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handoutvar06 - Handout on Blanchard-Quah(AER 1989 1...

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Handout on Blanchard-Quah (AER, 1989) . 1 Deriving a VMA representation: Aggregate supply (production function where θ t is labor produc- tivity and N t is employment): Y s t = θ t + N t (1) Aggregate demand curve (consumption depends on real money holdings and investment depends on productivity): Y d t = M t P t + αθ t (2) Goods Price Setting (real wages equated to labor productivity): P t = W t θ t (3) Wage Setting (nominal wages are set one period in advance so as to achieve expected full employment): W t = W ¯ ¯ { E t 1 N t = N } (4) Exogenous productivity process (productivity variations depend on unobservable mean zero, iid technology shocks): θ t = θ t 1 + ε s t (5) Exogenous money supply process (variations in money supply de- pend on unobservable mean zero, iid money shocks): M t = M t 1 + ε d t (6) Assumptions on the fundamental shocks: ε s t ε d t (i.e. independent) and σ 2 ( ε s t ) = 1 = σ 2 ( ε s t ). That is, var-covar matrix is I. De fi nitions: Y t = Y s t = Y d t , U t = N N t Endogenous variables: Y t , N t , U t , P t , W t . Exogenous variables ε s t and ε d t . 1
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Let’s start with (4). That is, wages are set so that E t 1 N t = N. From (1) then E t 1 N t = E t 1 [ Y t θ t ] = N (7a) Plugging (3) into (2) we have an expression for Y t = M t W t + (1 + α ) θ t (8) Thus (8) into (7a) yields E t 1 N t = E t 1 M t E t 1 W t + (1 + α ) E t 1 θ t E t 1 θ t = M t 1 + αθ t 1 E t 1 W t But since W t is set one period in advance, then
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