The standard wage decomposition methodology produces arbitrary results when attempting to estimate the separate contributions of sets of dummy variables to the unexplained portion of the wage decomposition: the estimates are not invariant with respect to the choice of reference groups. However, the estimated separate contributions of sets of dummy variables to the explained portion and the overall decomposition are shown not to be dependent upon the choice of left-out reference groups. A similar identification problem applies to continuous variables, although this may not be as likely to cause problems in practice.