Extended path and changes in income

Good afternoon everyone,

I was wondering when I do simulation with the extended path method, do agents see a unanticipated shock on their revenues as a permanent change or transitory change ? If I have a tax shock, the agent will be surprised by that shock at t but he knows that shocks will be 0 in the future. So, does he takes this income shock as permanent ?

In the case of a perfect foresight model with anticipated shocks, the response is straightforward. If I have shocks on that taxation for all periods, he will see these as permanent.

Any hint @sebastien ?

Thank you

First note that, in the perfect foresight case, having the shock on all simulation periods is not enough to make it permanent. You also need to change the terminal condition through the endval block.

In the extended path case, if you specify the shock on all simulation periods, then as you explained it will not be considered permanent, since at every period agents expect that the shock will no longer be there tomorrow.

In order to achieve a permanent shock, you need to do something that is not strictly speaking the extended path method (though technically it is implement with a sequence of perfect foresight simulations, but you need to do it by hand): at some period, the agents learn that the shock is permanent, i.e. they anticipate the shock in all future periods and also in the terminal condition. Note that after they learn this, there can be no further news in the future, so the period at which they learn this is also the last one for which you need to compute a perfect foresight simulation. And if they learn this in the first period, you are back to the pure perfect foresight case.

Hope this helps,

Thank you @sebastien . I think that in my case the shock is perceived as permanent because it changes the terminal condition. So I have a new SS. I’ve followed this (I did not used per se the extended path) for my m. file:

"At every period, compute endogenous variables by running a deterministic simulation with:

  • 􏰀 the previous period as initial condition
  • 􏰀 the steady state as terminal condition
  • 􏰀 a random shock drawn for the current period
  • 􏰀 but no shock in the future"

I did this for all my 17 periods

If the terminal condition corresponds to the new steady state (taking into account the permanent shock), then I think what you are doing is correct. I guess you should also set the shock to all the future periods (and not only for the current period as in “real” extended path).

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Yes, this is exactly what I’ve followed. Thank you!

Good morning,

I have another question concerning this method. Is it a usual output to have different dynamics in both method?

Thank you for the clarification

Why would you get the same answer? Imagine I told you that you would get 1000 dollars every month for the rest of your life. Would you behave the same way today, if I only told you you will get 1000 dollars next month? And then I surprise you the next month again?
The information structure is very different.

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Yes thank you. I analysed after all everything, and all good