[quote=“jpfeifer”]You have to think more about the intuition of what you are doing. In your present exercise, you assume that agents know in every period there can be a small shift in taxes. But suddenly a large shift happens that, according to the assumed shock volatility should never occur. In principle this is problematic. However, as you are using a first order approximation, variances will not matter for the decision rules due to certainty equivalence (agents act as if expected values of the variables would occur with certainty). Thus, unless you try to estimate the parameters of the tax process, you should be fine. The big problem is specifying this process. VAT increases are usually permanent, so you must use a unit root process, which introduces a whole bunch of econometric issue. Even a small variance can imply that your system moves very far away from the approximation point over time, introducing approximation errors. However, the latter depends on the setup. You might be able to detrend your model accordingly so that this is not an issue.
If you are going for perfect foresight, you can use the varexo_det command to specify the then fully anticipated VAT process.[/quote]
Dear Johannes,
Thank you for a quick answer. What you are saying was exactely my concern, and I was also thinking that certainty eqivalence introduced by first-order approximation would help here since higher moments drop out and the distribution assumptions do not matter. This is also why I did not try to model the tax rate, it is just a white noise process in my model. Thank you, I feel more confortable with what I am doing now.
Regarding the unit root, since I am modeling inflation this change in VAT will show up as an impulse dummy in my setting (of course, the price level would shift permanently). Thus, I don’t think it is a problem. However, that is why I asked how would one introduce a shift dummy variable (a structural break) in the model. There is a short discussion about that here: Structural break in Bayesian estimation and DYNARE syntaxis.
However, I don’t really grasp what Michel is saying there. It seems to me that he is suggesting to model a shift dummy as an AR process, but I don’t see how is how that is even possible. Of course, maybe I am missing something. Do you maybe have any opinion about this?
Thank you once again.