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

This paper describes the application of a semiparametric approach, known as a varying coefficients model (Hastie and Tibshirani 1993), to implement a Oaxaca-Blinder type of decomposition in the presence of self-selection into treatment groups for a continuum of comparison groups. The flexibility of this methodology may allow for detecting heterogeneity of the role of endowment and coefficient effects when analyzing endogenous dose treatments. The methodology is then used to revisit the impact of obesity on wages (Cawley 2004), using body mass index (BMI) as the continuous group variable. The results suggest that body weight does have a negative impact on wages for white women, but the impact decreases for higher BMI levels. For white men, the impact is also negative and significant, but positive for low levels of BMI, which explains why they are not significant in the linear instrumental variables approach.