
Parameter: λ13
Parameter: λ23 Identified
Algebraic Equations:
σ22λ23-σ23
Single Door Criterion:
{2} ⊥ {1,3} | {}
{2} ⊥ {3} | {1}
Parameter: λ34 Identified
Algebraic Equations:
σ13λ34-σ14
Instrumental Variable:
1 | {}
1 | {2}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω13
Parameter: ω22 Identified
Algebraic Equations:
-σ22+ω22
Parameter: ω24 Identified
Algebraic Equations:
σ14σ23-σ13σ24+σ13ω24
Parameter: ω33
Parameter: ω34 Identified
Algebraic Equations:
-σ14σ232+σ13σ23σ24+σ14σ22σ33-σ13σ22σ34+σ13σ22ω34
Parameter: ω44 Identified
Algebraic Equations:
-σ142σ33+2σ13σ14σ34-σ132σ44+σ132ω44
Total Effect of X1 on X4: λ13λ34
Total Effect of X2 on X4: λ23λ34 Identified
Each Parameter Identified
Constraint Set:
σ12
All constraints are determinantal
Trek-separation:
{1} ⊥ {2} | ({},{})
Parameter: λ23 Identified
Algebraic Equations:
σ22λ23-σ23
Single Door Criterion:
{2} ⊥ {1,3} | {}
{2} ⊥ {3} | {1}
Parameter: λ34 Identified
Algebraic Equations:
σ13λ34-σ14
Instrumental Variable:
1 | {}
1 | {2}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω13
Parameter: ω22 Identified
Algebraic Equations:
-σ22+ω22
Parameter: ω24 Identified
Algebraic Equations:
σ14σ23-σ13σ24+σ13ω24
Parameter: ω33
Parameter: ω34 Identified
Algebraic Equations:
-σ14σ232+σ13σ23σ24+σ14σ22σ33-σ13σ22σ34+σ13σ22ω34
Parameter: ω44 Identified
Algebraic Equations:
-σ142σ33+2σ13σ14σ34-σ132σ44+σ132ω44
Total Effect of X1 on X4: λ13λ34
Total Effect of X2 on X4: λ23λ34 Identified
Each Parameter Identified
Vanishing Ideal
Constraint Set:
σ12
All constraints are determinantal
Trek-separation:
{1} ⊥ {2} | ({},{})