  While data-driven decision-making is transforming modern operations, most
large-scale data is of an observational nature, such as transactional records.
These data pose unique challenges in a variety of operational problems posed as
stochastic optimization problems, including pricing and inventory management,
where one must evaluate the effect of a decision, such as price or order
quantity, on an uncertain cost/reward variable, such as demand, based on
historical data where decision and outcome may be confounded. Often, the data
lacks the features necessary to enable sound assessment of causal effects
and/or the strong assumptions necessary may be dubious. Nonetheless, common
practice is to assign a decision an objective value equal to the best
prediction of cost/reward given the observation of the decision in the data.
While in general settings this identification is spurious, for optimization
purposes it is only the objective value of the final decision that matters,
rather than the validity of any model used to arrive at it. In this paper, we
formalize this statement in the case of observational-data-driven optimization
and study both the power and limits of predictive approaches to
observational-data-driven optimization with a particular focus on pricing. We
provide rigorous bounds on optimality gaps of such approaches even when optimal
decisions cannot be identified from data. To study potential limits of
predictive approaches in real datasets, we develop a new hypothesis test for
causal-effect objective optimality. Applying it to interest-rate-setting data,
we empirically demonstrate that predictive approaches can be powerful in
practice but with some critical limitations.
