Instrumental variables with unordered treatments: Theory and evidence from returns to fields of study

Published in: Journal of Labor Economics, Forthcoming (2024). (with Eskil Heinesen and Christian Hvid and Lars Kirkebøen and Magne Mogstad)

We revisit the identification argument of Kirkeboen et al. (2016) 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 both observed and unobserved heterogeneity in treatment effects. We show that the key assumptions underlying their identification argument have testable implications, and provide a new characterization of the bias that may arise if these assumptions are violated. We apply these insights in a comparison of earnings payoffs to post-secondary fields of study in Norway and Denmark. In both countries, we find that field of study, not only education levels, is a key determinant of individual earnings. We also find a strong cross-country correlation in the payoffs to field of study, which is robust to removing fields with evidence of violations of the identifying assumptions. The relative rewards to specific types of human capital are therefore found to be comparable in two small open economies that differ distinctly in industry structure, but are broadly similar in education system, wage setting institutions, and tax-transfer system.

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