By Gang Gong
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Extra resources for Stochastic Dynamic Macroeconomics: Theory, Numerics, and Empirical Evidence
1) Compute the solution Vh i on i . (2) Evaluate the error estimates ηl . If ηl < tol for all l, stop. (3) Reﬁne all cells Cj with ηj ≥ θ max ηl , set i = i + 1, and go to (1). For more information about this adaptive gridding procedure and a com¨ parison with other adaptive dynamic programming approaches, see Grune ¨ and Semmler (2004a) and Grune (1997). In order to determine equilibria and approximately optimal trajectories, we need an approximately optimal policy, which in our discretization can be obtained in feedback form u∗ (x) for the discrete time approximation, using the following procedure.
2). 1), there might be a problem in accuracy. One possible way to deal with this problem is to start with different initial u0 . In chapter 2, when we turn to a practical problem, we will investigate these issues more thoroughly. 2 The Log-Linear Approximation Method Solving the nonlinear dynamic optimization model with log-linear approximation has been widely used and well documented. It has been proposed in particular by King et al. (1988a, 1988b) and Campbell (1994) in the context of RBC models.
This number might be the same as the number of observations in the sample. We denote this number by T . • Step 3. 3) to compute the solution of the model iteratively T times. This can be regarded as a one-time simulation. • Step 4. If necessary, detrend the simulated series generated in step 3 to remove its time trend. Often the HP-ﬁlter (see Hodrick and Prescott 1980) is used for this detrending. • Step 5. Compute the moment statistics of interest using, if necessary, a detrended series generated in step 4.