The global economy’s stumbles over the past year have been no surprise to the world’s purchasing managers and the people closely following the economic indexes that are produced from their views.

Global purchasing managers’ indexes, or PMIs, have come forth as a leading barometer of the health of the world’s major manufacturing sectors. Through most of last year, official forecasts like those from the Federal Reserve or International Monetary Fund held steady, and until the fourth quarter, the stock market climbed upward....