On Mon, 14 Sep 2020, Sven Schreiber wrote:
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
First, Jack, sorry, but as a general statement I actually think this is
wrong. Gretl can estimate these structural equations already, with TSLS
equation-per-equation. Of course that's not the efficient estimator
here, and I guess that's what you had in mind. But still it can be done,
since both equations are linear by themselves.
Of course you're right, you can use single-equation methods as long as all
equations are linear in the coefficients. But then, you have no way, at
present to (a) estimate the coefficients jointly (b) set cross-equation
restrictions (c) solve the model, unless all the variables are linear.
I'd even say you can go a long way with linear behavioral systems in the
sense that some variables only appear in logs (including log-differences
as growth rates) and others only in raw levels (including absolute
differences, e.g. for interest rates). This would be less general than
your example above where x and y appear both in levels as well as in
logs. Then you could estimate it in gretl as a system directly -- OK you
can't do FIML because the non-linear identities linking the logs and the
levels are not allowed. But that's not too bad IMHO.
It depends on your definition of "not too bad"; the large simultaneous
systems I've seen often include nonlinear identities.
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucche...@univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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