So what economics concepts you can apply in analyzing the objective of this policy and in measuring the effectiveness of such subsidies?
The key objective is to reduce the peak-hour crowd which put pressures on the public transport system. So are we saying that travelling before peak hour is a "merit goods" which generate positive externalities? Thus without government's intervention, it will be under consumed. Subsidies will lower the marginal private costs of travel during non peak hours and thus increase consumption so that we can reach the social optimal levels of non peak MRT rides. However, the demand for such ride is price inelastic as commuters are not rushing to take the early rides even it is free! Economics concepts of opportunity cost can help to explain such behaviour. The cost of waking up earlier far exceed the benefits of free rides, thus, commuters choose to "sleep" more!
Another questions we need to consider include that opportunity cost of such subsidies, which could be the project forgone by the government such as building one more school or Elder Care Center.
However, economics theory cannot always fully explain the rationales behind all policies. We still have to take into account of social and political needs as well.