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While it does fully remove the bias from estimates in DGP-1, in which the only difference between the non-heaped and heaped data is their mean, it does not fully remove the bias from estimates based on other DGPs.
The main takeaway from these results is that it is possible to obtain unbiased estimates by separately investigating non-heaped and heaped data.
Our simulation exercise also showed that an approach that focuses solely on heaped types can yield unbiased estimates where the data allow for such estimates.
Moreover, if there are a sufficient number of heaps within a reasonable bandwidth of the threshold, a researcher can separately analyze these data to obtain an unbiased estimate that captures a weighted average of the treatment effects for heaped and non-heaped types (as both are present at data heaps).
(32) Second, it induces a positive slope in order to bring the regression line closer to the heaped data at the edge of the bandwidth.
In this example, there may be heterogeneity in how individuals report their incomes--some individuals may report in dollars (non-heaped types), whereas others may report their incomes in tens of thousands of dollars (heaped types).
(9.) Note our earlier reference to [K.sup.*.sub.i], as an unobservable identifier that i is heaped. As we here consider a proxy variable indicating heaped types, then, we surmise that such a proxy may be arrived at in practice by institutional knowledge, or common practice (as might be the case in rounding leading to heaping, for example).
(13.) In particular, the average treatment effect across observations at heap points is contributed to by non-heaped and heaped types.