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Another Look at the Linear Probability Model and Nonlinear Index Models

Kaicheng Chen, Robert S. Martin, and Jeffrey M. Wooldridge


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.