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China’s long boom is over. Persistent weaknesses in productivity growth and a looming demographic catastrophe will hobble the country for decades to come.

Every society produces goods and services using workers, raw materials, and capital. Living standards rise as societies increase their use of these inputs—putting more people to work, making them work longer hours, extracting and consuming more raw materials, and investing in more machines and technological research—and get more efficient at transforming those inputs into things people actually want.

The Chinese economy has done an exemplary job of boosting its labor and capital inputs since Deng Xiaoping began the process of “reform and opening up” in 1978. It has done far less well at improving its use of those inputs. According to an estimate from Harry Xiaoying Wu of Japan’s Hitotsubashi University, China’s underlying efficiency has not improved at all since the mid-1980s. In fact, he estimates Chinese businesses are now 15% less productive than they were in 2007.

The problem is the government’s widespread and persistent interference in investment decisions—a problem that has been getting worse. Since the end of 2012, the share of new credit extended to China’s state-owned enterprises has soared from about 50% to more than 80%. China’s vibrant pockets of private innovation have been squeezed for political reasons. While it is possible the political situation could change, and therefore lead to a renewed burst of productivity growth, as in 1978, that is not the likeliest outcome. Zero productivity growth, or even continued declines, are far more likely.

Reforms to the Chinese political system are at least theoretically possible. A radical improvement in China’s demographic outlook, however, is not. Until recently, China’s demographics provided a significant growth impulse to the Chinese economy. The number of Chinese aged 20-59 nearly doubled between 1978 and the peak in 2013, from 434 million to 855 million. Essentially all of the growth in the total number of Chinese during this period was caused by the booming number of people of prime working age.

Simply adding people to a society doesn’t make that society richer, although it can lead to higher production of goods and services to satisfy the needs of additional consumers. Adding workers, however, does lead to greater productive capacity. It is easier to raise material living standards for everyone when there are relatively fewer children and old people to support.

Even more important is adding workers in the right age range. Young people are inexperienced, while the elderly are less likely to generate new ideas or adapt to new technologies. Economists have repeatedly found that changes in the share of people in their 40s can meaningfully affect productivity growth. Patents, for example, are overwhelmingly filed by people in their 40s, while the best managers tend to be neither too young nor too old.

This theory neatly links the emergence and subsequent aging of the baby-boom generation to changes in U.S. productivity growth since the 1960s. Economists have found the general relationship between a society’s age structure and productivity holds elsewhere, including Europe and Japan. Here, too, China’s population structure was a tailwind for growth. The proportion of Chinese aged 40-49 doubled between 1978 and its peak in 2013. More than a third of the total growth in China’s population during its boom years came from the massive growth in the number of Chinese in their most-productive decade.

The positive growth impulse from demography has already begun to reverse, however. The number of Chinese aged 20-59 has already shrunk by about 0.5% since the peak in 2013, while the number of Chinese in their 40s has plunged by 10%.

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Demographics are not destiny, but the baseline projections produced by the United Nations in its World Population Prospects imply things will only get worse. By 2049, the centenary of the founding of the People’s Republic and the target date set by the Communist Party for China to become a “modern socialist country that is prosperous,” the number of working-age Chinese will have shrunk by 25% from current levels, while the number of Chinese in their 40s will have dropped by another 30%.

China’s total population, however, is expected to remain relatively stable over this period. The rapid shrinkage of the working-age population is projected to be offset by the booming population of elderly Chinese as today’s workers age. The share of Chinese aged 70 and older is projected to rise from less than 7% today to 20% by 2049. That will place severe burdens on working-age Chinese, who will need to sacrifice their own consumption to support their elders.

The outlook for the second half of the century looks even grimmer. While population projections that far in advance can be prone to substantial errors, the baseline forecast is for the number of working-age Chinese to collapse by half over the next 80 years, even as the number of Chinese aged 70 or older nearly triples. No society has any experience with this kind of demographic transition, especially when starting from China’s low level of development.

It is difficult to imagine how China can become “prosperous” under these conditions, much less stay that way.

Write to Matthew C. Klein at matthew.klein@barrons.com