You're assuming that poverty doesn't cause impulsiveness, and that poor people don't face any costs that the middle classes don't.

Both of these assumptions are likely untrue. Poverty makes the cost of many things higher. Banking is non-trivially more expensive. Public transport often ends up more than the cost of a car, and that's assuming you can afford a season ticket. Those in poverty often cannot. Rental is over a lifetime normally more expensive than buying - and if you're in poverty, you can often expect rental to include large deposits which you often won't get back.

For the impulsive thing, see http://yalepress.yale.edu/yupbooks/book.asp?isbn=97803001209.... Essentially if you're poor, there's a good chance that your marginal utility curve is upward, rather than downward sloping. Which rewards impulsive behavior in a way that is not the case for those who meet the normal standard of living in their society.