The Labor Department reports that a seasonally adjusted 361,000 people sought unemployment aid the week ended Dec. 15, from a revised 344,000 the week before.

But the less-volatile four-week moving average fell 13,750 to 367,750, the lowest since late October, suggesting that the job market continues to grow modestly. Applications had surged after Superstorm Sandy, then fallen back.

Applications are a proxy for layoffs. So the drop of the four-week average suggests that companies are cutting fewer jobs, even if they aren’t hiring enough to lower the unemployment rate significantly. The economy has generated an average of 151,000 jobs a month in 2012, not enough to pull high unemployment down sharply.