This paper is organized as follows. In Section 2, we motivate and discuss the sequential testing approach. Section 3 discusses invariance principles of the past and present, and the CUSUM and fluctuation instability detectors. Section 4 contains some illustrative Monte Carlo experiments. A summary and concluding remarks are given in Section 5. Proofs are gathered into the Mathematical Appendix

We present results of a randomized trial testing alternative approaches of mapping student achievement into rewards for teachers. Teachers in 216 schools in western China were assigned to performance pay schemes where teacher performance was assessed by one of three different methods. We find that teachers offered “pay-for-percentile” incentives outperform teachers offered simpler schemes based on class-average achievement or average gains over a school year. Moreover, pay-for-percentile incentives produced broad-based gains across students within classes. That teachers respond to relatively intricate features of incentive schemes highlights the importance of paying close attention to performance pay design.