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Revisiting the Evidence for a Cardinal Treatment of Ordinal Variables

Author

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  • Carsten Schröder
  • Shlomo Yitzhaki

Abstract

Well‐being (i.e., satisfaction, happiness) is a latent variable, impossible to observe directly. Hence, questionnaires ask people to grade their well‐being in different life domains. The most common practice—comparing well‐being by means of descriptive analysis or linear regressions—ignores that the underlying collected well‐being information is ordinal. If the well‐being function is ordinal, then monotonic transformations are allowed. We demonstrate that treating ordinal data by methods intended to be used for cardinal data may give an incorrect impression of a robust result. Particularly, we derive the conditions under which the use of cardinal method to an ordinal variable gives an illusionary sense of robustness, while in fact one can reverse the conclusion reached by using an alternative cardinal assumption. The paper provides empirical applications.

Suggested Citation

  • Carsten Schröder & Shlomo Yitzhaki, 2015. "Revisiting the Evidence for a Cardinal Treatment of Ordinal Variables," SOEPpapers on Multidisciplinary Panel Data Research 772, DIW Berlin, The German Socio-Economic Panel (SOEP).
  • Handle: RePEc:diw:diwsop:diw_sp772
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    References listed on IDEAS

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    More about this item

    Keywords

    satisfaction; well-being; ordinal; cardinal; dominance;

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • I30 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being
    • I39 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Other

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