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 f 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)y ie lds E t 1 N t = E t 1 M t E t
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This note was uploaded on 08/06/2008 for the course ECON 387 taught by Professor Corbae during the Spring '07 term at University of Texas at Austin.

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

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