Recently I read "WHATEVER IT TAKES TO SAVE THE PLANET? CENTRAL BANKS AND UNCONVENTIONAL GREEN POLICY ".
In an appendix to their working paper, the author mentions that
“Equations (A.50)-(A.62) are functions of yB and pB only. This implies that we can find yb and pB by solving the following system of two equations (A.13 and A.3), using a numerical solver:”.
What I don’t understand about this is that if you use Fsolve and follow the author’s words “find yb and p B by solving the following system of two equations (A.13 and A.3),” We still need to know what the steady state of w,h, etc., is, but, for example, w(A.60) in turn depends on yG,pG,hG, and yG in turn depends on… This is a very long chain, even though it depends on yB and pB in the end. Therefore:
(1) When we actually use matlab and dynare, how should we calculate yB and pB according to the author’s meaning or by other methods?
(2) For environmental DSGE, what general steady-state solution steps do we have for solving steady-state solutions with green sector and brown sector models, or do other articles provide more steady-state solutions?
Thanks!
Finding a steady state always means solving a nonlinear equation system of N unknowns in N equations. What the paper you cite seems to indicate is that some part of this system can be solved independently of the rest. The solutions for these two variables can then be used to solve for the rest.
You could in principle try to solve the whole equation system with a numerical solver but that tends to be very challenging for larger models. Often, you need a clever approach to analytically compute the steady state. That often means you reduce the problem to a small nonlinear system you need to solve numerically. Everything else then follows recursively.
Thank you for your prompt reply.
Yes, you are right, when starting to solve the steady state, the authors list some variables that can be solved independently of the other parts (e.g., Π, r, A, etc.). However, the steady-state values of most of the remaining variables (from A.50 to A.62) are expressed by the authors as analytical expressions for {y,Pb}. So, can I understand that given a reasonable {y, Pb}, the steady state of the entire model can be solved easily, for example {y=1, Pb=1}?If so, do I not need to use Fsolve?But why does the author say “using a numerical solver” （This expression appears on page 48 of the author’s note.）.
Thank you very much!