In the second quarter of this year, official Chinese data showed economic growth of 6.2%, close to Beijing’s target and within a percentage point of what it has reported every quarter for the past 4½ years.

A few months earlier, satellites monitoring Chinese industrial hubs suggested parts of the world’s largest trading economy were contracting. An index of Chinese industrial production created by a multinational manufacturer was pointing to lower growth than official figures. And a web-search index used to gauge how many...