{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter12_Business_Cycles_040509

Chapter12_Business_Cycles_040509 - Business Cycles Juan...

Info icon This preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Business Cycles Juan Rubio-Ram°rez Duke University and Federal Reserve Bank of Atlanta April 5, 2009 Juan Rubio-Ram°rez (DUKE) Business Cycles April 5, 2009 1 / 38
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Business Cycle U.S. economy ±uctuates over time. 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 5, 2009 2 / 38
Image of page 2
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). Juan Rubio-Ram°rez (DUKE) Business Cycles April 5, 2009 3 / 38
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Observation Technology does not grow smoothly but randomly. We can see it in Solow²s residual. 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 5, 2009 4 / 38
Image of page 4
Intuition Let us think about Robinson Crusoe²s Economy. 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-Ram°rez (DUKE) Business Cycles April 5, 2009 5 / 38
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 Juan Rubio-Ram°rez (DUKE) Business Cycles April 5, 2009 6 / 38
Image of page 6
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. Juan Rubio-Ram°rez (DUKE) Business Cycles April 5, 2009 7 / 38
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Social Planner²s Problem max E 0 t = 0 β t log c t ° ψ l 1 + η t 1 + η ! s.t. c t + k t + 1 = y t + ( 1 ° δ ) k t y t = k α t ( e z t l t ) 1 ° α z t = ρ z t ° 1 + σε t , ε t ± N ( 0 , 1 ) Juan Rubio-Ram°rez (DUKE) Business Cycles April 5, 2009 8 / 38
Image of page 8
Equilibrium Conditions 1 c t ° ψ l 1 + η t 1 + η = β E t 1 c t + 1 ° ψ l 1 + η t + 1 1 + η ² 1 + α y t + 1 k t + 1 ° δ ³ ψ l η t = ( 1 ° α ) y t l t c t + k t + 1 = y t + ( 1 ° δ ) k t y t = k α t ( e z t l t ) 1 ° α z t = ρ z t ° 1 + σε t , ε t ± N ( 0 , 1 ) Juan Rubio-Ram°rez (DUKE) Business Cycles April 5, 2009 9 / 38
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Working with Equilibrium Conditions From second condition ψ l η t = ( 1 ° α ) y t l t ) ψ l 1 + η t 1 + η = 1 ° α 1 + η y t = 1 ° α 1 + η k α t ( e z t l t ) 1 ° α which gives us labor as a function of k t and z t .
Image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern