Measuring discrimination by decomposing earnings functions

An unrecognized problem is examined in a frequently used method for decomposing earnings functions in the measurement of discrimination. The conventional method decomposes changes in the log of the geometric mean of the distribution, as opposed to the correct quantity, which is the change in the log of the arithmetic mean. Using the log of the geometric mean involves decomposing both changes in the mean and the spread of the distribution. But the mean and the spread of many earnings functions are subject to change, so it is not quite clear what this decomposition achieves. Two examples illustrate timewise and cross-sectional comparisons.