Non-Existent Moments of Earnings Growth

The literature often relies on moment-based measures of earnings risk, such as the variance, skewness, and kurtosis (e.g., Guvenen, Karahan, Ozkan, and Song, 2019, Econometrica). However, such moments may not exist in the population under heavy-tailed distributions. We empirically show that the population kurtosis, skewness, and even variance often fail to exist for the conditional distribution of earnings growths. This evidence may invalidate the moment-based analyses in the literature. In this light, we propose conditional Pareto exponents as novel measures of earnings risk that are robust against non-existence of moments, and develop estimation and inference methods. Using these measures with an administrative data set for the UK, the New Earnings Survey Panel Dataset (NESPD), and the US Panel Study of Income Dynamics (PSID), we quantify the tail heaviness of the conditional distributions of earnings changes given age, gender, and past earnings. Our main findings are that: 1) the aforementioned moments fail to exist; 2) earnings risk is increasing over the life cycle; 3) job stayers are more vulnerable to earnings risk, and 4) these patterns appear in both the period 2007-2008 of the great recession and the period 2015-2016 of positive growth among others.