[R] maximum likelihood convergence reproducing Anderson Blundell 1982 Econometrica R vs Stata

[Alex Olssen]

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

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 <pdalgd at gmail.com> 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
>
>