I am working on a number of non-linear NK models, but up until now I mostly concentrated on producing results based on calibration. I started looking into the alternatives and realised that estimation of non-linear models is an order of magnitude harder than that of the linear ones, because of the incompatibility of the Kalman filter approach.
Now, given that time is a limited resource and developing new (/improving the current) estimation techniques is not the goal of my thesis, but rather to produce some empirical justification for the results that I obtain, herein lies the question. What is the simplest way to estimate a non-linear model (medium scale: around 60 endogenous variables, 25-30 parameters, 7 shocks; solved using 2nd order approximation and the non-linearities come in the form of LINEX adjustment costs - *)? When I say the simplest, I mean the simplest to implement in matlab/dynare given some knowledge on how to estimate linear models in dynare using MH or MCMC type algorithms (if that is of any use…).
Briefly skimming the relevant literature, I come accross Particle Filtered MCMC, Simulated Method of Moments (SMM), Generalised Method of Moments (GMM) and more.
Any recommendations in how to best approach this would be very helpful. Any relevant references are even more helpful. There seems to be a lot of recent work out there, but as things stand - most of it is highly user-unfriendly and requires more than a couple of months investment of time.
P.S. I have already looked into Born/Pfeifer (2014): “Risk Matters: A comment”.
Thank you in advance.*