PerpetualYouth_SL

# PerpetualYouth_SL - Perpetual youth Prof Lutz Hendricks...

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Perpetual youth Prof. Lutz Hendricks August 7, 2009 L. Hendricks () Perpetual youth August 7, 2009 1 / 27

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Perpetual youth The standard growth model is very tractable. But it has an important limitation: all households are identical. For some questions, it is important to have households of di/erent ages : models with life-cycle features: job search, matching, . .. An analytically tractable version of the OLG model is the Blanchard-Yaari model of perpetual youth. L. Hendricks () Perpetual youth August 7, 2009 2 / 27
Demographics At t = 0 , there are L ( 0 ) = 1 identical persons. At each instant, nL ( t ) identical persons are born. Each person dies at each instant with Poisson probabilty ν . The population growth rate is n ν > 0 : L ( t ) = exp ([ n ν ] t ) (1) L. Hendricks () Perpetual youth August 7, 2009 3 / 27

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Poisson Process The Poisson process is the continuous time analog of i.i.d. It is a counting process: it describes the distribution of the number of events occurring during a particular time interval. It is a one-parameter distribution, characterized by the arrival rate ν . The probability of no even over a period of length τ is exp ( ντ ) . At each instant, fraction ν of the population experiences an event. L. Hendricks () Perpetual youth August 7, 2009 4 / 27
Demographics The mass of persons aged t τ is L ( t j τ ) = exp ( ν ( t τ ) + ( n ν ) t ) = Pr ( live beyond t τ ) L ( τ ) Notation: x ( t j τ ) means x at t for those born at τ . L. Hendricks () Perpetual youth August 7, 2009 5 / 27

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Households are indexed by i . Conditional on surviving, households utility at date t is e ρ t ln ( c i ( t )) . The probability of being alive after t "periods" is exp ( ν t ) . Expected utility for date t is e ν t e ρ t ln ( c i ( t )) . Expected lifetime utility is
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## This note was uploaded on 10/29/2009 for the course ECON 720 at UNC.

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PerpetualYouth_SL - Perpetual youth Prof Lutz Hendricks...

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