Answer to Reparameterisation

Answer to Reparameterisation - Applied Econometrics (Answer...

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Applied Econometrics (Answer to Reparameteristion.doc) Mini exercise Q1: Demonstrate that each of the following is a reparameterisation of the other, and identify the relationships between the φ and θ parameters: 1 t Y 4 1 t X 3 t X 2 1 t Y - φ + - φ + φ + φ = (1) 1 t Y 4 1 t X 3 t X 2 1 t Y - θ + - θ + θ + θ = (2) A1: Starting from equation (2), we have 1 t 4 1 t 3 1 t t 2 1 1 t t Y X ) X X ( Y Y - - - - θ + θ + - θ + θ = - and so 1 t 4 1 t 2 3 t 2 1 t Y ) 1 ( X ) ( X Y - - θ + + θ - θ + θ + θ = and so 4 4 2 3 3 2 2 1 1 1 , , , θ + = φ θ - θ = φ θ = φ θ = φ Q2: How are these two models related to the following two-equation model? (Comment on the fact that there are 5 parameters in this model, but only 4 in each of the two above.) ) 4 ( ) Y Y ( X Y ) 3 ( X Y 1 t * 3 t 2 1 t 2 1 * - - γ + γ + γ = β + β = A2: Substituting (3) into (4) we obtain: 1 t 2 1 3 t 2 1 t ) Y X ( X Y - - β + β γ + γ + γ = (5) and so 1 t 2 3 t 2 1 3 1 t ) Y X ( X ) ( Y - - β γ + γ + β γ + γ = (6) 1 t 3 1 t
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