  Every design choice will have different effects on different units. However
traditional A/B tests are often underpowered to identify these heterogeneous
effects. This is especially true when the set of unit-level attributes is
high-dimensional and our priors are weak about which particular covariates are
important. However, there are often observational data sets available that are
orders of magnitude larger. We propose a method to combine these two data
sources to estimate heterogeneous treatment effects. First, we use
observational time series data to estimate a mapping from covariates to
unit-level effects. These estimates are likely biased but under some conditions
the bias preserves unit-level relative rank orderings. If these conditions
hold, we only need sufficient experimental data to identify a monotonic,
one-dimensional transformation from observationally predicted treatment effects
to real treatment effects. This reduces power demands greatly and makes the
detection of heterogeneous effects much easier. As an application, we show how
our method can be used to improve Facebook page recommendations.
