How to estimate a constant elasticity of substitution for a country in a solow model including human capital and scarce resources For my thesis I was looking for some help due to the facts of my little knowledge of econometrics. I appreciate any help whether its directly dealing with my question or literature advice. 

Basically I would construct the Solow Model with a CES production function including 2 more variables as mentioned human capital and another restricting variable representing a scarce resource such as oil. I would search for Data then for the needed variables and estimate the sigma. 

My question here is the technical part on how to actually estimate that parameter given the data. What kind of methods are there to get an approximate value and what kind of programs would be potentially useful to get the solutions?
macro123,

You might want to have a look at MRW (1992) https://academic.oup.com/qje/article-abstract/107/2/407/1838296/A-Contribution-to-the-Empirics-of-Economic-Growth and the literature on growth regressions in the handbook of economic growth and the handbook of macroeconomics. In addition, Acemoglu's textbook on economic growth will provide you with some useful references as well as a clear and concise introduction to the topic. Although, I believe that you'll also be a little bit disappointed as you'll find that something close to what you wish to do has already been done.