Programs for young children — whether you call them day care or preschool or even third grade — serve two purposes. On the one hand, they are educational settings that are supposed to help foster the kids’ long-term development. On the other hand, they are safe places where parents can put their children so they can go do other things during the day — things like work for a living. In an ideal world, of course, they do both. The best preschool programs have been shown to have significant lifelong benefits for their students, and they’re doubtless a huge help to parents too. But a sobering new analysis by Michael Baker, Jonathan Gruber (yes, that Jonathan Gruber), and Kevin Milligan of Quebec’s effort to expand access to child care on the cheap is a painful reminder that the two issues can come apart.