JFG, thanks for your questions and comments. First, the impact of education on GDP and productivity is not evidence of an externality. The increase in productivity is captured by the individual who was educated. It's only when the education of one person increases the productivity of another person that there is an externality. As I said in the post, there is some evidence of this, but the size of that externality is not bigger than the private benefit.
On your second point about vouchers, this is precisely the situation when we need to regulate these markets. A voucher system is a subsidy to the private sector. When we introduce vouchers, all sorts of private providers crop up (to make use of the subsidy). But there is very little research (much less policy actions) on the market structure and behavior of these providers. Yet, it is this behavior that will determine whether vouchers lead to better learning outcomes for schoolchildren.