handoutrcesp06 - Recursive Competitive Equilibrium Up to...

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Recursive Competitive Equilibrium Up to now, every problem has been formulated as an in f nite sequence prob- lem. Next we will focus on the equivalence of a recursive equilibrium formulation to the in f 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 f nite sequences. Instead of working with in f nite sequences, a recursive formulation de f nes a f nite number of functions (remember, however, that a function is in f nite dimensional). 1 Stochastic Growth Environment Technology shocks: z t follow a f 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 f eren- tiable. 2S e q u e n t i a l C E At the beginning of each period in history z t , households rent capital k t X to f rms, consume c t and invest i t .
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handoutrcesp06 - Recursive Competitive Equilibrium Up to...

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