Ridge regression estimation of the linear probability model (LPM) offers the possibility of eliminating the critical difficulty with the least squares estimated LPM, the generation of negative residual variance estimates. This study investigates the mean squared error (MSE) properties of this estimation method relative to the least squares methods proposed in the literature using theory and simulation.

The ridge existence theorems are shown to still hold for the heteroskedastic case of the LPM and the ridge regression estimator of the LPM is shown to be consistent. Simulation results indicate that the ridge regression estimator of the LPM produces smaller coefficient and prediction MSEs than do the proposed least squares estimators of the LPM. Finally, some empirical evidence is offered to show that the ridge estimated LPM may compare favorably with logit and probit models.