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Unformatted text preview: Department of Economics University of California, Berkeley Fall 2005 Economics 202A Suggested Solutions to Midterm 2005 George Akerlof, Marina Halac 1 Sargent model and stochastic processes Consider a simplified version of the Sargent model described by the folllowing equations: y t = γ [ p t- E t- 1 ( p t )] + u t ( Lucas AS curve ) m t = p t ( LM curve ) where u t is of the form: u t = αu t- 1 + t and t is a White Noise term t ∼ WN (0 ,σ 2 ). (a) Characterize the (linear) money supply rules that will minimize the variance of output y t in this economy. (Assume that agents have rational expectations and that the monetary authority does not have any knowledge unavailable to the public.) Answer: Since the Lucas AS supply implies that only unexpected changes in the money supply will affect the variance of output, any monetary rule that is a function of variables known at time t- 1 will minimize the variance of output. That is, the monetary policy that minimizes V ar [ y t ] is that with no random term. Note that if the monetary rule has a random term η t , then: y t = γ [ p t- E t- 1 ( p t )] + u t = γ [ m t- E t- 1 ( m t )] + u t = γη t + u t and thus V ar [ y t ] = V ar [ γη t + u t ] = γ 2 σ 2 η + 2 γcov ( η t ,u t ) + σ 2 u ....
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This note was uploaded on 08/01/2008 for the course ECON 202A taught by Professor Akerlof during the Fall '07 term at University of California, Berkeley.
- Fall '07