  We reassess the use of linear models to approximate response probabilities of
binary outcomes, focusing on average partial effects (APE). We confirm that
linear projection parameters coincide with APEs in certain scenarios. Through
simulations, we identify other cases where OLS does or does not approximate
APEs and find that having large fraction of fitted values in [0, 1] is neither
necessary nor sufficient. We also show nonlinear least squares estimation of
the ramp model is consistent and asymptotically normal and is equivalent to
using OLS on an iteratively trimmed sample to reduce bias. Our findings offer
practical guidance for empirical research.
