The word recursive is used to describe an equation that

The word recursive is used to describe an equation that has an impact on a simultaneous system without any feedback from the system to the equation. Which of the equations in the following systems are simultaneous, and which are recursive? Be sure to specify which variables are endogenous and which are predetermined:

a. Y_1t = β₀ + β₁Y_2t + β₂X_1t + β₃X_2t-1 + ε_1t

Y_2t = α₀ + α₁Y_3t + α₂Y_1t + α₃X_4t + ε_2t

Y_3t = Ω₀ + Ω₁X_2t + Ω₂X_1t-1 + Ω₃X_4t-1 + ε_3t

b. Z_t = β₀ + β₁X_t + β₂Y_t + β₃H_t + ε_1t

X_t = ­0 + α₁Z_t + α₂P_t-1 + ε_2t

H_t = Ω₀ + Ω₁X_2t + Ω₂B_t + Ω₃C_St + Ω₄D_t + ε_3t

c. Y_1t = β₀ + β₁Y_2t + β₂X_1t + β₃X_2t + ε_1t

Y_2t = α₀ + α₁Y_3t + α₂X_5t + ε_2t

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