R gmm package using exactly identified moment conditions - r

Question

For exactly identified moments, GMM results should be the same regardless of initial starting values. This doesn't appear to be the case however.
library(gmm)
data(Finance)
x <- data.frame(rm=Finance[1:500,"rm"], rf=Finance[1:500,"rf"])
# want to solve for coefficients theta[1], theta[2] in exactly identified
# system
g <- function(theta, x)
{
m.1 <- x[,"rm"] - theta[1] - theta[2]*x[,"rf"]
m.z <- (x[,"rm"] - theta[1] - theta[2]*x[,"rf"])*x[,"rf"]
f <- cbind(m.1, m.z)
return(f)
}
# gmm coefficient result should be identical to ols regressing rm on rf
# since two moments are E[u]=0 and E[u*rf]=0
model.lm <- lm(rm ~ rf, data=x)
model.lm
# gmm is consistent with lm given correct starting values
summary(gmm(g, x, t0=model.lm$coefficients))
# problem is that using different starting values leads to different
# coefficients
summary(gmm(g, x, t0=rep(0,2)))
Is there something wrong with my setup?

Answer 1

The gmm package author Pierre Chausse was kind enough to respond to my inquiry.
For linear models, he suggests using the formula approach:
gmm(rm ~ rf, ~rf, data=x)
For non-linear models, he emphasizes that the starting values are indeed critical. In the case of exactly identified models, he suggests setting the fnscale to a small number to force the optim minimizer to converge closer to 0. Also, he thinks the BFGS algorithm works better with GMM.
summary(gmm(g, x, t0=rep(0,2), method = "BFGS", control=list(fnscale=1e-8)))
Both solutions work for this example. Thanks Pierre!