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

[Alex Olssen]

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?

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