Computational Methods for the Study of Dynamic Economies by Ramon Marimon, Andrew Scott

By Ramon Marimon, Andrew Scott

I have to do a little parameterized expectation paintings. I learn bankruptcy 7. it isn't well-written. The authors first introduce the overall framework, after which introduce a chain of examples. humans will be caught on the basic framework half. they do not know WHY can we do this.

A larger approach to introduce this technique will be to take advantage of one or thoroughly labored out examples, paying specific consciousness to give an explanation for the tips at the back of doing what we're doing. this manner humans will be aware of the tips in the back of the strategy, even if now not inevitably the overall framework (who want to know the overall framework anyway?) Then introduce the final framework, and extra examples.

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142). The MATLAB command for computing C° is (null(C'))'. 10 Analysing nonlinear dynamic stochastic models 39 1. 21) is stable if and only if all eigenvalues ofP are less than unity in absolute value. 2. R is given by 3. Given P and R, let V be the matrix where 7/c is the identity matrix of size k x k. 26) where vec(-) denotes columnwise vectorization. 26) with V~l yields the unique solution for Q. 19). 27) are zero. 28) Again, the coefficient matrices on xt-\ and zt need to be zero. 28) and collecting terms in vec(£>) and vec(S) yields the formula for Q and S.

Analysing nonlinear dynamic stochastic models 43 One further generalization step can be made by using the QZ decomposition instead of a (generalized) diagonalization; see, in particular, Sims (1999). In particular, the QZ decomposition can deal with repeated eigenvalues easily, and is thus the preferred method. The next theorem shows how it works, but before stating it, we need an additional piece of notation. For any 2m x 2m matrix X, say, write its partition as where Xij denotes a submatrix of size m x m.

Analysing nonlinear dynamic stochastic models 35 Note that we use the dating convention kt-\ for capital created in period / — 1 and used in production in period t: in general, we shall date all variables with respect to the date at which they are known. This contrasts with the notational practice in parts of the literature, but there obviously is no substantial difference: it is just important to keep this in mind when applying the method. Note that all equations only contain variables dated t, t — 1 or, possibly, expectations as of time t of variables dated t + 1.

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