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On the Linear Probability Model as binary choice random utility model

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  • Delle Site, Paolo
  • Parmar, Janak

Abstract

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.

Suggested Citation

  • Delle Site, Paolo & Parmar, Janak, 2024. "On the Linear Probability Model as binary choice random utility model," Journal of choice modelling, Elsevier, vol. 52(C).
    • Handle: RePEc:eee:eejocm:v:52:y:2024:i:c:s175553452400037x
    DOI: 10.1016/j.jocm.2024.100505
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    References listed on IDEAS

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    1. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, November.
    2. André Palma & Karim Kilani, 2011. "Transition choice probabilities and welfare analysis in additive random utility models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 427-454, April.
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    5. Goebel Jan & Grabka Markus M. & Liebig Stefan & Kroh Martin & Richter David & Schröder Carsten & Schupp Jürgen, 2019. "The German Socio-Economic Panel (SOEP)," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 239(2), pages 345-360, April.
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    More about this item

    Keywords

    Constrained maximum likelihood estimators; Linear probability model; Prediction validity; Random utility; Welfare change;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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