Hello,

I have a bit of a silly problem in setting up Maximum Likelihood Estimation of Fixed Effects Linear Regression Model via Optimize routine on Mata, with the corresponding (Gaussian) log-likelihood being (in a simplified setting):

L = - NT / 2 * ln(sigma) - (1/sigma)*( y_h - x_h*beta' )'*( y_h - x_h*beta')

Where y_h and x_h are within-transformed variables from individual and time Fixed Effects inclusion and sigma is variance of IID disturbance term. However running estimating the above specification via the following routine on Mata:

mata

// UnConcentrated Log Likelihood Gaussian with Fixed and Time Effects

void spml_1_UN(todo, b, lnf,g,H)
{
external ya, xa, id
paninfo = panelsetup(id,1)
npanels = rows(paninfo)
t = mean(paninfo[,2]-paninfo[,1]:+1)
sigma = b[1]
beta = b[2..cols(xa)+1]
// Fixed Effects Within transformation Operator
i = J(t,1,1)
M0 = I(t) - (1/(t))*i*i'
//End
//Time Effects Within Transformation Operator
T = I(npanels) - (1/npanels)*(J(npanels,1,1)*J(npanels,1,1)')
//End
ya1 = colshape(colshape(ya,t)*M0,1)
xa1 = J(npanels*(t),cols(xa),0)
for (k = 1; k <= cols(xa); k++) {
xa1[,k] = colshape(colshape(xa[,k],t)*M0,1)
}
ya2 = colshape(T*colshape(ya1,t),1)
xa2 = J(npanels*t),cols(xa1),0)
for (k = 1; k <= cols(xa); k++) {
xa2[,k] = colshape(T*colshape(xa1[,k],t),1)
}
lnf = - (npanels*t)/2*ln(sigma) - 1/(2*sigma)*(ya2 - xa2*beta')'*(ya2 - xa2*beta')
}

real function rho1_1_UN(xa){
S = optimize_init( )
optimize_init_evaluator(S, &spml_1_UN())
optimize_init_which(S,"max")
optimize_init_evaluatortype( S, "gf0")
optimize_init_params(S, (J(1,1+cols(xa),0)) )
optimize_init_singularHmethod(S, "hybrid")
optimize_init_conv_maxiter(S, 100)
optimize_init_technique(S, "nr")
//optimize_init_tracelevel(S, "none")
//optimize_init_conv_warning(S, "off")
a = optimize(S)
return(a)
}

end

Unfortunately the above routine consistently gives me the following message : initial values not feasible. Any help would be most welcome. While yes there are closed form estimators for the paramters above, however I would like to successfuly estimate the full unconcentrated log-likelihood.