[Gretl-devel] Re: Simulate simultaneous equation model

On Mon, 14 Sep 2020, Adam Elderfield wrote: That's what the main difficulty is. At present, we have very good technology for estimating _linear_ simultaneous systems. If we keep within the realm of linearity, simulating from a simultaneous system is trivial if the system is static (just compute the reduced form and you're done) and only slightly more intricate if you have lags (you need to cast the reduced form into a finite-order VAR and use varsimul()). The real problem is that at present we don't have a way for representing, let alone estimating, systems with nonlinearities, eg something like this: y_t = a0 + a1 * x_t + u_t log(x)_t = b0 + b1 * log(y)_t + e_t The only way we have at present to estimate something like that is to write ad-hoc functions for representing the system and then using GMM (for nonlinear IV) or MLE (if you choose FIML/LIML). Then, once you have coefficients for the structural form, simulation entails calculating the endogenous variables for a given realisation of the exogenous variables (and possibly of the structural disturbances, but I digress), which has to be done via iterative methods; IIRC, Gauss-Seidel is the industry standard. Again, this can be written in Hansl, but it's far from trivial. In fact, we have an expert here among the mailing list members, that is Francesca Di Iorio. Francesca, would you like to comment? ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------