Comparing accuracy of second order approximation and dynamic programming

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Becker, Stephanie ; Grüne, Lars ; Semmler, Willi:
Comparing accuracy of second order approximation and dynamic programming.
Bayreuth , 2007

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Abstract

The accuracy of the solution of dynamic general equilibrium models has become a major issue. Recent papers, substituting second order for first order approximations, have shown to obtain significant differences in accuracy. Second order approximations have had some considerable success in solving for the decision variable of small as well as large scale models. Yet, the issue of accuracy is also relevant for the approximate solution of the value function. In numerous dynamic decision problems welfare needs to be computed through the approximation of the value function. Kim and Kim (2003), for example, find a reversal of welfare ordering by moving from first to second order approximations. Studies of the impact of monetary and fiscal policy on welfare have also to deal with the accuracy of the value function. Employing the base line stochastic growth model this paper compares the accuracy of the second order approximation and dynamic programming solution for both the decision variable as well as the value functions. We find that in a neighborhood of the equilibrium the second order approximation method peforms satisfactory while on larger regions dynamic programming performs better with respect to both.