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Testing the normality assumption in an ordered probit model using an artificial regression– some results for the LM-test

Author

Listed:
  • Joachim Wilde

    (Osnabrueck University, Department of Economics, Rolandstr. 8, 49069 Osnabrueck, Germany)

  • Sarah Forstinger

    (Osnabrueck University, Department of Economics, Rolandstr. 8, 49069 Osnabrueck, Germany)

Abstract

The key assumption of normally distributed error terms is usually not tested in empirical practice when using ordered probit models. Therefore, an artificial regression version of the LM test against the class of Pearson distributions is derived that can be implemented more easily than the well-known matrix version. A comprehensive simulation study analyses the properties of the LM test and of the t-statistics in the artificial regression that correspond to skewness and fat tails, respectively. For most designs a large power against skewness and a moderate power against fat tails are found. However, the t-statistics against skewness and fat tails exhibit notable size distortions. Therefore, new double indicators are proposed. The simulation results indicate that the double indicators avoid the size distortions and exhibit power characteristics similar to the original statistics for most designs.

Suggested Citation

  • Joachim Wilde & Sarah Forstinger, 2026. "Testing the normality assumption in an ordered probit model using an artificial regression– some results for the LM-test," IEER Working Papers 127, Institute of Empirical Economic Research, Osnabrueck University.
    • Handle: RePEc:iee:wpaper:wp0127
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    References listed on IDEAS

    as
    1. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    2. Bera, Anil K & Jarque, Carlos M & Lee, Lung-Fei, 1984. "Testing the Normality Assumption in Limited Dependent Variable Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(3), pages 563-578, October.
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    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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