handoutrcesp06 - Recursive Competitive Equilibrium Up to...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Recursive Competitive Equilibrium Up to now, every problem has been formulated as an in fi nite sequence prob- lem. Next we will focus on the equivalence of a recursive equilibrium formulation to the in fi nite sequence competitive equilibrium and characterize properties of the recursive equilibrium. Mehra and Prescott (1980, Econometrica) did this. The sequence problem is primitive, but it involves in fi nite sequences. Instead of working with in fi nite sequences, a recursive formulation de fi nes a fi nite number of functions (remember, however, that a function is in fi nite dimensional). 1 Stochastic Growth Environment Technology shocks: z t follow a fi nite state Markov Process π ( z t +1 ) = π ( z t +1 = z 0 | z t ) = π ( z t +1 = z 0 | z t = z ) π ( z t = z | z t 1 = b z ) · ·· The process { z t } is assumed to be stationary with bounded ergodic set Z , i.e., if z t Z then z t +1 Z with probability one. The transition probabilities π : Z × Z [0 , 1] . Productive Technology: Y t = z t F ( K t ) where F is CRS. Investment Technology: K t +1 = (1 δ ) K t + I t where K 0 is given and K t X R + where X is assumed to be closed and convex. Unit measure of ex-ante identical agents with preferences: P t =0 P z t β t π ( z t ) u ( c t ) where u is continuous, strictly increasing, strictly concave, and di ff eren- tiable. 2 Sequential CE At the beginning of each period in history z t , households rent capital k t X to fi rms, consume c t and invest i t .
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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