Tokyo — Share prices of groups dealing in luxury goods from Japan’s Shiseido to France’s LVMH fell after social media reports that China is stepping up customs checks on citizens bringing in goods from overseas, adding to jitters from a trade war with the US. Chinese consumers make up the lion’s share of growth for the luxury business and account for about a third of the industry’s sales, according to consultancy Bain. Many do the bulk of their high-end shopping during visits to Tokyo, Hong Kong and Paris. Unconfirmed reports on Chinese social networks that authorities are cracking down on goods such as Louis Vuitton totes and Kering’s Gucci loafers could lower the incentive to concentrate spending in the brands’ flagship stores. Shiseido, the Japanese maker of high-end cosmetics, dropped 4.7% in Tokyo on Thursday. The selling spread to Europe, with Kering down as much as 4.8%, LVMH falling as much as 3.3% and personal-care giant L’Oréal slumping 2.8%. The sell-off followed a China ...

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