  Prediction models can improve efficiency by automating decisions such as the
approval of loan applications. However, they may inherit bias against protected
groups from the data they are trained on. This paper adds counterfactual
(simulated) ethnic bias to real data on mortgage application decisions, and
shows that this bias is replicated by a machine learning model (XGBoost) even
when ethnicity is not used as a predictive variable. Next, several other
de-biasing methods are compared: averaging over prohibited variables, taking
the most favorable prediction over prohibited variables (a novel method), and
jointly minimizing errors as well as the association between predictions and
prohibited variables. De-biasing can recover some of the original decisions,
but the results are sensitive to whether the bias is effected through a proxy.
