What is the statistical program used in the Worldwide Governance Indicators? I am interested in understanding the algorithm/methodology of the WGI  (the most cited and popular corruption/governance) World Bank Methodology. They try to publish as detailed as possible to the public but I struggle to figure out how they manage to solve the maximisation at page 97-99 here Governance Matters VII: Aggregate and Individual Governance Indicators, 1996-2007

Basically, they end up with a maximum-likehood estimation with three unknown parameters and state that it is a standard estimation. I am not an expert in Stata/Mata/Mathlab but honestly I can't see the trivial point. 

Can anyone help and refer me to some statistical packages?
This isn't a matter of statistical packages as much as it is a matter of how to write a program to maximize/minimize a function. You can do this readily in Stata, Matlab, R, Python, etc. No matter what language you use, though, the process is basically the same. You write a function that specifies the functional form your trying to, say, minimize, set the parameters you're optimizing over as the function arguments, then call some built-in minimization routine on that function. Here is a primer for doing this in Stata and here is an introduction for R. Matlab and Python will both be very similar to R, with the primary exception being that you will have to declare the function in a different .m file for Matlab.