The article's argument doesn't seem logical to me.
The economists claim that poor blacks spend more on conspicuous consumption because they're competing with neighbors who earn roughly as much as they do, while poor whites have richer neighbors that they can't afford to compete with. The reasoning is, because black median income is lower than white median income, poor blacks will cluster while poor whites will be surrounded by wealthier neighbors.
But why should that be? The median income isn't necessarily the most common income, or the income of people living next to you. There's no reason to assume that whites don't cluster by income just as tightly. In other words, why should the $42,000 household be living near a $60,000 household?
One factor that the article didn't bring up was suburban vs. urban patterns of residence. Black people are more likely to live in cities, where their neighbors will actually see them daily (and their sneakers, designer clothes, and cars.)
The other thing is the education gap. For college- and graduate-educated adults, their children's schools and, yes, phonics toys, are status symbols.