* Annual fall in retail sales biggest since May 2009
* Low jobless, higher wages fail to lift consumption
* Germany eyes domestic demand boost as exports weaken (Adds economist comment, details)
By Noah Barkin
BERLIN, Jan 31 (Reuters) - The German labour market remains strong but it is not translating into a significant increase in private consumption, data showed on Thursday, raising doubts about the strength of an rebound in Europe's largest economy.
Federal Labour Office figures showed seasonally adjusted unemployment falling unexpectedly by 16,000 in January, breaking a long run of increases to take the jobless rate down to 6.8 percent, not far from a post-reunification low.
That news will be welcomed by the centre-right government of Chancellor Angela Merkel, who faces an election in September which could be strongly influenced by the state of the economy and its ability to avoid being sucked down by weakness in key European trade partners.
But the positive development of the labour market was clouded by other data showing retail sales had tumbled by their largest amount in over three years in December and a new forecast by the HDE retail association showing it expects sales to fall in real terms in 2013.
"These are disappointing numbers," Christian Schulz of Berenberg Bank said of the retail data. "Consumers are not opening up their wallets."
The notoriously volatile retail sales figures slid by 4.7 percent compared to a year ago, the weakest annual result since May 2009. On a monthly basis, the fall was a more modest 1.7 percent, still the biggest drop since May 2011.
Economists polled by Reuters had expected retail sales to fall by just 0.1 percent on the month and by 1.6 percent on the year.
Despite low unemployment and rising wages, private consumption remains subdued.
Gross domestic product (GDP) contracted by 0.5 percent in the fourth quarter of 2012, according to an early estimate from the Statistics Office, and the government is forecasting meagre growth of 0.4 percent this year.
Exports to big trading partners in Europe are slowing as the debt crisis enters its fourth year, and Berlin now expects foreign trade to be a drag on GDP in 2013.
According to a breakdown of the retail data, sales fell almost across the board in December, with food, drinks and tobacco down 4.1 percent on an annual basis, and clothes, shoes and textiles down 6.5 percent.
Still, some economists warned against reading too much into the data, pointing to anecdotal evidence from retailers that the holiday period was solid.
"The retailers did not report sensational Christmas sales, but they were broadly satisfied. It's hard to reconcile this with the strong decline we've seen here," said Alexander Koch of Unicredit.
The HDE said retail sales over in November and December had declined by 0.7 percent compared to the previous Christmas period. (Additional reporting by Rene Wagner; Writing by Noah Barkin; editing by Patrick Graham)