statistical measures of what individual teachers have contributed to learning of all students in their classrooms. This does not provide information on changes in achievement over time (the performance measure is purely ordinal), but the authors suggest that education authorities can benefit from treating the provision of incentives and the documenting of student progress as separate tasks.

It is not immediately obvious that agents will respond in the same way to a relative target where they know they must do better than a comparator group, but they do not have an anchor of a given target to shoot for. This might be too abstract a goal and greater effort might be obtained by having a very clear goal. The approach described in this paper is also based on a relative notion – aiming for the 67<sup>th</sup> percentile of the quantile regression, but then that relative performance is converted to an absolute value that agents try to achieve. For that reason, the estimated target must be calculated from data that are available at the beginning of the period. The “Pay for Percentile” incentive would not have to use information at the beginning of the period. Since the incentive plan is a competition, only the rules must be fully specified at the beginning of the period. The actual determination of the percentile performance index can be calculated at the end of the period, once the data become available.

While the Pay for Percentile proposal was made for education, it could be useful to explore parallels with incentive plans for decentralized decision making. The actors in education are school districts, schools and individual students. The actors in decentralized decision-making plans are national governments, state and district level governments, but there are obvious parallels with arrangements within the education sector.

# 7.  Conclusions

This paper has considered the problem of selecting a reasonable performance standard and has illustrated how quantile regressions could be used to help generate a target that reflects the different characteristics of individual agents. This approach is a bit more flexible than the approach that was followed with the JTPA program in that it does not assume that the adjustment for the agents’ characteristics would necessarily be the same at different percentiles of the distribution of the performance standard. It is no harder to implement.

It is worth noting that the differences between the empirical and the **CAP** distributions were not all that great. It would, perhaps, be disturbing if they were. One might be inclined to conclude that this ability to take note of an agent’s initial conditions does not add much. However, the value of being able to calculate the **CAP** distributions has both a tactical and a technical value. The ability to take note of initial conditions makes it harder for an agent (a school, district or state, depending on the unit of analysis) to dismiss information on the distribution of performance as being completely irrelevant for them because of some factor which was not taken into account. Whatever observable factor an agent thinks should be taken into account could be taken into account in coming up with the CAP distribution.

The evidence suggests that school performance in Portuguese proficiency improved in 2008 following the introduction of targets into public sector management. However, a thorough analysis of the response to the introduction of the new system lies beyond the scope of this paper, which is focused on the issue of 19