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

From: peter dalgaard <pdalgd_at_gmail.com>
Date: Sat, 07 May 2011 10:46:14 +0200

On May 6, 2011, at 14:29 , Alex Olssen wrote:

> Dear R-help,
>
> I am trying to reproduce some results presented in a paper by Anderson
> and Blundell in 1982 in Econometrica using R.
> The estimation I want to reproduce concerns maximum likelihood
> estimation of a singular equation system.
> I can estimate the static model successfully in Stata but for the
> dynamic models I have difficulty getting convergence.
> My R program which uses the same likelihood function as in Stata has
> convergence properties even for the static case.
>
> I have copied my R program and the data below. I realise the code
> could be made more elegant - but it is short enough.
>
> Any ideas would be highly appreciated.

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.

Apart from that, it seems that the conjugate gradient methods have difficulties with this likelihood, for some less than obvious reason. Increasing the maxit gets you closer but still not satisfactory.

I would suggest trying out the experimental optimx package. Apparently, some of the algorithms in there are much better at handling this likelihood, notably "nlm" and "nlminb".

>
> ## model 18
> lnl <- function(theta,y1, y2, x1, x2, x3) {
> n <- length(y1)
> beta <- theta[1:8]
> e1 <- y1 - theta[1] - theta[2]*x1 - theta[3]*x2 - theta[4]*x3
> e2 <- y2 - theta[5] - theta[6]*x1 - theta[7]*x2 - theta[8]*x3
> e <- cbind(e1, e2)
> sigma <- t(e)%*%e
> logl <- -1*n/2*(2*(1+log(2*pi)) + log(det(sigma)))
> return(-logl)
> }
> p <- optim(0*c(1:8), lnl, method="BFGS", hessian=TRUE, y1=y1, y2=y2,
> x1=x1, x2=x2, x3=x3)
>
> "year","y1","y2","x1","x2","x3"
> 1929,0.554779,0.266051,9.87415,8.60371,3.75673
> 1930,0.516336,0.297473,9.68621,8.50492,3.80692
> 1931,0.508201,0.324199,9.4701,8.27596,3.80437
> 1932,0.500482,0.33958,9.24692,7.99221,3.76251
> 1933,0.501695,0.276974,9.35356,7.98968,3.69071
> 1934,0.591426,0.287008,9.42084,8.0362,3.63564
> 1935,0.565047,0.244096,9.53972,8.15803,3.59285
> 1936,0.605954,0.239187,9.6914,8.32009,3.56678
> 1937,0.620161,0.218232,9.76817,8.42001,3.57381
> 1938,0.592091,0.243161,9.51295,8.19771,3.6024
> 1939,0.613115,0.217042,9.68047,8.30987,3.58147
> 1940,0.632455,0.215269,9.78417,8.49624,3.57744
> 1941,0.663139,0.184409,10.0606,8.69868,3.6095
> 1942,0.698179,0.164348,10.2892,8.84523,3.66664
> 1943,0.70459,0.146865,10.4731,8.93024,3.65388
> 1944,0.694067,0.161722,10.4465,8.96044,3.62434
> 1945,0.674668,0.197231,10.279,8.82522,3.61489
> 1946,0.635916,0.204232,10.1536,8.77547,3.67562
> 1947,0.642855,0.187224,10.2053,8.77481,3.82632
> 1948,0.641063,0.186566,10.2227,8.83821,3.96038
> 1949,0.646317,0.203646,10.1127,8.82364,4.0447
> 1950,0.645476,0.187497,10.2067,8.84161,4.08128
> 1951,0.63803,0.197361,10.2773,8.9401,4.10951
> 1952,0.634626,0.209992,10.283,9.01603,4.1693
> 1953,0.631144,0.219287,10.3217,9.06317,4.21727
> 1954,0.593088,0.235335,10.2101,9.05664,4.2567
> 1955,0.60736,0.227035,10.272,9.07566,4.29193
> 1956,0.607204,0.246631,10.2743,9.12407,4.32252
> 1957,0.586994,0.256784,10.2396,9.1588,4.37792
> 1958,0.548281,0.271022,10.1248,9.14025,4.42641
> 1959,0.553401,0.261815,10.2012,9.1598,4.4346
> 1960,0.552105,0.275137,10.1846,9.19297,4.43173
> 1961,0.544133,0.280783,10.1479,9.19533,4.44407
> 1962,0.55382,0.281286,10.197,9.21544,4.45074
> 1963,0.549951,0.28303,10.2036,9.22841,4.46403
> 1964,0.547204,0.291287,10.2271,9.23954,4.48447
> 1965,0.55511,0.281313,10.2882,9.26531,4.52057
> 1966,0.558182,0.280151,10.353,9.31675,4.58156
> 1967,0.545735,0.294385,10.3351,9.35382,4.65983
> 1968,0.538964,0.294593,10.3525,9.38361,4.71804
> 1969,0.542764,0.299927,10.3676,9.40725,4.76329
> 1970,0.534595,0.315319,10.2968,9.39139,4.81136
> 1971,0.545591,0.315828,10.2592,9.34121,4.84082
>
> ______________________________________________
> R-help_at_r-project.org mailing list
> 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.

-- 
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

______________________________________________
R-help_at_r-project.org mailing list
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.
Received on Sat 07 May 2011 - 08:48:50 GMT

This quarter's messages: by month, or sorted: [ by date ] [ by thread ] [ by subject ] [ by author ]

All messages

Archive maintained by Robert King, hosted by the discipline of statistics at the University of Newcastle, Australia.
Archive generated by hypermail 2.2.0, at Sat 07 May 2011 - 16:40:06 GMT.

Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help. Please read the posting guide before posting to the list.

list of date sections of archive