Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₂²λ₂₃-σ₁₂σ₁₃-σ₁₁σ₂₂λ₂₃+σ₁₁σ₂₃

Single Door Criterion:

{2} ⊥ {3,4} | {1}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₃₃λ₃₄-σ₃₄,
σ₂₃λ₃₄-σ₂₄,
σ₁₃λ₃₄-σ₁₄

Single Door Criterion:

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

Instrumental Variable:

1 | {}
1 | {2}
2 | {}
2 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

σ₁₁σ₁₃σ₂₂-σ₁₁σ₁₂σ₂₃+σ₁₂²ω₁₃-σ₁₁σ₂₂ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₁₂²σ₁₃²σ₂₂+2σ₁₂³σ₁₃σ₂₃-2σ₁₁σ₁₂²σ₂₃²+σ₁₁²σ₂₂σ₂₃²-σ₁₂⁴σ₃₃+2σ₁₁σ₁₂²σ₂₂σ₃₃-σ₁₁²σ₂₂²σ₃₃+σ₁₂⁴ω₃₃-2σ₁₁σ₁₂²σ₂₂ω₃₃+σ₁₁²σ₂₂²ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₃₄²-σ₃₃σ₄₄+σ₃₃ω₄₄,
σ₂₄σ₃₄-σ₂₃σ₄₄+σ₂₃ω₄₄,
σ₁₄σ₃₄-σ₁₃σ₄₄+σ₁₃ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Each Parameter Identified

Total Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄ Identified

Each Parameter Identified

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Back Door Criterion:


{2} ⊥ {3,4} | {1}

Vanishing Ideal

Constraint Set:

σ₂₄σ₃₃-σ₂₃σ₃₄,
σ₁₄σ₃₃-σ₁₃σ₃₄,
σ₁₄σ₂₃-σ₁₃σ₂₄

All constraints are determinantal

Trek-separation:

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