Sears, Roebuck and Co., the nation's biggest retailer, said today its third-quarter profits dropped 18.5 percent because of a soft economy and a slower rate of increase in personal disposable income.

Sears earnings declined to $262.2 million (71 cents a share) from $321.9 million (88 cents) in the comparable 1984 period, although sales rose to $10.04 billion from $9.65 billion.

Sears said it expects sales to improve in the final quarter because of promotions for the chain's 100th anniversary celebrations and an increase in business during the Christmas shopping season.

Nine-month consolidated net income fell 15.7 percent to $751 million ($2.03) from $891.7 million ($2.47), while revenue edged up to $28.65 billion from $27.46 billion.

Sears said income from its Allstate Insurance Group was down sharply to $128.9 million from $211.4 million in the 1984 third quarter, partly because of $33 million in insurance losses from hurricanes Elena and Gloria.

The Dean Witter financial services group incurred a third-quarter loss of $7 million, slightly improved from a loss of $7.6 million in the 1984 period. The results included an after-tax loss of $2.1 million related to introduction of the Discover credit card in September.

The Sears World Trade Inc. subsidiary also showed some improvement for the quarter, with a loss of $3.3 million compared with a loss of $7 million in the third quarter of 1984.