vob2
commented
3 years ago Good work, Jie! Yes, this make sense.
By expediting project this period a contractor not only benefit by receiving the reward this period faster, but also rewards in all subsequent periods faster. So there is greater incentive to exert effort if there are project has many activities/tasks remaining.
This will hold not just for two activities/tasks, as in the note, but in general. Probably relatively easy to prove using DP recursion.
There is another, more mechanical effect that works in the same direction (even without greater incentive to reduce time on task for earlier tasks). Assume that the reduction on every task is the same, and call this number dT. If there is one task remaining in the project scope when QP is adopted, the total reduction will be dT. If there are 10 tasks remaining when QP is adopted, the total reduction will be 10*dT.
Because we are measuring total reduction in project completion time (or increase), and we do not know the remaining scope, we cannot tell two effects apart, We might be able to see a highly non-linear dependence of reduction on the stage of the project. This will give us clue that the incentive effect is present. But realistically without knowing the remaining scope, it would be hard to attribute to one effect or another.
Regardless of the effect, this is a good motivation for why the remaining scope of the project matters in empirical analysis.
Too bad that the direction of the effect is to reduce completion time and we observe the opposite empirically. Can we come up with a theory that depends on the scope of the project remaining but predicts an increase in the completion time?
I have uploaded some preliminary analysis on the stage-dependent treatment effect. Please review and comment. Thanks!