Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃σ₂₃λ₁₄-σ₁₂σ₃₃λ₁₄+σ₂₄σ₃₃-σ₂₃σ₃₄,
σ₁₂σ₂₃²λ₁₄-σ₁₂σ₂₂σ₃₃λ₁₄+σ₂₂σ₂₄σ₃₃-σ₂₂σ₂₃σ₃₄

Instrumental Variable:

2 | {3}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₂λ₂₃-σ₁₃

Single Door Criterion:

{2} ⊥ {3} | {}
{2} ⊥ {3} | {1}

Instrumental Variable:

1 | {}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₂₃²λ₃₄-σ₂₃σ₂₄-σ₂₂σ₃₃λ₃₄+σ₂₂σ₃₄,
σ₁₃σ₂₃λ₃₄-σ₁₃σ₂₄-σ₁₂σ₃₃λ₃₄+σ₁₂σ₃₄

Single Door Criterion:

{3} ⊥ {1,4} | {2}
{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂ Identified

Algebraic Equations:

-σ₁₂+ω₁₂

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₃σ₁₄σ₂₃+σ₁₃²σ₂₄+σ₁₂σ₁₄σ₃₃-σ₁₁σ₂₄σ₃₃-σ₁₂σ₁₃σ₃₄+σ₁₁σ₂₃σ₃₄+σ₁₃σ₂₃ω₁₄-σ₁₂σ₃₃ω₁₄,
-σ₁₂σ₁₄σ₂₃²+σ₁₂σ₁₃σ₂₃σ₂₄+σ₁₂σ₁₄σ₂₂σ₃₃-σ₁₁σ₂₂σ₂₄σ₃₃-σ₁₂²σ₂₃σ₃₄+σ₁₁σ₂₂σ₂₃σ₃₄+σ₁₂σ₂₃²ω₁₄-σ₁₂σ₂₂σ₃₃ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-2σ₁₃σ₁₄σ₂₃σ₂₄σ₃₃+σ₁₃²σ₂₄²σ₃₃+2σ₁₂σ₁₄σ₂₄σ₃₃²-σ₁₁σ₂₄²σ₃₃²+2σ₁₃σ₁₄σ₂₃²σ₃₄-2σ₁₂σ₁₄σ₂₃σ₃₃σ₃₄-2σ₁₂σ₁₃σ₂₄σ₃₃σ₃₄+2σ₁₁σ₂₃σ₂₄σ₃₃σ₃₄-σ₁₁σ₂₃²σ₃₄²+σ₁₂²σ₃₃σ₃₄²-σ₁₃²σ₂₃²σ₄₄+2σ₁₂σ₁₃σ₂₃σ₃₃σ₄₄-σ₁₂²σ₃₃²σ₄₄+σ₁₃²σ₂₃²ω₄₄-2σ₁₂σ₁₃σ₂₃σ₃₃ω₄₄+σ₁₂²σ₃₃²ω₄₄,
-2σ₁₂σ₁₄σ₂₃²σ₂₄σ₃₃+σ₁₂σ₁₃σ₂₃σ₂₄²σ₃₃+2σ₁₂σ₁₄σ₂₂σ₂₄σ₃₃²-σ₁₁σ₂₂σ₂₄²σ₃₃²+2σ₁₂σ₁₄σ₂₃³σ₃₄-2σ₁₂σ₁₄σ₂₂σ₂₃σ₃₃σ₃₄-2σ₁₂²σ₂₃σ₂₄σ₃₃σ₃₄+2σ₁₁σ₂₂σ₂₃σ₂₄σ₃₃σ₃₄-σ₁₁σ₂₂σ₂₃²σ₃₄²+σ₁₂²σ₂₂σ₃₃σ₃₄²-σ₁₂σ₁₃σ₂₃³σ₄₄+2σ₁₂²σ₂₃²σ₃₃σ₄₄-σ₁₂²σ₂₂σ₃₃²σ₄₄+σ₁₂σ₁₃σ₂₃³ω₄₄-2σ₁₂²σ₂₃²σ₃₃ω₄₄+σ₁₂²σ₂₂σ₃₃²ω₄₄,
-2σ₁₂σ₁₄σ₂₂σ₂₃²σ₂₄σ₃₃+σ₁₂²σ₂₃²σ₂₄²σ₃₃+2σ₁₂σ₁₄σ₂₂²σ₂₄σ₃₃²-σ₁₁σ₂₂²σ₂₄²σ₃₃²+2σ₁₂σ₁₄σ₂₂σ₂₃³σ₃₄-2σ₁₂σ₁₄σ₂₂²σ₂₃σ₃₃σ₃₄-2σ₁₂²σ₂₂σ₂₃σ₂₄σ₃₃σ₃₄+2σ₁₁σ₂₂²σ₂₃σ₂₄σ₃₃σ₃₄-σ₁₁σ₂₂²σ₂₃²σ₃₄²+σ₁₂²σ₂₂²σ₃₃σ₃₄²-σ₁₂²σ₂₃⁴σ₄₄+2σ₁₂²σ₂₂σ₂₃²σ₃₃σ₄₄-σ₁₂²σ₂₂²σ₃₃²σ₄₄+σ₁₂²σ₂₃⁴ω₄₄-2σ₁₂²σ₂₂σ₂₃²σ₃₃ω₄₄+σ₁₂²σ₂₂²σ₃₃²ω₄₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₁₃σ₂₂-σ₁₂σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {2,3} | ({},{2})