They did at least try to control for wealth: “We find that the estimated effects are driven entirely by households with access to a car, consistent with car usage mattering directly. The effect is also concentrated in households where there is an adult male in the household, increasing the likelihood that both front seats are occupied by adults. Somewhat surprisingly, the effects are larger among households with higher income levels. This suggests that the pressures leading to reduced birthrates may not be entirely financial, or that these groups bear a greater burden through higher compliance rates.”
They did at least try to control for wealth: “We find that the estimated effects are driven entirely by households with access to a car, consistent with car usage mattering directly. The effect is also concentrated in households where there is an adult male in the household, increasing the likelihood that both front seats are occupied by adults. Somewhat surprisingly, the effects are larger among households with higher income levels. This suggests that the pressures leading to reduced birthrates may not be entirely financial, or that these groups bear a greater burden through higher compliance rates.”