Manipulation of information and/or behavior near salient points

A key assumption for the regression discontinuity model is that those just above and just below the threshold are otherwise almost identical (on average). That assumption won't hold if people know their potential score and then can work to change it. For the regression discontinuity analysis, sometimes all you need is an initial score, prior to any manipulation. More interestingly, the distribution of scores near the cutoff tells us about the presence of manipulation. As such, non-random heaping can provide fertile ground for studying when and how people manipulate information and behavior in response to the incentives provided at the threshold.

Examples include:

• Earnings just barely beating benchmarks. Three salient benchmarks are, positive profits (not a loss), last year’s earnings, and analyst's earnings expectations (Zeckhauser and others)
• Do incumbents win close votes? (Jason Snyder)
• Do lots of cars just barely pass their state's air pollution standard (Jason Snyder and others)
• Do lots of poor people barely qualify for welfare? (Emily Conover & Adriana Camacho “Manipulation of Social Program Eligibility" 2008)
• Do lots of students just barely pass a high-stakes exam?
• Are lots of employers just below the size threshold or emissions threshold that triggers stricter regulation?
• Do husbands report earnings just greater than their wives more often than wives report?
• What else?

A general approach is to study all potential regression discontinuity designs and see if the key assumption is met or if there is heaping on one side of the cutoff. If such heaping exists, an interesting question is whether it is due to information distortion or behavior change and, if the latter, if that behavior change is desired or not.