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Pregibit: a family of binary choice models

Author

Listed:
  • Chu-Ping C. Vijverberg

    (College of Staten Island
    City University of New York Graduate Center)

  • Wim P. M. Vijverberg

    (City University of New York Graduate Center
    Institute for the Study of Labor (IZA))

Abstract

The pregibit binary choice model is built on a distribution that allows symmetry or asymmetry and thick tails, thin tails, or no tails. Thus, the model is much more flexible than the traditional binary choice models: pregibit nests logit, approximately nests probit, loglog, cloglog, and gosset models and incorporates the linear probability model. Greater flexibility allows a more accurate estimation of the data-generating process, including asymmetric and thick/thin tails. We prove that the maximum likelihood estimator of the pregibit model is consistent and asymptotically normally distributed. A Monte Carlo analysis and two real-world examples show that probit and logit estimates may show misleading evidence in cases where a pregibit model is statistically preferred. One example concerns enrollment in post-secondary education in Belgium: The pregibit estimate of the enrollment gap between Belgian natives and foreign students is 50 % larger, and the type of high school (general, technical, catholic) is more influential. The second example examines the outcome of mortgage applications in the USA. Here, pregibit estimates assign a stronger role to variables that measure the financial strength of mortgage applicants and a weaker role to demographic characteristics including minority status. More importantly, the distribution of the disturbances proves to be seriously skewed: Pregibit indicates that even high-risk applicants (with a probit acceptance probability of nearly 0) have a positive probability of getting their mortgage application approved. Apparently, mortgage officers are more inclined to uncover reasons to make a mortgage deal than to send clients away empty-handed.

Suggested Citation

  • Chu-Ping C. Vijverberg & Wim P. M. Vijverberg, 2016. "Pregibit: a family of binary choice models," Empirical Economics, Springer, vol. 50(3), pages 901-932, May.
    • Handle: RePEc:spr:empeco:v:50:y:2016:i:3:d:10.1007_s00181-015-0951-x
    DOI: 10.1007/s00181-015-0951-x
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    References listed on IDEAS

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    More about this item

    Keywords

    Binary choice; Asymmetry; Logit; Probit; Post-secondary education; Mortgage application;
    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
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

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