Dynamic General Equilibrium Modelling: Computational Methods by Professor Burkhard Heer, Professor Alfred Maußner (auth.)

By Professor Burkhard Heer, Professor Alfred Maußner (auth.)

Modern enterprise cycle concept and development concept makes use of stochastic dynamic common equilibrium types. Many mathematical instruments are had to remedy those types. The ebook offers a variety of tools for computing the dynamics of basic equilibrium versions. partly I, the representative-agent stochastic progress version is solved with assistance from worth functionality generation, linear and linear quadratic approximation tools, parameterised expectancies and projection tools. so that it will practice those equipment, basics from numerical research are reviewed intimately. half II discusses equipment for fixing heterogeneous-agent economies. In such economies, the distribution of the person nation variables is endogenous. This a part of the e-book additionally serves as an advent to the trendy conception of distribution economics. purposes contain the dynamics of the source of revenue distribution over the enterprise cycle or the overlapping-generations version. via an accompanying domestic web page to this ebook, machine codes to all purposes could be downloaded.

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Note, however, that due to the discretization the stationary 15 See our discussion on page 12. 24 Chapter 1: Basic Models and Elementary Algorithms solution of the original problem can differ from the stationary solution of the approximate problem. Therefore, we must choose a state space [K, K] that includes [K0 , K ∗ ] (or [K ∗ , K0 ]). Once the policy function has been found, we can confirm our choice. If the optimal policy hits either the upper or the lower bound of the grid, the selected state space is too small.

L=1 For given zj the policy function is still monotonically increasing in K and the value function is still strictly concave in K, if the oneperiod utility function u and the production function f are strictly increasing and strictly concave. Thus, when we solve the maxi∗ mization problem for Ki we need only consider indices k ≥ ki−1 ∗ from the set {1, 2, . . n}, where ki−1 is the solution found for Ki−1 . 28). 2 to the stochastic case, we must include an additional loop over the indices j ∈ {1, 2, .

As soon as the problem becomes more complex, however, the computational time becomes a binding constraint. Of course, this will be the case as soon as the number of the continuous state variables increases. Therefore, the value function iteration approach introduced above may not be very satisfactory for many purposes. However, we may be able to get a much more accurate solution, if we allow the next-period state variable to be points off the grid. How do we accomplish this? 19) with respect to K .

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