Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃

Single Door Criterion:

{2} ⊥ {1,3,4} | {}
{2} ⊥ {3,4} | {1}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₂₃λ₃₄-σ₂₄

Instrumental Variable:

2 | {}
2 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

σ₂₄σ₃₃-σ₂₃σ₃₄+σ₂₃ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₂₄²σ₃₃+2σ₂₃σ₂₄σ₃₄-σ₂₃²σ₄₄+σ₂₃²ω₄₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Back Door Criterion:


{2} ⊥ {1,3,4} | {}
{2} ⊥ {3,4} | {1}

Vanishing Ideal

Constraint Set:

σ₁₄,
σ₁₃,
σ₁₂

All constraints are determinantal

Trek-separation:

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