Regression Discontinuity Reversed 

 I recently came across a new paper by David Card, Alexandre Mas, and Jesse Rothstein entitled " Tipping and the Dynamics of Segregation ." What's interesting from a methodological standpoint is that the authors use what may be called "inverted" regression discontinuity methods to test for race-based tipping in neighborhoods in American cities.  

 In a classic regression discontinuity design researchers commonly exploit the fact that treatment assignment changes discontinuously as a function of one or more underlying variables. For example scholarships may be assigned based on whether students exceed a test score threshold (like in the classic paper by Thistlethwaite and Campbell (1960)). Unlucky students who just miss the threshold are assumed to be virtually identical to lucky ones who score just above the cutoff value so that the threshold offers a clean identification of the counterfactual of interest (assuming no sorting).  

 In the Card et al. paper, the situation is slightly different because the authors have no hard-and-fast decision rule, but a theory that posits that whites' willingness to pay for homes depends on the neighborhood minority share and exhibits a tipping behavior. If the minority share exceeds a critical threshold, all the white households will leave. Since the location of the (city-specific) tipping point is unknown, the author's estimate it from the data and find that there are indeed significant discontinuities in the white population growth rate at the identified tipping points. Once the tipping point is located, they go on to examine whether rents or housing prices exhibit non-linearity around the tipping point but find no effects. They also try to explain the location of the tipping points by looking at survey data on racial attitudes of whites. Cities with more tolerant whites appear to have higher tipping points.  

 I think this is a very creative paper. The general approach could be useful in other contexts so take a look!