ps3macro2sp08 - Econ 387L Macro II Spring 2008 University...

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Econ 387L: Macro II Spring 2008, University of Texas Instructor: Dean Corbae Problem Set #3- Due 2/5/08 Using matlab, you are to obtain decision rules by the method of undetermined coefficients suggested in Christiano (2002) for the economy in Hansen (1985). In particular, the problem you are to solve is to choose { C t 0 t [0 , 1] ,K t +1 0 } t =0 to solve max E " X t =0 β t ¡ (1 α )log( C t )+ απ t ln(1 h ) ¢ # subject to C t + K t +1 = Z t K θ t ¡ π t h ¢ 1 θ +(1 δ ) K t (1) Z t =(1 ρ )+ ρZ t 1 + ε t (2) where K 0 is given, ε t are i.i.d. N (0 ε ) , and the steady state level of technology Z =1 . You are to use the calibration that we considered in class. In particular, θ δ (quar) ρ σ ε h β (quar) α 0 . 36 0 . 015 0 . 95 0 . 007 0 . 53 0 . 9921 0 . 666 1. Follow the steps we did in class to get decision rules: (i) Find the steady state; (ii) Linearize the equations characterizing an equilibrium (i.e. first order conditions and
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