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PLM package PGGLS strange behavior

Ruben de Bliek
When using the PLM package (version 1.2-8), I encounter the probem that
calling the FGLS estimator evokes strange behavior, when choosing the
"random" effects model. After calling the PGGLS function to estimate FGLS,
PLM gives me a warning, stating that the "random" model has been replaced
with the "pooling" model. I would, however, really like to estimate the
random model instead. For me, the problem is reproducable using one of the
examples from the PLM Jstatsoft article "Panel Data Econometrics in R: The
plm package" (pp.19-20):

data("EmplUK", package="plm")
zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
summary(zz)

Which for me results in the following warning:

WARNING: Warning: 'random' argument to pggls() has been renamed as 'pooling'

It then proceeds with estimating a pooled model. I've checked if PLM by any
chance does produce the right coefficient estimates, but the numbers do not
add up when compared to the estimates in the article. This problem perists
for any dataset I use. Any thoughts?

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PLM package PGGLS strange behavior

Millo Giovanni
Hello. No "strange behaviour" here, just a warning.

There is a difference between an "error" and a "warning", and between an
argument and a model. In this specific case, the warning is just there
to remind you that, as stated, 'the "random" **argument** has been
renamed to "pooling" ' (emphasis mine).

Both still work, but the former is deprecated. The estimator you get is
the same (a GGLS, or "Parks estimator"), everything works the way it
should and you can trust the numbers that come out, provided the
specification is clear to you and it is what you wanted (which for
instance is not entirely clear from your email).

The model underlying the General Feasible GLS estimator (GGLS) does not
really have "random effects"; therefore, after having initially named
the model without FEs "random" by contrast to the Fixed Effects GLS a la
Kiefer (1980), we later considered the denomination as inappropriate and
changed it to "pooling" which in effect it is: a pooled model with no
proper individual effects but a general error covariance structure. You
can get a better understanding of the specification if you read the
cited reference carefully (or even better, Wooldridge as referenced
therein).

Lastly, it is not clear what you mean by "the right estimates": the
numbers I get by using either 'model="pooling"' or ' model="random"' on
the given example are exactly those in the JSS paper. If on your system
you get anything else, I'll be grateful for a reproducible report, as
asked for in the posting guide.

PS if by chance you are just mistaking "General Feasible GLS" with
"Random Effects by GLS", then you should use 'plm(yourformula, yourdata,
model="random")' instead, and you'll get the standard RE model.

Best wishes,
Giovanni

Giovanni Millo, PhD
Research Dept.,
Assicurazioni Generali SpA
Via Machiavelli 4,
34132 Trieste (Italy)
tel. +39 040 671184
fax  +39 040 671160

--------------- original message ---------------

Message: 18
Date: Thu, 26 Apr 2012 14:07:16 +0200
From: Ruben de Bliek <[hidden email]>
To: [hidden email]
Subject: [R] PLM package PGGLS strange behavior
Message-ID:
       
<CAMjFNLVpiDsSVemYf=[hidden email]>
Content-Type: text/plain

When using the PLM package (version 1.2-8), I encounter the probem that
calling the FGLS estimator evokes strange behavior, when choosing the
"random" effects model. After calling the PGGLS function to estimate
FGLS,
PLM gives me a warning, stating that the "random" model has been
replaced
with the "pooling" model. I would, however, really like to estimate the
random model instead. For me, the problem is reproducable using one of
the
examples from the PLM Jstatsoft article "Panel Data Econometrics in R:
The
plm package" (pp.19-20):

data("EmplUK", package="plm")
zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
summary(zz)

Which for me results in the following warning:

WARNING: Warning: 'random' argument to pggls() has been renamed as
'pooling'

It then proceeds with estimating a pooled model. I've checked if PLM by
any
chance does produce the right coefficient estimates, but the numbers do
not
add up when compared to the estimates in the article. This problem
perists
for any dataset I use. Any thoughts?

------------------ end original message ---------------------

 
Ai sensi del D.Lgs. 196/2003 si precisa che le informazi...{{dropped:12}}

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Re: PLM package PGGLS strange behavior

Ruben de Bliek
Thank you Millo. I was a little confused by the random versus pooling
nomenclature used in PLM, thank you for clearing that up. I still have the
issue of not receiving the proper coefficient estimates for the example in
the paper though. My output is posted below; the estimates are
substantially different from the ones posted on page 20. My R version is
2.14.2.

library(plm)
> data("EmplUK", package="plm")
> zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
Warning message:
'random' argument to pggls() has been renamed as 'pooling'
> summary(zz)
 Random effects model
Call:
pggls(formula = log(emp) ~ log(wage) + log(capital), data = EmplUK,
    model = "random")
Unbalanced Panel: n=140, T=7-9, N=1031
Residuals
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
-1.80700 -0.36550  0.06181  0.03230  0.44280  1.58700
Coefficients
              Estimate Std. Error z-value  Pr(>|z|)
(Intercept)   2.023480   0.158468 12.7690 < 2.2e-16 ***
log(wage)    -0.232329   0.048001 -4.8401 1.298e-06 ***
log(capital)  0.610484   0.017434 35.0174 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 1853.6
Residual Sum of Squares: 402.55
Multiple R-squared: 0.78283
2012/4/27 Millo Giovanni <[hidden email]>

> Hello. No "strange behaviour" here, just a warning.
>
> There is a difference between an "error" and a "warning", and between an
> argument and a model. In this specific case, the warning is just there
> to remind you that, as stated, 'the "random" **argument** has been
> renamed to "pooling" ' (emphasis mine).
>
> Both still work, but the former is deprecated. The estimator you get is
> the same (a GGLS, or "Parks estimator"), everything works the way it
> should and you can trust the numbers that come out, provided the
> specification is clear to you and it is what you wanted (which for
> instance is not entirely clear from your email).
>
> The model underlying the General Feasible GLS estimator (GGLS) does not
> really have "random effects"; therefore, after having initially named
> the model without FEs "random" by contrast to the Fixed Effects GLS a la
> Kiefer (1980), we later considered the denomination as inappropriate and
> changed it to "pooling" which in effect it is: a pooled model with no
> proper individual effects but a general error covariance structure. You
> can get a better understanding of the specification if you read the
> cited reference carefully (or even better, Wooldridge as referenced
> therein).
>
> Lastly, it is not clear what you mean by "the right estimates": the
> numbers I get by using either 'model="pooling"' or ' model="random"' on
> the given example are exactly those in the JSS paper. If on your system
> you get anything else, I'll be grateful for a reproducible report, as
> asked for in the posting guide.
>
> PS if by chance you are just mistaking "General Feasible GLS" with
> "Random Effects by GLS", then you should use 'plm(yourformula, yourdata,
> model="random")' instead, and you'll get the standard RE model.
>
> Best wishes,
> Giovanni
>
> Giovanni Millo, PhD
> Research Dept.,
> Assicurazioni Generali SpA
> Via Machiavelli 4,
> 34132 Trieste (Italy)
> tel. +39 040 671184
> fax  +39 040 671160
>
> --------------- original message ---------------
>
> Message: 18
> Date: Thu, 26 Apr 2012 14:07:16 +0200
> From: Ruben de Bliek <[hidden email]>
> To: [hidden email]
> Subject: [R] PLM package PGGLS strange behavior
> Message-ID:
>
> <CAMjFNLVpiDsSVemYf=[hidden email]>
> Content-Type: text/plain
>
> When using the PLM package (version 1.2-8), I encounter the probem that
> calling the FGLS estimator evokes strange behavior, when choosing the
> "random" effects model. After calling the PGGLS function to estimate
> FGLS,
> PLM gives me a warning, stating that the "random" model has been
> replaced
> with the "pooling" model. I would, however, really like to estimate the
> random model instead. For me, the problem is reproducable using one of
> the
> examples from the PLM Jstatsoft article "Panel Data Econometrics in R:
> The
> plm package" (pp.19-20):
>
> data("EmplUK", package="plm")
> zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
> summary(zz)
>
> Which for me results in the following warning:
>
> WARNING: Warning: 'random' argument to pggls() has been renamed as
> 'pooling'
>
> It then proceeds with estimating a pooled model. I've checked if PLM by
> any
> chance does produce the right coefficient estimates, but the numbers do
> not
> add up when compared to the estimates in the article. This problem
> perists
> for any dataset I use. Any thoughts?
>
> ------------------ end original message ---------------------
>
>
> Ai sensi del D.Lgs. 196/2003 si precisa che le informazioni contenute in
> questo messaggio sono riservate ed a uso esclusivo del destinatario.
> Qualora il messaggio in parola Le fosse pervenuto per errore, La invitiamo
> ad eliminarlo senza copiarlo e a non inoltrarlo a terzi, dandocene
> gentilmente comunicazione. Grazie.
>
> Pursuant to Legislative Decree No. 196/2003, you are hereby informed that
> this message contains confidential information intended only for the use of
> the addressee. If you are not the addressee, and have received this message
> by mistake, please delete it and immediately notify us. You may not copy or
> disseminate this message to anyone. Thank you.
>
        [[alternative HTML version deleted]]


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R: PLM package PGGLS strange behavior

Millo Giovanni
Hello again.
This is really strange: I actually get the right numbers all the time. I tried now and got
 
> data("EmplUK", package="plm")
> zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
Warning message:
'random' argument to pggls() has been renamed as 'pooling'
> summary(zz)
 Random effects model
 
Call:
pggls(formula = log(emp) ~ log(wage) + log(capital), data = EmplUK,
    model = "random")
 
Unbalanced Panel: n=140, T=7-9, N=1031
 
Residuals
      Min.    1st Qu.     Median       Mean    3rd Qu.       Max.
-1.8440000 -0.3908000  0.0388700  0.0005525  0.4153000  1.4920000
 
Coefficients
              Estimate Std. Error z-value Pr(>|z|)    
(Intercept)   1.751448   0.180100  9.7249  < 2e-16 ***
log(wage)    -0.132986   0.054292 -2.4495  0.01431 *  
log(capital)  0.629621   0.018483 34.0648  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 1853.6
Residual Sum of Squares: 386
Multiple R-squared: 0.79176

exactly as expected.
Which is your system? (please post the output of Sys.info) .... although I'd be surprised if this were system dependent!
 
You might also update the package to the last version if it isn't yet, although I can't remember bugs in this function since a very long time.
Thx for feedback
Best,
G.

________________________________

Da: Ruben de Bliek [mailto:[hidden email]]
Inviato: venerdì 27 aprile 2012 16.28
A: Millo Giovanni
Cc: [hidden email]
Oggetto: Re: [R] PLM package PGGLS strange behavior


Thank you Millo. I was a little confused by the random versus pooling nomenclature used in PLM, thank you for clearing that up. I still have the issue of not receiving the proper coefficient estimates for the example in the paper though. My output is posted below; the estimates are substantially different from the ones posted on page 20. My R version is 2.14.2.

library(plm)
> data("EmplUK", package="plm")
> zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
Warning message:
'random' argument to pggls() has been renamed as 'pooling'
> summary(zz)
 Random effects model
Call:
pggls(formula = log(emp) ~ log(wage) + log(capital), data = EmplUK,
    model = "random")
Unbalanced Panel: n=140, T=7-9, N=1031
Residuals
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
-1.80700 -0.36550  0.06181  0.03230  0.44280  1.58700
Coefficients
              Estimate Std. Error z-value  Pr(>|z|)    
(Intercept)   2.023480   0.158468 12.7690 < 2.2e-16 ***
log(wage)    -0.232329   0.048001 -4.8401 1.298e-06 ***
log(capital)  0.610484   0.017434 35.0174 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 1853.6
Residual Sum of Squares: 402.55
Multiple R-squared: 0.78283

2012/4/27 Millo Giovanni <[hidden email]>


        Hello. No "strange behaviour" here, just a warning.
       
        There is a difference between an "error" and a "warning", and between an
        argument and a model. In this specific case, the warning is just there
        to remind you that, as stated, 'the "random" **argument** has been
        renamed to "pooling" ' (emphasis mine).
       
        Both still work, but the former is deprecated. The estimator you get is
        the same (a GGLS, or "Parks estimator"), everything works the way it
        should and you can trust the numbers that come out, provided the
        specification is clear to you and it is what you wanted (which for
        instance is not entirely clear from your email).
       
        The model underlying the General Feasible GLS estimator (GGLS) does not
        really have "random effects"; therefore, after having initially named
        the model without FEs "random" by contrast to the Fixed Effects GLS a la
        Kiefer (1980), we later considered the denomination as inappropriate and
        changed it to "pooling" which in effect it is: a pooled model with no
        proper individual effects but a general error covariance structure. You
        can get a better understanding of the specification if you read the
        cited reference carefully (or even better, Wooldridge as referenced
        therein).
       
        Lastly, it is not clear what you mean by "the right estimates": the
        numbers I get by using either 'model="pooling"' or ' model="random"' on
        the given example are exactly those in the JSS paper. If on your system
        you get anything else, I'll be grateful for a reproducible report, as
        asked for in the posting guide.
       
        PS if by chance you are just mistaking "General Feasible GLS" with
        "Random Effects by GLS", then you should use 'plm(yourformula, yourdata,
        model="random")' instead, and you'll get the standard RE model.
       
        Best wishes,
        Giovanni
       
        Giovanni Millo, PhD
        Research Dept.,
        Assicurazioni Generali SpA
        Via Machiavelli 4,
        34132 Trieste (Italy)
        tel. +39 040 671184 <tel:%2B39%20040%20671184>
        fax  +39 040 671160 <tel:%2B39%20040%20671160>
       
        --------------- original message ---------------
       
        Message: 18
        Date: Thu, 26 Apr 2012 14:07:16 +0200
        From: Ruben de Bliek <[hidden email]>
        To: [hidden email]
        Subject: [R] PLM package PGGLS strange behavior
        Message-ID:
       
        <CAMjFNLVpiDsSVemYf=[hidden email]>
        Content-Type: text/plain
       
        When using the PLM package (version 1.2-8), I encounter the probem that
        calling the FGLS estimator evokes strange behavior, when choosing the
        "random" effects model. After calling the PGGLS function to estimate
        FGLS,
        PLM gives me a warning, stating that the "random" model has been
        replaced
        with the "pooling" model. I would, however, really like to estimate the
        random model instead. For me, the problem is reproducable using one of
        the
        examples from the PLM Jstatsoft article "Panel Data Econometrics in R:
        The
        plm package" (pp.19-20):
       
        data("EmplUK", package="plm")
        zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
        summary(zz)
       
        Which for me results in the following warning:
       
        WARNING: Warning: 'random' argument to pggls() has been renamed as
        'pooling'
       
        It then proceeds with estimating a pooled model. I've checked if PLM by
        any
        chance does produce the right coefficient estimates, but the numbers do
        not
        add up when compared to the estimates in the article. This problem
        perists
        for any dataset I use. Any thoughts?
       
        ------------------ end original message ---------------------
       
         
        Ai sensi del D.Lgs. 196/2003 si precisa che le informazioni contenute in questo messaggio sono riservate ed a uso esclusivo del destinatario. Qualora il messaggio in parola Le fosse pervenuto per errore, La invitiamo ad eliminarlo senza copiarlo e a non inoltrarlo a terzi, dandocene gentilmente comunicazione. Grazie.
       
        Pursuant to Legislative Decree No. 196/2003, you are hereby informed that this message contains confidential information intended only for the use of the addressee. If you are not the addressee, and have received this message by mistake, please delete it and immediately notify us. You may not copy or disseminate this message to anyone. Thank you.
       



        [[alternative HTML version deleted]]


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Re: PLM package PGGLS strange behavior

Ruben de Bliek
Hi. I can confirm my version of R to be of number 2.14.2, PLM 1.2-8. My
system:

X86 Pentium dualc. t2390 32bit, 3gb internal memory. Windows 7 build 7601,
Service Pack 1. This machine has actually just received a clean Windows 7
install. The estimated estimates do not match the correct ones.
Furthermore, I can confirm the coefficient estimates are also off using R
at my office, which also has R 2.14.2 alongside PLM 1.2-8 installed. This
is a similar machine to the one above, the only difference being the cpu
(amd).

Update: I have just downloaded and installed the latest version of R, 2.15,
on the above machine, just to see if that would fix the problem. The
wrongly estimated coefficients remain, unfortunately. I've also checked
some other examples from the JSS paper. It would appear, that the examples
using a different dataset than the EmplUK data, such as the Grunfeld
dataset, are all correctly estimated on my machine. However, I can also
reproduce the GMM results on page 18,  using the EmplUK data. The FGLS
estimator example is the only one that is not consistent with the paper,
for me. It would appear that the total sum of squares is correct, but the
residual is not.
2012/4/27 Millo Giovanni <[hidden email]>

> **
> Hello again.
> This is really strange: I actually get the right numbers all the time. I
> tried now and got
>
> > data("EmplUK", package="plm")
> > zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
> Warning message:
> 'random' argument to pggls() has been renamed as 'pooling'
> > summary(zz)
>  Random effects model
>
> Call:
> pggls(formula = log(emp) ~ log(wage) + log(capital), data = EmplUK,
>     model = "random")
>
> Unbalanced Panel: n=140, T=7-9, N=1031
>
>  Residuals
>       Min.    1st Qu.     Median       Mean    3rd Qu.       Max.
> -1.8440000 -0.3908000  0.0388700  0.0005525  0.4153000  1.4920000
>
>  Coefficients
>               Estimate Std. Error z-value Pr(>|z|)
> (Intercept)   1.751448   0.180100  9.7249  < 2e-16 ***
> log(wage)    -0.132986   0.054292 -2.4495  0.01431 *
> log(capital)  0.629621   0.018483 34.0648  < 2e-16 ***
>
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> Total Sum of Squares: 1853.6
> Residual Sum of Squares: 386
> Multiple R-squared: 0.79176
> exactly as expected.
> Which is your system? (please post the output of Sys.info) .... although
> I'd be surprised if this were system dependent!
>
> You might also update the package to the last version if it isn't yet,
> although I can't remember bugs in this function since a very long time.
> Thx for feedback
> Best,
> G.
>  ------------------------------
> *Da:* Ruben de Bliek [mailto:[hidden email]]
> *Inviato:* venerdì 27 aprile 2012 16.28
> *A:* Millo Giovanni
> *Cc:* [hidden email]
> *Oggetto:* Re: [R] PLM package PGGLS strange behavior
>
>   Thank you Millo. I was a little confused by the random versus pooling
> nomenclature used in PLM, thank you for clearing that up. I still have the
> issue of not receiving the proper coefficient estimates for the example in
> the paper though. My output is posted below; the estimates are
> substantially different from the ones posted on page 20. My R version is
> 2.14.2.
>
> library(plm)
> > data("EmplUK", package="plm")
> > zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
> Warning message:
> 'random' argument to pggls() has been renamed as 'pooling'
> > summary(zz)
>  Random effects model
> Call:
> pggls(formula = log(emp) ~ log(wage) + log(capital), data = EmplUK,
>     model = "random")
> Unbalanced Panel: n=140, T=7-9, N=1031
> Residuals
>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
> -1.80700 -0.36550  0.06181  0.03230  0.44280  1.58700
> Coefficients
>               Estimate Std. Error z-value  Pr(>|z|)
> (Intercept)   2.023480   0.158468 12.7690 < 2.2e-16 ***
> log(wage)    -0.232329   0.048001 -4.8401 1.298e-06 ***
> log(capital)  0.610484   0.017434 35.0174 < 2.2e-16 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> Total Sum of Squares: 1853.6
> Residual Sum of Squares: 402.55
> Multiple R-squared: 0.78283
> 2012/4/27 Millo Giovanni <[hidden email]>
>
>> Hello. No "strange behaviour" here, just a warning.
>>
>> There is a difference between an "error" and a "warning", and between an
>> argument and a model. In this specific case, the warning is just there
>> to remind you that, as stated, 'the "random" **argument** has been
>> renamed to "pooling" ' (emphasis mine).
>>
>> Both still work, but the former is deprecated. The estimator you get is
>> the same (a GGLS, or "Parks estimator"), everything works the way it
>> should and you can trust the numbers that come out, provided the
>> specification is clear to you and it is what you wanted (which for
>> instance is not entirely clear from your email).
>>
>> The model underlying the General Feasible GLS estimator (GGLS) does not
>> really have "random effects"; therefore, after having initially named
>> the model without FEs "random" by contrast to the Fixed Effects GLS a la
>> Kiefer (1980), we later considered the denomination as inappropriate and
>> changed it to "pooling" which in effect it is: a pooled model with no
>> proper individual effects but a general error covariance structure. You
>> can get a better understanding of the specification if you read the
>> cited reference carefully (or even better, Wooldridge as referenced
>> therein).
>>
>> Lastly, it is not clear what you mean by "the right estimates": the
>> numbers I get by using either 'model="pooling"' or ' model="random"' on
>> the given example are exactly those in the JSS paper. If on your system
>> you get anything else, I'll be grateful for a reproducible report, as
>> asked for in the posting guide.
>>
>> PS if by chance you are just mistaking "General Feasible GLS" with
>> "Random Effects by GLS", then you should use 'plm(yourformula, yourdata,
>> model="random")' instead, and you'll get the standard RE model.
>>
>> Best wishes,
>> Giovanni
>>
>> Giovanni Millo, PhD
>> Research Dept.,
>> Assicurazioni Generali SpA
>> Via Machiavelli 4,
>> 34132 Trieste (Italy)
>> tel. +39 040 671184
>> fax  +39 040 671160
>>
>> --------------- original message ---------------
>>
>> Message: 18
>> Date: Thu, 26 Apr 2012 14:07:16 +0200
>> From: Ruben de Bliek <[hidden email]>
>> To: [hidden email]
>> Subject: [R] PLM package PGGLS strange behavior
>> Message-ID:
>>
>> <CAMjFNLVpiDsSVemYf=[hidden email]>
>> Content-Type: text/plain
>>
>> When using the PLM package (version 1.2-8), I encounter the probem that
>> calling the FGLS estimator evokes strange behavior, when choosing the
>> "random" effects model. After calling the PGGLS function to estimate
>> FGLS,
>> PLM gives me a warning, stating that the "random" model has been
>> replaced
>> with the "pooling" model. I would, however, really like to estimate the
>> random model instead. For me, the problem is reproducable using one of
>> the
>> examples from the PLM Jstatsoft article "Panel Data Econometrics in R:
>> The
>> plm package" (pp.19-20):
>>
>> data("EmplUK", package="plm")
>> zz <- pggls(log(emp)~log(wage)+log(capital),data=EmplUK, model="random")
>> summary(zz)
>>
>> Which for me results in the following warning:
>>
>> WARNING: Warning: 'random' argument to pggls() has been renamed as
>> 'pooling'
>>
>> It then proceeds with estimating a pooled model. I've checked if PLM by
>> any
>> chance does produce the right coefficient estimates, but the numbers do
>> not
>> add up when compared to the estimates in the article. This problem
>> perists
>> for any dataset I use. Any thoughts?
>>
>> ------------------ end original message ---------------------
>>
>>
>> Ai sensi del D.Lgs. 196/2003 si precisa che le informazioni contenute in
>> questo messaggio sono riservate ed a uso esclusivo del destinatario.
>> Qualora il messaggio in parola Le fosse pervenuto per errore, La invitiamo
>> ad eliminarlo senza copiarlo e a non inoltrarlo a terzi, dandocene
>> gentilmente comunicazione. Grazie.
>>
>> Pursuant to Legislative Decree No. 196/2003, you are hereby informed that
>> this message contains confidential information intended only for the use of
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>> by mistake, please delete it and immediately notify us. You may not copy or
>> disseminate this message to anyone. Thank you.
>>
>
>
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