Revisiting gender identity and relative income within households: a cautionary tale on the potential pitfalls of density estimators

We show that Bertrand et al.'s (QJE 2015) finding of a sharp drop in the relative income distribution within married couples at the point where wives start to earn more than their husbands is unstable across different estimation procedures and varies across contexts. We apply the estimators by McCrary (JoE, 2008, McC) and Cattaneo et al. (JASA, 2020, CJM) to administrative data from the US and Germany and compare their performance in a simulation. Large bins cause McC to substantially overreject the null hypothesis, and mass points close to the potential discontinuity affect McC more than CJM.