By Ramon Marimon, Andrew Scott
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Additional resources for Computational Methods for the Study of Dynamic Economies
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. These unit roots typically already show up as an undetermined steady state: any of the possible steady states can then serve as a starting point for the dynamic calculation, keeping in mind that a simulation based on the dynamics calculated here will eventually wander away too far to be numerically useful.
An earlier version of this chapter was completed while visiting the Institute for Empirical Macroeconomics at the Federal Reserve Bank of Minneapolis: I am grateful for the Institute's hospitality. Any views expressed here are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. This is an updated version of Discussion Paper 101 at the Institute for Empirical Macroeconomics and of CentER DP 9597. Further work was done while visiting the Institute for International Economic Studies in Stockholm: thanks are due to colleagues there, in particular Paul Klein.
Finally we calculate the steady-state values for both the endogenous and the exogenous state variables and for the control variables, (z, s, d). 3 illustrates this procedure. 2 and compute the steady state of the deterministic version of this economy as a function of parameters (a, p, S, p, cr£2). Solution: To compute the steady state, it is easier to consider the maximization problem, which in this case is the following: such that Substituting the shocks by their unconditional means and dropping the expectations operator, this problem becomes: such that Computing the first-order conditions for this problem and substituting out the Lagrange multipliers, we obtain the following Euler equation: Imposing the steady-state condition, ct = ct+\ = c, this expression becomes: Finally, after solving for k, we obtain the steady state, (z, /c, i), given by: 14 For an example where this transformation is carried out explicitly, see Hansen and Prescott (1995).