THE tsunami of 2011 left gaping holes reminiscent of war zones in the landscape along the coast of Tohuku, in the north-east of Honshu, Japan’s main island. Car navigation systems gave directions to landmarks that had vanished into the sea. The subsequent reconstruction effort hit an unexpected roadblock: missing landowners. Officials were stunned to find that hundreds of plots were held in the names of people who were dead or unknown.

The deluge threw the problem into particularly sharp relief in Tohuku, but it is widespread elsewhere too. A report last year for the government by a panel of experts estimated that about 41,000 sq km of land, or 11% of Japan’s surface, was unclaimed, most of it in rural regions. By 2040, it warned, the area could more than double. The cumulative cost in lost productivity could be as high as ¥6trn ($56bn).

The countryside is littered with vacant plots and empty houses. Some date from Japan’s great post-war migration to coastal cities; others were abandoned more recently, as urbanisation continued and as the population has shrunk and aged. Ownership has often passed through several generations and the thread may have been lost. Some titles in Tohoku had not changed since the 1860s.

One reason is that, unlike most other developed countries, Japan does not require changes of land ownership to be registered. The tax for changing title deeds is 0.4% of the assessed value, and the change must be done by notaries, who charge steep fees. If there is more than one heir, the cost is higher. Those who inherit land often do not bother to update the records.

As she grieved for her mother four years ago, Rie Nakaya discovered that she had inherited the family’s ancestral home in rural Shikoku, the smallest of Japan’s four main islands. But the seeming windfall has become a burden. Demolishing the tottering house on the 300-square-metre plot would be expensive—and pointless, since she cannot dispose of the land at any price. Living hundreds of miles away in Tokyo, her only remaining tie to it is the annual property-tax bill that plops through her letterbox.

Ms Nakaya’s inheritance points to a bigger issue: that many plots are simply valueless. The price of land in Japan peaked in the early 1990s, along with that of houses and shares. Then all these bubbles burst. Valuations in prime parts of Tokyo eventually recovered, but in the depopulated countryside much land is worth next to nothing. Absent an implausible wave of immigration, that is unlikely to change.

When bureaucrats take the time to track down owners, says Uichirou Masumoto of the land ministry, they almost always find them. But that detective work takes time and trouble. Officials spend thousands of hours a year searching through yellowing property records to find owners when they want to build a road, say. In one case, they travelled the country trying to contact over 600 descendants of a single landowner, without success. According to Yasushi Asami of the University of Tokyo, who advises the government on the problem of vacant land, some Japanese people even fear that “hostile” foreign governments (read: China) could buy up swathes of empty countryside.

The government is considering a few moves that might help. One is to make the registration of inherited land compulsory. That, at least, would force new owners to pay taxes. Faced with vast, complicated public-works projects such as rebuilding Tohoku, it has lowered the legal barriers to seizing vacant land, and become more aggressive in doing so. This is simply an acknowledgment that the legal system is creaking, says Mr Masumoto.

Yet more action will be needed. Overgrown lots, many hosting decrepit houses, are popping up in towns and even some big cities across Japan, says Hiroya Masuda, a former minister of internal affairs who helped draw up the report. As more people die and pass on titles to unwitting or unwilling relatives—the number of deaths in Japan is expected to peak at 1.67m in 2040—the growing swathes of unclaimed land could overwhelm the state, he fears.

The best way forward, says Peter Matanle of Britain’s University of Sheffield, may be for Japan to re-wild much of its vacant countryside with forests and parks. Having shown Asia how to develop in the 20th century, he thinks, Japan could lead the way in dealing with an ageing, shrinking society in this one.