How to assess whether the approximation method does well?


I was wondering if there is some way to know whether relying on low-order perturbation method provides a good enough approximation of the actual optimal decision rule in some specific model ?

How can we see which one of first-order, second-order or third order approximation is more appropriate for solving a specific model and whether it is appropriate at all ?

I had a look at the residuals in my model’s equations when simulating the model over a large number of periods, but I don’t know what is considered as a high residual or not.

Is there some better way to assess this ?

Thanks a lot !

Usually, one goes for Euler errors that have a somewhat better interpretation. See e.g.