  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. We also provide a new
characterization of the bias that may arise if these assumptions are violated.
Taken together, these results allow researchers not only to test the underlying
assumptions, but also to argue whether the bias from violation of these
assumptions are likely to be economically meaningful. Guided and motivated by
these results, we estimate and compare the earnings payoffs to post-secondary
fields of study in Norway and Denmark. In each country, we apply the
identification argument of Kirkeboen et al. (2016) to data on individuals'
ranking of fields of study and field-specific instruments from discontinuities
in the admission systems. We empirically examine whether and why the payoffs to
fields of study differ across the two countries. We find strong cross-country
correlation in the payoffs to fields of study, especially after removing fields
with violations of the assumptions underlying the identification argument.
