Re: [R] recommended reading for manual maximum likelihood of a system of equations

From: Arne Henningsen <>
Date: Thu, 24 Mar 2011 12:11:30 +0100

Hi Alex

On 24 March 2011 04:47, Alex Olssen <> wrote:
> I am looking for some recommended reading.
> I want to read up on the estimation systems of linear equations using
> maximum likelihood?

For a comprehensive review of estimating systems of linear equations, see:

   Greene, Econometric Analysis, 6th ed., 2008, chapter 10.

For ML estimation in R, see:

For ML estimations of systems of linear equations, see:

   Greene, Econometric Analysis, 6th ed., 2008, section 13.6.2.

Please note that the iterated SUR estimator should converge to the ML estimator.

> I have a strongly applied bias, I want to be able to do such estimation myself.
> Reading with examples would be great.
> Something which also works through a concentrated maximum likelihood
> estimation would be even better!
> I want to use a likelihood ratio test to compare some nested models of
> linear simultaneous equations.
> I have estimated the systems using   systemfit()   and
> nlsystemfit().  systemfit()   can be used with   lrtest()   which
> automatically obtains the log-likelihood values.
> Unfortunately one of my models requires nonlinear coefficient
> restrictions and   lrtest()   does not seem to be usable with
> nlsystemfit().

Yes. Please note: in contrast to systemfit(), the function nlsystemfit() is still under development; it has convergence problems rather often and only a few methods have been implemented yet.

> I decided it would be a good idea to program the likelihood estimation myself.
> This would solve the problem and would also be a great learning experience.

You are invited to implement the ML estimation in the "systemfit" package. You could join the developer team at R-Forge.

Best wishes from Copenhagen,

Arne Henningsen

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