The conditions under which ordinary least squares (OLS) is an unbiased and consistent estimator of the linear probability model (LPM) are unlikely to hold in many instances. Yet the LPM still may be the correct model or a good approximation to the probability generating process. A sequential least squares (SLS) estimation procedure is introduced that may outperform OLS in terms of finite sample bias and yields a consistent estimator. Monte Carlo simulations reveal that SLS outperforms OLS, probit and logit in terms of mean squared error of the predicted probabilities.
Horrace, William C. and Oaxaca, Ronald L., "New Wine in Old Bottles: A Sequential Estimation Technique for the LPM" (2003). Economics - Faculty Scholarship. 139.
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