Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3,4} | {}
{1} ⊥ {2,3} | {4}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₂λ₂₃-σ₁₃

Single Door Criterion:

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

Instrumental Variable:

1 | {}
1 | {4}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

-σ₃₄+ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₄₄+ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}
{1} ⊥ {2,3} | {4}

Vanishing Ideal

Constraint Set:

σ₂₄,
σ₁₄,
σ₁₃σ₂₂-σ₁₂σ₂₃

All constraints are determinantal

Trek-separation:

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