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Ordinal Decomposition

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Abstract

The famous Blinder-Oaxaca decomposition estimates the statistically "explained" proportion of a between-group difference in means, but ordinal variables have no mean. A common approach assigns cardinal values 1,2,3,... to the ordinal categories and runs the conventional OLS-based decomposition. Surprisingly, we show such results are numerically identical to a decomposition of the survival function when estimating the counterfactual using OLS-based distribution regression, even if the cardinalization is wrong. Still, reporting the counterfactual helps transparency and wide-sense replication, and to mitigate functional form misspecification, we describe and implement a nonparametric estimator. Empirically, we decompose U.S. rural-urban differences in mental health.

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  • David M. Kaplan & Qian Wu, 2024. "Ordinal Decomposition," Working Papers 2404, Department of Economics, University of Missouri.
    • Handle: RePEc:umc:wpaper:2404
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    Keywords

    Blinder-Oaxaca decomposition; counterfactual distribution; distribution regression; survival function;
    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
    • I14 - Health, Education, and Welfare - - Health - - - Health and Inequality

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