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.

Economists and psychologists argue that individuals skew personal beliefs to accord with their own interests. To test for the presence of self-serving beliefs, we surveyed 1,200 members of the Mormon Church about tithing. A tithe is a voluntary contribution equal to 10 percent of income. Since respondents must decide privately what income items to tithe, we observe how the income definition depends on an individual's religious and financial incentives. We find surprisingly little evidence that an individual's financial situation influences beliefs about what counts as income for the tithe. However, ambiguity increases the role for self-serving biases.