[Gretl-users] Re: gretl vs Stata: different WLS estimates for weights=0

IMO, there's another point we should consider here, if you want to compare our results with Stata's, namely computation of the sample size, which may become relevant for the computation of the covariance matrix with small samples. Consider the following example (adapted from Artur's): <hansl> set verbose off open greene12_1.gdt list lx = const income ownrent selfemp set seed 100 # generate a weights series with a few zeros in z = uniform() < 0.1 w = abs(normal()) w0 = z ? 0 : w w1 = z ? 1.0e-9 : w wls w0 expend lx stata_se = $stderr * sqrt(($nobs - $ncoeff)/($T - $ncoeff)) print stata_se wls w1 expend lx foreign language=stata --send-data reg expend income ownrent selfemp [aw=w0] reg expend income ownrent selfemp [aw=w1] end foreign </hansl> The two series w0 and w1 are, for all intents and purposes, identical. Therefore, the estimates of the coefficients are the same. It just makes sense that the standard error should also be the same (like we do). However, Stata skips zeros when computing the effective sample size: the vector stata_se reproduces stata's algorithm. This introduces an inconsistency in stata when using the w1 series. The estimates are the same, but the standard errors are quite different. Of course, the inconsistency vanishes for large sample sizes, but it has to be taken into account when comparing results.