Chapter12_Business_Cycles_040709

Chapter12_Business_Cycles_040709 - Business Cycles Juan...

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Business Cycles Duke University and Federal Reserve Bank of Atlanta April 7, 2009 Business Cycles April 7, 2009 1 / 39
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Business Cycle How can we build models to think about it? Do we need di/erent models than before to do so? Traditionally, the answer was yes. Nowadays, the answer is no. We will focus on equilibrium models of the cycle. Juan Rubio-Ram±rez (DUKE) Business Cycles April 7, 2009 2 ² 39
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Stochastic Neoclassical Growth Model Cass (1965) and Koopmans (1965). Brock and Mirman (1972). Kydland and Prescott (1982). Hansen (1985). King, Plosser, and Rebelo (1988a,b). Business Cycles April 7, 2009 3 / 39
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Observation Technology does not grow smoothly but randomly. Let us suppose that we have an economy that is hit over time by productivity shocks with the same characteristics that the ones that hit the US economy. How does this economy behave over time? In particular, how do the variances and covariances of the main variables in our economy compare with those observed in the US economy? Juan Rubio-Ram±rez (DUKE) Business Cycles April 7, 2009 4 / 39
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Intuition How will Robinson do if he wakes up and today is a sunny day? And if it is rainy? Basic idea: intertemporal substitution. We will have an initial shock: change in preferences, technology or policy. Then we will have a propagation mechanism: intertemporal labor substitution and capital accumulation. We will have ±uctuations as an equilibrium outcome. Juan Rubio-Ram²rez (DUKE) Business Cycles April 7, 2009 5 / 39
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Households Labor supply choice. Preferences (Greenwood-Hercowitz-Hu/man): E 0 t = 0 β t log c t ψ l 1 + η t 1 + η ! No wealth e/ects. Alternatives: ( cv ( l )) 1 γ 1 1 γ if γ > 0, γ 6 = 1 log c + log v ( l ) if γ = 1 Business Cycles April 7, 2009 6 ± 39
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Technology Production function: y t = k α t ( 1 + g ) t e z t l t ± 1 α z t changes over time. It follows the AR(1) process: z t = ρ z t 1 + σε t , ε t ± N ( 0 , 1 ) with zero unconditional mean. Interpretation of ρ and σ . Let me set g = 0 to simplify algebra. Business Cycles April 7, 2009 7 / 39
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max E t s = 0 β t + s log c t + s ψ l 1 + η t + s 1 + η ! s.t. c t + k t + 1 = k α t ( e z t l t ) 1 α + ( 1 δ ) k t z t = ρ z t 1 + σε t , ε t ± N ( 0 , 1 ) Juan Rubio-Ram±rez (DUKE) Business Cycles April 7, 2009 8 / 39
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max E t s = 0 β t + s log c t + s ψ l 1 + η t + s 1 + η ! + λ t + s c t + s + k t + 1 + s k α t + s ( e z t + s l t + we take decisions over c t , l t , and k t + 1 . Juan Rubio-Ram±rez (DUKE)
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This note was uploaded on 05/13/2010 for the course ECON 110D taught by Professor Schmitt-grohe during the Spring '08 term at Duke.

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Chapter12_Business_Cycles_040709 - Business Cycles Juan...

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