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

[peter dalgaard]

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