# 3rd order approximation with varexo_det

Hi all,

I have an application where I have to combine stochastic and deterministic shocks and want to use higher order approximations in a stochastic simulation. It works fine with 2nd but I get an error with the 3rd, and it has to do with the fact that I use varexo_det (I’m sure because if I pass these deterministic exogenous variables as parameters the problem goes away). The question then is, is 3rd order stoch_simul compatible with varexo_det?

No, it is not. It only work up to order=2

Thanks for the prompt response Johannes. Is this a math issue (i.e. theory isn’t there yet) or you just haven’t added the functionality? I am a much better coder than econometrician and it seems that I could program this myself.

More generally, I’m trying to understand whether I should bother with higher order approximations or 1st order is enough. I’m just doing a simple simulation of a standard NK model with a few twists, but I’m not doing any welfare calculations or have asset multiplicity or even capital in the model, so I’m not really bothered with volatility. In short, I don’t think I’m affected by any of the issues that render the certainty equivalence of first-order approximations problematic. My only concern is that I’m feeding a very large shock which in principle should throw me off steady-state - but would higher order approximations help there anyway?

It’s a matter of theory. I don’t think it’s too complicated, but people have not used this and therefore have not yet worked out the math.

If you need higher order depends very much on the degree of nonlinearity. If you have big shocks, using a higher order approximation might theoretically help. But in practice, you often need to resort to pruning to make simulations stable. If I were you, I would compare first and second order to see whether results are seriously affected.

Thanks Johannes; the shocks are indeed big and the results a lot more dramatic with 2nd order (while very reasonable for 1st), even with pruning. Variables do eventually return to steady state, but after an unreasonably long amount of time. I’m hence not sure what to choose, particularly because I’m not concerned with risk or rolatility in this application (which seems to be the major justification of higher order approximations).

It’s hard to give any guidance here. But this sounds like a case where local approximations are not really suitable and you may want to consider a global solution technique.

Hi, if you are not concerned with risk/volatility and interested in expected/non expected shocks it would make sense to consider perfect foresight models (see section 4.12 in the reference manual) instead of stochastic models.

Best,
Stéphane.