Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₂λ₁₃-σ₂₃,
σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3,4} | {}
{1} ⊥ {3} | {2}

Instrumental Variable:

2 | {}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₃₃λ₃₄-σ₃₄,
σ₁₃λ₃₄-σ₁₄,
-σ₁₂σ₁₄+σ₁₁σ₂₃λ₃₄

Single Door Criterion:

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

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂ Identified

Algebraic Equations:

-σ₁₂+ω₁₂

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

-σ₂₄σ₃₃+σ₂₃σ₃₄+σ₃₃ω₂₄,
σ₁₄σ₂₃-σ₁₃σ₂₄+σ₁₃ω₂₄,
σ₁₂σ₁₄-σ₁₁σ₂₄+σ₁₁ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃,
σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₃₄²-σ₃₃σ₄₄+σ₃₃ω₄₄,
σ₁₄σ₃₄-σ₁₃σ₄₄+σ₁₃ω₄₄,
σ₁₂σ₁₄σ₃₄-σ₁₁σ₂₃σ₄₄+σ₁₁σ₂₃ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {3,4} | {}

Vanishing Ideal

Constraint Set:

σ₁₄σ₃₃-σ₁₃σ₃₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

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