Estimation with first or second-order


I am trying to do welfare analysis for different monetary policy rules for a Latin American country, to do this, my plan is to estimate the parameters with data from the country, however, the estimation of parameters with second order approximation is very time consuming (the model that I’m trying to estimate has more than 50 equations).I’ve read some discussions on the forum, but it’s still not clear to me what is the best solution.

Is it (at least partially) correct to estimate the parameters with a first order approximation and then do the welfare analysis with a second order? What is the path that literature or researchers have followed in this regard? Trade accuracy for computational efficiency?

I’ve seen many papers that estimate parameters and then do welfare analyzes without specifying if they do the estimation with a second-order approximation, but my guess is that they rely on a first order approximation. Is there a paper that discusses this trade-off in depth? or in the end, is it left to the discretion of the researcher?

The most common approach is to indeed estimate the model at first order and then do a second order welfare analysis. The only paper I am aware of is the one by An: (628.8 KB)