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

From: Alex Olssen <alex.olssen_at_gmail.com>
Date: Sat, 07 May 2011 00:29:42 +1200

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.

## 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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