There is not an equivalent for charities. The agency problem becomes more severe as the charity moves away from visible, easily measured efforts (distributing clean water to hurricane victims) to more complex endeavors (funding long term research programs). We can also observe more severe problems as charities become bigger and the monitoring is more expensive for the donors. This might account for what I perceive to be a lower rate of misbehavior in local churches compared to larger scale, national ministries. (This could also simply be because we don’t hear about smaller scale misbehavior as it isn’t as newsworthy or caught as often.)
I’ve found my own charitable giving has shifted more toward organizations that I have enough knowledge about to be confident that they are engaged in actually using the resources I donate for the purpose for which they are donated. (I feel particularly good about the Linderman/Russell families’ efforts in Albania and the Universidad Francisco Marroquin in Guatemala, if you are looking for recommendations.) How charities resolve the agency problem is a puzzle that hasn’t been solved yet. But one solution seems to be to foster connections between the people giving the money and those spending it – perhaps we’re less likely to cut corners on both the giving and the spending when we know to whom our money goes and from whom it comes.