GMM non-negativity constraints with --lbfgs option
by Alecos Papadopoulos
gretl 2024b. Windows 10 64-bit.
Is there a way to impose a non-negativity/positivity constraint on the
gmm command for an estimated parameter *when using the --lbfgs option*?
I am trying to estimate variance(scale) parameters of a distribution.
The theoretical moment condition is
qw^2 + qu^2 = (1/n)sum res^2
(sum of squared residuals estimates the population variance, which is
the sum of two separate variances, so we need both qw>0, qu>0).
I wrote one of the two related orthogonality conditions as
series eq2 = (res2 - (sqrt(qw))^4 - (sqrt(qu))^4 ) *(1/obsn)
(obsn = n) .
/Without/ the --lbfgs option, it appears that the positivity constraint
imposed implicitly through the use of the square root, is respected.
But when I include the --lbfgs option in the gmm command, the estimator
does not seem to be bothered with the square root any more; I get for
example (with --lbfgs)
...
Iteration 2: GMM criterion = 1.45609463344 (steplength = 0.0197114)
Parameters: 0.26238 0.26007
Gradients: -0.87662 1.0848 (norm 5.06e-001)
Iteration 3: GMM criterion = 0.911545264969 (steplength = 13)
Parameters: 0.041548 0.51495
Gradients: -0.019980 1.4100 (norm 6.03e-001)
Iteration 4: GMM criterion = NA (steplength = 0.6875)
Parameters: -0.57965 1.3822
Gradients: -0.019980 1.4100 (norm 9.90e-001)
Iteration 5: GMM criterion = NA (steplength = 0.6875)
Parameters: -1.2008 2.2495
Gradients: -0.019980 1.4100 (norm 1.26e+000)
Iteration 6: GMM criterion = NA (steplength = 0.6875)
Parameters: -1.8220 3.1169
Gradients: -0.019980 1.4100 (norm 1.49e+000)
...
--- FINAL VALUES:
GMM criterion = NA (steplength = 0.6875)
Parameters: -51.518 72.501
Gradients: -0.019980 1.4100 (norm 7.19e+000)
I detect that once one parameter becomes negative, the values of the
gradients do not change anymore, which may say something about the inner
workings of the gmm command with --lbfgs
--
A last-minute thought: in gretl's guide (in chapter 37 for numerical
methods) we read
/<< The primary case for using L-BFGS-B, however, is constrained
optimization: this algorithm supports constraints on the parameters in
the form of minima and/or maxima. In gretl this is implemented by the
function BFGScmax (‘c’ for constrained). The syntax is basically similar
to that of BFGSmax, *except that the first argument must followed by
specification of a “bounds” matrix. >>*/
So, maybe, because when lbfgs is used as an option in gmm we do not
specify this "bounds" matrix, this creates the issue?
But regardless, how can it happen that it takes a negative number, puts
it inside a square root, and doesn't at least abort if not move away,
but keeps on trying negative candidates?
--
Alecos Papadopoulos PhD
Affiliate Researcher
Dpt of Economics, Athens University of Economics and Business
Foundation for Economic and Industrial Research (IOBE)
web: alecospapadopoulos.wordpress.com/
ORCID:0000-0003-2441-4550
2 years, 1 month
- 2
- 1
New Dataset Collection Available - Introduction to Modern Time Series Analysis
by Artur T.
Dear gretl users,
I'm pleased to announce that a new collection of datasets is now
available in gretl. These datasets are from the textbook:
Title: Introduction to Modern Time Series Analysis
Authors: Gebhard Kirchgässner, Jürgen Wolters, Uwe Hassler
URL: https://link.springer.com/book/10.1007/978-3-642-33436-8
You can easily access these datasets in two ways:
1. Through the gretl menu:
File -> Open data -> sample file -> Press icon 'Look on server' and
install
2. Using the hansl command:
pkg install hassler.tar.gz
This package is available from the gretl data server at
https://gretl.sourceforge.net/gretl_data.html.
We extend our sincere thanks to Uwe Hassler for providing the raw data,
making this valuable resource available to the gretl community.
Happy analyzing!
Artur
2 years, 1 month
- 1
- 0
next gretl release coming up, translation updates welcome
by Cottrell, Allin
Hello all,
We're planning to release gretl 2024c before long, probably next week.
For anyone who works on a translation of gretl, this would be a good
time to update. Thanks in advance!
Allin
2 years, 1 month
- 1
- 0