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Quantile Regression with Log(0) Outcomes

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Abstract

We consider quantile regression when the outcome is the log of a non-negative variable that can equal zero. Unlike the analogous mean regression, this is well-defined if the quantile level is not low enough to include the extensive margin, but "log-like" transformations are used in practice due to computational obstacles. We provide computational solutions and diagnostics, as well as theoretical results including identification, coefficient interpretation under proper specification, characterization of the misspecified log-linear model's estimand, and sensitivity of this estimand to changes in the conditional distribution. To illustrate these results, we revisit an empirical study of armed-group and civilian violence.

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  • Xin Liu & David M. Kaplan, 2025. "Quantile Regression with Log(0) Outcomes," Working Papers 2509, Department of Economics, University of Missouri.
    • Handle: RePEc:umc:wpaper:2509
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    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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