“…To address this issue, a number of empirical strategies have been developed to consistently estimate the impact of a misclassified binary regressor, many of which make use of an instrumental variable (e.g. , Card 1996;Kane, Rouse, and Staiger 1999;Black, Berger, and Scott 2000;Frazis and Lowenstein 2003;Mahajan 2006;Lewbel 2007;Hu 2008;Chen, Hu, and Lewbel 2008a,b;Battistin, De Nadai, and Sianesi 2014;DiTraglia and Garcia-Jimeno 2019;Calvi, Lewbel, and Tomassi 2017;Yanagi 2019).…”