Rob, thanks for your probing questions and comments. On the Blattman et al. study, the training and facilitation in getting together was given to all groups, but only a random sample of these groups were given the money. In other words, the control group also received training, so it was the cash and not the training that explained the difference between the treatment group and the control group. [They note that having to prepare a proposal may have served as a commitment device]. Furthermore, having received the money, the treatment group spent only a small part of the grant on further skills training, and most of it in tools and materials.
On your question about supply-side responses to demand-strengthening programs, there is now quite a bit of evidence on the effects of school vouchers in poor areas. In places as diverse as the slums of Bogota, Colombia (Angrist et al., American Economic Review, 2002) and rural Bangladesh (the Female Secondary School Assistance Program), these have been shown to increase the quantity and quality of education. Perhaps the most compelling evidence is the proliferation of low-cost private schools in many developing countries (India, Pakistan, South Africa, etc.). If the private sector responds without there being cash transfers, think how much more it will respond with such transfers. I am not too optimistic about "combining [cash transfers] with supply-side strengthening programs," however. The reason we are advocating cash transfers is that the government's supply interventions are not working (witness teacher absenteeism, lack of materials, etc.) Indeed, this is why low-cost private schools are cropping up. If the government was failing to provide these services to begin with, why do we think a program to strengthen them will now succeed?
Best regards, Shanta