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

Sat May 7 17:51:56 CEST 2011

There is something strange in this problem.  I think the log-likelihood is incorrect.  See the results below from "optimx".  You can get much larger log-likelihood values than for the exact solution that Peter provided.

## 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)))  # it looks like there is something wrong here
  return(-logl)
}

data <- read.table("e:/computing/optimx_example.dat", header=TRUE, sep=",")

attach(data)

require(optimx)

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

# the warnings can be safely ignored in the "optimx" calls
p1 <- optimx(start, lnl, hessian=TRUE, y1=y1, y2=y2,
+ x1=x1, x2=x2, x3=x3, control=list(all.methods=TRUE, maxit=1500))

p2 <- optimx(rep(0,8), lnl, hessian=TRUE, y1=y1, y2=y2,
+ x1=x1, x2=x2, x3=x3, control=list(all.methods=TRUE, maxit=1500))

p3 <- optimx(rep(0.5,8), lnl, hessian=TRUE, y1=y1, y2=y2,
+ x1=x1, x2=x2, x3=x3, control=list(all.methods=TRUE, maxit=1500))

Ravi.
________________________________________
From: r-help-bounces at r-project.org [r-help-bounces at r-project.org] On Behalf Of peter dalgaard [pdalgd at gmail.com]
Sent: Saturday, May 07, 2011 4:46 AM
To: Alex Olssen
Cc: r-help at r-project.org
Subject: Re: [R] maximum likelihood convergence reproducing Anderson    Blundell 1982 Econometrica R vs Stata

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
>
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--
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

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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.