Despite prime minister Shinzo Abe’s efforts to reinvigorate it, Japan’s economy remains in the doldrums. Now, experts are warning of a “lost generation” — a whole tier of Japanese children who are growing up in families where the parents — or, often, a single parent — work but do not earn enough to break through the poverty line. The number of families living on an income lower than the public welfare assistance level more than doubled in the 20 years after the asset price bubble popped in 1992, according to a study by Kensaku Tomuro of Yamagata University. Now 16 percent of Japanese children live below the poverty line, according to the health ministry statistics, but among single-parent families, the rate hits 55 percent. Poverty rates in Osaka are among the worst. The falling birthrate means that the population, currently 127 million, is set to drop below 100 million by 2060, and one-third of Japanese will be older than 65.