In addition, we implement a difference in difference identification strategy allowing us to
control for time invariant firm level differences. Given this identification strategy, the key
assumption required to identify the impact of CDHP offer is that firms choosing to offer a CDHP
(treatment firms) in the study period would, on average, have had the same time trend in costs as
firms choosing not to offer, had the treatment firms not offered CDHPs. Although we cannot
directly test this assumption, we mitigate any violations by controlling for time-varying changes
in employee composition through a novel application of a machine learning technique in order to
5
develop weights that balance firms’ health plan enrollee composition over time