R help - Jul 2017 - Question on Simultaneous Equations & Forecasting

Frances,

I would not advise Gauss-Seidel for non linear models. Can be quite tricky, slow
and diverge.

You can write your model as a non linear system of equations and use one of the
nonlinear solvers.
See the section "Root Finding" in the task view NumericalMathematics
suggesting three packages (BB, nleqslv and ktsolve). These package are certainly
able to handle medium sized models.
(https://cran.r-project.org/web/views/NumericalMathematics.html)

Write a function with the system of equations with each equation written as 

 y[..] <- lefthandside - (righthandside)

You can then include identities naturally.

You would have to make the model dynamic but that shouldn't be too difficult
using vector indexing.

Berend Hasselman
> On 13 Jul 2017, at 10:06, Pfaff, Bernhard Dr. <Bernhard_Pfaff at
fra.invesco.com> wrote:
> 
> Hi Frances,
> 
> I have not touched the system.fit package for quite some time, but to solve
your problem the following two pointers might be helpful:
> 
> 1) Recast your model in the revised form, i.e., include your identity
directly into your reaction functions, if possible.
> 2) For solving your model, you can employ the Gau?-Seidel method (see
https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method).
> This has not only the advantage of generating forecasts, in terms of your
exogenous variables, but you can also compute 'dynamic ex post'
forecasts. This is probably the most powerful testing for dynamic simultaneous
equation systems, given that you provide only your predetermined variables as
starting values and then apply the Gauss-Seidel method (recursively) in-sample.
The progressions of your endogenous variables should then not depart too much
from your observed in-sample endogenous variables, i.e., you are assessing the
stability of your model. Because forecast-errors cumulate over time in a dynamic
ex-post forecast, this is a rather good and stringent model-test.
> 
> Incidentally, when you use simultaneous equation models on a larger scale
(say, between 200-300 equations, like medium-sized macroeconomic models), the
only route to go for, is by estimating your reaction equations separately and
then putting all your pieces - including identities and/or technical equations -
together in a format suitable for applying the Gauss-Seidel method. Hence,
forget about 2SLS or 3SLS and Haavelmo-bias.
> 
> Best wishes,
> Bernhard   
> 
> -----Urspr?ngliche Nachricht-----
> Von: R-help [mailto:r-help-bounces at r-project.org] Im Auftrag von
OseiBonsu, Frances
> Gesendet: Mittwoch, 12. Juli 2017 22:36
> An: r-help at r-project.org
> Betreff: [EXT] [R] Question on Simultaneous Equations & Forecasting
> 
> Hello,
> 
> I have estimated a simultaneous equation model (similar to Klein's
model) in R using the system.fit package.
> 
> I have an identity equation, along with three other equations. Do you know
how to explicitly identify the identity equation in R?
> 
> I am also trying to forecast the dependent variables in the simultaneous
equation model, while incorporating the identity equation in the forecasts. Is
there a way to do this in R?
> 
> The only way that I have been able to forecast the dependent variables has
been by getting the predictions of each variable, converting them to time series
uni-variables, and forecasting each variable individually.
> 
> Any help would be appreciated.
> 
> Best Regards,
> 
> Frances Osei-Bonsu
> Summer Analyst, Research and Strategy
> LaSalle Investment Management
> 333 West Wacker Drive, Suite 2300, Chicago IL 60606 Email frances.oseibonsu
at lasalle.com<mailto:frances.oseibonsu at lasalle.com>
> Tel +1 312 897 4024
> lasalle.com<http://www.lasalle.com/>
> 
> 
> 
> This email is for the use of the intended recipient(s) only. If you have
received this email in error, please notify the sender immediately and then
delete it. If you are not the intended recipient, you must not keep, use,
disclose, copy or distribute this email without the author's prior
permission. We have taken precautions to minimize the risk of transmitting
software viruses, but we advise you to carry out your own virus checks on any
attachment to this message. We cannot accept liability for any loss or damage
caused by software viruses. The information contained in this communication may
be confidential and may be subject to the attorney-client privilege. If you are
the intended recipient and you do not wish to receive similar electronic
messages from us in the future then please respond to the sender to this effect.
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> *****************************************************************
> Confidentiality Note: The information contained in this ...{{dropped:10}}
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

Who was speaking about non-linear models in the first place???
The Klein-Model(s) and pretty much all simultaneous equation models encountered
in macro-econometrics are linear and/or can contain linear approximations to
non-linear relationships, e.g., production functions of the Cobb-Douglas type.

Best,
Bernhard

-----Urspr?ngliche Nachricht-----
Von: Berend Hasselman [mailto:bhh at xs4all.nl] 
Gesendet: Donnerstag, 13. Juli 2017 10:53
An: OseiBonsu, Frances
Cc: Pfaff, Bernhard Dr.; r-help at r-project.org
Betreff: [EXT] Re: [R] Question on Simultaneous Equations & Forecasting

Frances,

I would not advise Gauss-Seidel for non linear models. Can be quite tricky, slow
and diverge.

You can write your model as a non linear system of equations and use one of the
nonlinear solvers.
See the section "Root Finding" in the task view NumericalMathematics
suggesting three packages (BB, nleqslv and ktsolve). These package are certainly
able to handle medium sized models.
(https://cran.r-project.org/web/views/NumericalMathematics.html)

Write a function with the system of equations with each equation written as 

 y[..] <- lefthandside - (righthandside)

You can then include identities naturally.

You would have to make the model dynamic but that shouldn't be too difficult
using vector indexing.

Berend Hasselman
> On 13 Jul 2017, at 10:06, Pfaff, Bernhard Dr. <Bernhard_Pfaff at
fra.invesco.com> wrote:
> 
> Hi Frances,
> 
> I have not touched the system.fit package for quite some time, but to solve
your problem the following two pointers might be helpful:
> 
> 1) Recast your model in the revised form, i.e., include your identity
directly into your reaction functions, if possible.
> 2) For solving your model, you can employ the Gau?-Seidel method (see
https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method).
> This has not only the advantage of generating forecasts, in terms of your
exogenous variables, but you can also compute 'dynamic ex post'
forecasts. This is probably the most powerful testing for dynamic simultaneous
equation systems, given that you provide only your predetermined variables as
starting values and then apply the Gauss-Seidel method (recursively) in-sample.
The progressions of your endogenous variables should then not depart too much
from your observed in-sample endogenous variables, i.e., you are assessing the
stability of your model. Because forecast-errors cumulate over time in a dynamic
ex-post forecast, this is a rather good and stringent model-test.
> 
> Incidentally, when you use simultaneous equation models on a larger scale
(say, between 200-300 equations, like medium-sized macroeconomic models), the
only route to go for, is by estimating your reaction equations separately and
then putting all your pieces - including identities and/or technical equations -
together in a format suitable for applying the Gauss-Seidel method. Hence,
forget about 2SLS or 3SLS and Haavelmo-bias.
> 
> Best wishes,
> Bernhard   
> 
> -----Urspr?ngliche Nachricht-----
> Von: R-help [mailto:r-help-bounces at r-project.org] Im Auftrag von 
> OseiBonsu, Frances
> Gesendet: Mittwoch, 12. Juli 2017 22:36
> An: r-help at r-project.org
> Betreff: [EXT] [R] Question on Simultaneous Equations & Forecasting
> 
> Hello,
> 
> I have estimated a simultaneous equation model (similar to Klein's
model) in R using the system.fit package.
> 
> I have an identity equation, along with three other equations. Do you know
how to explicitly identify the identity equation in R?
> 
> I am also trying to forecast the dependent variables in the simultaneous
equation model, while incorporating the identity equation in the forecasts. Is
there a way to do this in R?
> 
> The only way that I have been able to forecast the dependent variables has
been by getting the predictions of each variable, converting them to time series
uni-variables, and forecasting each variable individually.
> 
> Any help would be appreciated.
> 
> Best Regards,
> 
> Frances Osei-Bonsu
> Summer Analyst, Research and Strategy
> LaSalle Investment Management
> 333 West Wacker Drive, Suite 2300, Chicago IL 60606 Email 
> frances.oseibonsu at lasalle.com<mailto:frances.oseibonsu at
lasalle.com>
> Tel +1 312 897 4024
> lasalle.com<http://www.lasalle.com/>
> 
> 
> 
> This email is for the use of the intended recipient(s) only. If you have
received this email in error, please notify the sender immediately and then
delete it. If you are not the intended recipient, you must not keep, use,
disclose, copy or distribute this email without the author's prior
permission. We have taken precautions to minimize the risk of transmitting
software viruses, but we advise you to carry out your own virus checks on any
attachment to this message. We cannot accept liability for any loss or damage
caused by software viruses. The information contained in this communication may
be confidential and may be subject to the attorney-client privilege. If you are
the intended recipient and you do not wish to receive similar electronic
messages from us in the future then please respond to the sender to this effect.
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> *****************************************************************
> Confidentiality Note: The information contained in this 
> ...{{dropped:10}}
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

> On 13 Jul 2017, at 12:55, Pfaff, Bernhard Dr. <Bernhard_Pfaff at
fra.invesco.com> wrote:
> 
> Who was speaking about non-linear models in the first place???
> The Klein-Model(s) and pretty much all simultaneous equation models
encountered in macro-econometrics are linear
That's really not true. Klein model is linear but Oseibonsu did not say that
explicitly.
"Klein like" can just mean same size or same variables.
> and/or can contain linear approximations to non-linear relationships, e.g.,
production functions of the Cobb-Douglas type.
> 
One can indeed sometimes approximate without too much harm. But not always.

Berend
> Best,
> Bernhard
> 
> -----Urspr?ngliche Nachricht-----
> Von: Berend Hasselman [mailto:bhh at xs4all.nl] 
> Gesendet: Donnerstag, 13. Juli 2017 10:53
> An: OseiBonsu, Frances
> Cc: Pfaff, Bernhard Dr.; r-help at r-project.org
> Betreff: [EXT] Re: [R] Question on Simultaneous Equations & Forecasting
> 
> Frances,
> 
> I would not advise Gauss-Seidel for non linear models. Can be quite tricky,
slow and diverge.
> 
> You can write your model as a non linear system of equations and use one of
the nonlinear solvers.
> See the section "Root Finding" in the task view
NumericalMathematics suggesting three packages (BB, nleqslv and ktsolve). These
package are certainly able to handle medium sized models.
> (https://cran.r-project.org/web/views/NumericalMathematics.html)
> 
> Write a function with the system of equations with each equation written as
> 
> y[..] <- lefthandside - (righthandside)
> 
> You can then include identities naturally.
> 
> You would have to make the model dynamic but that shouldn't be too
difficult using vector indexing.
> 
> Berend Hasselman
> 
>> On 13 Jul 2017, at 10:06, Pfaff, Bernhard Dr. <Bernhard_Pfaff at
fra.invesco.com> wrote:
>> 
>> Hi Frances,
>> 
>> I have not touched the system.fit package for quite some time, but to
solve your problem the following two pointers might be helpful:
>> 
>> 1) Recast your model in the revised form, i.e., include your identity
directly into your reaction functions, if possible.
>> 2) For solving your model, you can employ the Gau?-Seidel method (see
https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method).
>> This has not only the advantage of generating forecasts, in terms of
your exogenous variables, but you can also compute 'dynamic ex post'
forecasts. This is probably the most powerful testing for dynamic simultaneous
equation systems, given that you provide only your predetermined variables as
starting values and then apply the Gauss-Seidel method (recursively) in-sample.
The progressions of your endogenous variables should then not depart too much
from your observed in-sample endogenous variables, i.e., you are assessing the
stability of your model. Because forecast-errors cumulate over time in a dynamic
ex-post forecast, this is a rather good and stringent model-test.
>> 
>> Incidentally, when you use simultaneous equation models on a larger
scale (say, between 200-300 equations, like medium-sized macroeconomic models),
the only route to go for, is by estimating your reaction equations separately
and then putting all your pieces - including identities and/or technical
equations - together in a format suitable for applying the Gauss-Seidel method.
Hence, forget about 2SLS or 3SLS and Haavelmo-bias.
>> 
>> Best wishes,
>> Bernhard   
>> 
>> -----Urspr?ngliche Nachricht-----
>> Von: R-help [mailto:r-help-bounces at r-project.org] Im Auftrag von 
>> OseiBonsu, Frances
>> Gesendet: Mittwoch, 12. Juli 2017 22:36
>> An: r-help at r-project.org
>> Betreff: [EXT] [R] Question on Simultaneous Equations & Forecasting
>> 
>> Hello,
>> 
>> I have estimated a simultaneous equation model (similar to Klein's
model) in R using the system.fit package.
>> 
>> I have an identity equation, along with three other equations. Do you
know how to explicitly identify the identity equation in R?
>> 
>> I am also trying to forecast the dependent variables in the
simultaneous equation model, while incorporating the identity equation in the
forecasts. Is there a way to do this in R?
>> 
>> The only way that I have been able to forecast the dependent variables
has been by getting the predictions of each variable, converting them to time
series uni-variables, and forecasting each variable individually.
>> 
>> Any help would be appreciated.
>> 
>> Best Regards,
>> 
>> Frances Osei-Bonsu
>> Summer Analyst, Research and Strategy
>> LaSalle Investment Management
>> 333 West Wacker Drive, Suite 2300, Chicago IL 60606 Email 
>> frances.oseibonsu at lasalle.com<mailto:frances.oseibonsu at
lasalle.com>
>> Tel +1 312 897 4024
>> lasalle.com<http://www.lasalle.com/>
>> 
>> 
>> 
>> This email is for the use of the intended recipient(s) only. If you
have received this email in error, please notify the sender immediately and then
delete it. If you are not the intended recipient, you must not keep, use,
disclose, copy or distribute this email without the author's prior
permission. We have taken precautions to minimize the risk of transmitting
software viruses, but we advise you to carry out your own virus checks on any
attachment to this message. We cannot accept liability for any loss or damage
caused by software viruses. The information contained in this communication may
be confidential and may be subject to the attorney-client privilege. If you are
the intended recipient and you do not wish to receive similar electronic
messages from us in the future then please respond to the sender to this effect.
>> 
>> 	[[alternative HTML version deleted]]
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide 
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>> *****************************************************************
>> Confidentiality Note: The information contained in this 
>> ...{{dropped:10}}
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide 
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>