NPR looks at how the jobs and incomes of parents influence the same outcomes among their children:

After some poking around, we figured out how to settle the argument. It allowed us to look at the same group of people in 1979 and 2010 — from a time when most were teenagers to the time when they were middle-aged and, for the most part, gainfully employed…

Based on this chart, it looks like the jobs of parents that are linked to better outcomes for their children require more education and are higher-skilled. This would seem to line up with findings from the Pew Economic Mobility Project about what traits are linked to upward social mobility:

This research reveals:

• College graduates were over 5 times more likely to leave the bottom rung than non-college graduates.
• Dual-earner families were over 3 times more likely to leave the bottom rung than single-earner families.
• Whites were 2 times more likely to leave the bottom rung than blacks.

Additionally, Pew’s analysis examined the intersection between income and wealth, and found that the health of family balance sheets—including accumulated savings and wealth—are related to income mobility prospects. Households with financial capital, such as liquid savings or other readily available assets such as stocks, were more likely to leave the bottom of the economic ladder. In other words, movement up the income and wealth ladders was connected, and economically secure families were also the most likely to be upwardly mobile.

So in addition to parental education and the type of job one’s parent has, going to college, having two-income families, race, and wealth matter quite a bit. Overcoming these factors is not necessarily easy: “In fact, 43 percent of Americans raised at the bottom of the income ladder remain stuck there as adults, and 70 percent never even make it to the middle.”