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This paper presents an extension to the Oaxaca–Blinder decomposition with continuous groups using a semiparametric approach known as varying coefficients model. To account for potential self-selection into the continuum of groups, the use of inverse mills ratios is expanded upon following the literature on endogenous selection. The flexibility of this methodology may allow detecting heterogeneity when analyzing endogenous dose treatments effects, as well as correcting for endogeneity when analyzing the heterogeneous partial effects across the continuous group variable. For illustration, the methodology is used to revisit the impact of body weight on wages, using body mass index (BMI) as the continuum of groups, finding evidence that body weight has a negative, but decreasing impact on wages for both white men and women.

A Semi-Parametric Approach to the Oaxaca–Blinder Decomposition with Continuous Group Variable and Self-Selection