Comment: Summarizing Income Mobility with Multiple Smooth Quantiles Instead of Parameterized Means

Abstract

Studies of economic mobility summarize the distribution of offspring incomes for each level of parent income. Mitnik and Grusky (2020) highlight that the conventional intergenerational elasticity (IGE) targets the geometric mean and propose a parametric strategy for estimating the arithmetic mean. We decompose the IGE and their proposal into two choices: (1) the summary statistic for the conditional distribution and (2) the functional form. These choices lead us to a different strategy—visualizing several quantiles of the offspring income distribution as smooth functions of parent income. Our proposal solves the problems Mitnik and Grusky highlight with geometric means, avoids the sensitivity of arithmetic means to top incomes, and provides more information than is possible with any single number. Our proposal has broader implications: the default summary (the mean) used in many regressions is sensitive to the tail of the distribution in ways that may be substantively undesirable.