Using recently published U.S. long-run microdata (SCF+), we document that — for people born in the first half of the 20th century — median wealth used to increase from one ten-year birth cohort to another. For people born in the second half, median wealth successively declined from cohort to cohort and wealth inequality within birth cohorts has markedly increased. Shifts in observable household characteristics, life expectancy, length of educational paths or the repercussions of the Great Recession cannot conclusively explain these wealth patterns. A synthetic saving approach suggests that the growing wealth gap across and within cohorts is mainly caused by diverging savings, which are driven by changes in income levels and, importantly, saving rates. We hypothesize that shifts in economic circumstances, rather than preferences, are the main reason behind the declining saving rates of low- and median-wealth households.