Instrumental Variables with Unordered Treatments: Theory and Evidence from Returns to Fields of Study

Eskil Heinesen, Christian Hvid, Lars Kirkebøen, Edwin Leuven and Magne Mogstad

Journal of Labor Economics, 2026, vol. 44, issue 3, 823 - 854

Abstract: We revisit the 2016 identification argument of Kirkeboen and colleagues, who showed how one may combine instruments for multiple unordered treatments with information about individuals’ ranking of these treatments to achieve identification while allowing for heterogeneity in treatment effects. We show that the key identifying assumptions have testable implications and provide a new characterization of the bias that may arise if these assumptions are violated. We estimate and compare the earnings payoffs to postsecondary fields of study in Norway and Denmark. We empirically examine whether and why the payoffs to fields of study differ across the two countries.

Date: 2026
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