essays in public finance and industrial organization a dissertation ...

CHAPTER 2. HEALTH PLAN CHOICE 81
where rf denotes the average risk of employees in firm f, which the insurer forecasts
using the available demographic information, xf. 16
We model expected plan bids as a mark-up over expected cost. So plan j’s bid
for firm f is:
Bjf = δj · (aj + bj · (E[rf|xf] − 1)) + νjf, (2.7)
where νjf is an independent mean zero random variable. The new parameter intro-
duced in the bid model is the mark-up, δj. We constrain the mark-up to be constant
across the plans offered by a particular insurer. Although in theory an insurer could
vary the mark-up across its different plans, because the cost data are at the insurer-
firm level, we are unable to identify separately the mark-up and the fixed costs for
each plan offered by an insurer. Naturally we expect the mark-up parameters to be
larger than one.
Employer Contribution Setting
The last part of our model specifies how employers set required plan contributions.
We adopt a simple model in which employers pass on a fraction of their cost for the
lowest cost plan, and then a fraction of the incremental cost for higher cost plans. We
allow these fractions, denoted β and γ, to vary across firm-years and coverage tiers.
Let B lf denote the minimum bid received for coverage tier l in firm-year f, de-
note plan j’s bid for coverage tier l in firm-year f as Bjlf. We model the required
contribution as:
pjlf = βlf · B lf + γlf · (Bjlf − B lf)+ξjlf. (2.8)
This model describes employer behavior in our data remarkably well. The resid-
uals from the linear regression (2.8) have a standard deviation of 7.64, and the R-
squared is 0.99. As noted above, approximately half of the firms in our data choose
a ”proportional pass-through” strategy where β = γ. The others choose an ”incre-
mental pass-through” strategy in which β