {3}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₂-σ₁₂σ₂₄+σ₁₂ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₂₂+2σ₁₂σ₁₄σ₂₄-σ₁₂²σ₄₄+σ₁₂²ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₃₄,
σ₂₃,
σ₁₃

All constraints are determinantal

Trek-separation:

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