On the Linear Probability Model as binary choice random utility model

The econometrics of the Linear Probability Model (LPM) cast as binary choice random utility model and where probabilities are constrained in the [0,1] interval is unexplored. The paper fills this gap. Assumptions are identified under which constrained maximum likelihood estimators exist and are unique, consistent and asymptotically normal. A consistent estimator of the covariance matrix is provided. Statistics that can be used to evaluate the prediction validity of binary choice models are reviewed. With income independent choices, the LPM has the merit of closed-form welfare change measure for the sub-population of consumers shifting from one alternative to the other. Two datasets illustrate the theoretical insights. One from the Swiss Mobility and Transport Microcensus related to choices between teleworking and commuting, one from the German Socio-Economic Panel related to add-on health insurance subscription. The signs and statistical significance at 5% level of the coefficients are concordant across LPM, Logit and Probit. Model prioritization based on prediction validity is data specific and dependent on the statistics used.