By John S. McClenahen For the week ending Jan. 3, 2004, initial claims for unemployment insurance rose to 353,000, some 14,000 higher than the previous week's figure of 339,000, the U.S. Labor Department reported Jan. 8. Last week's figure also is 8,000 higher than the 345,000 level that economists generally expected. However, the weekly figure was well below the 400,000 mark that separates an improving U.S. labor market from a deteriorating one. What's more, the Labor Department's four-week moving average for initial claims fell by 5,500 last week to 350,250. That's significant because the four-week average smoothes out week-to-week changes and may be a better indicator of underlying labor market conditions.