maximum likelihood convergence reproducing Anderson Blundell 1982 Econometrica R vs Stata

Z <- princomp(cbind(x1,x2,x3))$scores
Z <- as.data.frame(princomp(cbind(x1,x2,x3))$scores)
names(Z)<- letters[1:3]
optimx(rep(0,8),lnl, hessian=TRUE, y1=y1, y2=y2,

Hi Mike,

Mike said
"is this it, page 1559?"

That is the front page yes, page 15*6*9 has the table, of which the
model labelled 18s is the one I replicated.

"did you actually cut/paste code anywhere and is your first
coefficient -.19 or -.019?
Presumably typos would be one possible problem."

-0.19 is not a typo, it is pi10 in the paper, and a1 in my Stata
estimation - as far as I can tell cutting and pasting is not the
problem.

"generally it helps if we could at least see the equations to check your
code against typos ( note page number ?) in lnl that may fix part of the
mystery.  Is full text available
on author's site, doesn't come up on citeseer AFAICT,"

Unfortunately I do not know of any place to get the full version of
this paper that doesn't require access to a database such as JSTOR.
The fact that this likelihood function reproduces the published
results in Stata makes me confident that it is correct - I also have
read a lot on systems estimation and it is a pretty standard
likelihood function.

"I guess one question would be " what is beta" in lnl supposed to be -
it isn't used anywhere but I will also mentioned I'm not that familiar
with the R code ( I'm trying to work through this to learn R and the
optimizers).

maybe some words would help, is sigma supposed to be 2x2 or 8x8 and what are
e1 and e2 supposed to be?"

The code above is certainly not as elegant as it could be - in this
case the beta is rather superfluous.  It is just a vector to hold
parameters - but since I called all the parameters theta anyway there
is no need for it.  e1 and e2 are the residuals from the first and
second equations of the system.  Sigma is a 2x2 matrix which is the
outer product of the two vectors of residuals.

Kind regards,

Alex



On 9 May 2011 23:12, Mike Marchywka <marchywka at hotmail.com> wrote:

----------------------------------------

Date: Mon, 9 May 2011 22:06:38 +1200
From: alex.olssen at gmail.com
To: pdalgd at gmail.com
CC: r-help at r-project.org; davef at otter-rsch.com
Subject: Re: [R] maximum likelihood convergence reproducing Anderson Blundell 1982 Econometrica R vs Stata

Peter said

"Ahem! You might get us interested in your problem, but not to the
level that we are going to install Stata and Tsp and actually dig out
and study the scientific paper you are talking about. Please cite the
results and explain the differences."

Apologies Peter, will do,

The results which I can emulate in Stata but not (yet) in R are reported below.

did you actually cut/paste code anywhere and is your first coefficient -.19 or -.019?
Presumably typos would be one possible problem.

They come from Econometrica Vol. 50, No. 6 (Nov., 1982), pp. 1569

is this it, page 1559?

http://www.jstor.org/pss/1913396

generally it helps if we could at least see the equations to check your
code against typos ( note page number ?) in lnl that may fix part of the
mystery.  Is full text available
on author's site, doesn't come up on citeseer AFAICT,


http://citeseerx.ist.psu.edu/search?q=blundell+1982&sort=ascdate

I guess one question would be " what is beta" in lnl supposed to be -
it isn't used anywhere but I will also mentioned I'm not that familiar
with the R code ( I'm trying to work through this to learn R and the optimizers).

maybe some words would help, is sigma supposed to be 2x2 or 8x8 and what are
e1 and e2 supposed to be?

TABLE II - model 18s

coef std err
p10 -0.19 0.078
p11 0.220 0.019
p12 -0.148 0.021
p13 -0.072
p20 0.893 0.072
p21 -0.148
p22 0.050 0.035
p23 0.098

The results which I produced in Stata are reported below.
I spent the last hour rewriting the code to reproduce this - since I
am now at home and not at work :(
My results are "identical" to those published. The estimates are for
a 3 equation symmetrical singular system.
I have not bothered to report symmetrical results and have backed out
an extra estimate using adding up constraints.
I have also backed out all standard errors using the delta method.

. ereturn display
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
a |
a1 | -.0188115 .0767759 -0.25 0.806 -.1692895 .1316664
a2 | .8926598 .0704068 12.68 0.000 .7546651 1.030655
a3 | .1261517 .0590193 2.14 0.033 .010476 .2418275
-------------+----------------------------------------------------------------
g |
g11 | .2199442 .0184075 11.95 0.000 .183866 .2560223
g12 | -.1476856 .0211982 -6.97 0.000 -.1892334 -.1061378
g13 | -.0722586 .0145154 -4.98 0.000 -.1007082 -.0438089
g22 | .0496865 .0348052 1.43 0.153 -.0185305 .1179034
g23 | .0979991 .0174397 5.62 0.000 .0638179 .1321803
g33 | -.0257405 .0113869 -2.26 0.024 -.0480584 -.0034226
------------------------------------------------------------------------------

In R I cannot get results like this - I think it is probably to do
with my inability at using the optimisers well.
Any pointers would be appreciated.

Peter said "Are we maximizing over the same parameter space? You say
that the estimates from the paper gives a log-likelihood of 54.04, but
the exact solution clocked in at 76.74, which in my book is rather
larger."

I meant +54.04 > -76.74. It is quite common to get positive
log-likelihoods in these system estimation.

Kind regards,

Alex

On 9 May 2011 19:04, peter dalgaard  wrote:

On May 9, 2011, at 06:07 , Alex Olssen wrote:

Thank you all for your input.

Unfortunately my problem is not yet resolved.  Before I respond to
individual comments I make a clarification:

In Stata, using the same likelihood function as above, I can reproduce
EXACTLY (to 3 decimal places or more, which is exactly considering I
am using different software) the results from model 8 of the paper.

I take this as an indication that I am using the same likelihood
function as the authors, and that it does indeed work.
The reason I am trying to estimate the model in R is because while
Stata reproduces model 8 perfectly it has convergence
difficulties for some of the other models.

Peter Dalgaard,

"Better starting values would help. In this case, almost too good
values are available:

start <- c(coef(lm(y1~x1+x2+x3)), coef(lm(y2~x1+x2+x3)))

which appears to be the _exact_ solution."

Thanks for the suggestion.  Using these starting values produces the
exact estimate that Dave Fournier emailed me.
If these are the exact solution then why did the author publish
different answers which are completely reproducible in
Stata and Tsp?

Ahem! You might get us interested in your problem, but not to the level that we are going to install Stata and Tsp and actually dig out and study the scientific paper you are talking about. Please cite the results and explain the differences.

Are we maximizing over the same parameter space? You say that the estimates from the paper gives a log-likelihood of 54.04, but the exact solution clocked in at 76.74, which in my book is rather larger.

Confused....

-p

Ravi,

Thanks for introducing optimx to me, I am new to R.  I completely
agree that you can get higher log-likelihood values
than what those obtained with optim and the starting values suggested
by Peter.  In fact, in Stata, when I reproduce
the results of model 8 to more than 3 dp I get a log-likelihood of 54.039139.

Furthermore if I estimate model 8 without symmetry imposed on the
system I reproduce the Likelihood Ratio reported
in the paper to 3 decimal places as well, suggesting that the
log-likelihoods I am reporting differ from those in the paper
only due to a constant.

Thanks for your comments,

I am still highly interested in knowing why the results of the
optimisation in R are so different to those in Stata?

I might try making my convergence requirements more stringent.

Kind regards,

Alex

--
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com