handouteppsp06 - Mehra and Prescott's Equity Premium Puzzle...

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Mehra and Prescott’s Equity Premium Puzzle Can the 6% equity premium over riskless debt be explained using a version of the stochastic growth model? Answer: No. A good illustration of a quantitative exercise. 1 Environment Just a growth version of Lucas (1978) Preferences U ( c )= c 1 ψ 1 ψ Technologies (Endowments vary stochastically according to an n -state Markov process in growth rates ): y t +1 = x t +1 y t where x t +1 { λ 1 , ..., λ n } and π ij =Pr[ x t +1 = x j | x t = x i ] 2 Equilibrium Asset Pricing Just as in Lucas: p t = βE " μ y t y t +1 ψ ( y t +1 + p t +1 ) | x t ,y t # (1) ⇐⇒ P ( y,i )= β n X j =1 π ij μ y λ j y ψ [ λ j y + P ( λ j y,j )] Clearly P ( y,x ) is homogeneous of degree one in y :T oseeth i s , P ( γy,i )= β n X j =1 π ij μ 1 λ j ψ [ λ j γy + P ( λ j γy,j )] = γP ( y,i ) Given that P ( y,x ) is homogeneous of degree 1, then conjecture a solution of the form P
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handouteppsp06 - Mehra and Prescott's Equity Premium Puzzle...

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