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 final framework, after which introduce a chain of examples. humans will be caught on the common framework half. they do not know WHY can we do this.

A greater option to introduce this technique will be to exploit one or thoroughly labored out examples, paying specific recognition to give an explanation for the guidelines in the back of doing what we're doing. this fashion humans will recognize the tips in the back of the strategy, even if now not unavoidably the overall framework (who want to know the overall framework anyway?) Then introduce the overall framework, and extra examples.

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The method above then still permits calculation of an equilibrium which satisfies the nonlinear equilibrium conditions at least locally. In particular, in models involving more than one agent or sector or country, one may find as many unit roots as there are more agents (sectors, countries) than one since shocks may affect the relative wealth (capital) of any two agents (sectors, countries) and thus may result in permanent changes in their consumption paths (or capital stocks): in these cases, the method above allowing for unit roots still gives useful results, which obviously should then be used with some care.

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.

4 provide the desired recursive equilibrium law of motion. 3 Log-linearization and model formulation Log-linearizing the necessary equations characterizing the equilibrium is a well-known technique. In the context of real business cycle models, log-linearization has been proposed in particular by King et al. (1987) and Campbell (1994). 26). Analysing nonlinear dynamic stochastic models 33 appears frequently in text books such as Obstfeld and Rogoff (1996, pp. 503-505). Nonetheless, the technique often seems to create more headaches than it should.

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