By Ramon Marimon, Andrew Scott
I must perform 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 sequence of examples. humans will be caught on the basic framework half. they do not know WHY will we do this.
A higher strategy to introduce this system will be to take advantage of one or thoroughly labored out examples, paying specific realization to give an explanation for the guidelines in the back of doing what we're doing. this manner humans will understand the information in the back of the strategy, although no longer unavoidably the overall framework (who want to know the final framework anyway?) Then introduce the final framework, and extra examples.
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Additional info for Computational Methods for the Study of Dynamic Economies
Note, for example, that for any given A and any three real numbers a,b,c satisfying a1 + be = k2, all matrices 19 Another approach to select a unique solution is given in McCallum (1983), who suggests using those roots that can be obtained continuously from the zero roots of the equation * />2 — TP — a 6) for a = 0, as a changes from 0 to 1. However, not only is following these roots as functions of a computationally very demanding, it is also the case that uniqueness is lost once two or more such paths cross each other.
Let C+ be the pseudo-inverse^1 ofC. Let C be an (I — n) x / matrix whose rows form a basis for the null space12 ofC'. 3. The case / < n can be treated as well: the easiest approach is simply to "redeclare" some other endogenous variables to be state variables instead - that is, to raise m and thus lower n - until I = n. "Thepseudo-inverseofthematrixCisthenx/matrixC+satisfyingC + CC + = C+andCC+C = C. Since it is assumed that rank(C) > n, one obtains C+ = (C'C)~1C'\ see Strang (1980, p. 138). The MATLAB command to compute the pseudo-inverse is pinv(C).
18 Note that the certainty equivalence principle only holds when the objective function is quadratic and the constraints are linear. It does not characterize stochastic control problems in general. 21) into a quadratic form in [1 WT]. 21). Specifically, we have to find a rectangular matrix B of dimension (1 + nz +ns) x (1 +nz+ns +«) that satisfies F' — B[l WT]T. 2. 22) Note that henceforth we no longer need to consider any constraints because we have substituted them into the utility function.