Let’s postulate a society with several identifiable ethnic groups. All other things being equal, the group with highest birth rates would be considered the poorest simply because their members would be overwhelmingly young. A 20 year old typically earns less than a 40 year old simply because of lesser experience and skill set. A population segment in which 20 year olds have kids and average family has three children is going to look less wealthy than one where the first child is delayed until age 30 and an average family has two kids.
Of course, not everything is equal, so people who get better education and upbringing typically earn more. A family with two kids can invest more in each than a family with three. Moreover, a population that produces few high-investment offspring would be more risk-averse, on average. So you would have the difference between relatively well-educated individuals working in industries where opportunity does not decline with age (examples of which would be the military) and those who are less educated, may initially work in more dangerous environment by choice…the per capita wealth difference should not be surprising. At the same time, barring excessive mortality, the less wealthy population would be greatly more numerous within a couple of generations.
A population with more kids also benefits more from social services. As the kids grow up — assuming no change in the orientation towards large families — their increased voting weight enables them to get more transfer payments and the cycle becomes self-reinforcing. In reality, such a cycle would be diluted by age groups acting in concert across ethnic divides, by changes in fertility rates and other factors. That’s why sociology is such an “inexact science” — more of a philosophy than a science — pure, categorized data is hard to get and controlled experiments on a meaningful scale are difficult.