Deriving the low-energy effective action in string theory

Question

Does an explicit derivation of the 10 Dimensional supergravity actions from string theory exist? All the textbooks that I looked at say that the low-energy action can be computed by calculating S-matrix elements in string theory. However, the books then mention the 11D Supergravity (again, without a derivation) and then do a dimensional reduction on a circle to get the IIA supergravity 10D action. I need to work out these details. I find it hard to accept results without a derivation especially if these results are important in what I'm doing (I'm studying string compactifications). Do graduate students in string theory actually derive these actions? Why don't the textbooks derive them? 

Comments

I found a chapter-long treatment of the derivation of the low energy effective action in the textbook "Basic concepts in string theory". It derives it by doing many S-matrix calculations using the polyakov path integral.