The state of the world is improving at an astonishing rate. That might have served as the title of a valuable new report on global incomes from the Pew Research Center. In a spirit of glass-half-full restraint, the center instead announced that “A Global Middle Class Is More Promise Than Reality.”

Well, that’s one way of looking at it. For the purposes of this study, Pew defines the global middle class as people with incomes (adjusted for inflation and purchasing power) of between $10 and $20 a day. As a proportion of the total, this group almost doubled between 2001 and 2011, from 7 percent to 13 percent. Yes, that’s still a small share. The middle class, defined this way, remains but a sliver of the planet’s population. Even so, a doubling in 10 years is a nice rate of increase.

Here’s another way of looking at global trends. In the same period, the proportion of the world’s population living in poverty — on $2 a day or less — halved, from 29 percent to 15 percent, according to the report. The unjaded observer might regard that as a staggering improvement.

Granted, the proportion who are only slightly better off — those with incomes between $2 and $10 — went up, from 50 percent to 56 percent, because many of the poorest moved over the $2 threshold. Combining the two groups, people living on less than $10 a day fell from 79 percent of the global population to 71 percent. To repeat, this was in just 10 years, a decade that included a global crash.

To be clear, there’s no cause for complacency in these statistics. Most of the world is still very poor by rich-country standards, and the toll of suffering contained in that fact should always be kept in mind. And Pew is right: The emerging middle class that companies everywhere see as a potentially vast new market doesn’t yet come close to rivaling the scale of the rich-country market. For now, moreover, this new middle class is a preponderantly Asian phenomenon.

No cause for complacency, then — but grounds, nonetheless, for optimism. In the span of world history, this is a remarkable age.