Where the first term of the right-hand side measures the part of the gap attributed to the existence of differential returns to the same characteristics. The second term reflects the part of the gap explained by differences in observed characteristics. The third term measures the interaction between differences in observed characteristics and differences in returns to those characteristics
This way the gap in mean outcomes can be thought of as deriving from a gap in coefficients (C), a gap in endowments (E), and a gap arising from the interaction of endowments and coefficients (CE). Thus, Equations (9) and (10) can be seen as special
cases in which:
where the first term of the right-hand is usually called ―the explained part‖ and the second term ―the unexplained part‖.
In (9) the interaction effect is placed in the unexplained part and in (10) it is placed in the explained part. Regarding interpretation it can be said that in (9) it is assumed that natives are exposed to risk according to their employment characteristics, whereas immigrants are inexplicably exposed to higher levels of risk. By contrast in (10) is assumed that immigrants are exposed to risk according to their employment characteristics, whereas natives are unexpectedly exposed to lower levels of risk.
5.2. Oaxaca decomposition results
The first block of Table 6 presents the average of the transformed exposure to risk variable (z), the average of the original exposure to risk variable (O*Net) and the gap between immigrants and natives mean exposure to risk. The second block shows the explained and unexplained portions of the output outcome gap using both methods (Equation (9) and (10) respectively). Table 6 presents results for the whole sample and men and women treated as separate groups.