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I already know that expanding the grids of state variables around the steady states works, however in my toy model it's hard to get steady states analytically, so I cannot determine the boundary for variables. Is there any other method to set the grid even without steady states?

Barry
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1 Answers1

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In that case, I think you can try to approximate the value of the steady-state $k^*$. If your capital accumulation function is implicitly defined, say $k_{t+1}=\phi(k_{t+1},k_t)$:

  • You can still prove the existence of a steady state by using the Intermediate Value Theorem.
  • To show the convergence of dynamics, maybe it is enough to prove $\phi' > 0, \phi'' < 0$. (see Galor, O., & Ryder, H. E. (1989). Although the theory was developed for the class of OLG model, I think its relevance can still be applied here).

After making sure that you indeed have a steady state, you are entitled to use a numerical solution. I think you can use the fsolve function in Matlab to obtain a numerical approximation of that point, and then it's possible to create a grid as usual.

Please correct me if I'm wrong.

teddi
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