By Ramon Marimon, Andrew Scott
I have to perform a little parameterized expectation paintings. I learn bankruptcy 7. it's not well-written. The authors first introduce the final framework, after which introduce a sequence of examples. humans will be caught on the normal framework half. they do not know WHY will we do this.
A larger option to introduce this system will be to exploit one or thoroughly labored out examples, paying specific recognition to give an explanation for the tips at the back of doing what we're doing. this manner humans will be aware of the guidelines at the back of the tactic, even if no longer inevitably the overall framework (who want to know the final framework anyway?) Then introduce the overall framework, and extra examples.
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Extra info for Computational Methods for the Study of Dynamic Economies
The next section skips directly to step 3 of the procedure outlined above and describes how to log-linearize nonlinear equations without explicit differentiation. 1 studies Hansen's (1985) benchmark real business cycle model as a prototype example, in which calculation of the Euler equations, the steady state and the log-linearization is carried out to see how this method works. 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.
Replace a variable Xt with Xt — Xex', where xt is a real number close to zero. Likewise, let yt be a real number close to zero. Take logarithms, where both sides of an equation only involve products, or use the following three building blocks, where a is some constant: up to a constant For example, these building blocks yield up to a constant up to a constant Constants drop out of each equation in the end, since they satisfy steady-state relationships, but they are important in intermediate steps: compare, for example, the two equations above.
22) Note that henceforth we no longer need to consider any constraints because we have substituted them into the utility function. 23) where matrix [Q + /3BTPnB]is a square, symmetric and negative semi-definite matrix arid, therefore, the expression inside the braces is indeed quadratic in z, s and d. 279 19 Note that to perform this transformation the constraints s' = A(z,s,d) andz' = L(z) must be linear in ( z , s , d ) . 23) is quadratic in (z, s,d) the first-order conditions are linear in (z, s).