This paper shows how difficult it is to study the roles of discrimination and unobserved skills when studying changes in racial and gender wage gaps over time by examining merits and shortcomings of a popular decomposition method by Juhn, Murphy and Pierce (1991). The JMP method shows that wage dispersion can offer a compelling explanation of the wage gap. However, JMP have to rely on a few strong assumptions in order to derive their decomposition equation which introduces wage inequality as the price of unobserved skills (the standard deviation of the residuals) into their decomposition equation.