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handoutudcsp06

# handoutudcsp06 - Solving RBC models by Christiano's method...

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Solving RBC models by Christiano’s method of undetermined coe cients This handout is meant to provide a simple introduction to Christiano (2002), “Solving Dynamic Equilibrium Models by a Method of Undetermined Coe - cients”, Computational Economics , Vol. 20, p. 21-55. Note that I have made some notational changes from Christiano’s paper. Recall that the Euler equation for the savings decision generates the fol- lowing second order di ff erence equation in b k t : E t · Y C b z t +1 + K C μ θ Y K + (1 δ ) b k t +1 K C b k t +2 ¸ (1) · Y C b z t + K C μ θ Y K + (1 δ ) b k t K C b k t +1 ¸ (1 β (1 δ )) E t h b z t +1 (1 θ ) b k t +1 i Letting ζ t (the greek character for z ) denote the endogenous state variable (in this case ζ t = b k t +1 , notice the dating re fl ects when information is known) and letting s t denote the exogenous state variable (in this case s t = b z t ), then we can write (1) as E t £ α 0 ζ t +1 + α 1 ζ t + α 2 ζ t 1 + β 0 s t +1 + β 1 s t ¤ = 0 (2) This is Christiano’s (2.2) with

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handoutudcsp06 - Solving RBC models by Christiano's method...

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