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

Joachim Wilde () and Sarah Forstinger ()
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Joachim Wilde: Osnabrueck University, Department of Economics, Rolandstr. 8, 49069 Osnabrueck, Germany
Sarah Forstinger: Osnabrueck University, Department of Economics, Rolandstr. 8, 49069 Osnabrueck, Germany

No 127, IEER Working Papers from Institute of Empirical Economic Research, Osnabrueck University

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.

Keywords: ordered probit model; normality assumption; Lagrange multiplier test; artificial regression (search for similar items in EconPapers)
JEL-codes: C25 (search for similar items in EconPapers)
Pages: 40 pages
Date: 2026-03-11
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