policy-it - Short notes on a simple global solution method1...

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Short notes on a simple global solution method 1 Consider the following recursive maximization problem: V ( a, e )=max c,a 0 ( u ( c )+ β P e 0 { e 1 ,e 2 } π ( e 0 | e ) V ( a 0 ,e 0 ) ) subject to c e +(1+ r ) a a 0 a 0 ≥− φ The Euler equation (substituting in the budget constraint) is u 0 ( e +(1+ r ) a a 0 ) β X e 0 { e 1 ,e 2 } π ( e 0 | e ) V a ( a 0 ,e 0 ) with equality if a 0 > 0 . TheEnve lopecond it ionis V a ( a, e )= u 0 ( e +(1+ r ) a a 0 )(1 + r ) We are looking for a decision rule a ( a, e ) for savings (given values for r and φ ) . 1. Construct a grid on a = { a 1 ,a 2 ...a n } . Set a 1 = φ. 2. Guess a vector of values ˆ V a for all combinations for a and e on the grid: ˆ V a = n ˆ V a ( a 1 ,e 1 ) , ˆ V a ( a 2 ,e 1 ) , ..., ˆ V a ( a n ,e 1 ) , ˆ V a ( a 1 ,e 2 ) ,..., ˆ V a ( a n ,e 2 ) o (e.g. ˆ V a =1 ) 3. Take the f rst point on the grid ( a 1 ,e 1
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This note was uploaded on 11/10/2011 for the course ECON 601 at Cornell University (Engineering School).

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policy-it - Short notes on a simple global solution method1...

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