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* S.Korea official says unclear whether economy has bottomed
* Industrial production under threat from rising won (Adds comment from finance ministry official, details on data)
SEOUL, Feb 7 (Reuters) - South Korea warned on Thursday that its economy may have further to fall after estimating record declines in sales at top department and discount stores last month, emphasizing the severity of headwinds now facing Asia's fourth-largest economy.
"It's not clear whether the economy has bottomed," said Choi Sang-mok, director-general of economic policy at the Ministry of Strategy and Finance. "Some indicators have improved but we need to monitor the data trends a bit more."
Sales at department stores run by Hyundai Department Store , Lotte Shopping and Shinsegae fell by 8.4 percent from a year earlier, the finance ministry estimated in a monthly report, compared with a 0.2 percent decline in December and marking the biggest decline going back to 2005.
Sales at the country's top three discount store chains last month also fell by a record 24.3 percent from a year earlier, according to the estimates, compared with a 5.0 percent decline in December.
The data highlights weak prospects for South Korea in the first quarter as feeble private consumption at home adds to challenges facing exporters. The won's continued appreciation against the yen is already eating into some firms' profitability, which may lead to job losses and reduced corporate investment.
The ministry said South Korea's industrial production could be weighed by slowing daily overseas shipments growth for key export products such as electronics and cars.
Meanwhile, sales of locally-produced cars rose by 1.6 percent from a year earlier in January, easing from a 7.5 percent rise in December as tax breaks expired at the end of 2012.
Sale of gasoline by volume rose by 2.7 percent from a year earlier in January, rebounding form a 2.8 percent decline in December.
Some of the weakness in department and discount store sales in January was attributed to the fact that the Lunar New Year holidays are in February this year. The Ministry of Knowledge Economy will release revised data on the sales later this month.
Reporting by Se Young Lee; Additional reporting by Lee Shin-hyung; Editing by Eric Meijer