“…1 Introduction Heckman and Vytlacil (1999) introduced the marginal treatment effect (MTE) as a unifying concept for program and policy evaluation. 1 Since then, MTE methods have become a fundamental tool for empirical work, and have been applied in a variety of different settings including the returns to schooling (Moffitt, 2008;Carneiro, Heckman, and Vytlacil, 2011;Carneiro, Lokshin, and Umapathi, 2016;Nybom, 2017) and its impacts on wage inequality (Carneiro and Lee, 2009), discrimination (Arnold, Dobbie, and Yang, 2018;Arnold, Dobbie, and Hull, 2020), the effects of foster care (Doyle Jr., 2007), the impacts of welfare (Moffitt, 2019) and disability insurance (Maestas, Mullen, and Strand, 2013;French and Song, 2014;Autor, Kostøl, Mogstad, and Setzler, 2019) programs on labor supply, the performance of charter schools (Walters, 2018), health care (Kowalski, 2018;Depalo, 2020), the effects of early childhood programs (Kline and Walters, 2016;Cornelissen, Dustmann, Raute, and Schönberg, 2018;Felfe and Lalive, 2018), the efficacy of preventative health products (Mogstad, Santos, and Torgovitsky, 2017), the quantity-quality theory of fertility (Brinch, Mogstad, and Wiswall, 2017), and the effects of incarceration (Bhuller, Dahl, Løken, and Mogstad, 2020), among many others. Mogstad and Torgovitsky (2018) provide a recent review of the MTE methodology and its connection to other instrumental variable (IV) approaches.…”